Lorentz derivation of length contraction in electrodynamics

In summary, Lorentz's theory of length contraction was developed to explain the negative results of the Michelson-Morley experiment and rescue the hypothesis of a stationary aether. This was considered an ad hoc hypothesis until Einstein's theory of special relativity removed the need for a stationary aether and explained length contraction using transformations of space and time. Today, length contraction is derived using the special theory of relativity and Lorentz transformations, and is recognized as a fundamental concept in modern physics. Lorentz's hypothesis of intermolecular forces being electromagnetic was eventually proven to be true, adding further support to his theory of length contraction. However, the question of how matter not held together by electromagnetic forces would be affected by length contraction was
  • #1
Babbeus
2
0
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?
 
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  • #2
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>
 
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  • #3
drvrm said:
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>

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
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.
 

1. What is the Lorentz derivation of length contraction in electrodynamics?

The Lorentz derivation of length contraction is a mathematical explanation for the observed phenomenon of objects appearing shorter in the direction of motion when traveling at high speeds. It is a crucial component of Einstein's theory of special relativity and is based on the principles of electromagnetism.

2. How does the Lorentz contraction formula work?

The Lorentz contraction formula is given by L = L0 / γ, where L is the contracted length, L0 is the rest length of the object, and γ is the Lorentz factor. This formula takes into account the relative velocity of the object and the observer and shows that the length of an object decreases as its velocity increases.

3. What is the significance of the Lorentz contraction in electrodynamics?

The Lorentz contraction is significant because it helps us understand the effects of relativity on the measurements of length. It also shows that the laws of physics, specifically electromagnetism, are the same for all observers regardless of their relative velocities, as long as they are moving at a constant speed.

4. Can the Lorentz contraction be observed in everyday life?

Yes, the Lorentz contraction can be observed in everyday life, although it is most noticeable at very high speeds. For example, particles in particle accelerators appear shorter than they actually are due to their high velocities. It is also taken into account when designing high-speed trains and airplanes.

5. Are there any exceptions to the Lorentz contraction in electrodynamics?

Yes, the Lorentz contraction does not apply to objects that are not moving at a constant speed. It also does not apply to objects that are accelerating or decelerating. Additionally, it only applies to objects that are traveling at speeds close to the speed of light, as the effects become more significant at higher velocities.

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