Lorentz derivation of length contraction in electrodynamics

  • #1
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Here is a quote 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.
lattice_at_rest.png

The equilibrium was disturbed if the entire object was set in motion. 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.

lattice_moving.png

My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?
 

Answers and Replies

  • #2
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Length contraction was postulated by George FitzGerald and H.A Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether .

It was considered an ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones.

Eventually, Albert Einstein (1905) was the first to completely remove the ad hoc character from the contraction hypothesis, by demonstrating that this contraction did not require motion through a supposed aether, but could be explained using special relativity, which changed our notions of space, time, and simultaneity.

Now a days the special theory of relativity and Lorentz Transformations are used to derive contraction as a consequence of STR.
one can see details of historical development in <https://en.wikipedia.org/wiki/Length_contraction> [Broken]
 
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  • #3
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Length contraction was postulated by George FitzGerald and H.A Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether .

It was considered an ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones.

Eventually, Albert Einstein (1905) was the first to completely remove the ad hoc character from the contraction hypothesis, by demonstrating that this contraction did not require motion through a supposed aether, but could be explained using special relativity, which changed our notions of space, time, and simultaneity.

Now a days the special theory of relativity and Lorentz Transformations are used to derive contraction as a consequence of STR.
one can see details of historical development in <https://en.wikipedia.org/wiki/Length_contraction> [Broken]

Thank you very much for your reply.
If I understand well what happened I would say the objections of "ad hoc" hypothesis addressed to Lorentz actually vanished not just because of Einstein's revolution but also because Loretnz's hypothesis that intermolecular forces are electromagnetic turned out to be true. Is this right? So it makes sense to consider the possibility that Lorentz derivation was indeed sound/correct and if it is so maybe it would be remarkable enough to deserve to be treated in textbook today. Is this the case?
 
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  • #4
Ibix
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The question that Lorentz left open but Einstein answered is what happens to matter that is not held together by electromagnetic forces. Michelson and Morley's interferometer was built on a solid base. But what would happen to an interferometer with mirrors floating freely in vacuum? Einstein says that it will behave the same way as the one with the solid base. But the argument you laid out above gives no reason to expect the distance between free-floating unconnected mirrors to change. That makes it a detailed application of Einstein's more general argument to the case of solid matter, I think.
 

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