# Einstein holding Maxwell's equations above Newton's equations

I'm learning electrodynamics and one of the speakers I'm learning from said that when faced with the incompatibility of retaining both Newton's equations (based on mass, distance and time) and Maxwell's equations (based on charge, E and B) unchanged, Einstein had to choose one or the other. The speaker said that Einstein chose Maxwell's equations as definitive, meaning that he kept charge, E and B unchanged. Newton's equations became malleable, so that mass, length and time became malleable. I hope I'm not embellishing his point here.

The speaker added that Einstein's choice was a reinforcement, at least for him, of the fundamental nature of the conversation of charge.

In any event, I hadn't heard this perspective before, and was curious if those more familiar with electrodynamics and the roots of relativity could help explain why Maxwell's equations might hold preference over Newton's equations, or why charge, E and B would go unchanged while mass, time and distance are modified.

Nabeshin
At the time Einstein formulated special relativity, phenomenon such as length contraction were already known. Additionally, concepts such as transverse and longitudinal mass had already been noted in the 1890's. So Einstein didn't really have a choice; he was merely following experimental evidence.

I'm learning electrodynamics and one of the speakers I'm learning from said that when faced with the incompatibility of retaining both Newton's equations (based on mass, distance and time) and Maxwell's equations (based on charge, E and B) unchanged, Einstein had to choose one or the other. The speaker said that Einstein chose Maxwell's equations as definitive, meaning that he kept charge, E and B unchanged. Newton's equations became malleable, so that mass, length and time became malleable. I hope I'm not embellishing his point here.

The speaker added that Einstein's choice was a reinforcement, at least for him, of the fundamental nature of the conversation of charge.

In any event, I hadn't heard this perspective before, and was curious if those more familiar with electrodynamics and the roots of relativity could help explain why Maxwell's equations might hold preference over Newton's equations, or why charge, E and B would go unchanged while mass, time and distance are modified.

Most people at Einstein's time tried to coordinate the classical view of spacetime with Maxwell's equations but that gave rise to a lot of problems.Einstein finally discarded the classical view of spacetime and built a new theory upon Maxwell's equations and the special relativitistic principle.

But he did this not because he wanted to.It was because the experiments done by physics before Einstein suggested that this was the only way to solve the problem.

And E、B are not unchanged.They are relativistically covariant.

bcrowell
Staff Emeritus
Gold Member
This is an interesting perspective. Is the person claiming that this was historically how Einstein thought about it, or is this merely the person's own interpretation?

It's true that SR is latent in Maxwell's equations.

On the other hand, I don't really buy this part: "Newton's equations became malleable, so that mass, length and time became malleable." Length and time occur in both Newton's laws and Maxwell's equations. In both cases, the frame-dependence of length and time forces a reinterpretation of the equations, compared to their traditional interpretations. Traditionally, Newton's laws were interpreted in terms of absolute time and instantaneous action at a distance. Traditionally, Maxwell's equations were interpreted in terms of an aether.

And the way we treat mass today is usually that we consider it a frame-independent quantity, just like charge, although it's true that Einstein originally treated mass as being frame-dependent.

So Einstein didn't really have a choice; he was merely following experimental evidence.

Thanks for the insight. So does this mean that it would not have been possible for Einstein to have changed Maxwell's equations instead of Newton's to fit the data? Or is my asking such a question perhaps missing the point or otherwise misinterpreting what he did?

This is an interesting perspective. Is the person claiming that this was historically how Einstein thought about it, or is this merely the person's own interpretation?

He actually didn't specify that, but spoke about it as if this was well-known in the history of science, which I suppose isn't quite true. He said that Einstein had a choice. Either he could keep Newton's equations unscathed, and then he wrote down "(m,l,t)" or keep Maxwell's equations unscathed, and he wrote down "(q,E,B)". He added that Einstein decided that Maxwell's equations could not be wrong, and then he crossed out m,l,t on the board, leaving q,E and B untouched.

I have heard before that Einstein was so convinced of the intrinsic veracity of Maxwell's equations, especially the fixed c for all observers that they seem to necessitate, that he dismissed other interpretations, such as Lorentz's, which argued that m,l and t only appeared to change, and that c only appeared to be the same for all observers, as unsatisfactory. But I'm not sure if this is what this speaker had in mind.

