Classical to Quantum

Classical to Quantum | Galileo's Principle: a shadow over modern physics? | Wild Egg Maths

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Before we can get properly to grips with Einstein's seminal 1905 paper on Special Relativity, we need to acknowledge some painful truths about modern physics (i.e. the last few hundred years) and its relation to Galileo's Invariance Principle.

Unfortunately, most of physics after Galileo and before Einstein was not able to properly incorporate Galileo's Principle. In many cases, the physics is pretty well in direct conflict with at least the spirit of Galileo's understanding. This was very clear to late 19th century physicists in the context of electromagnetism and Maxwell's laws, and provided a key motivation for the novel approach of Einstein.

The consequence of this reasoning is that many notions of fundamental high school physics and indeed university level physics are at best only provisional: as they self-evidently conflict with the fundamental historical understanding of Galileo. So who was right? Was it Newton and Euler and Lagrange and Hamilton and Gauss and Faraday and Maxwell? Or was it Galileo?

It was Galileo.

From this point of view, Einstein's revolution was waiting to happen for hundreds of years. Special Relativity was necessary to bridge the unreasonable gap that had been allowed to develop between Galileo and the rest of physics, and ultimately to reassert the primacy of Galileo's Invariance Principle over all others in physics.

This is one of the Classical to Quantum series of lectures which will aim to reconsider a lot of modern physics from a more purely mathematical point of view.

0:02

hello everyone I'm Norman warburger

0:03

thanks for joining me on this adventure

0:05

we're looking at physics

0:07

quantum mechanics ultimately but

0:09

currently special relativity of Einstein

0:12

we're wanting to understand Einstein's

0:15

foundational 1905 paper I've just had a

0:18

look at the first section called

0:21

definition of simultaneity and my

0:23

ambition is to look at that very

0:25

carefully from a mathematical point of

0:28

view before I do that though there is an

0:31

important discussion that we need to

0:33

have and that's concerning the

0:36

foundational

0:39

underpinning

0:42

observation that underlies this entire

0:45

subject which is Galileo's invariance

0:49

principle that the laws of physics

0:53

seem to be invariant under changes of

0:58

coordinate frames if you have one ship

1:00

which is stationary and another ship

1:02

which is moving at uniform velocity with

1:05

respect to that stationary one then

1:08

the laws of physics are the same in both

1:11

ships

1:13

and in particular

1:15

you cannot tell if you're just inside

1:18

the ship not looking outside you cannot

1:20

tell whether you are the stationary ship

1:23

or the moving ship

1:25

now this is such a profound a profound

1:30

understanding okay in some sense it's

1:33

perhaps the the underpinning

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foundation for modern physics it

1:40

predates Newton it predates his laws of

1:44

motion and all subsequent mechanics and

1:46

then indeed electromagnetism but

1:49

remarkably perhaps

1:51

most of the subsequent developments in

1:55

physics starting with Newton and working

1:57

their way into the beginning of the 20th

1:59

century when Einstein takes his position

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almost all of that is

2:07

somehow independent of Galileo's

2:11

principle in other words

2:14

modern physics has done its best to sort

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of avoid dealing with the consequences

2:21

of Galileo's understanding even though

2:24

he very clearly enunciated it at the

2:27

beginning of the 1600s essentially 400

2:30

years ago so we want to talk about that

2:33

today

2:34

and this raises a very big Shadow you

2:37

know over the subject it calls into

2:40

question a lot of the foundational

2:42

physics that you learned in high school

2:43

and also that you further developed an

2:47

undergraduate level and indeed it

2:49

actually also calls into question a lot

2:51

of issues in modern 20th century physics

2:57

you see once we are fully on board with

3:02

Galileo's principle

3:04

the consequences that we are not able to

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say whether we're stationary and that

3:11

means that we cannot

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really logically talk about a point in

3:16

space

3:17

you see

3:19

because we don't know whether we are

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moving or not or to what extent we are

3:24

moving we can talk about whether we're

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moving with relation to something else

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but in an absolute sense it's impossible

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for us

3:33

to determine whether we're moving or

3:36

stationary so just to say that you know

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this is a point in space

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the end of my finger there that's as if

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I say consider this point in space right

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here

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that's ultimately a meaningless

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statement because

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in fact it may appear as if that's not

3:52

moving okay but in fact of course we are

3:55

rotating uh the Earth is rotating around

3:58

its axis you know once every 24 hours

4:01

the whole earth is orbiting the Sun once

4:04

a year going 200 kilometers per second

4:06

or something like that

4:08

the sun itself is making some kind of

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circular motion around the center of the

4:15

Milky Way galaxy

4:17

the Galaxy itself is part of a a local

4:20

cluster part of the Virgo supercluster

4:23

and it as such the Galaxy itself is

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moving with respect to the

4:29

the the center let's say or the you know

4:31

the mass of the supercluster that it's

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in and then there are lots of other

