A Portal Special Presentation- Geometric Unity: A First Look
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hello you found the portal I'm your host Eric Weinstein and I think that today's must be the most unusual episode yet of
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a podcast that has been marked by almost regular unusual episodes now this is the
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first podcast that I'm recording at home I don't really have a home recording studio so we're really doing this from
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chicken wire and masking tape but I am sheltering in place because of the worldwide kovat pandemic and what we've
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been asked by the state of California and by the federal government is to shelter in place for an upcoming month
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because today is April 1st now during a pandemic I can assure you that no one is
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interested in April Fool's jokes so the question is what to do with the April Fool's tradition in a situation in which
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nobody wants a prank I thought that this was probably the best time to launch an
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idea that I've been playing with for years and that idea is that it is dangerous to have a world in which we
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are afraid to talk about what we think is true when I think about what happened
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during the beginning of the kovat pandemic I find that we were in general
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intimidated from sharing our fears about the virus we were told that if we wore
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masks that we were acting in a peculiar fashion if we refused to shake hands that we were behaving in a strange and
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unpleasant social way we did not want to be alarmist we did not want to be seen as Chicken Little and in fact it was
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extremely important that we not be seen as xenophobic given that the outbreak was originating in Wuhan China in fact
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perhaps the most dangerous idea was that this outbreak might have been connected to some research being done in a lab
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perhaps a bioweapons lab we really don't know where this epidemic began what is
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the etiology of something that is causing the entire world economy to effectively shut down what I believe is
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that that silence has been deadly we have many people who have now lost their lives because we did not feel free to
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exchange ideas to think and to talk and in fact many of the people who warned us first were the freest members of society
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having been previously canceled by standard mainstream institutions and their associated media so what I thought
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would be important for in April Fool's Day that no one wants to actually participate in was to deal with an idea
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that maybe one day a year we should all be free to share crazy ideas that are
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going around between our ears and in our head we're having conversations with ourselves wondering is anyone else
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seeing the same thing that I'm seeing but we are too afraid because the social stigma for actually believing in things
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that maybe things are possible or perhaps there's a conspiracy somewhere perhaps we are ill-prepared for example
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I believe that our current pandemic is exacerbated because our government and
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our readiness czars failed to stock adequate supplies and that these supplies were called for in
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the academic literature for years there was absolutely no excuse not to have personal project protective equipment
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stocked for doctors and nurses and hospitals to say nothing of all of the people who are in the frontlines of
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treating patients sick with code now currently I don't believe that you can
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trust the World Health Organization absolutely not I don't think you can trust the Surgeon General of the United
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States and I absolutely don't think you can trust the CDC because they are all covering for our inadequacy this was a
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problem that we always knew was coming and we at one point had stocks which apparently were depleted under a
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previous administration and not restocked under this administration in fact our fear of dealing with a
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pervasive institutional incompetence has blinded us to the degradation in our
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society across all major institutions as I've discussed before on the program I
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believe that this has a singular etiology that is that because of embedded growth obligations coming from
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the previous era of unsustainable post-war growth from about nineteen forty five to nineteen seventy one
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seventy three something like that we built in expectations to our system that cannot currently be met we will not have
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technology that follows the same break neck pace of innovation as a result we
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have a system whereby the head of our organizations are forced to cover for their inadequacies because growth is
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built into the system that cannot be sustained therefore there is not the funding the manpower there is not the
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wherewithal to continue many of our programs because we do not actually have the ability to continue to simply grow
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our way out at least so far so what's today's program about well I thought
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that what I would do is to let go of something that I've been keeping pretty
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close for I think about 37 years when I
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was around 19 I started it's hard to
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talk about when I was around 18 or 19 I was at the University of Pennsylvania and I thought I saw a glimmer of hope I
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thought I saw that some new equations that were being played with might actually provide a solution to some of
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the problems that had bedeviled Einstein and others for years in the quest for a
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unified field theory now it's an embarrassing thing to say that one is a unified field theorist it
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is effectively equivalent to saying I'm interested in perpetual motion machines
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or that I have a private cure for cancer that I'm trying on rabbits in my
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backyard however I actually think that it's important to fess up because that's
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exactly what this is now in my situation I have an extremely unusual history and
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I really don't want to get bogged down in all of the things that happened while I was a student trying to develop this
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theory because it is not a particularly happy story I believe that this theory is an incredibly joyous one now in this
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situation I want to talk about what it means to have a theory of everything
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we've never seen one and in fact not only have we never seen a theory of everything we've never even seen I
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believe a candidate for a theory of everything and because a theory of everything would have to
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different characteristics they might believe every theory that has gone before we don't think enough about what
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the difference is between what we would normally call in physics and effective theory and a fundamental one now if
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you're familiar with the MC Escher drawing called drawing hands it is a
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lithograph of two hands apparently drawing each other into existence on
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some kind of a canvas or piece of paper that is sometimes referred to as a
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strange loop but it in fact is an attempt to answer the question what is
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the fire that lights itself this is the problem that be devils us when we search
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for a unified theory that doesn't bedevil us in my opinion in any previous effective theory now why is that well
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many people confuse a theory of everything is if they imagine that it's a theory in which you can compute every
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eventualities and it is absolutely not that because the computational power is very different than the question of
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whether or not the rules are effectively given I've analogized it to a game of chess and knowing all of the rules is
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equivalent to a theory of everything knowing how to play chess well is an entirely different question but in the
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case of a theory of everything or a unified field theory if you will many people also take it to be an answer to
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the question why is there something rather than nothing and I don't think that this is in fact what a theory of
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everything is meant to be either now why is that well because I believe at some
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level it is impossible for most of us to imagine a an airtight argument
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mathematically speaking which coaxes out of an absolute void a something however
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there's a different question which I think might actually animate us and which is the right question to ask of a
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potential candidate and that is how does one get everything from almost nothing
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in the MC Escher drawing or lithograph hands drawing hands or
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hands what we see is that the paper is presupposed that is if you could imagine
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a theory of everything it would be like saying if I posit the paper can the paper will the ink into being such that
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the ink gives rise to the pens and the pens draw the hands which in fact manipulate the pens to use the ink that
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kind of a problem is one which is of a very different character than everything that is gone before it is also in my
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opinion an explanation of why the physics community has been stalled for nearly 50 years since around 1973 when
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the standard model was intellectually in place now consider this we have never
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had in modern times the drought where no person working in pure fundamental
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theory has taken a trip to Stockholm just as a rough indicator for
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contributing to the standard model no one in my opinion since let see Frank will check was born in 1951 no one born
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after that time has in fact contributed to the standard model in a clear and profound way that is not to say that no
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work has been done but for the most part the current generation of physicists has for more than 40 years in almost 50
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years remained stagnant within the standard paradigm of physics which is positing theories that are then verified
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by experiment now my belief which is relatively radical is that there is no
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way to get to our final destination using the tools that have gotten us to where we are now in other words what got
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you here cannot get you there and in particular one of the biggest problems we have is the political economy of
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science we have effectively starved our scientific enterprise for resources
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creating a dire and cutthroat competition which is completely deranged
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the scientific tradition and so one of the things that's going to happen in this lecture this is that I'm simply
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going to announce that I have broken and have broken for many years with just
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about every expectation of standard science that is not to say that the equations or the style of present
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is going to be foreign quite the contrary I have every intention of writing up some results in standard
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terminology wherever possible using popular mathematical typesetting programs but it goes far deeper than
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this my belief is that what we've created is a career structure a journal structure an employment structure an
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access structure that cannot possibly complete the job and why is that well
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what if in the last leg in fact we had a situation by which an attempt at the
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fundamental theory would result almost certainly in career suicide now if you
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think of that as an explanation you would realize that it has the power to synchronize failure across many
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seemingly independent experiments and I believe that that's exactly what's been going on through the so called string
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theory revolutions one two and perhaps three now in that case what happened was
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a theory became fixed in the minds of really the baby boom generation of
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physicists because it allowed for infinite elaboration within a mathematical work more particularly a
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geometric context and those supposed physicists spent their time submitting
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papers to what's called the high energy section of the so-called preprint
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archive but in fact most of these papers have nothing to do with high energy physics whatsoever and if you're looking
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for the the designation it's hep th high energy physics - theory now if you look
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through those papers they don't seem to have much to do with particles they don't seem to have to do with forces in space-time they seem to have to do with
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very strange and obscure mathematical issues and in the years since the string
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theory program got particularly reanimated I guess that would be around 1984 with
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the anomaly cancellation of Greene and Schwartz what you'll find is is that physics became very active and
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simultaneously ground to a halt it it failed to remain a physical subject it
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became something like a medieval quest for the number of angels to dance on the head of a pit now in this circumstance I
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think it's very important to realize that this is not a paper and we're not submitting to the archive in fact the
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archive requires people who are not employed at universities to get permission from some member of the
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community which is called an endorsement which I find absolutely insulting and I refuse to go along furthermore we are
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expected to cite papers sometimes which are behind paywalls and I think that it's absolutely immoral