On the other hand, I don't really buy this part: "Newton's equations became malleable, so that mass, length and time became malleable."

That's probably my misinterpretation of what the speaker said, although this might have been what he meant,judging from the above.

Either way, one thing that does mystify me is how a fixed c for all observers is a logically necessary outcome of Maxwell's equations. Could you help explain? Thanks again for your help

Either way, one thing that does mystify me is how a fixed c for all observers is a logically necessary outcome of Maxwell's equations. Could you help explain? Thanks again for your help

My interpretation is that Maxwell's equations predict that the speed of light is a function of the permitivity and permeability of space and independent of the velocity of emitter. The last point is the key point. Once you establish that the speed of light is independent of the velocity of the emitter relative to the observer and if you accept that the laws of physics are same in all reference frames, then it follows that the Lorentz transformations are the logical outcome and the consequence of those transformations is that time and space are not absolute.

And E、B are not unchanged.They are relativistically covariant.

yes.

The speaker added that Einstein's choice was a reinforcement, at least for him, of the fundamental nature of the conversation of charge
."

Coulombs law must be modified as well for relativistic effects... so the statement(s) attributed by the OP to his lecturer are inaccurate in a number of respects.

I've tried to find just what Einstein's thinking was as he developed special and general relativity. I don't have a full picture.

"....why Maxwell's equations might hold preference over Newton's equations..."

Intuition, for one. Einstein was also a founder of quantum mechanics and he sure did NOT like "spooky action at a distance"....Newton "assumed" instantaneous action at a distance and I believe Maxwell's finite fixed speed of light must have appealed to Einstein...

My interpretation is that Maxwell's equations predict that the speed of light is a function of the permitivity and permeability of space and independent of the velocity of emitter."

This might be a key point, however, the "luminiferous ether" was still all the rage when Einstein was in college...According to one account, apparently his old school electromagnetism professor would not even mention the "new" Maxwell's equations...this infuriated Einstein who was apparently "attracted" to the new theory while still an undergraduate.

Lee Smolin, or one other of the big popular physicsts, mentions in a book reading Einstein's original notes (in German) and notes many, many, many fits and starts (errors) but Einstein was very persistent and eventually came around, found his error and proceeded.

I understand that as a teenager Einstein tried to picture what light would look like if he caught up with it...and somehow he came to conclude that the speed of light is constant....I'm guessing Maxwell's theory answered that conundrum for him... then Einstein concluded contrary to thousands of years of science, space and time cannot be constant!

So while he did have many others to "lean on", like Maxwell, Lorentz, Fitzgerald, he also might have choosen the wrong road to follow...his genius seems to have been properly interpreting physical situations.....

atyy
One thing that may have motivated Einstein is the principle of relativity - basically that you can drink coffee on the aeroplane - which we all know is true, and would like to be true (it isn't, at least not in general relativity, but let's stick to special relativity here). I'm not sure if these ideas are exactly correct, but just a sketch for where to look.

Newton's mechanics and the prinicple of relativity are compatible.

Maxwell's equations and the principle of relativity are compatible.

Maxwell's and Newton's equations are not jointly compatible with the principle of relativity.

So we must modify Maxwell or Newton or both, if we wish to keep the principle of relativity. Maybe we can justify modifying Newton, if there is no way to modify Maxwell to be compatible with Newton and the principle of relativity. Special relativity is a modification of Newton to be compatible with Maxwell and the principle of relativity.

Does anyone know a way to modify Maxwell to be compatible with Newton and the principle of relativity? If that is possible, then Einstein did have a choice whether to modify Newton or Maxwell. If it is not possible, then Einstein had no choice but to modify Newton. (It is possible to keep Newton and Maxwell unmodified, but then the principle of relativity has to go.)

I just stumbled across the following....seems Einstein surely would have known about this in the early 1900's....but who accepted it and who did not is another question....

