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Quoting from this website:

What Lorentz was able to show was that Maxwell's theory of electromagnetism predicted precisely this much longitudinal contraction.To get this result, Lorentz modeled matter composing a body as a large collection of electric charges, all held together in equilibrium by electric and magnetic forces.
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Moving electric charges create magnetic fields that in turn act back of electric charges. All these changes settle out into a new equilibrium configuration. What Lorentz could show was that new configuration consists in a contraction of the body in the direction of motion in just the amount needed to eradicate a possible result from the Michelson Morley experiment.

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My questions:

1) Is this derivation of length contraction considered to be sound and correct today? Is it treated in modern textbooks?

2) What if there are 2 masses (and therefore chargs) at rest with empty space between them? Would electrodynamics predict lenght contraction also in this case?

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  • $\begingroup$ This description of length contraction seems incorrect, because it implies that length contraction is a dynamic effect involving things changing their equilibrium positions as they speed up. But length contraction has nothing to do with dynamics. It's a purely kinematic effect. $\endgroup$ – knzhou Aug 19 '16 at 3:02
  • $\begingroup$ @knzhou "seems" incorrect or "is" incorrect? $\endgroup$ – Marco Disce Aug 19 '16 at 14:49
  • $\begingroup$ Possible duplicate :Is it possible to derive Lorentz transformation equation without Einstein's postulates? $\endgroup$ – sammy gerbil Aug 19 '16 at 16:17
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The webpage which you are quoting from points towards the answers to your questions. You need to read the whole of the webpage.

At the time this seemed like a perfectly satisfactory resolution of the puzzle of the failure of all ether drift experiments. It is only if you know what is coming next that you find the resolution awkward. Or, if you are Einstein, you see more in the resolution than others then did.

This is telling you that Lorentz' explanation is not accepted today. The webpage has the title of Origins of Special Relativity. This gives you a big clue that the explanation accepted today is not that of Lorentz but that of Einstein in his Theory of Special Relativity.

Lorentz made the ad hoc assumption that a fixed Aether medium exists, in order to predict a contraction in length of all experimental apparatus which explains why we can never detect the Aether. The only role the Aether plays in this theory is to explain why it cannot be detected!

Moreover, the Aether must have contradictory properties : it must be infinitely stiff in order to transmit vibrations of light at such tremendous speed, while also being so weak that the Earth can slip through it without being slowed down noticeably over centuries. The only consistent property it does have is that it does not move in any direction.

Instead of a fixed Aether, Einstein assumed that the speed of light is the same for all observers in relative motion. Although both assumptions (or hypotheses) are consistent with relevant experimental results, and neither can be proven, Einstein's hypothesis is considered to be superior. It avoids being ad hoc - ie it does not assume the existence of something which it proposes to explain or explain away. It is more consistent with the rest of physics, and is more 'useful' in making other testable predictions, as explained here.

The wikipedia article on the Lorentz Ether Theory summarizes the modern view of Lorentz' hypothesis :

Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length contraction and time dilation for all phenomena in a "preferred" frame of reference, which plays the role of Lorentz's immobile aether, leads to the complete Lorentz transformation (see the Robertson–Mansouri–Sexl test theory as an example). Because the same mathematical formalism occurs in both, it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable aether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.

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  • $\begingroup$ The point of my question was not if Lorentz "Aether theory" was accepted: I was asking about Lorentz derivation of length contraction in the frame of Maxwell Electrodynamics alone. If it was actually possible to derive it only from Maxwell's equation's then Lotentz actually did explain the experiment for anybody who just believed in Maxwell's equation, with or without Aether. So the point is only if Loretz did a mistake in that explanation or not. His argument doesn't need Aether: he just consider a moving system of charges satisfying Maxwell's equation. $\endgroup$ – Marco Disce Aug 19 '16 at 15:05
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    $\begingroup$ 1. The website you quoted is U. of Pittsburgh, Dept of History and Philosophy of Science. A well-established academic institution, and an appropriate dept for this topic. So it can be taken as reliable. 2. Although, as the wiki article points out, the prediction is the same (the Aether cannot be detected) and the Lorentz Contraction formula is the same, the 2 theories are fundamentally different, based on different physical principles. Lorentz contraction is not taught today as an alternative view of SR, only as an historical attempt to explain why the Aether cannot be detected. $\endgroup$ – sammy gerbil Aug 19 '16 at 15:22
  • $\begingroup$ See wiki article, especially section on "local time." Lorentz contraction cannot be derived from Maxwell's equations alone. Lorentz had to make other assumptions as well, based on the existence of some kind of Aether. One was the idea of "local time," the time co-ordinate for a moving observer. He regarded this as a 'mathematical trick' and length contraction as a real physical effect. SR regards both length contraction and time dilation as the result of consistent co-ordinate transformations between 2 observers : neither are physical effects; no physical explanation is necessary. $\endgroup$ – sammy gerbil Aug 19 '16 at 15:59

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