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to ask people to pay outside the system to read the papers to cite other people's work I can go on about the
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number of things that are currently wrong with the system but instead what I would like to do is to simply joyously
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reject it I have every intention of simply sharing this with you and
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jealously guarding my right to Shepherd this through now what is that in two
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previous episodes we've had interactions with academics which I think are interesting in bear scrutiny in the
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first case in a in an interview with The Economist's Tyler Cowen I talked to
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Tyler about the fact that the Boskin Commission was in fact committing economic malpractice now why was that it
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was because they decided that they needed to transfer a trillion dollars over ten years and that they had found a
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devious way of doing it which is to adjust the CPI by backing out the amount
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of adjustment needed to get a trillion dollars they decided that a 1.1 percent overstatement in the CPI would cause a
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reduction in entitlements that is Medicare and Medicaid payments together with Social Security as well as an
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increase in taxes because tax brackets are also indexed now to my mind it is
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absolutely unconscionable to say that you have a right to Train for wealth cryptically by adjusting a
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fundamental barometer that would be like saying in order to meet our global
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warming targets we have to recalibrate all the thermometers to show that in fact things had cooled one simply can't
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do that at science but Tyler's response I found was very interesting his
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perspective was that this was in fact not a terrible thing because it was quote directionally correct and in
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general he believed that because the CPI should be considered overstated that this was not the world's most terrible
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thing to do as an economist I respect Tyler a great deal and I enjoy his company but I have to say that I am
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absolutely of a different opinion my belief is is that one has no rights and
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no ability as a scientist to fudge the data to meet social goals in this fashion
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another interesting interaction was the interaction with Professor ACMA scholar of the University of Chicago now when
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she listened to episode 19 about Brett Weinstein she found that it was a very
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compelling episode but strangely even though the point of the episode was to
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surface breaths long forgotten theory because Brett had not been acknowledged as having predicted that laboratory mice
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would in particular have radically elongated telomeres where it was thought that all mice had long radically
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elongated telomeres which has incredible potential implications for a drug
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testing and all of the work that is done on laboratory rodents as model organisms
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this is an episode you should definitely listen to if you haven't already but Agnes's perspective was very
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different than mine her feeling was that because we were in a situation in which
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the work actually surfaced that the system worked even if it was the case that Brett's name was erased from the
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history of the development and that his theory was put in a situation in which
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it was not able to carry the day because in fact there was no record of the fact that a prediction
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been made now I disagreed with Agnes on that program facili but what I found was
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is that it was very telling in general our academic population has given up on the previous and quaint idea of decency
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propriety truth fairness because there simply isn't the resource for everyone
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now I believe that current science is not necessarily unsalvageable but it
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will be unsalvageable if we don't get the very people that I rail against far more money and I know that's very
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confusing but my belief is as the inadequate resources that we have put aside are very similar to the inadequate
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masks that we have put aside for our doctors we have asked some of the world's most gifted and smartest people
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to devote their lives to the study of science and technology and we've inadequately prepared them we've put
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their lives and their families lives under incredible pressures and what I wish to do is to in fact point to the
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very people who I have been most angry at for years and say the part of the problem is that we need to take a hard
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look at how we've invested in science and technology and give the very people that I'm most angry at more money I will
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explain more about this later but I do want to give you an introduction to this episode what I will
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be doing is to screen a very unusual and somewhat awkward lecture at the
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University of Oxford now why is it so awkward well first of all I had left
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standard research perhaps 20 years earlier almost further I'm not a
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physicist and I have only taken one or two courses in the physics major
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sequence I think I've taken one semester of mechanics and perhaps I took an advanced general relativity course in
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college but in general no one goes into a theoretical physics department and
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attempts to lecture physics physicists on physics and why is that well because physics is incredibly demand
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and this is almost certainly the world's most interesting and most accomplished intellectual community these are guys
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that don't miss a trick there are so many things to know and it is such a difficult field that it is effectively
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almost impossible to contribute from outside chemists don't do it and once in
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a blue moon mathematicians will attempt to talk about actual real physics so one
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thing that you're seeing is a very unusual circumstance where somebody is trying to figure out how to give their
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first lecture in a physics department and it concerns the possibility of a theory which attempts to solve the
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problem of how does a fire light itself another thing that you'll see is is that
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it's relatively difficult to read my handwriting I'm not going to make any bones about it I've been very vocal
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about having learning differences dysgraphia dyslexia all sorts of different issues symbols come extremely
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difficult to me I don't want to spend this time making excuses what I do want to say is the following I will be
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attempting to record a short PowerPoint presentation for after the lecture to
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say at least some of what some of the constructions are more clearly this is not meant to be the actual presentation
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of the theory what this is is an introduction a down payment and above all a historical account of what
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happened seven years ago at the University of Oxford when I tried to present these ideas I've talked before
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about the twin nuclei problem and our need to get off of this planet and if we
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have a hope of getting off of this planet it really comes from fundamental physics you see a hundred years ago or
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perhaps 105 when Albert Einstein gave us general relativity he effectively consigned us for life to the solar
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system why is that well his model his geometric model of
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space and time effectively creates a speed limit known as C or the speed of
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light now there are three rocks that are at least interesting for habitation by
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humans although two of them are marginal the Moon and Mars one of them of course is unbelievable the earth but I doubt
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that we're going to be able to steward the through our new godlike powers which I've called it - a nucleotide problem of
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cell and atom we've unlocked the power of both and I don't think we have the wisdom to stay all in one place so the
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question that I had was if there is any ability to escape to the cosmos that we can see in the night sky where would it
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come from we are almost positive that Albert Einstein's theory of relativity is in
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some weird way incomplete the Schwarzschild singularities which give us black holes and the initial
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singularities of the robertson-walker Freedman universe which are associated with the Big Bang are some clue that
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there is some subtle flaw united Stein's theory so how to go beyond Einstein I
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mean what Einstein did to Newton was to recover Newton as a special case of a more general theory that is more
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flexible and in fact this is the same problem that we have because Albert Einstein's theory is so fundamental we
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effectively begin every theory of physics seminar with a statement about space-time in other words Albert
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Einstein is locked in at the ground floor so if we can't get below the ground floor to the foundations it's
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very difficult to make progress this is one of the things that is making it almost impossible for us to go beyond
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the initial revolutions of the 20th century do I know that this new theory
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if it works will allow us to escape I do not there's no one who can I can
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say that and I don't think I have the skills to develop the physical consequences of the theory even if the
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theory turns out to be mostly right what I will say is that I think that the
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theory is the first of its kind that I've seen I believe that in part what
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you will see is that at a minimum it is like fool's gold
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it appears to explain why we think we see three or three generations but it
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also says that perhaps they aren't really three generations of matter perhaps there are only two even though
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physicists tell us that there are at least three or perhaps more I believe that physics tells us that the universe
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is chiral that is left-right asymmetric but the theory is itself not chiral instead it chooses
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to present a different idea which is that perhaps chirality is emergent much the way our hands are individually
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left-right asymmetric as our pinky is not a reflection of our thumb but the thumb on each hand is a pairing to the
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other one as is the pinky now what does that mean it means that if perhaps there is matter
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and there is force that is decoupled from our ordinary world that that matter
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might restore the parody or the chirality rather would break the
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chirality and restore parody between these two halves the matter we see in the matter that is missing there are a
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good number of other things that happen in the theory it replaces space time with what I've termed an observers now
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an observers is an unusual gadget in that it's thought of as two separate places where physics takes place
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connected by a map that means effectively that we are in something
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like a stadium where there is there are stands and there is a pitch and the playing field that we think we see may
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not in fact be where most of the action is taking place in fact not all of the fields live on the same space so when we
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see waves and particles dancing around they may have separate origins in each of the two components of the observers
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what I hope to do after this is to gracefully and gradually develop the
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theory under my leadership now why do I say that there is a belief in physics
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and in most fields that the field should behave in a communal fashion and that people should put forward their ideas
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and other people should joyously build upon them and that the community should be allowed to name the various
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accomplishments for whoever they say accomplish those things there's not a
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way there's not a way in hell that I'm letting that happen my experience with this community is is that it simply
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can't be trusted to behave equitably given the fact that it is so resource starved and constrained people simply do
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not have the freedom to be generous kind and accurate as to who did what furthermore there is an incredible
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premium on cherry topping that is who finished something off is considered bizarrely
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much more important than who found something to begin with imagine you located an island and you
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named the island after the first person who could plant the flag on the top of the highest peak this is patently
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offensive and ridiculous there's a story years ago about how Hilbert almost
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scooped Einstein by giving the Hilbert action from which Einstein's equations could be recovered really not a chance
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so if Hilbert came up with the Hilbert action and recovered Einstein's equations so what I mean the real theory
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actually takes place in Einstein and Grossman before Albert Einstein even works out a lot of the flaws in the
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original theory it's about the ideas it's not about the formulas and it's not about racing to the final form now I
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know that the community won't agree with that but think about this what I'm doing is taking an incredible risk I'm
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addressing you here on April Fool's Day and I'm saying that if there is a fool it is certainly me because I have sat on
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this theory for almost 40 years now I've never known is it true is it false it's
