# Why was Lorentz transformation known before Einstein explained clock synchronisation

#### lalbatros

The constancy of the speed of ligth is a result of the Maxwell's equations.
And the Lorentz transformation is an invariance of Maxwell's theory that was known before the special theory of relativity was discovered.

Why and how did the physics of the 19th century (particularly Maxwell) built a Lorentz-invariant theory? And how and when did they implicitely define the coordinate system they used? Specially the clock synchronisation?

Thanks,

Michel

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Maxwell took the existing laws discovered by Ampere, Faraday, and Henry and contributed his own displacement current to respect the law of conservation of energy. That gave him his equations; he didn't set out to make it Lorentz covariant, but it was eventually apppreciated that his theory was not Galilean invariant, and this motivated Lorentz to develop the transformations. that bear his name

#### Office_Shredder

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I thought the lorentz transformation came about because Lorentz looked at the ether experiment, and realized everything would work out perfectly if the length was dilated along the axis of motion.

#### JesseM

Office_Shredder said:
I thought the lorentz transformation came about because Lorentz looked at the ether experiment, and realized everything would work out perfectly if the length was dilated along the axis of motion.
I think you also need time dilation to explain the Michelson-Morley results, although you don't need to worry about synchronization conventions because the MM experiment measured the two-way speed of light rather than the one-way speed, so only a single clock is required. The full lorentz transformation also implies the relativity of simultaneity, so even if you had thought up time dilation and length contraction it wouldn't be quite enough to derive it. As selfAdjoint said, I think the Lorentz transformation was discovered in a more purely mathematical way, by noticing that this was the transformation you'd need in order for Maxwell's laws to remain the same in each coordinate system; I'm not sure if this was noticed before or after the proposal of genuine physical length contraction and time dilation in order to explain the MM results, though.

#### nakurusil

lalbatros said:
The constancy of the speed of ligth is a result of the Maxwell's equations.
And the Lorentz transformation is an invariance of Maxwell's theory that was known before the special theory of relativity was discovered.

Why and how did the physics of the 19th century (particularly Maxwell) built a Lorentz-invariant theory? And how and when did they implicitely define the coordinate system they used? Specially the clock synchronisation?

Thanks,

Michel
The first instance of the Lorentz transforms is the 1904 paper entitled " Electromagnetic phenomena in a system moving with any velocity less than light"
In this paper, Lorentz attacks the issue of the invariance of the Maxwell equations. He starts with the Galilei transforms , though it was already known that they do not preserve the invariance and proceeds by fiddling with the transforms in such a fashion that they leave the Maxwell equations invariant. Because he had to deal with the $${\sqrt{1 - \frac{v^2}{c^2}}$$ term, Lorentz sets forward the fact that the new theory is valid for v<c, hence the title of his paper.
Satisfied with the fact that the new transforms leave the Maxwell equations invariant, Lorentz proceeds to explain the null result of the MMX via the Lorentz (length) contraction.
MMX needs only the length contraction as an additional postulate. Kennedy Thorndike needs length contraction and the added postulate of time dilation. The simplicity of Einstein's theory won over Lorentz's explanation (fewer postulates is always better)

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#### yogi

Quite correct Nakurusil - the Kennidy-Thorndike experiment eliminated theories that depended only upon length contraction but left intact those theories that incorporated both length contraction and time dilation, which included both modified Lorentz Ether theory and SR.

#### lalbatros

Dear All,

What strikes me is precisely this:

Maxwell took the existing laws discovered by Ampere, Faraday, and Henry and contributed his own displacement current to respect the law of conservation of energy.
How is it that the laws of Ampère, Faraday and Henry, that are based on experimental results in non-relativistic situations have led to the special theory of relativity. How is it that this forced Einstein to reconsider how spacetime is represented, while the forerunners of the EM theory did not need to think about it. How is it that the coordinate system implicitely used in the Maxwell's equation is compatible with the special relativity? Does that not mean that the constraints encountered when designing the EM theory are somehow equivalent to the theory of relativity? Where can we see that, if it is true?

Thanks,

Michel

#### robphy

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lalbatros said:
How is it that the laws of Ampère, Faraday and Henry, that are based on experimental results in non-relativistic situations have led to the special theory of relativity.
As in many instances in the history of physics, experiments give us glimpses of how nature works. Then, hopefully, someone comes along and sees the bigger picture...leading to predictions in new [say, relativistic] situations not yet tested.

lalbatros said:
How is it that this forced Einstein to reconsider how spacetime is represented, while the forerunners of the EM theory did not need to think about it.
He looked at the bigger picture [the general principles] rather than the fine details of an experiment. As you pointed out, the forerunners were focused on their various laws and associated phenomena. In addition, it's probably fair to say that physics and mathematical thinking had not yet advanced to appreciate symmetries, like relativistic invariance. [I think that Felix Klein's Erlangen program was a major advance in this direction.]

An interesting paper on issues like this is
http://dx.doi.org/10.1119/1.12239
"If Maxwell had worked between Ampère and Faraday: An historical fable with a pedagogical moral"
Max Jammer, John Stachel
American Journal of Physics -- January 1980 -- Volume 48, Issue 1, pp. 5-7

#### Office_Shredder

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lalbatros said:
How is it that the laws of Ampère, Faraday and Henry, that are based on experimental results in non-relativistic situations have led to the special theory of relativity. How is it that this forced Einstein to reconsider how spacetime is represented, while the forerunners of the EM theory did not need to think about it. How is it that the coordinate system implicitely used in the Maxwell's equation is compatible with the special relativity? Does that not mean that the constraints encountered when designing the EM theory are somehow equivalent to the theory of relativity? Where can we see that, if it is true?
The real simple explanation, is electricity moves faster, and has a stronger force, than gravity and large masses. So effects are easier to notice

#### bernhard.rothenstein

JesseM said:
I think you also need time dilation to explain the Michelson-Morley results, although you don't need to worry about synchronization conventions because the MM experiment measured the two-way speed of light rather than the one-way speed, so only a single clock is required. The full lorentz transformation also implies the relativity of simultaneity, so even if you had thought up time dilation and length contraction it wouldn't be quite enough to derive it. As selfAdjoint said, I think the Lorentz transformation was discovered in a more purely mathematical way, by noticing that this was the transformation you'd need in order for Maxwell's laws to remain the same in each coordinate system; I'm not sure if this was noticed before or after the proposal of genuine physical length contraction and time dilation in order to explain the MM results, though.
Please have a critical look at
arXiv.org > physics > physics/0510178

Physics, abstract
physics/0510178

Date: Wed, 19 Oct 2005 17:32:24 GMT (312kb)

Subj-class: Physics Education

Considering that the rays in the Michelson-Morley interferometer perform the radar detection of its mirrors, we use a relativistic diagram that displays, at a convenient scale, their location and the path of the rays. This approach convinces us that the rays that come from the two arms interfere with zero phase difference without using the usual ingredient, length contraction.
Full-text: PDF only
sine ira et studio

#### Ich

Office_Shredder said:
The real simple explanation, is electricity moves faster, and has a stronger force, than gravity and large masses. So effects are easier to notice
For the derivation of Maxwell's Equations, electrons don't have to move fast.
But electricity has an incredible strength, which is masked by the fact that charges balance out. If you experiment with slowly moving charges, relativistic effects shift that perfect balance for a minute amount. Because electricity is so strong, its easy to detect those effects.

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