# How did Lorentz come up with his ether theory?

1. Jul 22, 2012

### Lamarr

I'm quite confused on this.

According to Lorentz's ether theory, he used the immobile stationary ether as an absolute frame of reference.

In that case, why would the Lorentz transforms be required, since there are no relative reference frames?

2. Jul 22, 2012

### ghwellsjr

There was another thread recently they touched on this subject which I think may provide the answer you are looking for. Go to Was Einstein's postulate for the speed of light a consequence of Maxwell's equations? and scroll down to lugita15's excellent post #8 and the subsequent discussion.

3. Jul 23, 2012

### harrylin

Hi welcome to physicsforums.
There is an ambiguity in your first statement that may be at cause. People use relatively moving inertial reference systems as reference and according to Lorentz's model, there exists an inertial frame that is at rest in the ether.
It's easy if you understand Newton's "absolute space" which Newton used as "absolute" reference: you could have asked similarly "why would according to Newton's theory the Galilean transforms be required, since there are no relative reference frames?"

4. Jul 23, 2012

### Lamarr

true. so lorentz came up with the math and einstein showed that it was not due to an ether?

5. Jul 23, 2012

### harrylin

No. Lorentz found in 1904 the transformations by combining his model with the relativity principle and Einstein derived in 1905 the same transformations in a more straightforward manner. Instead of the ether model he merely used the light principle which was based on Maxwell-Lorentz. Later, Lorentz came to promote Einstein's way of deriving the transformations as it was more elegant and simpler.

Be aware that Lorentz and Einstein knew of no "Lorentz ether theory" and that label has led to confusion. We also had a discussion of Einstein's 1907 summary of their 1904 and 1905 papers:

Last edited: Jul 23, 2012
6. Jul 23, 2012

### ghwellsjr

You might find the wikipedia article History of Lorentz transformations helpful.

7. Jul 23, 2012

### harrylin

Yes, that's a nice overview, it may be very helpful. It also has a link to a more elaborate discussion of the history.

Note however that - contrary to what that article suggests - Voigt mapped the sound and light waves to a mathematical space (and back to physical space), for ease of calculation, as also some textbooks still do for sound. That confusion between mathematical convenience and physical effects may have started with Lorentz but continues up to this day.

Last edited: Jul 23, 2012
8. Jul 23, 2012

### DrGreg

I don't understand what's supposed to be the difference between a "mathematical space" and a "physical space".

9. Jul 23, 2012

### harrylin

Such a mathematical space does not directly match observed distances; a better known variant is conformal mapping*. You transform to a more convenient space for calculations, do your calculations, and then transform back to the real world.

To get back to the topic: Lorentz admitted that he might have been inspired by the transformations of Voigt when searching for solutions, just as some modern textbooks on acoustics have been inspired by the Lorentz transformation - and so the inspiration came full circle!

* http://en.wikipedia.org/wiki/Conformal_map

10. Jul 23, 2012

### DrGreg

Thanks. That's not the terminology I'd use, but I understand the point being made.

11. Jul 24, 2012

### PhilDSP

As an alternate to Conformal maps, you can think of what Voigt first did and then Lorentz was to use the simple technique of solving more difficult PDE's through the substitution of variables to arrive at equations of simpler form:

http://en.wikipedia.org/wiki/Change_of_variables_(PDE)

But the disconnect with their use of both Conformal maps and substitution of variables is that you must normally perform the inverse transformation to "undo" your original transformation to arrive at the resulting complete solution. So as Harrylin indicates, since they didn't do that, the space of the transformed or mapped variables isn't the same type of space as our classical space.

12. Jul 24, 2012

### harrylin

Right.
No. again: Voigt also used it for acoustics and he did do the inverse transformation (because it was just a substitution of variables) but Lorentz didn't do that. That was what I tried to explain, their applications such not be confounded.

And regretfully, there is reason to believe that Lorentz himself didn't see this clearly. That is both suggested by the way that he referred to Voigt, and by his later admission that he thought of the transformed quantities as "simple auxiliary quantities whose introduction is only a mathematical artifice." - https://en.wikipedia.org/wiki/Relativity_priority_dispute#Lorentz

Last edited: Jul 24, 2012
13. Jul 24, 2012

### PhilDSP

Hmmm, I definitely don't agree that Voigt used the inverse transformation in his application of the procedure for light waves, but I'll scrutinize his paper again to be doubly sure.

http://en.wikisource.org/wiki/On_the_Principle_of_Doppler

One thing Voigt didn't do that Lorentz did do was to normalize a factor of $\gamma$ away from the vector directions that are normal to the velocity to move the $\gamma$ factor into the vector directions that are parallel to the velocity. That could cause some confusion. Also worth noting is a postscript footnote Voigt left with the paper several years after it was published that indicates that with that normalization, his result is equivalent to that of Lorentz.

P.S. Maybe we're both half right. Voigt doesn't seem to re-generate the wave equation in a Doppler accommodating form (as I'd expect since he's substituting variables into the wave equation). But he does arrive at the simple formula for the space dilation:

$\frac{\partial^2 \delta}{\partial t^2} = \omega^2 \Delta \delta \ \ \ \ \$ with $\ \ \ \ \ \delta = \frac {R}{r}f(t - \frac {r - R}{\omega})$

Last edited: Jul 24, 2012
14. Jul 24, 2012

### harrylin

It's a bit off-topic but I'm happy if you can go through it with me.

"The solution is most comfortable when we use a temporary co-ordinate system X1, Y1, Z1
[...].
If we pass from the assumed special co-ordinate system X1, Y1, Z1 to the general X, Y, Z, [..] we finally get [..]. it contains what is usually understood by the principle of Doppler"

Next for a moving observer he makes instead a transformation to X', Y', Z' and how he does that is a bit obscure (at least to me!). However, he nowhere proposes or suggests to be doing anything in conflict with Newtonian mechanics. Thus, further on, when he talks about "introduction of relative coordinates against the moving luminous point", I think that he uses a Galilean transformation.

Also:
" the analogous problems of the acoustics of fluids [..] The introduction of the substitutions (10), (12) or (13) always gives, if δ is given by the constraints along a given surface as an arbitrary function of time, the transition from the effect of a stationary source to the effect when it is in translational motion. "

15. Jul 24, 2012

### PhilDSP

I've actually been intending to write a review paper on the subject. I'd certainly welcome working with a co-author. A full evaluation and re-expression of Voigt's paper and the issues involved might be a bit too much to take on in one thread here and I think it would be best not to be overly hasty in making any pronouncements. But it is an exciting and mysterious subject with no doubt some very interesting findings. Maybe the moderators can venture an opinion on the wisdom of saying much more on this here.

16. Jul 26, 2012

### harrylin

As it's separate from the topic of Lorentz, let's continue that discussion between the two of us.