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impossible to tell when you're only talking to yourself but in this situation what I've done is I've taken a
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tremendous amount of risk and now I'm trying to share it with you hopefully I know that well Newton did
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his greatest work when he was sheltering sheltering from a Great Plague in England and I would like to think that
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perhaps whether or not this is correct simply the act of somebody trying honestly to share hope and some path
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forward would be uplifting now under the worst circumstances if this doesn't work
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what do I think is a question I'm asked frequently there are two things that I'll say many years ago around 1987 I
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put forward some equations that I thought might become my thesis at the Harvard Department of Mathematics and
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they were disallowed for a variety of reasons those let equations were later discovered in I believe 1994 and I sat
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in a lecture in which I saw these equations go up on a board the very end at MIT and I looked at
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those equations and I said huh those are the exact equations I was told could never work why is the leading physicist
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in the world placing them on the board and saying that these are the equations from which all of something called donaldson theory can be derived what I'm
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giving you at least at a minimum had the ability years earlier to provide those equations
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from a different source there's something called Seibert Witten theory which I have no claim on but the
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actual equations that are called the cyber quittin equations came originally as an outgrowth from investigations of
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this theory so at a bare minimum the cyber Witten revolution should have
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happened at Harvard rather than Princeton and it should have been recognized that this theory was capable
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of at least at a minimum giving birth to that as a side project the other thing
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that I think is incredibly important is is that we've never seen how a universe that looks like ours could possibly
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emerge from almost no assumptions whatsoever and I believe that even if this theory
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were to turn out to be wrong which I don't think is likely I believe that it would give us something to go on
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we would at least have a first candidate of how a hopeful theory of everything
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would look and how it would go wrong so under any circumstance I think that I'm going to be fine if the theory doesn't
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work out I will have at least taken my shot on goal and I think that that's probably more than almost anyone can ask
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from a life to attempt to make contact with the deepest question that we've ever had which is what is this place and
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what brought it into being lastly I want to just talk about a personal aspect of
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this which is what does it mean to come to an end whether or not this theory in
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fact does what I claim I think it does I don't know but I do know that sooner or
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later in the era of intercontinental exploration someone found the last
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landmass and that must have been a very strange moment when there was nothing left to do I think whether or not this
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theory in fact accomplishes that is one question but we all have to plan for what it is that we think will happen
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when man at last learns his own source code in fact this was the last edge
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question that I answered for Jon Brockman which is does something unprecedented happen when man at last
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learns his own source code I don't know the answer of this but I want to return
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to the same spirit that I started this when I was 18 or 19 which is that of joyous investigation of brave open
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hearted undertakings and I also want to bring back a different style of
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scientific investigation there has been far too much communalism in fact there
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is a belief that there are no lone researchers and that everything is produced by a community and pardon my
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french but this is absolute horseshit I have been so long alone with these
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principles equations and ideas that I don't even know what my adult life will
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look like once I discourage them and I begin to talk about them with the
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community at large I've talked to many theoretical physicists who've taken some interest in them but I've never put out
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enough to absolutely ensure that people are seeing what it is that I'm seeing so
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whether or not the April Fool's joke is on me I cannot tell you but I can promise you that I'm not trying to play
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one on you what I hope to show you is a lecture that was the first of three versions of this lecture that were
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delivered in Oxford over the course of a week and one of the things that has held
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me back is is that I have a great number of people who I have to thank for effectively being my Underground
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Railroad when my career got into serious trouble to make sure who made sure that I always
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had an opportunity to fight another day and some of the most important of those
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people one of whom occurs on this video is Marcus - so toy and Marcus I just
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wanted to say thank you for your brave your courage your friendship and your encouragement I know I've been absolutely impossible to you I've made
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you wait for this and I just want to say how much I love you I also want to thank Isadora singer for effectively saving me
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from not getting a PhD I think putting pressure on the Harvard Department and
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for coming to my assistance making sure that I got a postdoc at MIT despite not
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having any publications at all I'd like to think Raul Bhatt who's no longer with us who I should have invited to my
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wedding I was very angry at him but I didn't realize that he was saving me in a very difficult situation against the
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department that probably just wanted to see me gone I'd like to thank Peter Thiel one of my closest friends is like
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a brother to me for allowing me these seven years since this lecture to lick my wounds to get
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strong to have a 401k to buy a house and to begin coming back to regular society
33:25
after a very difficult and strained career I'd like to thank Adil Abdul Ali
33:31
and Michel Grossberg the two greatest best friends from college a guy could
33:36
have I'd like to thank my grandfather Harry Rubin who believed in things that
33:43
couldn't possibly be true and made some of them happen I'd like to thank my parents Karen and les Weinstein for all
33:49
the good things that they did I'd like to thank my brother Brett Weinstein and his family Heather and the kids for
33:54
sticking by me and I'd like to thank my in-laws in Bombay and yeah I hope you
34:00
guys are well and lastly I would very much like to thank my wife and my two
34:07
kids for putting up with a lot of lost weekend's a lot of lost vacations and
34:13
believing that just maybe there was something to this and sticking by me all these years so I hope everybody really
34:20
enjoys this it may not be comprehensible and after this video finishes I'll do a
34:27
short presentation of some of the constructions that took place not all of the equations and things
34:32
I think some of them were sort of botched on the board they became disoriented the night before and
34:38
rearranged things in a way that probably wasn't optimal but I I'll attempt to
34:44
clarify these things going forward and to begin to present the theory as I see
34:50
whether or not I can bring myself to once again work on it somewhat close to full time as a 54 year old father of two
34:58
so sit back relax and coming up next is the first of my three lectures at Oxford
35:06
University on geometric unity be well
35:18
[Music] well welcome to this special Simoni
35:25
lecture and my name is Marcus DeSoto I'm a professor of mathematics here and the Simoni professor for the public
35:31
understanding of science and Chancellor mone prepared a manifesto when he in dealt this chair to guide the holder of
35:38
the professorship in their mission and I'd like to read one part of that manifesto to you
35:43
it said scientific speculation when so labeled and when the concept of speculation and its place in the
35:50
scientific method has been made clear to the audience can be very exciting it is
35:55
a very effective communication tool and it is by no means discouraged and it is
36:01
in the spirit of this part of my mission there's a Simoni professor that I would like to introduce today's Simoni special
36:07
lecture I first met Eric vine Stein when we were both postdocs at the Hebrew University just over 20 years ago
36:15
and I had the feeling then that he was working on something big but it wasn't
36:20
until two years ago that Eric met me in a bar in New York and we began he began to explain the mathematics that he'd
36:26
been working on in private for the last 20 years as he took me through the
36:31
equations he had been formulating I began to see emerging before my eyes potential answers to many of the major
36:38
problems in physics it was an extremely exciting daring proposal and also
36:44
mathematically so natural that it started to work its magic on me over the
36:49
last two years I have had the privilege of being taken through the twists and turns of Eric's ideas after our postdocs
36:56
in Israel when I went the academic route getting my professorship here in Oxford Eric went to more independent roots
37:03
working in economics government and finance so he comes here today as something of an insider and an outsider
37:10
a difficult place from which to propose bold ideas but having spent time seeing
37:16
how powerful these ideas appear to be I felt it was time that Eric shared his ideas more widely as I believe his
37:23
perspective could give the scientific community a new story to explain some of the big questions on the side
37:29
books and therefore very happy to provide a platform here in Oxford for Eric to share his ideas on a new theory
37:35
he calls geometric unity the lecture will be approximately 17 minutes after
37:41
which we will have a period to ask questions Eric so it's it's a great
37:53
pleasure to be here in Oxford for those of you who are not aware it is possible
38:00
that no other university in the world has kept so tightly and kept the faith for so long with Einstein's great vision
38:08
of a final theory for physics as a theory of pure geometry a sort of
38:14
elegance and simplicity of the highest order and the names that are associated with Oxford that weigh heavy on me are
38:21
attea Penrose Siegel Woodhouse Hitchin it's a very long list of people who even
38:27
when fashion did not hold those ideas in favor always kept the faith that there
38:34
was much to be learned from the geometric perspective on physics of course unified field theory and some
38:40
sense acquired a stigma with Einsteins failure to find it in the sense that even someone like Einstein being tempted
38:48
by the siren song of geometry might lose their footing and go astray and in the
38:54
years since we've had a replacement theory which is that what is really calling our generations is the is the
39:01
quest to quantize general relativity and gravity and I'd like to to go back to
39:08
the sort of earlier perspective that there's no evidence to date in my mind
39:14
that we are being called to quantize general relativity directly in fact
39:21
there's been more effort spent on that quest without very tangible results then
39:27
Einstein spent as one man searching for years for a unified field theory so we
39:33
have to in some sense begin to undo some of what we think we know in order to
39:38
truly reconsider and allow me to put some of these Diaz before you today Marcus asked me to
39:47
begin presenting these ideas here and hopefully this is the first opportunity
39:53
but if the ideas are not good then lighting on the aisles will lead you to
40:00
safety and your exits may be behind you but in the event of a good flight
40:05
hopefully this will begin a conversation rather than n1 I feel in some sense that
40:11
I'm presenting the works of another man a younger man someone who came of age
40:18
right in the middle of the Great string theory boom with the anomaly
40:23
cancellation in 1984 and I look at this work and I see a young person struggling
40:29
with the idea why can't I see that string theory is going to answer all of these questions over the next 10 years
40:34
as we were told at the time and making a very dangerous decision which was I
40:40
think I'm not going to follow that particular path and I'm going to follow another and it's not clear where this
40:46
path is going to lead us but we're going to explore it today and see as best we
40:52
can so in some sense I've been able to polish some of that young man's work but I'm also struggling to reconstruct it because as someone
40:59
spending full time on that theory he knew a lot of things that I no longer know so with that as a beginning I'm
41:08
just gonna say one disclaimer which is that this is not a usual talk and whatever contract a speaker usually has
41:16
with the audience right now we're going to break that contract this is a this is
41:21
a talk about ideas and some of these ideas are bold some of them may offend some people because there's a sense that
41:28
you don't have a right to be considering those ideas but I go back to the admonition of Jim Watson that said if
41:33
you're going to try to make progress big progress you are by definition unqualified to be doing whatever it is
41:39
that you're doing so in that spirit let us begin what is physics to
41:49
today how do they see it different from the way in which we might imagine the
41:54
lay person sees physics ed Witten was asked this question in a talk he gave on
42:01
physics and geometry many years ago and he pointed us to three fundamental
42:08
insights which were his big three insights in physics and they correspond
42:14
to the three great equations so the first one is is that somehow physics takes place in an arena and that arena
42:23
is a manifold X together with some kind
42:30
of semi roumanian metric structure something that allows us to take length
42:37
and angle so that we can perform measurements at every point in this space-time or higher dimensional
42:45
structure leaving us a little bit of headroom the equation most associated
42:51
with this is the Einstein field equation
43:11
and of course I've run in to the market
43:17
so it says that a piece of the Riemann
43:27
curvature tensor the Ricci tensor - an even smaller piece the scalar curvature
43:32
multiplied by the metric is equal or plus the cosmological constant is equal
43:38
to some amount of matter and energy the stress energy tensor so it's
43:43
intrinsically a curvature equation the second fundamental insight I'm going to
43:51
begin to start drawing pictures here as well so if this is the space-time
43:56
manifold the arena the second one concerns symmetry groups which cannot
44:06
necessarily be deduced from any structure inside of the arena they are additional data that come to us
44:13
out of the blue without explanation in
44:19
these symmetries form a non abelian group which is currently su3 color cross
44:38
su - weak isospin cross u1 weak hypercharge which breaks down to su 3
44:44
cross u1 where the broken u1 is the electromagnetic symmetry this equation
44:55
is also a curvature equation the corresponding equation and it says that
45:01
this time the curvature of an auxiliary structure known as a gage potential
45:10
when differentiated in a particular way is equal again to the amount of stuff in
45:24
the system that is not directly involved in the left-hand side of the equation so it has many similarities to the above
45:31
equation both involve curvature one involves a projection or a series of projections the other involves a
45:37
differential operator the Third Point
45:47
surrounds the matter in the system and
45:57
here we have a Dirac equation again
46:03
coupled to a connection but one of the
46:12
great insights is is that because the reason for the lightness of matter in
46:17
the natural mass scale of physics has to do with the fact that this sigh really