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super clusters forming larger units

4:39

which are no doubt also moving with

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respect to each other so

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even if we just go up several levels we

4:45

see that there's motions on top of

4:48

motions on top of motions Etc so you

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know

4:52

what this point is actually doing you

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know if you looked at it from some other

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galaxy outside of our super cluster the

5:01

actual motion of this this thing that

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I'm pointing at would be you know wildly

5:06

complicated

5:07

and you would not agree that it makes

5:10

even any sense to talk about this point

5:14

in space

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so it's a consequence of that in fact

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you don't have to have had that that

5:20

rather large-scale understanding of our

5:22

you know our Cosmic framework which was

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not available to to Galileo or Newton

5:28

Etc but even just thinking about things

5:31

in terms of ships on

5:34

the earth's surface in the ocean it's

5:38

clear that

5:39

from a physics point of view from an

5:41

observational point of view the the idea

5:44

of a point in space is problematic

5:47

so another way to say that is that the

5:50

concept of here

5:52

is not really a logically tight notion

5:56

in physics

5:58

and one of the things that Einstein is

6:00

doing is morphing that into a parallel

6:04

discussion about now he's showing that

6:07

in a parallel fashion in fact very

6:09

closely parallel fashion there is no

6:12

such thing really as now it's not a

6:14

clearly defined concept

6:19

now

6:21

that that has a lot of consequences

6:24

because if we look at the history of

6:26

physics after Galileo starting notably

6:29

with Newton and his Laws of Motion we

6:32

see that Notions of velocity in

6:36

particular play a crucial role all right

6:41

velocity is crucial to Define momentum

6:44

which is mass times velocity it's

6:47

crucial to Define kinetic energy

6:48

one-half MV squared

6:51

the law of conservation of momentum

6:54

involves the momentum which involves

6:56

velocities

6:58

the

7:00

conservation of energy which involves a

7:03

kinetic part and also a potential part

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both of those also involve positional

7:10

questions that are actually impossible

7:13

to Define properly or to pin down

7:16

properly once you adopt Galileo's point

7:19

of view in other words there's no such

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thing as an absolute velocity it doesn't

7:24

make sense to say oh look look at this

7:26

eraser I wonder what its velocity is

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it's a meaningless statement according

7:32

to Galileo

7:34

it makes sense perhaps to say oh I

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wonder what its velocity is with respect

7:39

to me or with respect to the center of

7:42

our galaxy or perhaps with respect to

7:45

the center of the Virgo supercluster but

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just by itself what is the velocity now

7:52

of this eraser

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doesn't make sense

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that means that

8:01

Newtonian physics actually logically

8:05

doesn't really

8:07

hang together properly right it needs to

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be modified or it needs to be qualified

8:13

by the statement that we're adopting a

8:16

relative point of view at all times

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and that then becomes a very um

8:22

significant aspect of the

8:24

electrodynamics developed in the 19th

8:27

century

8:28

um it's accommodating in Maxwell's loss

8:30

which were sort of patently also not

8:34

invariant under changes of reference

8:38

frame because you know I'm moving uh

8:42

Electric

8:44

particle creates a magnetic field a

8:47

moving magnetic field creates an

8:50

electric electric field so the the

8:53

notion of movement is critical in the

8:58

formulation of Maxwell's loss and if you

9:00

don't have a proper notion of movement

9:02

like an invariant notion of movement

9:04

then all those things are in question

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and

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it was this realization you know that

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ultimately physicists in the later part

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of the

9:14

19th century started coming to that was

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a motivation for some of the work

9:19

predating Einstein in particular the

9:22

transformations of Lorenz okay where he

9:25

was interested in in trying to describe

9:28

what what how are the

9:31

equations of Maxwell actually changing

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if we change uh reference frame and then

9:37

the work of poincare who analyzed um

9:41

Lorenzo's Transformations and saw quite

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clearly that these things are very

9:48

intimately connected with changes of

9:50

reference frames in fact Point array's

9:52

work is um in my view not given enough

9:56

credit here and it's worth examining

9:58

that uh quite a lot

10:00

so I I want to make this point okay that

10:04

when we approach Einstein's

10:06

foundational paper okay we should be

10:09

aware that there are serious

10:12

definitional issues

10:14

that we cannot take for granted that we

10:18

know what we mean by a point in space a

10:21

point in time we shouldn't take for

10:23

granted that the notion of velocity is

10:26

something that we all understand that

10:28

Notions of distance and time are

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predetermined we are obliged to define

10:35

those things

10:36

and then even more problematically we

10:39

also have to think about Mass we have to

10:42

think about Force we have to think about

10:46

energy

10:47

and all these concepts are ones that we

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first must pay attention to in terms of

10:55

what their definition is before we can

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really have a careful foundational

11:00

discussion about their role in physics

11:07

lots to think about