In PART VI of his 1864 paper which is entitled 'ELECTROMAGNETIC THEORY OF LIGHT'[2], Maxwell combined displacement current with some of the other equations of electromagnetism and he obtained a wave equation with a speed equal to the speed of light. He commented:

The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.[3]
http://en.wikipedia.org/wiki/Electromagnetic_wave_equation

This seems to substantiate that ether WAS still popular at the time Einstein launched SR...and maybe even after:

Contemporary scientists were aware of the problems, but aether theory was so entrenched in physical law by this point that it was simply assumed to exist. In 1908 Oliver Lodge gave a speech in behalf of Lord Rayleigh [6] to the Royal Institution on this topic, in which he outlined its physical properties, and then attempted to offer reasons why they were not impossible. Nevertheless he was also aware of the criticisms, and quoted Lord Salisbury as saying that "aether is little more than a nominative case of the verb to undulate". Others criticized it as an "English invention", although Rayleigh jokingly corrected them to state it was actually an invention of the Royal Institution.[citation needed]

By the early 20th Century, aether theory was in trouble. A series of increasingly complex experiments had been carried out in the late 1800s to try to detect the motion of earth through the aether, and had failed to do so. A range of proposed aether-dragging theories could explain the null result but these were more complex, and tended to use arbitrary-looking coefficients and physical assumptions. Lorentz and Fitzgerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable (length contraction), but if their equations were correct, the new special theory of relativity (1905) could generate the same mathematics without referring to an aether at all.

http://en.wikipedia.org/wiki/Luminiferous_ether

Did not realize it was that early:

The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University. Its results are generally considered to be the first strong evidence against the theory of a luminiferous aether.
http://en.wikipedia.org/wiki/Michaelson-Morley_experiment

Anyway, Einstein appears to have had lots of choices....depending on what information he had (this WAS before Al Gore's invention of the internet, after all)

My interpretation is that Maxwell's equations predict that the speed of light is a function of the permitivity and permeability of space and independent of the velocity of emitter. The last point is the key point.

Thanks kev. I suppose what I still need guidance on is what aspect of Maxwell's equations necessitate that all observers will measure c to be the same, regardless of the velocity of the source of the emitter relative to them. I'm familiar w/ Maxwell's laws at this point, and to some degree the wave equations, Poynting vector and so on, but it's still not clear to me how they necessitate the "independent of the velocity of the emitter" part of the above. Could you help explain if you have time or point me to an explanation perhaps?

Thanks kev. I suppose what I still need guidance on is what aspect of Maxwell's equations necessitate that all observers will measure c to be the same, regardless of the velocity of the source of the emitter relative to them. I'm familiar w/ Maxwell's laws at this point, and to some degree the wave equations, Poynting vector and so on, but it's still not clear to me how they necessitate the "independent of the velocity of the emitter" part of the above. Could you help explain if you have time or point me to an explanation perhaps?

If permittivity and permeability of space are Lorentz invariant, then they will give the same value when measured in any intertial frame and the constancy of locally measured c follows. Now, one of the LT invariants of the EM field is $-4E\cdot B$. If we make a leap and say that E depends linearly on $\epsilon_0$ and B depends on $\mu_0$ then the product $\epsilon_0\mu_0$ is an invariant. That is speculative but gives the right answer.

mgb_phys
Homework Helper
You also have to consider that Einstein had the Maxwell's Equations t-shirt.

It's interesting how close Maxwell came to inventing SR, not sure if it was the acceptance of the aether or he was just happy being a millionaire VC on his yacht that stopped him going further.

atyy
You also have to consider that Einstein had the Maxwell's Equations t-shirt.

It's interesting how close Maxwell came to inventing SR, not sure if it was the acceptance of the aether or he was just happy being a millionaire VC on his yacht that stopped him going further.

I think he fell off his yacht after a bit too much whisky. If he had lived longer, we might even have quantum gravity by now.

If c2 = 1/u0e0

then apparently the product of the right hand terms is invarient...but nobody knew that when Maxwell developed his equations...special relativity had not been discovered...