46:24
should have two components and the differential operator should map to one component on the other side of the
46:30
equation but the mass operator should map to another and so if one of the components is missing if the equation is
46:37
intrinsically lopsided chiral asymmetric then the mass term and the differential
46:44
term have difficulty interacting which is sort of overcompensating for the mass
46:49
scale of the universe so you get to a point where you actually have to define a massless equation but then just like over shooting a putt it's easier to
46:57
knock it back by putting in a Higgs field in order to generate and as if fundamental mass through the Okawa
47:03
couplings
47:22
so matter is asymmetric and therefore
47:27
light and then interestingly he went on
47:37
to say one more thing he said of course these three central observations must be supplemented with the idea that this all
47:44
takes place treated in a quantum
47:52
mechanical fashion our quantum field theory so it's a bit of an aftermarket
47:58
modification rather than in his opinion at the time one of the core insights I
48:06
actually think that that's in some sense about right now one of my differences
48:13
with with the community in some sense is that I question whether the quantum
48:19
isn't in good enough shape that we don't know whether we have a serious quantum mechanical problem or not we know that
48:24
we have a quantum mechanical problem the quantum field theory attic problem relative to the current formulations of
48:29
these theories but we know that in some other cases the quantum becomes incredibly natural sometimes sort of
48:36
almost magically natural and we don't know whether the true theories that we
48:42
will need to be generalizing in some sense have beautiful quantum mechanical
48:47
treatments whereas the affective theories that we're dealing with now may not survive the quantization so what I
48:54
want to do is I want to met imagine a different
48:59
sort of incompatibility so let's take our great three theories and just
49:05
visually treat them as the vertices of a triangle so I'm going to put general
49:15
relativity in Einstein's formulation and
49:20
I'm gonna put the probably won't write this again yang-mills Maxwell Anderson
49:25
Higgs Theory over here and I'm gonna
49:32
write the Dirac theory what I want to
49:40
explore is the incompatibility is not at the quantum level but the geometric
49:47
input all three of these are geometric theories and the question is what are
49:52
the compatibilities are incompatibilities at the level of geometry before the theory is treated
49:57
quantum mechanically well in the case of
50:02
Einstein's general relativity we can rewrite the Einstein theory by saying
50:08
that there's a projection map due to Einstein of a curvature tensor where I'm
50:15
going to write that curvature tensor as I would in the yang-mills theory that
50:23
should be an LC for lemme chavita so the Einstein projection of the curvature tensor of the leve chavita
50:29
connection of the metric on this side and on this side I'm going to write down
50:36
this differential operator the adjoint of the exterior derivative coupled to a connection and you begin to see that
50:50
we're missing an opportunity potentially what if the FAs were the same in both
50:55
contexts then you're applying to separate operators 1 0 with order and
51:00
destructive in the sense that it doesn't see the entire curvature tensor the other inclusive but a first-order
51:09
and so the question is is there any opportunity to do anything that combines these two but the problem is is that the
51:18
hallmark of the yang-mills theory is the freedom to choose the data the internal quantum numbers that give all the
51:25
particles their personalities beyond the mass and the spin additional to all of
51:35
that freedom is some means of taking away some of the redundancy that comes with that freedom which is the action of
51:42
the gauge group now we can allow the gauge group of symmetries to act on both sides of the equation
51:47
but the key problem is is that if I act
52:03
on connections on the right and then take the Einstein projection this is not
52:11
equal to first taking the projection
52:26
and then conjugating with the gauge action so the problem is is that the
52:34
projection is based on the fact that you have a relationship between the
52:39
intrinsic geometry if this is an add value to form the to form portion of
52:45
this and the adjoint portion of this are both associated to the structure group
52:50
of the tangent bundle but the gauge rotation is only acting on one of the two factors yet the projection is making
52:57
use of both of them so there is a fundamental incompatibility in the claim that Einstein's theory is a gauge theory
53:04
relies more on analogy than an exact mapping between the two theories what
53:11
about the incompatibilities between the einstein theory of general relativity and the Dirac theory of matter I was
53:20
very struck that if we're going to try to quantize gravity and we associate gravity with the spin to field G mu nu
53:31
we actually have a pretty serious problem which is if you think about
53:38
spinners electrons quarks as being waves in a medium and you think about photons
53:46
as being waves in a different medium photons medium does not depend on the
53:54
existence of a metric one forms are defined whether or not a metric is
53:59
present yet spinners are not so if we are going to take the spin to G mu nu
54:05
field to be quantum mechanical if it blinks out and does whatever the quantum does between observations in the case of
54:13
the photon it's saying that the waves may blink out but the ocean need not blink out in the case of the Dirac
54:19
theory it is the ocean the medium in which the waves live that becomes uncertain itself so even if you're
54:25
comfortable with the quantum to me this becomes a bridge too far so the question
54:31
is how do we liberate the definition
54:46
how do we get the metric out from its responsibilities it's been assigned far too many responsibilities its
54:52
responsible for a volume form for differential operators it's responsible for measurement it's responsible for
55:00
being a dynamical field part of the field content of the system lastly we
55:07
have the compatibility comparing yang-mills and in the Dirac theory these may be the most mild of the various
55:13
incompatibilities but it is an incompatibility of naturality where the
55:19
direct field Einsteins field and the connection fields are all geometrically well motivated we push a lot of the
55:27
artificiality that we do not understand into the potential for the scalar field that gives everything its mass so we
55:34
tended to treat it as something of a mysterious fudge factor so the question is if we have a Higgs field why is it
55:45
here and why is it geometric it has long
55:52
been the most artificial sector of our models the proposal that I want to put
56:00
to you today is that one of the reasons that we may be having trouble with
56:05
unification is is that the duty our duty may be to generalize all three vertices
56:15
before we can make progress that's
56:23
daunting because in each case it would appear that we can make an argument that
56:29
this that and the other vertex are the simplest possible theories that could
56:34
live at that vertex we know for example the Dirac operator is the most
56:40
fundamental of all the elliptic operators in Euclidean signature generating all of a Tia singer theory we
56:47
know that einstein's theory is in some sense a unique spin to massless field
56:52
capable of communicating gravity which can be arrived at from field theoretic rather than geometric considerations in
56:58
the yang-mills case it can be argued that the yang-mills theory is the simplest theory that can possibly result
57:03
where we're taking the simplest lagrangian in the Einstein case looking only at the scalar curvature in the
57:09
yang-mills case we have no substructure and so we're doing the most simple-minded thing we can do by taking the norm square of the curvature and
57:16
saying whatever the field strength is let's measure that size so if each one of these as simple as possible doesn't
57:22
Occam's razor tell us that if we wish to remain in geometric field theory that we've already reached bottom and that
57:28
what we're being asked to do is to abandon this is merely an effective theory that's possible and I would say
57:35
that that in some sense represents a lot of conventional wisdom but there are
57:40
other possibilities there are other possibilities that while each of these may be simplest in its category they are
57:47
not simplest in their interaction for
57:54
example we know that Dirac famously took
58:00
the square root of the klein-gordon equation to achieve the Dirac equation
58:06
he actually took two square roots one of the differential operator and another of the algebra on which it acts but could
58:14
not could we not do the same thing by reinterpreting what we saw in Donaldson theory the insurance Simon's theory and
58:21
finding that there are first-order equations that imply second-order equations that are nonlinear and in the
58:26
curvature so let's imagine the following we replace the standard model with a
58:33
true second-order theory we imagine that general relativity is replaced by a true
58:39
first-order theory and then we find that the true second-order theory admits of a
58:45
square root and can be linked with the true first-order theory this would be a
58:50
program for some kind of unification of de rocks type but in the force sector
59:00
the question is does this really make any sense are there any possibilities to do any such thing
59:10
so what I'd like to do is I'd like to talk a little bit about what the geometric unity proposal is so we have a
59:34
division into intrinsic theories and auxiliary theories between physics and
59:48
mathematics more specifically geometry an intrinsic physical theory would be
59:54
general relativity an auxiliary physical theory would be the yang-mills theory
1:00:02
with the freedom to choose internal quantum numbers at the mathematical level an intrinsic Theory would be to be
1:00:11
a little fastidious the older semi
1:00:20
Romani in geometry a study of manifolds with length and angle but auxiliary
1:00:27
geometry is really what's taken off of late since the revolution partially begun at Oxford when is singer brought
1:00:34
insights from Stony Brook to the UK and so we're gonna call this fiber bundle
1:00:39
theory or modern gauge theory geometric
1:00:49
unity is the search for some way to break down the walls between these four boxes what's natural to one theory is
1:00:55
unnatural to another semi romani and geometry is dominated by these
1:01:00
projection operators as well as the ability to use the levy chavita
1:01:07
connection now some aspects of this are less explored torsion tensors are definable in semi romani in geometry but
1:01:13
they are not used to the extent that you might imagine in the case of fiber bundle theory
1:01:18
the discovery of physicists that the gauge group was fantastically important
1:01:24
came as something of a shock to the mathematicians who had missed that structure and have since exploited it to
1:01:32
great effect so what we'd like to do is we'd like to come up with some theory that is intrinsic but allows us to play
1:01:39
some of the games that exist in other boxes how can we how can we try to have our cake eat it and use all the full
1:01:48
suite of techniques that are available to us so our perspective is is that it
1:01:55
is the quantum that maybe the comparatively easy part and that the unification of the geometry which is not
1:02:02
occurred maybe what we're being asked to do so let's try to figure out what would a final Theory even look like when I was
1:02:12
a bit younger I remember reading this question of Einstein which he said I'm
1:02:18
not really interested in some of the details of physics what really concerns me is whether the creator had any choice
1:02:24
in how the world was constructed and some people may have read that as a
1:02:30
philosophical statement but I took that as an actual call for a research program so I'd like to describe that research
1:02:36
program and try to unpack what I think he was saying
1:02:45
we talk a lot about unification but we hardly ever actually imagine if we had a
1:02:50
unified theory what would it look like
1:02:56
let us imagine that we cannot figure out the puzzle of why is there something rather than nothing but if we do have a
1:03:02
something that that something has this little structure as possible but still
1:03:08
invites us to work mathematically so to me the two great theories that we have mathematically and in physics are
1:03:14
calculus and linear algebra if we have calculus and linear algebra I mean imagine that we have some manifold at
1:03:22
least one of dimension four but it's not a space-time it doesn't have a metric it's not broken down into two different
1:03:29
kinds of coordinates which then have some bleed into each other but still
1:03:34
maintains a distinction it's just some sort of flabby proto space-time and in
1:03:41
the end it's got to fill up with stuff and give us some kind of an equation so
1:03:50
let me write an equation
1:04:12
so I have in mind differential operators parameterised by some fields Omega which
1:04:19
when composed are not of second-order if these are first-order operators but at zero with order and some sort of further
1:04:28
differential operator saying that whatever those two operators are in
1:04:34
composition is in some sense harmonic is
1:04:41
such a program even possible so if the
1:04:46
universe is in fact capable of being the fire that lights itself is it capable of
1:04:52
managing its own flame as well and closing up what I'd like to do is to set
1:04:59
ourselves an almost impossible task which is to begin with this little data in a sandbox to use the computer science
1:05:09
concept so if here's physical reality
1:05:19
standard physics is over here we're
1:05:27
going to start with the sandbox and all
1:05:35
we're going to put in it is x4 and we're going to set ourselves a straight
1:05:42
jacketed task of seeing how close we can come to dragging out a model that looks
1:05:47
like the natural world that follows this trajectory
1:05:54
while it may appear that that is not a particularly smart thing to do I would like to think that we could agree that
1:06:02
it is quite possible that if that were to be the case we might say that this is
1:06:08
what Einstein meant by a creator which was his anthropomorphic concept for necessity and elegance and design having
1:06:16
no choice in the making of the world so with that let us begin to think about
1:06:23
what we mean today by geometric unity Jihu comes in four flavors but I'm only
1:06:30
getting one shot to do this so I'm going to do the most exciting of them to me
1:06:35
there's a completely exhaust flavor and
1:06:42
what I'm going to do is I'm going to take the concept of observation and I'm going to break the world into two pieces
1:06:48
a place where we do our observation and a place where most of the activity takes
1:06:54
place and I'm going to try to do this without loss of generality so in this
1:07:01
case we have x4 and it can map into some other space and we're going to call this an observers the idea of an observer is
1:07:16
a bit like a stadium you have a playing field and you have stands they aren't distinct entities they're coupled and so
1:07:23
fundamentally we're going to replace one space with two excitedness model simply
1:07:29
means that U is unrestricted although larger than x4 so any manifold of four dimension higher that is capable of
1:07:35
admitting export as an immersion the
1:07:41
next model we have is the bundle theoretic in which case use sits over X
1:07:50
as a fiber bundle
1:07:56
the most exciting which is the one we'll deal with today is the endogenous model
1:08:02
where x4 actually grows the space you
1:08:08
where the activity takes place so we talked about extra dimensions but these are in some sense not extra dimensions
1:08:14
their implicit dimensions within x4 and last to proceed without loss of
1:08:20
generality we have the tautological model in that case X 4 equals u and the
1:08:28
immersion is the identity and without loss of generality we simply play our games on one space okay now we need
1:08:37
rules and the rules are sorry feedback no
1:08:46
choice of fundamental metric so we imagine that Einstein was presented with
1:08:52
the fork in the road and it's always disturbing not to follow Einsteins path
1:08:59
but we're in fact going to turn Einsteins game on its head and see if we can get anywhere with that right so it's
1:09:05
also a possibility that because Einstein's theory is so perfect that if there's anything wrong with it it's very hard to untap of it so let's make no
1:09:15
choice of fundamental metric and in fact let's go more ambitious and let's say we're going to reverse the logic of Einstein Einstein the metric is
1:09:21
fundamental but the levy chavita connection from which we deduce the curvature is emergent right so the
1:09:27
fundamental theorem of romani and geometry is is that every connection causes every metric causes a connection
1:09:35
to emerge and then the curvature is built on the connection we turn this around we imagine we're looking for a connection and we wish it to build a
1:09:40
metric because connections are amenable to quantization in a way that metrics are not the next point is that we always
1:09:49
want to have a plan to return to finite dimensions without losing sight of the
1:09:54
quantum and lastly we want to liberate matter from its dependence on the metric
1:10:02
for its very existence so what we now need to build fermions
1:10:07
onto our four dimensional manifold in some way without ever choosing a metric if we're even having to have any
1:10:14
hope of playing a game involving matter starting from this perspective of no information other than the most bare
1:10:21
information let's get started we take x4 you need metrics we have none
1:10:28
we're not allowed to choose one so we do the standard trick as we choose them all
1:10:35
so we allow you 14 to equal the space of metrics on X for point wise therefore if
1:10:45
we propagate on top of this and you call this the projection operator if we
1:10:50
propagate on you 14 we are in some sense following a Fineman like idea of propagating over the space of all
1:10:55
metrics but not at a field level that a point wise tensorial level is there a
1:11:03
metric on you 14 well we both want one and don't want one if we had a metric from the space of all metrics we could
1:11:09
