Classical to Quantum

Classical to Quantum | Einstein's Special Relativity (Intro) and Galileo's Principle | Wild Egg Math

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We begin to have a look at Einstein's famous 1905 paper "On the Electrodynamics of Moving Bodies" which initiated the subject of Special Relativity. However we are going to have a non-standard view of this development, touching base importantly with Galileo's Invariance Principle: that the laws of nature are the same in two inertial reference frames moving with uniform speed with respect to each other.

This is a beginning video in a series on Classical to Quantum physics, seen through the eyes of pure mathematics.

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Hello everyone I'm Norman Wildberger thanks for joining me on this adventure Classical to Quantum

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an important part of this story is the major shift

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initiated by Albert Einstein from classical Newtonian mechanics to

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special relativity it turned out that special relativity and quantum mechanics were to have

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a very important connection and it's impossible perhaps to really give an overview of quantum

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mechanics without talking about special relativity which is of course of independent interest so I'm

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going to propose to do something rather Elementary here I propose to actually look at this most

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famous of papers called "On the Electrodynamics of Moving Bodies" by Albert Einstein

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written June 30th 1905 which probably has some legitimate claim to being the most important paper

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written in the history of physics it certainly propelled an entire New World View ultimately no

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of course not initially initially people didn't really understand what Einstein was trying to

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say but ultimately it led to a revolutionary a new understanding of our world and our position in it

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and when you look at 20th century physics most physicists will say that there are really these

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two great Innovations in that century quantum mechanics and special relativity I think there's

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also a third one okay that um associated with the name of Paul Dirac and that's the discovery of the

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matter anti-matter symmetry or Duality that's um just as equally remarkable in my view as these two

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theories but we'll get to that later but I want to have a look at this first paper now quantum

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mechanics has a very wide range of interpretations the basic equations of quantum mechanics are

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pretty well accepted by all practitioners but the interpretation of quantum mechanics is widely and

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wildly different there are really dramatically separate and almost contradictory ways of

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interpreting or assigning meaning to what's going on with equations of quantum mechanics

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with special relativity it's much less so there is a happy sort of uniformity of thought

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about the meaning of the equations that Einstein introduced but I think this Conformity of opinion

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is misplaced and I think we need to have a wider discussion of the actual meaning of Einstein's

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special relativity and general relativity is another issue and so to initiate that discussion

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I'm proposing to actually look very carefully at this foundational paper now this is or should be

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of independent interest to all students of physics all students of physics should at one point or

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another have read this paper and should have read it rather carefully so we're going to do that but

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we're going to do it in stages okay and I'm just going to deal with the first section today and I'm

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also going to introduce to you a rather radical idea that despite the remarkable originality

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and and profound Insight contained in this paper undeniably by without doubt the greatest

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Genius of modern physics after Newton nevertheless there are aspects of this paper which are

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logically problematic from a mathematician's point of view and so having a mathematical

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orientation rather than a physical one allows me to look at things in perhaps unusual light

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so my physics background admittedly is not very deep okay but I have a lot of experience with

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mathematics and with just this basic idea of orienting ourselves towards a subject and being

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very mindful of the importance of definitions and that's going to turn out to be a crucial

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aspect of understanding this entire story so I'm going to ultimately show you a alternative

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quite different interpretation of Einstein's special relativity okay

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and then the question will arise well is this new interpretation really different and does it have

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applications or implications to the way we think about ourselves and the universe in which we're

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in and I believe that it does okay but at first I just want to present this paper and I want to

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sort of allow you the possibility of engaging with it yourselves of thinking well does this

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make sense to me? You know if it was 1905 and I was reading this paper for the very first time

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does this does this make sense is it convincing okay so we're going to do that and along the way

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I'm actually going to introduce another famous person in this story which often doesn't get

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enough credit I think and that's Galileo okay so let's start with on the electrodynamics of a

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moving bodies by Albert Einstein it is known that Maxwell's electrodynamics as usually understood at

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the present time when applied to moving bodies leads to asymmetries which do not appear to be

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inherent in the phenomena take for example the reciprocal electrodynamic action of a magnet and