Thanks kev. I suppose what I still need guidance on is what aspect of Maxwell's equations necessitate that all observers will measure c to be the same, regardless of the velocity of the source of the emitter relative to them. I'm familiar w/ Maxwell's laws at this point, and to some degree the wave equations, Poynting vector and so on, but it's still not clear to me how they necessitate the "independent of the velocity of the emitter" part of the above. Could you help explain if you have time or point me to an explanation perhaps?

You probably know more about maxwell's equations than I do, but I will try and explain my informal reasoning. When Maxwell formulated his equations he assumed a medium that light traveled in called the "luminiferous aether" back then. Even if it was conjectured that the permitivity and pearmeability of the aether changed from the point of view of an observer moving relative to the aether, we only need to know the point of view of an observer at rest with the aether. It seems reasonable that the motion of an emitter relative to aether does not change the permitivity and permeabilty of the medium from the point of view of an observer at rest with the medium. His equations show than the speed of light depends only on the permitivity and permeabilty and we can conclude that that the speed of light in the medium is independent of the velocity of the emitter relative to the medium. Once we know that and using the first postulate "that the laws of physics are the same in alll reference frames" then Lorentz transformations fall into place and the frame invariance of the speed of light from the point of view of any observer with any velocity relative to the medium follows. Einstein later removed the requirement to consider the hypothetical medium but the Lorentz Ether theory retains it and is compatible in its predictions with those of Special Relativity.

Maxwell's and Newton's equations are not jointly compatible with the principle of relativity.

So we must modify Maxwell or Newton or both, if we wish to keep the principle of relativity.

Does anyone know a way to modify Maxwell to be compatible with Newton and the principle of relativity?

Thanks for the response and insight. From what I gather, it's possible that this is what Lorentz and Fitzgerald tried to do when they used the same length-time contraction/dilation equation (The Lorentz transformations) that Einstein later used, but they argued that the speed of light only appeared to be the same for all observers, due to the contraction of the measuring instrument and the dilation of its clock as it moved through the ether.

So from the Lorentz-Fitzgerald perspective, they had retained a Newton-Maxwell compatible world view. But I suppose Occam's razor won out, since Einstein didn't need their ether to make the same, and many more, predictions, and although I hear of someone now and then that still supports the Lorentz-ether rather the Einstein interpretation, most consider the Lorentz theory antiquated and fringe at this point, from what I gather. I don't know enough physics yet to really pass any intelligent judgment though.

atyy
Thanks for the response and insight. From what I gather, it's possible that this is what Lorentz and Fitzgerald tried to do when they used the same length-time contraction/dilation equation (The Lorentz transformations) that Einstein later used, but they argued that the speed of light only appeared to be the same for all observers, due to the contraction of the measuring instrument and the dilation of its clock as it moved through the ether.

So from the Lorentz-Fitzgerald perspective, they had retained a Newton-Maxwell compatible world view. But I suppose Occam's razor won out, since Einstein didn't need their ether to make the same, and many more, predictions, and although I hear of someone now and then that still supports the Lorentz-ether rather the Einstein interpretation, most consider the Lorentz theory antiquated and fringe at this point, from what I gather. I don't know enough physics yet to really pass any intelligent judgment though.

The Lorentz-Fitzgerald perspective is still good - if not in detail, certainly in spirit. The idea is that "matter" changes - and this is retained in the idea that the laws of governing "matter" have Poincare invariance. It's pointless really to ask which is better - since the two views are equivalent - after all to formulate the Poincare invariant laws, one uses the Minkowski spacetime metric. But on the other hand, there would be no observable spacetime if not for matter! So perhaps we would like to have spacetime be a sort of matter and matter a sort of spacetime. General relativity comes very close to this, where the metric is just a field, like the matter and force fields. However, it is still different in that it is the only field that does not have local stress-energy-momentum.

Einstein's achievement is not a view different from Lorentz's or Poincare's. Rather it is the modification of Newton's second law, and accordingly, the Lorentz force law, for consistency with Maxwell's equations and the principle of relativity.

Einstein's achievement is not a view different from Lorentz's or Poincare's. Rather it is the modification of Newton's second law, and accordingly, the Lorentz force law, for consistency with Maxwell's equations and the principle of relativity.