define fermions but we would also lock out any ability to do dynamics we want
1:11:14
some choice over what this metric is but we don't want full choice because we want enough to be able to define the
1:11:20
matter fields to begin with it turns out that if this is X 4 and this is this
1:11:29
particular endogenous choice of U 14 we
1:11:35
have a 10 dimensional metric along the fibers so we have a G 10 mu nu further
1:11:46
for every point in the fibers we get a metric downstairs on the base space so
1:11:53
if we pull back the cotangent bundle we
1:11:59
get a metric G 4 mu nu on pi star of the
1:12:05
cotangent bundle of X we now define the
1:12:12
chimeric bundle right and the chimeric bundle is the sum of the
1:12:19
vertical tangent bundle along the fibers with the pullback which we're going to call the horizontal bundle from the base
1:12:25
space so the chimeric bundle is going to
1:12:33
be the vertical tangent space of ten dimensions to you direct sum the
1:12:42
four-dimensional cotangent space which we're going to call horizontal to you
1:12:48
and the great thing about the chimeric bundle is is that it has an a priori metric it's kind of metrics on the floor
1:12:55
metric on the ten we can always decide that the two of them are naturally perpendicular to each other furthermore it is almost canonically
1:13:02
isomorphic to the tangent bundle of the cotangent bundle because we either have four out of 14 or 10 out of 14
1:13:07
dimensions on the nose so the question is what are we missing and the answer is
1:13:13
that we're missing exactly the data of a connection so this bundle chimeric see
1:13:21
we have c is equal to the tangent bundle of you up to a choice of a connection
1:13:29
theta and this is exactly what we wanted we have a situation where we have some
1:13:37
field on the manifold X in the form of a connection which is amenable more
1:13:42
friendly to quantization which is now determining a metric turning around the levee chavita game and the only problem
1:13:48
is is that we've had to buy ourselves into a different space than the one we thought we wanted to work on but now as
1:13:55
theta changes the fermions are defined on the chimeric bundle and it's the
1:14:01
isomorphism from the chimeric bundle to the tangent bundle of the space U which
1:14:07
is varying which means that the fermions no longer depend on the metric they no longer depend on the theta connection
1:14:13
they are there if things go quantum mechanical and we've achieved our objective of putting the matter fields
1:14:18
and the spin one fields on something of the same footing
1:14:26
but and I want to emphasize this one
1:14:32
thing most of us we think a lot about final theories and and about unification
1:14:39
but until you actually start daring to try to do it you don't realize what the
1:14:44
process of it feels like now try to imagine conducting your life or you have
1:14:50
no children let's say and no film tropic urges what you want to do is you want to use all of your money for yourself and
1:14:58
die penniless right like a perfect finish assuming that that's what you
1:15:03
wanted to do it would be pretty nerve-wracking at the end right how many days left do I have how many dollars
1:15:09
left I have this is the process of unification in physics you start giving away all of your most valuable
1:15:15
possessions and you don't know whether you've given them away too early whether you've husband them too long and so in
1:15:22
this process what we've just done is we've started to paint ourselves into a corner we got something we wanted but
1:15:28
we've given away freedom we're now dealing with a fourteen dimensional world now let me just sum this up by
1:15:41
saying
1:15:52
between fundamental and emergent
1:15:57
standard model and gr let's do G our
1:16:04
fundamental is the metric Mergent is the connection here in GU it is the
1:16:15
connection that's fundamental and the metric that's emergent in the next unit
1:16:23
of G u so this is sort of the first unit of G you there any quick questions having to do with confusion or may I
1:16:30
proceed to the next unit okay the next
1:16:37
unit of G U is the unified field content what does it mean for our fields to become unified there are in fact only at
1:16:50
this moment two fields that know about X
1:16:55
theta which is the connection that we've just talked about and a section Sigma
1:17:01
that takes us back so that we can
1:17:10
communicate back and forth between U and X we now need field content that only
1:17:18
knows about you which now has a metric depending on theta
1:17:29
a particular member of the audience is a hedge fund manager who taught me that
1:17:35
there is something of a universal trade and a universal trade has four components you have to have a view you
1:17:41
have to have a trade expression you have to be able to calculate your cost of carry and you need a catalyst our view
1:17:48
is going to be that somebody doesn't understand what trade is possible and we're going to make a trade that looks
1:17:54
like one of the worst trades of all time and hopefully if we if we have enough conviction we're gonna have a catalyst
1:17:59
to show that we actually got the better part of the deal what is that trade what is it that we think has been blocking
1:18:06
progress in gr and romani and geometry
1:18:19
as we've said we have the projection operators and we also have the levy chavita connection in the auxiliary
1:18:31
theory we have freedom to choose our
1:18:37
field content and we have the ability to get rid of much excess through the
1:18:45
symmetries of the gauge group we are going to take particle theory we're
1:18:52
going to make a bad trade or what appears to be a bad trade which is that we are going to give away the freedom to
1:18:59
choose our field content which is already extremely as I think I said in the abstract Baroque with all of the
1:19:06
different particle properties and we are going to lose the ability to use the
1:19:12
gauge group because we're going to trade it all
1:19:25
you have the family cow and you have
1:19:31
some magic beans so it's now time to
1:19:40
trade the family cow for the magic beans and bring them home and see whether or not we got the better of the deal okay
1:20:06
what is it that we get for the leve chavita connection well not much
1:20:12
one thing we get is that normally the space of connections is an affine space
1:20:18
not a vector space but in affine space almost a vector space a vector space up to a choice of origin but with the leve
1:20:27
chavita connection rather than having an infinite plane with an ability to take differences but no real ability to have
1:20:33
a group structure you pick out one point which then becomes the origin that means that any connection a has a torsion
1:20:43
tensor a which is equal to the connection minus the levy chavita connection so we get a tensor that we
1:20:52
don't usually have gauge potentials are not usually well-defined they're only
1:20:57
defined up to a choice of gauge so that's one of the things we get for our levy chavita connection but because the
1:21:02
gauge group is going to go missing this has terrible properties from with respect to the gauge group it almost
1:21:09
looks like a representation but in fact if we let the gauge group act there's going to be an affine shift furthermore
1:21:21
as we've said before the ability to use projection operators together with the
1:21:26
gauge group is frustrated by virtue of the fact that these two things do not commute with each
1:21:32
so now the question is how are we going to prove that we're actually making a
1:21:38
good trade okay first thing we need to
1:21:48
do is is that we still have the right to choose intrinsic field content we have an intrinsic field theory so if you
1:21:55
consider the structure bundle of The
1:22:00
Spinners right we built the chimeric bundle so we can define dirac spinors on the chimeric
1:22:09
bundle for in Euclidean signature a $14
1:22:14
of dimension to to the dimension of the space / - right so two to the 14 / - 2
1:22:21
to the seventh is 128 so we have a map
1:22:27
into a structure group of you 128 at
1:22:36
least in Euclidean signature we can get to mix signatures later from that we can
1:22:42
form the associated bundle
1:22:52
and sections of this bundle are either
1:23:00
depending upon how you want to think about it the gauge group H or C a space
1:23:14
of Sigma fields nonlinear there's no
1:23:25
reason that we can't choose this as field content again we're being led by
1:23:30
the nose like a bowl if we want to make use of the symmetries of the theory we
1:23:36
have to promote some symmetry to being part of the theory and we have to let it be subjected to dynamical laws we're
1:23:42
gonna lose control over it but we're not dead yet right we're fighting for our life to make sure that this trade has some hope so potentially
1:23:50
by including symmetries as field content we will have some opportunity to make
1:23:56
use of the projection so for those of you who so when I was thinking about
1:24:07
this I to be amazed by ships and bottles I must confess that I never figured out
1:24:13
what the trick was for ships in bottles but once I saw it I remembered thank you that's really clever so if you've never
1:24:21
seen it you have a ship which is like a curvature tensor and imagine that the mast is is the Ricci curvature if you
1:24:30
just try to shove it into the bottle you're undoubtedly gonna snap the mast
1:24:37
so you imagine you've transformed your gauge fields you've kept track of where the Ricci curvature was you try to push
1:24:44
it from one space like add value to forms into another space like add valued
1:24:50
one forms where connections live that's not a good idea instead what we do is
1:24:56
the following imagine that you're carrying around group theoretic information and what you do is you do a transformation based on
1:25:03
the group Theory so you lower the mast you push it through the neck having some
1:25:09
string attached to the mast and then you undo the transformation on the other side this is exactly what we're going to
1:25:19
hope is going to save us in this bad trade that we've made because we're
1:25:24
going to add field content that has the ability to lower the mast and bring the mast back up we're going to hope to have
1:25:31
a theory which is going to create a commutative situation but then once we've had this idea we start to get a
1:25:36
little bolder let's think about unified
1:25:44
content we know that we want a space of
1:25:51
connections a for our field theory but we know because we have a levee chavita
1:25:57
connection that this is going to be equal on the nose to add valued one forms as a vector space the gauge group
1:26:04
represents an ad valued one forms so if we also have the gauge group but we
1:26:10
think of that instead as a space of Sigma fields what if we take the semi
1:26:17
direct product at a group theoretic level between the two and call this a
1:26:23
our group of interest well by analogy we've always had a problem with the
1:26:29
Pangkor a group being too intrinsically tied to rigid flat minkovski space what
1:26:36
if we wanted to do quantum field theory in some situation which was more amenable to a curved space situation
1:26:43
it's possible that we should be basing it around something more akin to the gauge group and in this case we're
1:26:48
mimicking the construction where C here would be analogous to the Lorentz group
1:26:54
fixing a point in in Minkowski space and AD valued one forms would be analogous
1:27:00
to the Momentum's when we take in the semi direct product to create the in homogeneous Lorentz group otherwise
1:27:06
known as the Pangkor a group or rather it's double cover to allow spin so we're
1:27:12
going to call this the inhomogeneous gauge group or Iggy
1:27:21
and this is going to be a really interesting space because it has a couple of properties one is it has a
1:27:29
very interesting subgroup now of course H includes into G by just including on
1:27:38
to the first factor but in fact there's a more interesting homomorphism brought
1:27:47
to you by the levy chavita connection so this magic bean trade is going to start to enter more and more into our
1:27:53
consciousness if I take an element H and I map that in the obvious way into the
1:27:58
first factor but I map it onto the more
1:28:13
ore cart and for I think that's what I wish I remembered more of this stuff into the second factor it turns out that
1:28:21
this is actually a group homomorphism and so we have a non-trivial embedding
1:28:27
which is in some sense diagonal between the two factors that subgroup we are
1:28:34
going to refer to as the tilted gauge group and now our field content at least
1:28:39
in the bosonic sector is going to be a group manifold an infinite dimensional
1:28:45
function space lead group but a group nonetheless and we can now look at G mod
1:28:52
the Tilted gauge group and if we have
1:29:00
any interesting representation of H we can form homogeneous vector bundles and
1:29:05
work with induced representations and that's what the fermions are going to be so the fermions and our theories are
1:29:12
going to be H modules and the idea is that we're going to work with vector
1:29:17
bundles curly e of the form in
1:29:23
homogeneous gauge group
1:29:29
product it over the Tilted gage group
1:29:46
now just as in the finite-dimensional case we have a linear and a nonlinear component right because that topological
1:29:54
level this is just a cartoon Cartesian product so if we wish to take products
1:29:59
of fermions of spin oriole fields we have a place to accept them we can't
1:30:04
figure out necessarily how to map them into the nonlinear sector but we don't want to so just the way when we look at
1:30:10
supersymmetry we can take products of the spin 1/2 fields and map them into the linear sector we can do the same
1:30:17
thing here so what we're talking about is something like a super symmetric
1:30:23
extension of the inhomogeneous gauge group analogous to super symmetric extensions of the double cover of the
1:30:30
inhomogeneous Lorentz or plonker a go further because this construction is at
1:30:37
the level of groups we've left a slot on the left hand side on which to act so
1:30:43
for example if we want to take regular representations on the group we can act by the group G on the left hand side
1:30:52
because we're allowing the tilted gage group to act on the right hand side so it's perfectly built for representation
1:30:58
theory and if you think back to Vig neurs classification and the concept that a particle should correspond to an
1:31:04
irreducible representation of the in homogeneous gauge group in homogeneous Lorentz group we may be able to play the
1:31:10
same games here up to the issue of infinite dimensionality so right now our
1:31:15
field content is looking pretty good it's looking unified in the sense that
1:31:22
it has an algebraic structure that is not usually enjoyed by field content and the field content from different sectors
1:31:28
can interact and know about each other provided we can drag something of this
1:31:34
out of this with meaning now what would it mean to be able to use a
1:31:43
gauge group in an intrinsic theory like this we would be talking about something
1:31:51
like an action let's say a first-order action and it would take the group G
1:31:57
let's say to the real numbers invariant
1:32:06
not under the full group but under the tilted gauge subgroup and now the
1:32:13
question is do we have any such actions that are particularly nice and could we
1:32:20
recognize them the way Einstein did by trying to write down not the action in
1:32:25
Hilbert was the first one to write that down but I you know I always feel defensive because I think Einstein and
1:32:31
Grossman did so much more to begin the theory and that the Lagrangian that got written down was really just an
1:32:37
inevitability so just humor me for this talk and let
1:32:42
me call it the Einstein Grossman Lagrangian Hilbert certainly done fantastic things and has a lot of credit
1:32:48
elsewhere and he did do it first but here what we we had was that Einstein
1:32:55
thought in terms of the differential of the action not the action itself so what
1:33:01
we're looking for is equations of motion
1:33:07
or some field alpha where alpha belongs to the one forms on the group now in
1:33:22
this section of G you unified field content is only one part of it but what
1:33:29
we really want
1:33:35
is unified field content plus a toolkit
1:33:41
so we've restricted ourselves to one gauge group this big unitary group on
1:33:47
the spinners using whatever sort of inner product naturally exists on the spinners and not spinners value in an
1:33:53
auxiliary structure but intrinsic spinners the toolkit that we have is
1:34:02
that the adroit bundle looks like the
1:34:18
clifford algebra at the level of vector spaces which is just looking like the
1:34:28
exterior algebra on the chimeric bundle that means that it's graded by degrees
1:34:36
chimeric bundle has dimension 14 so there's a zero part of one part a two part all the way up to 14 plus we have
1:34:43
forms in the manifold and so the question is if I want to look at Omega I
1:34:51
valued in the adjoint bundle there's
1:34:56
going to be some element Phi I which is
1:35:05
pure trace right because it's the same
1:35:13
representations appearing where in the usually auxiliary directions as well as
1:35:18
the geometric directions so we get an entire suite of invariants together with
1:35:26
trivially associated invariants that come from using the Hodge star operator
1:35:31
on the form so I'm just going to call them for completeness I'm going to deal with them
1:35:39
now this is a tremendous amount of freedom that we've just gained normally we keep losing freedom but this is the
1:35:46
first time we actually begin to see that we have a lot of freedom and we're gonna actually retain some of this freedom
1:35:51
through the it to the end of the talk but the idea being that I can now start to define operators which correspond to
1:36:00
the ship in the bottle problem I can take field content epsilon and PI where
1:36:08
epsilon where these are elements of the
1:36:14
in homogeneous gauge group in other words epsilon is a is a gauge transformation and pi is an is a gauge
1:36:22
potential and I can start to define
1:36:28
operators I'm using so in this case if I
1:36:49
have a Phi which is one of these invariants in the form piece I can either take a contraction or I can take
1:36:56
a wedge product in the Lee algebra piece I can either take a Lee product or
1:37:02
because I'm looking at the unitary group there's a second possibility which is I can multiply everything by I and go from
1:37:09