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a conductor the observable phenomena here depends only on the relative motion of the conductor and

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the magnet whereas the customary view draws a sharp distinction between the two cases in which

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either the one or the other of these bodies is in motion for if the magnet is in motion and the

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conductor at rest there exists in the neighborhood of the magnet an electric field with a certain

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definite energy producing a current at the places where parts of the conductor are situated

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but if the magnet is stationary and the conductor in motion no electric field arises

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in the neighborhood of the magnet in the conductor however we find an electromotive Force to which

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in itself there is no corresponding energy but which gives rise assuming equality a relative

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motion in the two cases discussed two electric currents of the same path and intensity as those

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produced by the electric forces in the former case so let me just interject something here so

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he's drawing upon Maxwell's famous theory of electromagnetism and the way that electric

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and magnetic fields interact with each other okay and what he's saying here is that the usual story

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of what happens in in a certain situation when you have some some movement maybe in

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one case the the description is in terms of an electric field but in another case it is when

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you take a the point of view of one of the other objects which are moving maybe the phenomena is

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best expressed in terms of a magnetic field so electric field in one case magnetic field in

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another case but it's really the same phenomena from this point of view that it shouldn't really

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depend on whether we think of this thing as stationary or this thing is stationary

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so to carry on examples of this sort together with the unsuccessful attempts to discover any

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motion of the Earth relative to the light medium suggests that the phenomena of electrodynamics as

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well as of mechanics possess no properties corresponding to the idea of absolute rest

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let me say that again suggests that the phenomena of electrodynamics as well as of mechanics possess

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no properties corresponding to the idea of absolute rest they suggest rather that as has

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already been shown to the first order of small quantities the same laws of Electrodynamics and

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Optics will be valid for all frames of reference for which the equations of mechanics hold good

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and there's a footnote here the preceding

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Memoir by Lorentz was not at this time known to the author

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We will raise this conjecture the purport of which we'll Hereafter be called the principle

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of Relativity to the status of a postulate and also introduce another postulate which is only

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apparently irreconcilable with the former namely that light is always propagated in empty space

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with a definite velocity C which is independent of the state of motion of the emitting body these two

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postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of

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moving bodies based on Maxwell's theory for stationary bodies the introduction of

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a luminiferous ether will prove to be Superfluous in as much as the view here to be developed will

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not require an absolutely stationary space provided with special properties nor assign

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a vector velocity to a point of the empty space in which electromagnetic processes take place

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now he's referring here of course to the previous 19th century view of The Ether

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that since light was seen as a wave and waves always have a medium in which they they pass

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or they the energy is transferred so it was felt that light as it passes through empty space really

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ought to be vibrating something and that was called The Ether

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but a famous experiment Michaelson and Morley in the 1870s I think showed that

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you couldn't detect a difference in the speed of light in the direction of motion of the Earth

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um as opposed to a transverse a direction uh suggesting that the Ether perhaps

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doesn't exist and so that's a that's part of the motivation here that he's drawing upon

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for this principle of equivalence and I'll just finish the paragraph before I say something else

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really important in this direction the theory to be developed is based like all electrodynamics

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on the kinematics of the rigid body since the assertions of any such theory have to do with

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the relationships between rigid bodies systems of coordinates clocks and electromagnetic processes

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insufficient consideration of this circumstance lies at the root of the difficulties which

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the electrodynamics of moving bodies at present encounters I admit that I don't

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quite understand that paragraph very well but I do want to say something a little bit about the

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the previous paragraph where this important principle of Relativity is enunciated okay

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okay so let me say I think some important words about this principle relativity so what

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he's saying here um at least in the context of mechanics is really a reiteration of a principle

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that was firmly established or at least firmly enunciated by Galileo okay in the in the 1500s and

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um I'm going to show you that okay and perhaps interestingly I'm going to call on my friend

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um chatGPT 4 okay to uh to find a quote so I've asked to chatGPT 4 can you find

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Galileo's quote on the invariance of physical laws with regard to uniformly moving Observers

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GPT4 tells me: Certainly! Galileo Galilei made an important observation that laid the groundwork for