Thanks, you're definitely more aware of what was going on at that time, I'll have to do more reading on the history of physics during that period. Thanks again for your thoughts on this, I'll keep reading up on it.

atyy
Thanks, you're definitely more aware of what was going on at that time, I'll have to do more reading on the history of physics during that period. Thanks again for your thoughts on this, I'll keep reading up on it.

Well, there are multiple views on this. Rindler, I think takes a slightly different view in his textbook. But see also John Bell's "How to teach special relativity" in the collection "Speakable and Unspeakable in Quantum Mechanics", as well as Weinberg's introductory chapter in his text from the 70s on gravitation.

It seems reasonable that the motion of an emitter relative to aether does not change the permitivity and permeabilty of the medium from the point of view of an observer at rest with the medium.

Agree, that makes good sense to me.

His equations show than the speed of light depends only on the permitivity and permeabilty and we can conclude that that the speed of light in the medium is independent of the velocity of the emitter relative to the medium.

Still with you, that certainly follows.

Once we know that and using the first postulate "that the laws of physics are the same in alll reference frames" .

This is where I get tripped up. It at least seems that up to this point the argument has been dependent on a medium independent of the emitter carrying waves at a speed dependent on the properties of that medium. But if there were such a medium, then by definition the laws of physics, at least of optics anyway, would not be the same for all observers moving at different speeds relative to that medium. Or am I missing a possibility here? I must be, of course, because they are, or at least appear to be, b/c c is always measured to be the same.

Einstein later removed the requirement to consider the hypothetical medium but the Lorentz Ether theory retains it and is compatible in its predictions with those of Special Relativity.

Agree.

Well, there are multiple views on this. Rindler, I think takes a slightly different view in his textbook. But see also John Bell's "How to teach special relativity" in the collection "Speakable and Unspeakable in Quantum Mechanics", as well as Weinberg's introductory chapter in his text from the 70s on gravitation.

Thanks atyy, I'll see if I can get my hands on those and get more informed.

Once we know that (the speed of light is independent of the velocity of the emitter) and using the first postulate "that the laws of physics are the same in all reference frames" .
This is where I get tripped up. It at least seems that up to this point the argument has been dependent on a medium independent of the emitter carrying waves at a speed dependent on the properties of that medium. But if there were such a medium, then by definition the laws of physics, at least of optics anyway, would not be the same for all observers moving at different speeds relative to that medium. Or am I missing a possibility here? I must be, of course, because they are, or at least appear to be, b/c c is always measured to be the same.

I think you might be missing that the Lorentz ether has certain physical properties (unlike the the classic passive aether), but the end result is that there is "conspiracy of effects" that makes the Lorentz ether undetectable. Having established that the speed of light is independent of the velocity of the emitter relative to the ether, it is probably best to ignore the ether.

Now take a look at this paper (http://arxiv.org/PS_cache/physics/pdf/0302/0302045v1.pdf). The paper describes a generalised transformation that guarantees the laws of physics are the same in all reference frames. It has a generalised time dilation factor of:

$$t = \frac{t '}{\sqrt{1-K v^2}}$$

It turns out using dimensional analysis that the only two reasonable values for K are 0 and 1/c^2. When K = 0, you get the Galilean Transformation (t=t') and when K =1/c^2 you get the Lorentz transformation. The generalised transformation also yields a generalised velocity addition equation :

$$w = \frac{(u+v)}{(1+K u v)}$$

Now if u is the velocity of the emitter and v is set to the speed of light (c), then w=c for any value of u, if K=1/c^2 and w = u+c if K=0. If we agree that the speed of light is independent of the velocity of the emitter (w=c) then that identifies 1/c^2 as the only valid value for the K parameter. In turn, this indentifies the Lorentz transformation as the correct solution and eliminates the Galilean Transformation.

In summary, the first postulate, combined with the knowledge that the speed of light is independent of the velocity of the emitter (from Maxwell's equations), points to Relativity and the Lorentz transformations being a better description of nature, than Newton's laws.

Some texts specify a third postulate that "A particle at rest or with constant velocity in one inertial frame will bea t rest or have constant velocity in all inertial frames" (uniform motion is invariant), but that is getting onto a new subject.