skew-hermitian to hermitian and take a Jordan product using anticommutator x' rather than commutator so I actually
1:37:15
have a fair amount of freedom and I'm going to use a magic bracket notation which in whatever situation I'm looking
1:37:21
for knows what it wants to be is does it want to do contractions is wanting to wedge product leap product Jordan
1:37:27
product but the point is I now have a suite of ways of moving forms around so
1:37:34
for example I can define a Shia operator
1:37:41
that takes I forms valued in the adjoint bundle
1:37:58
to much higher degree forms value than the adjoint bundle so for this in this
1:38:05
case for example it would take a to form to a D minus 3 plus 2 or a D minus 1
1:38:12
form so curvature is an add value to form and if I had such a she AB operator
1:38:22
it would take add value to forms to add
1:38:27
value D minus 1 forms which is exactly the right space to be an alpha coming
1:38:33
from the derivative of an action this is exactly what Einstein was doing he took
1:38:40
the curvature which was large and he bent it back and he sheared off the viol
1:38:45
curvature and they took that part and he pushed it back along the space of
1:38:50
metrics to give us something which we nowadays call Ricci flow an ability for the curvature to direct us to the next
1:38:57
structure well we're doing the same thing here we're taking the curvature
1:39:03
and we can now push it back onto the space of connections
1:39:37
three plus I so in this case the idea is
1:39:47
that we've actually got something for our magic beans we have an ability now
1:39:52
to get equations of motion which go along the group in some sense it's as if
1:40:00
it was a gradient vector field except we're using forms rather than vectors but now what are the transformation
1:40:05
properties well because the curvature so
1:40:21
you have XI AB because the curvature of
1:40:29
a connection hit by a gauge transformation is equal on the nose to
1:40:41
the adjoint action on the Lee algebra of the curvature we know that if we have
1:40:48
two possible actions of conjugation under a bracket and the bracket respects
1:40:57
the action of the gauge group we know that this is going to be well preserved in other words we're going to get a form
1:41:03
that is gauge invariant relative to the tilted gauge group and so as a result we
1:41:09
now have the possibility for equations of motion which are well defined even
1:41:15
though they involve projection operators because we built the symmetries into the theory and we're working on a group
1:41:21
manifold to begin with what about the
1:41:26
torsion can we rescue the torsion here again we have good news
1:41:32
the torsion is problematic but if I look at a different field which I'm going to
1:41:38
call the Augmented torsion and I define it to be the regular torsion which would be pi minus this expression this turns
1:41:53
out to be beautifully invariant again so neither this term nor this term is gauge
1:42:00
invariant but there they failed to be gauge invariant in exactly the same way so an important principle of life which
1:42:07
I took too long to realize is that if you have one disease you're in real trouble but if you have two diseases you always
1:42:13
have the possibility of having one disease kill the other disease this is true and renormalization theory it's true in black-scholes theory it's true
1:42:20
all over the place so what we have here is we've got more diseases into the theory but an even number of diseases
1:42:26
allow us to have no disease at all so now we have two great tensors we've got 1 tensor coming from the curvature and
1:42:32
the shiaa operator we have another tensor coming from the torsion and it's augmentation
1:42:52
no we're doing okay
1:43:06
okay we're not doing physics yet we're just building tools we've built
1:43:11
ourselves a little bit of freedom we have some reprieves we've still got some very big debts to pay back for this magic beans trade we're in the wrong
1:43:18
dimension we don't have good field content we're stuck on this one spinner we've built ourselves some projection
1:43:24
operators we picked up some symmetric nonlinear Sigma field what can we write
1:43:33
down in terms of equations of motion let's start with einstein's concept if
1:43:40
we do xi AB of the curvature tensor of
1:43:46
the gage potential hit with an operator defined by the epsilon Sigma field plus
1:43:57
the star operator acting on the
1:44:04
Augmented torsion of the pair this contains all of the information when PI
1:44:11
is zero in Einstein's tensor in other
1:44:16
words there is a spin Oriole analog of the viol curvature Aspen Oriole analog of the traceless Ricci curvature and
1:44:22
Aspen Oriole analog of the scalar curvature this operator should shear off
1:44:29
the analog of the viol purva Chur just the way Einstein is projection shears off the viol curvature when you're
1:44:35
looking at the tangent bundle in this tournament which is now gauge invariant may be considered as containing a piece
1:44:45
that looks like lambda times G mu nu or a cosmological constant in this piece
1:44:51
here
1:44:58
can be made to contain a piece that looks like Einstein's tensor and so this
1:45:04
looks very much like the vacuum field equations but we have to add in
1:45:11
something else I'm gonna be a little bit vague because I'm still giving myself some freedom as we write this up but
1:45:24
we're going to define whatever tensor we need for this term these terms here this
1:45:30
is gauge invariant this is gauge invariant and this is gauge invariant
1:45:37
with respect to the tilted gauge group these two tensors together should be
1:45:45
exact and this tensor on its own should be exact
1:45:51
we're going to call the exact tensor the swerve ature so the particular she have
1:46:00
operator we call the swerve so that it's swerve curvature plus the adjustment needed for exactness and another gauge
1:46:09
invariant term which is not usually gauge invariant so that's pretty cool if
1:46:19
that works we've now taken the Einstein equation
1:46:24
and we've put it not on the space of metrics but we've put a generalization in an analogue on the space of gauge
1:46:30
potentials much more amenable to quantization with much more algebraic structure and symmetry in the form of
1:46:37
the in homogeneous gauge group in its homogeneous vector bundle some of which may be super symmetric now the question
1:46:44
is we've we've integrated so tightly with the matter field we have to ask
1:46:51
ourselves the question can we see unification here let's define matter
1:47:01
content in the form of Omega zero tenser than the spinners which is a fancy way
1:47:06
of saying spinners together with a copy
1:47:14
of the one forms tenser than the spinners and let me come up with two
1:47:21
other copies of the same data so I'll
1:47:32
make Omega D minus one just by duality so imagine that there's a Hodge star
1:47:37
operator and there's a little kid I had
1:47:46
the soma cube I don't know if you ever played with one of these things they're fantastic and I later found out that
1:47:51
this guy who invented the soma cube which you had to put the others pieces there was one piece that looked like
1:47:56
this this object and he was like this amazing guy in the resistance during
1:48:02
world war ii so I would like to name this the somatic complex after I guess his name is P at Hine I think so this
1:48:10
this complex I'm going to choose to start filling in some operators the
1:48:17
exterior derivative coupled to a connection but on the case of spinors we're gonna put a slash through it let's
1:48:23
make this the identity we'd now like to come up with a second operator here and
1:48:29
this second operator here should have the property that the complex should be exact
1:48:34
than the obstruction to it being a true complex to know potency should be
1:48:41
exactly the generalization of the Einstein equations thus unifying the spin oriole matter
1:48:50
with the intrinsic replacement for the curvature equations well we know that da
1:49:02
composed with itself is going to be the curvature and we know that we want that
1:49:08
to be hit by a Shia operator and if she
1:49:14
has a derivation you can start to see that that's gonna be curvature so you want something like FA followed by she
1:49:22
AB over here to cancel then you think okay well how am I going to get at
1:49:28
getting this augmented torsion and then you realize that the information in the
1:49:33
in homogeneous gauge group you actually have information not for one connection but for two connections so in one case I
1:49:43
can do plus star to pick up the a sub PI
1:49:57
but I'm also gonna have a derivative operator if I just do a star operation so I need another derivative operator to
1:50:04
kill it off here so I'm going to take minus the derivative with respect to the
1:50:09
connection H inverse da not H which
1:50:16
defines a connection one form as well as having the same derivative cup coming
1:50:23
from the levy chavita connection on you so in other words I have two derivative operators here I have to add valued one
1:50:28
forms the difference between them is going to be of zero with order and it's going to be precisely the augmented
1:50:33
torsion that's the same game I'm going to repeat here
1:50:51
so I'm going to do the same thing here I'm going to define a bunch of terms
1:50:57
where in the numerator I'm going to pick up the pie as well as the derivative in
1:51:02
the denominator because I have no derivative here I'm going to pick up
1:51:08
this H inverse da not an H I'm going to
1:51:17
do that again on the other side they're
1:51:31
gonna be plus and minus signs but it's a magic bracket that knows whether or not should be a plus sign or a minus sign and I apologize for that but I'm not
1:51:37
able to keep that straight and then there's gonna be one extra term where
1:51:47
all these T's have the epsilon and PI's okay so some crazy series of
1:51:53
differential operators on the northern route so if you take the high road or you take the low road when you take the
1:51:59
composition of the to the differential operators fall out and you're left with an obstruction term that looks like the
1:52:07
Einstein field equations well that's
1:52:20
pretty good if true can you go farther
1:52:27
well look at how close this field content is to the picture from
1:52:34
deformation theory that we learned about in low dimensions the low dimensional
1:52:41
world works by saying that symmetries map to field content map to equations
1:52:51
usually in the curvature and when you linearize that if you're in low enough dimensions you
1:52:58
have Omega 0 Omega 1 sometimes I make a zero again and then something that comes
1:53:05
from Omega 2 and if you can get that sequence to terminate by looking at something like a half signature at theorem or a bent back to Ram complex in
1:53:13
the case of dimension 3 you haven't a tee a singer theory and remember we need some way to get out of infinite
1:53:18
dimensional trouble all right you have to have someone to call when things go wrong overseas you have to be able to
1:53:24
get your way home and in some sense we call it a tee and singer and say we're in some infinite dimensional space can't
1:53:29
you cut out some finite dimensional problem that we can solve even though we start getting ourselves into serious
1:53:34
trouble and so we're going to do the same thing down here we're going to have a mega
1:53:41
zero add Omega 1 add direct sum Omega
1:53:49
zero add Omega D minus 1 ad and it's
1:54:03
almost the same operators and this is
1:54:08
now not just a great guess it's actually the information for the deformation
1:54:15
theory of the linearized replacement of the einstein field equations so this is
1:54:23
computing the director iski tangent space just as if you were doing self-dual theory or chern-simons theory
1:54:29
you've got two somatic complexes right one of them is bose one of them is
1:54:36
firming the obstruction to both of them is a common generalization of the
1:54:43
Einstein field equations what's more is if you if you start to think about this
1:54:50
this is some version of Hodge theory with funky operators so you can ask
1:54:56
yourself well what are the harmonic forms in a fractional spin context well
1:55:04
they're different depending upon whether you take the degree 0 piece together with the degree
1:55:09
P so you take the degree one piece let's just take the degree one piece you get
1:55:16
some kind of equation so I'm going to decide that I have a Zeta field which is
1:55:22
an Omega 1 tensor spinors and a field
1:55:27
new jewelry strikes me as a kiddush
1:55:33
field new is omega 0 tensor s ok what
1:55:46
equation would they solve if we were doing Hodge theory relative to this complex the equation would look
1:55:54
something like this
1:56:09
there'd be one equation that was very simple and then there'd be one equation
1:56:14
that would be like really hard to guess
1:56:43
kahshanna I hope I'm not screwing this up but look all these words and I still
1:56:57
feel like I'm managing to run out of room
1:57:47
now if you have something like that that would be a hell of a Dirac equation right you've got differential operators
1:57:53
over here you've got differential operators I guess I didn't write them in
1:58:07
but you would have two differential operators over here and you'd have this differential operator coming from this
1:58:13
more cartoon form so I apologize and being a little loose here but the idea is you have two of these terms or
1:58:20
zeroeth order three of these terms would be first-order and on this side one term would be first-order and that's not
1:58:32
there that's right that was a mistake oh no sorry that was a mistake
1:58:39
calling it a mistake these are two separate equations right so you have two separate fields nu and Zeta and you have
1:58:48
a couple set of differential equations that are playing the role of the Dirac theory coming from the Hodge theory of a
1:58:55
complex whose obstruction to being calm ology theory would be the replacement to the Einstein field equations which would
1:59:02
be rendered gauge invariant on a group relative to a tilted sub group okay what
1:59:11
would so now we've dealt with two of the three sectors is there any generalization of the yang-mills equation well if we were to take the
1:59:20
Einstein field equations ation and take the norm square of it oh there's some
1:59:27
point I should make here just one second I've been treating this as if everything
1:59:33
is first-order well what really happens here
1:59:39
is that you've got symmetries you've got symmetric field content you've got
1:59:51
ordinary connections and we're
2:00:00
neglecting to draw the fact that there have to be equations here too these equations are first-order so why
2:00:10
do we get to call this a first-order theory if there are equations here which are of second-order well it's not a pure
2:00:17
first-order theory but when I say a first-order theory in this context what I really mean is that the second-order
2:00:23
equations are completely redundant on the first-order equations by virtue of the symmetry principle that is any
2:00:29
solution of the first-order equations should automatically apply imply a
2:00:34
solution of the second order equations so from that perspective I can pretend
2:00:39
that this isn't here because it is sufficient to solve the first-order equations so I can now look let's call
2:00:52
that entire replacement which we
2:00:58
previously called alpha I miss that alpha equal to epsilon because I've actually been using Absalon the portion
2:01:04
of it that is just the first-order equations and take the norm square of that that gives me a new Lagrangian and
2:01:10
if I solve that new Lagrangian it leads to equations of motion that look like
2:01:17
exactly what we said before
2:01:26
and it ends up defining an operator that looks something like this da star the
2:01:35
adjoint of the Shehab operator so in
2:02:01
other words this piece gives you some portion that looks like right from the
2:02:06
swerve ature tensor there's going to be some component that's playing the role of Einsteins field equations directly
2:02:12
and the Ricci tensor but generalized and then you're gonna have some differential operator here so that the replacement
2:02:20
for the yang-mills term instead of da star of fa you've got these two XI a band at XI AB and an adjoint XI AB
2:02:27
together in the center generalizing the yang-mills theory then you say well how
2:02:34
come we don't just see the yang-mills theory why don't we see general relativity as well but in the full
2:02:39
expansion there's also a term that zeroeth order that's effectively acting like the identity which hits this as
2:02:45
well so you have one piece that looks like the yang-mills theory and in these second-order equations you also have a
2:02:50
piece that looks like the Einstein theory and this is in the vacuum
2:02:56
equations so then the question is how do
2:03:02
you see the Dirac theory coming out of this and so what we're just trying to
2:03:08
put together now before we come out with the manuscript for this is putting these
2:03:14
two elliptic complexes together the direct terms go between the two complexes right so the idea is that the
2:03:21
stress-energy tensor should be the up and back term and the Dirac equations should come out of the term that goes up
2:03:29
and over versus the term that goes over and up and you need some cancellations
2:03:34
to make sure that everything is of zero width order properly invariant etc and that's taking
2:03:39
little time because frankly I'm not good keeping track of indices minus signs left right - it's a learning-disabled
2:03:45
nightmare
2:03:52
so we've got one more unit to go I mean
2:04:00
there's a fifth unit that has to do with mathematical applications but this is sort of a physics talk for today is
2:04:05
there any questions before we go into the last unit and then really handle questions for real all right let me show
2:04:13
you the next a little bit we've got
2:04:18
problems we're not in four dimensions we're in 14 we don't have great field content because we've just got these
2:04:24
unadorned spinners and we're doing gauge transformations effectively on the
2:04:29
intrinsic geometric quantities not on some safe auxiliary data that's tensor
2:04:36
product with what are our spinners are how is it that we're gonna find anything
2:04:41
realistic and then we have to remember everything we've been doing recently has been done on you we've forgotten about X
2:04:57
how does all of this look to X so X is
2:05:04
sitting down here and all the action is happening up here on you 14 there's a
2:05:10
projection operator I've used PI twice it's not here the field contents just projection and I've got a Sigma which is