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the principle of Relativity which Albert Einstein would later generalize in his theory of relativity

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Galileo's Insight is often captured in a thought experiment involving observations made inside a

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smoothly sailing ship here's a passage from his work dialogue concerning the Two Chief World

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Systems that captures this idea so this is Galileo talking you know you know 400 almost 400 years

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before the 20th century. "Shut yourself up with some

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friend in the main cabin below decks on some large ship and have with you there some flies

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butterflies and other small flying animals have a large bowl of water with some fish in it hang

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up a bottle that empties drop by drop into a wide vessel beneath it with the ship standing

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still observe carefully how the little animals fly with equal speed to all sides of the cabin

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the fish swim indifferently in all directions the Drops Fall Into The Vessel beneath and in

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throwing something to your friend you need throw it no more strongly in One Direction than another

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the distance is being equal jumping with your feet together you pass equal spaces in every direction

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when you have observed all these things carefully though doubtless when the ship

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is standing still everything must happen in this way have the ship proceed with any speed you like

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so long as the motion is uniform and not fluctuating this way and that

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you will discover not the least change in all the effects named

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nor could you tell from any of them whether the ship was moving or standing still"

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I claim that it's this paragraph here which is really at the heart of Special Relativity

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okay and I'm going to show you in subsequent videos that a good part of special relativity,

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in fact the majority of it, could have been established okay by a thoughtful

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physical slash mathematical person carefully by just thinking about the consequences of

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this paragraph of Galileo even before Maxwell's equation so even without that strong motivation

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from electromagnetism. Let me just continue here with chatGPT this illustrates the idea that the

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laws of physics are the same in any inertial non-accelerating frame of reference that is if

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you're inside a ship moving at a constant velocity and you had no windows to look out of there'd be

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no experiment you could do to determine whether the ship was moving or stationary this idea is a

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foundational principle in physics and I want to also say ask the following did Galileo come up

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with the Transformations between inertial frames that are usually attributed to him

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so here they are below here so no Galileo did not come up with the transformation equations

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that are sometimes attributed to him known as the Galilean Transformations however he

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did implicitly recognize the conceptual underpinnings of these Transformations

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okay here's a mathematical description of the relatively simple Transformations that you go from

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one coordinate system in a moving frame to another coordinate system in in say the stationary frame

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but there's some various assumptions built into this particular um this particular formulation

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of these Transformations that is not really implicit in Galileo's reasoning okay Galileo

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is not making any Claim about how to transfer measurements from one of these uniform motions

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to the stationary one he is just saying that the laws of physics are observationally the same in

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both of them okay so I would not actually want to attribute these transformations to Galileo

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because it turns out that these are not actually the correct Transformations really that these

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Transformations themselves already assume a kind of um naivete okay or um an assumption

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about the world which is not justifiable or at least not intrinsically uh really obvious

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and we're going to talk about that okay so um just to continue where TNT primary events in the

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stationary and moving frames so while Galileo did not write down these Transformations explicitly

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the principle behind them that the laws of motion are the same in any uniformly moving frame is

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evident in his thought experiment involving the ship as mentioned earlier this principle underlies

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the Galilean transformations it was the inability of the Galilean transformations to correctly

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describe the behavior of light as determined by Maxwell's equations that led to Einstein's

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special theory of relativity and the Lorentz Transformations which supersede the Galilean

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Transformations and velocities close to the speed of light so I object to this because this

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is ascribing a wrong point of view or at least a a limited point of view to Galileo. Galileo did

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not come up with these Transformations and to say that Einstein's equations sort of superseded the

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Galilean ones is a misunderstanding: it's more accurate to say that Galileo had his finger on

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the essential fact of special relativity, which is this invariance of physical laws with regard

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to uniformly moving reference frames okay so I have a big task ahead of me to to explain to you

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why special relativity could in principle have been discovered you know at any time after after

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Galileo it could have been discovered at any time especially after Newton enunciated his his

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loss but in fact even even before that and so to make progress in that direction in my next video

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we're going to look at that first section of Einstein's paper Okay so we're gonna go

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to the to the kinematical part the definition of simultaneity I hope you'll be joining me for that!