2:05:16
a section what does Zeta
2:05:27
pulled back or new pulled back look like
2:05:38
on x4
2:06:04
okay let's try to think about how we would come up with this filled content
2:06:11
starting from first principles let's imagine that there's nothing to begin
2:06:17
with then you have one copy of matter whatever it is that we see in our world
2:06:24
the first generation in order for that to become interesting it has to have an
2:06:32
equation so it has to get mapped somewhere then we've seen the muon and
2:06:39
all the rest of the matter that comes with it we have a second generation then in the mid-1970s pearl finds the tau
2:06:47
particle and we start to get panicked that we don't understand what's going on
2:06:53
one thing we can do is we could move these equations around a little bit and
2:06:58
move the equation for the first generation back and then we could start
2:07:05
adding particles let's imagine that we could guess what particles we'd add we'd add a pseudo generation of 16 particles
2:07:13
spin three halves never-before-seen not necessarily superpartners but we read a
2:07:19
Schwinger matter with familiar internal quantum numbers but potentially so that they're flipped so that matter looks
2:07:24
like antimatter to this generation then we add just for the heck of it
2:07:32
144 spin 1/2 fermions which contain a bunch of particles with familiar quantum
2:07:38
numbers but also some very exotic looking particles that nobody's ever seen before now we start doing something
2:07:47
different we make an accusation one of our generations isn't a regular
2:07:53
generation it's an imposter at low energy in a cooled state potentially it
2:07:58
looks just the same as these other generations but were we somehow able to turn up the energy imagine that it would
2:08:06
unify differently with this new matter that we've posited rather than simply
2:08:11
unifying onto itself so two of the generations would unify into themselves but this third generation
2:08:17
would fuse with the new particles that we've already added we consolidate
2:08:23
geometrically we can add some 0 with order terms and we imagine that there is
2:08:30
an elliptic complex that would govern the state of affairs we then choose to
2:08:36
add some stuff that we can't see it all that's dark and this matter would be
2:08:43
governed by forces that were dark to there might be dark electromagnetism and dark strong and dark weak it might be
2:08:51
that things break in that sector completely differently and it doesn't break down to an su 3 cross su 2 cross u
2:08:56
1 because these are different su 3 s su 2 s nu ones and it may be that there would be like a high energy su 5 you
2:09:04
know or some p'tee Salam Model imagine then that chirality was not fundamental but it was
2:09:11
emergent that you had some complex and as long as there were cross terms these two halves would talk to each other but
2:09:18
if the cross terms went away the two terms would become decoupled and just the way we have a left hand and we have
2:09:24
a right hand and you asked me right imagine you have a neurological condition and in Oliver Sacks sort of an
2:09:30
idiom if somebody's only aware of one side of their body they say oh my god I'm deformed I'm asymmetric right but we
2:09:37
actually have a symmetry between the two things that can't see each other then we
2:09:43
would still have a chiral world but the chirality wouldn't be fundamental there'd be something else keeping the
2:09:49
fermions light and that would be the absence of the cross strands now if you look at what happens in our replacement
2:09:55
for the Einstein field equations the term that would counterbalance the scalar curvature if you put these
2:10:02
equations on a sphere they wouldn't be satisfied if the T term had a zero
2:10:07
expectation value because there would be non-trivial scalar curvature and the curtain to swerve ature terms but
2:10:13
there'd be nothing to counterbalance so it's fundamentally the scalar curvature that would coax the valve on the
2:10:20
Augmented torsion out of the vacuum to have a nonzero level and if you pumped
2:10:25
up that sphere and it smeared out the curvature which you can't get rid of because of topological consider Asians let's say from churned a theory
2:10:33
you would have a very diffuse very small turn and that term would be the term
2:10:40
that was playing the role of the cosmological constant so in a large universe you'd have a curvature that was
2:10:46
spread out and things would be very light and things would get very dark due to the absence of curvature linking the
2:10:53
sectors and that turns out to be exactly
2:11:01
our complex so in other words just to
2:11:08
recap starting with nothing other than a four manifold we built a bundle you the
2:11:16
bundle you had no metric but it almost had a metric and had a metric up to a connection there was another bundle on
2:11:23
top of that bundle called the chimeric bundle the chimeric bundle had an intrinsic metric we built our spinners
2:11:29
on that we restricted ourselves to those spinners we moved most of our attention
2:11:35
to the emergent metric on u14 which gave gave us a map between the chimeric
2:11:42
bundle and the tangent bundle of u14 we built a tool kit allowing us to choose
2:11:50
symmetric field content to define equations of motion on the cotangent
2:11:55
space of that field content to form a homogeneous vector bundle with the fermions to come up with unifications of
2:12:04
the einstein field equations yang-mills equations and Dirac equations we then
2:12:10
broke those things apart under decomposition pulling things back from u14 and we found a three generation
2:12:17
model where nothing has been put in by hand and we have a 10 dimensional normal
2:12:22
component which looks like the spin 10 theory
2:12:32
I can tell you where there are problems in this story I can tell you that when
2:12:38
we move from Euclidean metric to minkovski metric we seem to be off by a sign somewhere or I could be mistaken I
2:12:44
could tell you that the propagation in 14 dimensions has to be worked out so
2:12:50
that we would be fooled into thinking we were in a four dimensional world there are lots of things to ask about this
2:12:55
theory but I find it remarkable that tying our hands we find ourselves with
2:13:02
new equations unifications and three generations in a way that seems
2:13:07
surprisingly rich certainly unexpected
2:13:13
and I think I'll stop there thank you very much for your time [Applause]
2:13:24
so thanks for watching that video but I thought I would do since that was the
2:13:30
first time I'd really presented the theory at all in public and I'd gotten somewhat turned around on my trip to
2:13:37
England and trying probably stupidly to do last-minute Corrections got me a bit confused in a few places and I wrote
2:13:44
some things on the board I probably shouldn't have I thought I would try a partial explainer for technically
2:13:51
oriented people so that they're not mystified by the video and any errors
2:13:58
here of my own I'm known to make many so hopefully they won't be too serious but
2:14:05
we'll find out so this is a supplementary explainer for the geometric unity talk at Oxford that you
2:14:12
just saw first of all I think the most important thing to begin with is to ask what new
2:14:18
hard problems arise when you're trying to think about a fundamental theory that aren't found in any earlier theory now
2:14:26
every time you have an effective theory which is a partial theory there is always the idea that you can have
2:14:33
recourse to a lower-level strata so you don't have to explain in some sense everything coming from very little or
2:14:40
nothing I think that the really difficult issue that people don't talk
2:14:46
enough about is the problem of the fire that lights itself and I think this was beautifully demonstrated by MC Escher in
2:14:53
his famous lithograph drawing hands where he takes the idea of the canvas or
2:15:00
the paper as a given but somehow he imagines that the canvas could will into
2:15:06
existence the ink needed to draw the hands that move the pen to draw the
2:15:12
hands that concept is actually the super tricky part in my opinion about going
2:15:19
from effective theories to any attempt at a fundamental theory so with that said what I want to think about is what
2:15:27
antecedents does this concept have in physics and I find that there really
2:15:33
aren't any candidate theories of everything are unified field theories that I can find that plausibly
2:15:40
give us an idea of how a canvas would will an entire universe into being and
2:15:47
so that really to me is the conceptual problem that I think b-doubles this and makes the step quite a bit more
2:15:55
difficult than some of the previous technical steps if you ask for antecedents however there is one that at
2:16:02
least within physics is relatively famous and that is by John Archibald wheeler and it is a picture in some
2:16:09
sense of the universe contemplating itself and so this idea that somehow the universe would contemplate itself into
2:16:16
existence maybe the letter U is in some sense analogous to the paper and somehow
2:16:22
the eye rather than the hand is drawn across to look at a different part of
2:16:28
the of the U and whether or not that has meaning is intrinsically always a
2:16:33
question people are animated by it but I don't know that people have actually worked on it the quote of Einstein's I
2:16:40
think that really speaks to me often the most and maybe even was my thesis problem was he asked whether the creator
2:16:49
had any choice in how the universe was constructed and so I think if you believe that the canvas is itself the
2:17:01
that which generates all of the content and all of the action you're you're left
2:17:08
with a puzzle as to how would you move forward from this it might be easier in a mathematical sense to temporarily put
2:17:16
the U on its back to put it more in line with a standard picture that many
2:17:21
mathematicians and physicists will be familiar with in sector one of the
2:17:29
geometric unity theory space-time is replaced and recovered by the observers
2:17:36
contemplating itself and so there are several sectors of G U and I wanted to
2:17:41
go through at least four of them in Einstein's space-time we have not
2:17:49
only four degrees of freedom but also a spacetime metric representing rulers and protractors if we're going to replace
2:17:56
that it's very tricky because it's almost impossible to think about what would be underneath einstein's theory
2:18:02
now there's a huge problem in the spin oriole sector which I don't know why more people don't worry about which is
2:18:09
that spinners aren't defined for representations of the double cover of gl4 are the general linear groups
2:18:17
effective spin analog and as such if we imagine that we will one day quantize
2:18:23
gravity we will lose our definition not of the electrons but let's say of the
2:18:29
medium in which the electrons operate that is there will be no spin oriole bundle until we have an observation of a
2:18:36
metric so one thing we can do is to take a manifold X D as the starting point and
2:18:43
see if we can create an entire universe from no other data and not even with a metric so since we don't choose a metric
2:18:52
what we instead do is to work over the space of all possible point wise metrics so not quite in the Fineman sense but in
2:18:59
the sense that we will work over a bundle that is a quite larger quite a
2:19:08
bit larger dimension so for example if X was a four-dimensional therefore D
2:19:14
equals four then Y in this case would be d squared which would be 16 + 3 D which would be
2:19:21
12 making 28 divided by 2 which would be 14 so in other words a four-dimensional
2:19:26
universe or sorry a four-dimensional proto spacetime not a spacetime but a proto space-time with no metric would
2:19:33
give rise to a 14 dimensional observers
2:19:38
portion called Y now I believe that in the lecture in Oxford I called that you
2:19:45
so I'm sorry for the confusion but of course this shifts around every time I take it out of the garage and that's one
2:19:51
of the problems with working on a theory in solitude for many years so we have two separate spaces and we
2:19:59
have fields on the two spaces now what I'm going to do is I'm gonna refer to fields on the XD space by hebrew letters
2:20:08
so instead of g mu nu for a metric i just wrote gimel mem noon and the idea being that i
2:20:16
want to separate latin and greek fields on the y space from the rather rarer
2:20:23
field that actually lived directly on X so this is a little bit confusing one way of thinking about it is to think of
2:20:30
the observer s-- as the stands plus the pitch in a stadium I think I may have
2:20:37
said that in the in the lecture but this is what replaces the questions of where and when in the newspaper story that is
2:20:45
a fundamental theory where and when correspond to space and time who and what correspond to bosons and fermions
2:20:51
and how and why correspond to equations
2:20:57
and the Lagrangian that generates them so if you think about those six quantities you'll realize that that's really what the content of a fundamental
2:21:04
theory is assuming that it can be quantized properly most fields and in
2:21:09
this case we're going to call the collection of two tuples Omega so the
2:21:15
inside of Omega that will be in the first tuple will have epsilon and PI written a sort of a non-traditional
2:21:22
variation of how we write this symbol for pi in the second tuple we'll have the letters nu and Zeta and I would like
2:21:31
them not to move because they honor particular people who are important so most fields in this case Omega are
2:21:38
dancing on Y which was called you in the lecture unfortunately but they are
2:21:44
observed via pull back as if they lived on X in other words if you're sitting in the stands you might feel that you're
2:21:49
actually literally on the pitch even though that's not true so what we've done is we've taken the U of wheeler
2:21:55
we've put it on its back and created a W structure and the W structure is meant to say that there's a bundle on top of a
2:22:02
bundle again geometric unity is more flexible than this but I wanted to make the most concrete approach to the
2:22:09
possible for at least this introduction and sometimes we don't knit we don't
2:22:15
need to state that why would in fact be a bundle you could be an immersion of X
2:22:21
into any old manifold but I'd like to go with the most ambitious version of GU first so the two projection maps are PI
2:22:29
2 and PI 1 and what we're going to say up top is is that we're going to have a a symbol Z and an action of a group row
2:22:39
on Z standing in for any bundle associated to the principal bundle which
2:22:45
is generated as the unitary bundle of the spin of the spinners on the chimeric
2:22:51
tangent bundle 2y that's a bit of a mouthful but the key issue was that on the manifold Y there happens to be a
2:22:59
bundle which is isomorphic non canonical e to the tangent bundle of Y which can
2:23:04
has a definite and canonical metric and in fact there that carries the spinners
2:23:12
so this is the way in which we get spinners without ever having to choose a metric but we pick up some technical
2:23:17
debt to use the computer science concept by actually having to now work on two different spaces x and y and we're not
2:23:25
merely working on x anymore this leads
2:23:30
to the Mark of Zorro that is we know that whenever we have a metric by the fundamental theorem of Romani in
2:23:36
geometry we always get a connection it happens however that what is missing to turn the canonical chimeric bundle on Y
2:23:45
into the tangent bundle of Y is in fact a connection on the space X so there is
2:23:52
one way in which we've reversed the fundamental theorem of Romani in geometry where a connection on X leads
2:23:58
to a metric on Y so if we do the full transmission mechanism out and gimel on
2:24:03
x leads to alpha sub gimel for the leve chavita connection on x alpha sub gimel
2:24:10
live leads to g sub alpha which is or sorry the G sub Aleph I'm not used to
2:24:18
using Hebrew in math so jisub
2:24:23
Alif then is a metric on why and that creates a levy chavita connection of the
2:24:32
metric on the space Y as well which then B induces one on the spin oriole bundles
2:24:37
in Sector two the in homogeneous gauge group on Y replaces the Pangkor a group
2:24:44
and the internal symmetries that are found on X and in fact you use a
2:24:50
fermionic extension of the inhomogeneous gauge group to replace the supersymmetric punker a group and that
2:24:56
would be with field content 0 forms 10 surd and spinner tensor with spinners
2:25:02
direct some one forms tensor two spinners all up on Y as the fermionic
2:25:08
field content so that gets rid of the biggest problem because the internal
2:25:14
symmetry group is what causes the failure I think of supersymmetric particles to be seen in nature which is
2:25:20
we have two different two different origin stories which is a little bit like lilith and in Genesis we can't
2:25:29
easily say we have a unified theory if space-time and the SU 3 cross su 2 cross
2:25:34
u one group that lives on space-time have different origins and cannot be related in this situation we tie our
2:25:41
hands and we have no choice over the the group content so just to fix bundle
2:25:47
notation we let H be the structure group of a bundle piece of H over a base space
2:25:55
B we use PI for the projection map we've reserved the variation in the PI
2:26:02
orthography for the field content and we try to use write principle actions I'm
2:26:08
terrible with left and right but we do our best we use H here not G because we
2:26:15
want to reserve G for the inhomogeneous extension of H once we move to function
2:26:20
spaces so with function spaces we can take the bundle of groups using the
2:26:28
adjoint action of H on itself form The Associated bundle and then
2:26:35
moved to C infinity sections to get the so-called gage group of automorphisms we
2:26:41
have a space of connections typically denoted by a and we're going to promote Omega 1 tensor in the adjoint bundle to
2:26:51
notation of script n as the affine group
2:26:57
which acts directly on the space of
2:27:03
connections now the in homogeneous gauge
2:27:09
group is formed as the semi direct product of the gauge group of automorphisms together with the affine
2:27:15
group of translations of the space of connections and you can see here is a
2:27:22
version of an explicit group multiplication well I hope I got that one right and then we have an action of
2:27:28
G that is the inhomogeneous gauge group on the space of connections because we have two different ways to act on
2:27:35
connections we can either act by gauge trans transformations or we can act by affine translations so putting them
2:27:42
together gives us something for the inhomogeneous gauge group to do we then
2:27:48
get a bi connection in other words because we have two different ways of pushing a connection around if we have a
2:27:53
choice of a base connection we can push the base connection around in two different ways according to the portion
2:28:00
of it that is coming from the gauge transformations curly H or the affine
2:28:07
translations coming from curly n we can
2:28:12
call this map the BI connection which gives us two separate connections for
2:28:18
any point in the in homogeneous gauge group and we can notice that it can be
2:28:24
viewed as a a section of a bundle over
2:28:32
the base space to come when we find an interesting embedding of the gauge group
2:28:37
that is not the standard one in the in homogeneous gauge group so our summary
2:28:42
diagram looks something like this take a look at the Tau sub a knot we
2:28:47
will find a homomorphism of the gauge group into its inhomogeneous extension that isn't simply inclusion under the
2:28:55
first factor we and I'm realizing that I
2:29:00
have the wrong pipe reduction just be a simple PI projecting down we have a map
2:29:05
from the gate in homogeneous gauge group via the by connection to a cross a
2:29:11
connections across connections and that that behaves well according to the difference operator Delta that takes the
2:29:18
difference of two connections and gives an honest add value at 1/4 ok the
2:29:23
infinitesimal action of the gauge transformation of a gauge transformation or at least an infinitesimal one on a
2:29:29
point inside of the group is given by a somewhat almost familiar expression
2:29:35
which should remind us of how the first term in the gauge deformation complex
2:29:42
for self-dual yang-mills actually get started and so by acting via this interesting
2:29:52
embedding of the inhomogeneous gauge group on sorry the embedding of the
2:29:58
gauge group inside it's in homogeneous extension but the non-trivial one we get something very close to the original
2:30:05
first step of the two step deformation complex now in Sector 3 there are
2:30:11
payoffs to the magic beans trade the big issue here is is that we've forgone the privilege of being able to choose and
2:30:18
dial in our own field content and we've decided to remain restricted to anything
2:30:23
we can generate only from XD in this case X 4 so we generated y 14 from X 4
2:30:30
and then we generated chimeric tangent bundles on top of that we built spinners
2:30:35
off of the chimeric tangent bundle and we have not made any other choices so
2:30:41
we're dealing what I think it's u 128 u u 2 to the seventh that is our structure
2:30:51
group and we it's fixed by the choice of X for not anything else
2:30:57
so what do we get well as promised there is a tilted homomorphism which takes the
2:31:05
gauge group into its inhomogeneous extension it acts as inclusion on the first factor but it uses the levy
2:31:12
chavita connection to create a second sort of more cartan form I hope I remember the terminology right it's been
2:31:18
a long time the map is injective because it's injective under the first factor but it
2:31:24
actually gives us a non trivial embedding of the gauge group in its in
2:31:29
homogeneous extension which makes the whole theory work we then get to see I
2:31:35
have operators now a shiev operator is a map from the group crossed the ad valued
2:31:41
I forms in this case the particulars about operators were interested in is
2:31:47
mapping I forms 2d minus 3 plus I forms so for example it would map a to form 2d
2:31:59
minus 3 plus I so if d for example were
2:32:05
14 then and and i were equal to 2 then
2:32:11
14 minus 3 is equal to 11 plus 2 is
2:32:17
equal to 13 so that would be an ad valued 14 minus 1 form which is exactly
2:32:26
the right place for something to form a current that is the differential of a
2:32:32
Lagrangian on this space now the
2:32:37
Augmented torsion the torsion is a very strange object it's introduced sort of right at the beginning of learning
2:32:44
differential geometry but it really doesn't get used very much one of the reasons it doesn't get used in gauge theory is that it's not gauge invariant
2:32:50
it has a gauge invariant piece to it but then a piece that spoils the gauge invariance but we because we have two
2:32:57
connections one of the ideas was to introduce two diseases and then to take
2:33:03
a difference and as long as the disease is the same in both the difference will
2:33:08
not have the disease because both diseases are in polluted but with a minus sign between them so the Augmented torsion is
2:33:15
relatively well behaved relative to this particular slanted or tilted embedding
2:33:22
of the gauge group in its inhomogeneous extension which this is very nice
2:33:28
because now we actually have a use for the torsion we have an understanding of why it may never figured particularly
2:33:35
into geometry is that you need two of two connections rather than one to see the advantages of torsion at all so
2:33:43
here's an example of one ship-in-a-bottle operator I think this would be sort of analogous if I'm not
2:33:48
mistaken to trying to take the Ricci curvature from the entire Riemann
2:33:54
curvature but if you think about what Einstein did Einstein had to go further and reduce the Ricci curvature to the
2:34:01
scalar curvature and then sort of dial the components of the traceless Ricci
2:34:07
and the scalar curvature to get the right proportions so there are many Xie
2:34:12
operators and you have to be very careful about which one you want and once you know exactly what it is you're
2:34:18
trying to hit you can choose the Shehab operator to be bespoke and get the
2:34:25
contraction that you need now I've I've
2:34:31
made you guys sit through a lot so I wanted to give you sort of humorously a a feeling of positivity for the
2:34:39
exhaustion so the years of anxious searching in the dark with their intense longing their intense alternations of
2:34:46
confidence in exhaustion and the final emergence into the light only those who have experienced it can understand it I
2:34:52
just always thought this was like the most sensitive and beautiful quote and I wish it were one of his better known
2:34:58
quotes but I think it's so singular that it's hard to it's hard to feel what it
2:35:03
was that he was talking about because in fact he sort of explains this in the last line so given that you've been on a
2:35:11
long journey here is something of what geometric unity equations might look
2:35:16
like so in the first place you have the swerved curvature the Shi AB applied to
2:35:21
the curvature tensor that in general does not work out to be exact so you can't have it as the
2:35:28
differential of a Lagrangian and in fact that we talk about swirls swerves twirls
2:35:34
Eddie's there has to be a quadratic Eddy tensor that I occasionally forget when I
2:35:40
pull this thing out of mothballs and the two of those together make up what I call the total swerve ature and on the
2:35:48
other side of the equation you have the displaced torsion which I've called dysplasia and to get rid of the pesky
2:35:55
sort of minus sign and Hodge star operator this would be the replacement
2:36:01
for the Einstein equation not on X where we would perceive it but on Y before
2:36:07
being pulled back on to the manifold X so a condensation of that would be very
2:36:14
simple in simplest terms we would be saying that the swerve ature is equal to
2:36:19
visit to the dysplasia and at least in this sector of the four main equations of theoretical physics this would be the
2:36:26
replacement for the Einstein equations again on Y before being pulled back to X
2:36:32
next is the sketch of the fermionic field content I'm not sure whether that
2:36:38
should have been sector for sector three but it's gonna be very brief I showed some pictures during the lecture and I'm
2:36:46
not gonna go back through them but I wanted to just give you an idea of where this mysterious third generation I think
2:36:52
comes from so if we review the three
2:36:58
identities here we see that if we have a space V thought of like as a tangent
2:37:05
bundle and then you have spinners built on the tangent bundle when you product tensor product the tangent bundle with
2:37:13
its own spinners it breaks up into two pieces one piece is the so-called cart
2:37:18
and product which is sort of the some of the highest weights and the other is a second copy of the spinners gotten
2:37:25
through the Clifford contraction so that's well known but now what I think fewer people know many people know that
2:37:33
the spinners have a sort of an exponential property that is the spinners of a direct song
2:37:38
are the tensor product of the spinners of the two summons of the direct Sun so
2:37:45
that's a very nice sort of version of an exponential and exponential would take a sum and turn it into a product what
2:37:52
happens when you're trying to think about a tangent space in Y is being
2:37:59
broken up into a tangent space along an immersed X together with its normal
2:38:04
bundle so imagine that x and y are the tangent space to X and a normal bundle
2:38:10
so there were read a Schwinger piece that is the spin three-halves piece has
2:38:16
a funny kind of an almost exponential property that is they're worried to
2:38:22
Schwinger content of a direct sum of vector spaces is equal to the rita
2:38:28
Schwinger of the first tensor product did with the ordinary spinners in the
2:38:34
second direct sum with the ordinary spinners in the first tensor product it with the Ricci with this re they worry -
2:38:40
winger content of the second son man but then there's this extra interesting term which is the spinners on the first sum
2:38:49
and tensor product did with the spinners on the second Samantha now recalling that when I started my career we did not
2:38:57
know that neutrinos were massive and I figured that they probably had to be massive because I desperately wanted a
2:39:02
16 dimensional space of internal quantum numbers not 15 because my my ideas only
2:39:08
work if the space of internal quantum numbers is of dimension 2 to the N and
2:39:13
one of my favorite equations at the time was 15 equals 2 to the fourth not
2:39:19
literally true but almost true and thankfully in the late 1990s the case
2:39:24
for 16 particles in a generation was strengthened when neutrinos were found
2:39:30
to have mass but that remaining term in the south-east corner the spinners on X
2:39:38
tensor spinners and why looks like the term above it in line 2.15 and that in
2:39:47
fact is the third generation of matter in my opinion that is it is not a true generation it
2:39:56
is broken off and would unify very differently if we were able to heat the universe to the proper temperature so
2:40:04
starting to sum up this is not the full theory I'm just presenting this in part
2:40:09
to dip my toe back into the water it's a daunting task to try to address people about something you've been thinking
2:40:14
about for a long time and if no idea whether it's even remotely correct this
2:40:19
is the Einsteinian replacement and it must be pulled back to X that's the first thing the yang-mills Maxwell peace
2:40:25
comes from a direct square of the Einstein replacement that is I don't believe that we're really looking for a
2:40:32
unifying equation I think we're looking for a unifying Dirac Square direct famously took the square root of the
2:40:38
client Gordon equation and he gave us the Dirac equation and in fact I believe
2:40:44
that the Dirac equation and the Einstein equation are to be augmented and fit
2:40:50
into the square root part of a direct Square and I believe that the yang-mills
2:40:56
content and Higgs version of the klein-gordon equation would go in the
2:41:02
square part of the Dirac Square so two of these equations unified differently than two others and the two pairs are
2:41:10
unified in the content of a direct square the Dirac piece will be done
2:41:18
separately elsewhere when I get around to it and contains the Rita Schwinger
2:41:23
field content which is fundamental and new there are only two generations in
2:41:28
this model I think people have accepted that there are three but I don't believe that there are three I think that there
2:41:34
are two and that the third unifies with other matter at higher energies the quartic Biggs piece comes from the Dirac
2:41:41
squaring of a quadratic remember there's a Eddy tensor which is quadratic in the Augmented torsion the metric does
2:41:49
multiple duties here is it's the main field in this version of G U with the
2:41:56
sort of strongest assumptions as field content on that is originally on X
2:42:02
whereas most of the rest of the field content is on but it also acts as the observer pulling
2:42:08
back the full content of Y onto X to be
2:42:13
interpreted as if it came from X all along generating the internal the the sort of illusion of internal quantum
2:42:19
numbers and I should say that the p'tee Salam theory which is usually advertised as think su for cross su 2 across su 2
2:42:27
is really much more naturally spin 6 cross spin for when the trace portion of
2:42:35
the space of metrics is put in with the proper sign if you're trying to generate
2:42:41
the sector that begins as X 1 comma 3 remember XD where X where D equals 4 is
2:42:50
the generic situation but you have all these different sectors I believe that these sectors probably exist if this
2:42:56
model is correct but we are trapped in the 1 3 sector so you have to figure out what the implications are for pushing that
2:43:03
indefinite signature up into an indefinite signature on the y manifold
2:43:08
and there are signatures that make it look like the p'tee salam rather than
2:43:13
directly in the spin 10 su 5 line of thinking so we will attempt to present
2:43:20
the full theory shortly and shortly keep in mind this took seven years to just bring me to want to come back to this
2:43:27
but it must be reassembled from decades of notes and that's part of the problem when you're working alone and you're not
2:43:33
really expecting to talk to anybody so I want to thank you for your patience and your time and I just want to read a
2:43:40
bunch of names that people who matter to me and if I have done anything wrong this is not no reflection on them marcos
2:43:46
de Soto Peter teal is the door singer Raul bot Michael Grossberg Adil Abdul Ali Harry
2:43:52
and Sophie Rubin Brett Weinstein and family Heather hanging and Zach and Toby
2:43:58
Peter fried Scott Axelrod Nima our Connie Hamed Luiz Alvarez Gamay Edward
2:44:04
Frenkel drawer Barnett on slow mo Sternberg David Koch Don Daniel Barr k
2:44:10
kharon and less Weinstein Haynes Miller Ralph Camry John Tate Sidney Coleman
2:44:15
Graham Siegel Robert Herman and here mr. Milani errors and omissions because
2:44:20
I've too many people to thank our are all my own as for the claims that should
2:44:27
reflect badly on no one else other than myself and most especially I just want
2:44:32
to say that I've asked a tremendous amount from my family to stick with me on this quixotic quest and I want to
2:44:39
thank Pia Milani nyla Weinstein and Zev Weinstein I love you all very much and thank you for making this possible I do
2:44:48
want to leave you with one thought I really think that we've gotten completely bent out of shape about
2:44:53
trying to court formalize and routinize science and it doesn't work you cannot
2:44:59
mandate science as social engineering you can't decide that science is always in the zeitgeist and done by committee
2:45:06
in fact it is essential to understand that science will not conform to what
2:45:12
you want one of the things that I I'm very proud of I think it's quite true is
2:45:17
the saying that great science has the scientific method as its radio edit I
2:45:24
don't think that great science is actually done the way we say it's done and I think that directs 1963 Scientific
2:45:31
American article should be read by absolutely absolutely everyone every time major theories have come out
2:45:38
they've almost always been wrong but they're not wrong in an important way
2:45:43
and I think that we have to fix the political economy of people racing to
2:45:48
correct theories or point out that there is no agreement with the experiment we
2:45:54
are killing many of our best ideas by creating a terrible and combative environment which already attempts to
2:46:01
apportion credit for work and more importantly risk undertaken by
2:46:08
individuals and I just think that I want people to understand that I've always
2:46:15
wanted to share this but I I I detest the culture that I saw that cropped up
2:46:21
around what has now become known as the cyber Whidden equations when they were put forward there was a period of time
2:46:27
where I watched people as if it a feeding trough trying to stay up around the clock to
2:46:33
use a new machine tool that had been given to them to claim credit and it
2:46:39
profoundly pushed me away from the community we have to become more ethical
2:46:45
and we have to honor the people who are trying to speak and act imaginatively
2:46:50
now if this doesn't work if it's silly I'll have egg on my face and I'll go on
2:46:55
I'll be fine but I'm very worried that maybe that some of the best ideas are
2:47:01
between the ears of people without the confidence in the hutzpah and just the
2:47:06
sort of almost psychotic drive to push things across the finishing line we've
2:47:13
got to be kinder and nicer and more decent and stop stealing people's lives their credit their future and their
2:47:21
ability to have families and make a living and that's absolutely essential to me and I look forward to finding out
2:47:28
whether this theory has merit to it or is without merit but I guarantee that if I'm going to go down with the ship I'm
2:47:34
also not going to be knocked off the ship as I was many years ago completely unfairly and I won't dwell on it but the
2:47:42
amount of power you professors have is absolutely almost without parallel
2:47:48
because nobody really understands enough to adjudicate disputes that happen in academics I'm going to insist that we
2:47:55
fund you better and that you are nicer to the people who depend upon you in
2:48:01
this beautiful chain that we call science scientific method and most
2:48:07
particularly American science which i think is still the envy of the world so
2:48:12
you've been through the portal I know it was a long slog I hope you found it interesting and enjoyable and we'll see
2:48:18
you again soon be well everybody stay safe
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