# Alternate derivation of Lorentz Trans.

1. Oct 16, 2004

### timetraveldude

Has anybody come up with a way to derive the LT not based on the constantcy of the speed of light in all inertial reference frames?

2. Oct 16, 2004

### HallsofIvy

WHY would one want to? The constancy of the speed of light was the experimental data that led to the Lorenz transformation. If the speed of light was not constant why would one want or need the Lorenz transformation?

3. Oct 16, 2004

### Fredrik

Staff Emeritus
I'm not sure what you (timetraveldude) have in mind here. The Lorentz tranformation is equivalent to the statement that the speed of light is the same to all inertial observers. I don't think the question really makes sense. Any postulate that you can use as a starting point for a derivation of the Lorentz tranformation will include that stuff about the speed or light, whether it's apparent or not.

4. Oct 16, 2004

### arildno

I think Lorentz himself had another way...
If I remember correctly, he made some ad-hoc assumption that objects contracted in the direction of motion.
This is of course only of historical interest; I think Lorentz attempted to account for the Michelson-Morley experiment while simultaneously saving the ether hypothesis.

Einstein, of course, presented a far more elegant, and convincing, chain of argument for the necessity of the Lorentz transformation.

5. Oct 16, 2004

### timetraveldude

I am not sure if you are correct. As I understand it, Maxwell's equations were not invariant under the Galilean transformations. Einstein felt that the laws are physics should be the same in all inertial reference frames. So either the Galilean transformations were wrong or Maxwell's equations.

6. Oct 16, 2004

### timetraveldude

Simultaneity post

Maybe you should see my other post in this forum. The relativity of simultaneity argument is based on light but if you use sound instead of light all inertial observers will agree whether two events were simultaneous. On the other hand if you can derive the Lorentz transformations without using the 2nd postulate (i.e. through a different means) then the relativity of simultaneity is preserved.

7. Oct 16, 2004

### timetraveldude

This is not true. The Lorentz transformations only describe distance and time transformations between coordinate systems if there is a universal speed limit.

The impression I get from the people here is that they have memorized the details but do not know how to think critically. I have proved that you can derive the Lorentz transformations without utilizing the 2nd postulate of SR. Am I the only one? There was a paper in 1972 that did this exact thing but using a different method from mine. The idea is basically that if you are teaching a mechanics course and want to incorporate SR without reference to electro-dynamics you need a different way of introducing the Lorentz transformations.

8. Oct 16, 2004

### jcsd

The problem is for you argument to have any validity you need something that travels on a null worldline, light does whereas sound does not.

9. Oct 16, 2004

### Fredrik

Staff Emeritus
OK. When I think of "the speed of light" I don't even think of light. To me "the speed of light" is just a name that represents the universal speed. That's why I thought your suggestion sounded so strange. But OK, you don't want to do a derivation that doesn't involve a universal speed, you want to do a derivation that doesn't involve light (or anything else from the classical or quantum theory of electrodynamics). That's a different story.

I've seen a derivation like that once, or at least a part of it. Unfortunately I don't remember who wrote it. Their idea was to assume nothing at all about the properties of space, except rotational and translational invariance, and try to determine the most general rule for addition of velocities. The result they got was of course not the non-relativistic "u+v" but a relativistic-looking formula (u+v)/(1+Kuv), where K was a non-negative real number that couldn't be determined from the postulates they had started with.

The constant K can of course be identified with 1/cĀ², but there's no need to do that just yet. Instead, we can use the velocity addition formula as the starting point of a derivation of the rest of special relativity, including the Lorentz transformation.

10. Oct 16, 2004

### timetraveldude

My argument is perfectly valid. Again you are using as evidence what I am questioning. If you want to remain in the realm of logical thinkers you need to understand this is not acceptable.

11. Oct 16, 2004

### jcsd

The problem is that sound is totally irrelevant to considerations of simultaneity in relativity. Special relativty is inertanally self-consistent so any questioning of well-know results such the fialure of simulatenity at distance cannot come from poniticating it must come from experimental evidmnece, yet you offer none.

12. Oct 16, 2004

### cragwolf

To answer the OP, yes, there are many alternative derivations of the Lorentz Transformations, some of which do not assume the constancy of the speed of light. I'll just list a few that don't assume the constancy of the speed of light:

Y.P.Terletskii, "Paradoxes in the Theory of Relativity", Plenum Press, New York, 1968, P17
R.Weinstock, "New Approach to Special Relativity", Am. J. Phys. 33 640-645 (1965)
A.R.Lee and T.M.Kalotas, "Lorentz Transformation from the First Postulate", Am. J. Phys. 43 434-437 (1975)
J.M.Levy-Leblond, "One more Derivation of the Lorentz Transformation", Am. J. Phys. 44 271-277 (1976)
A.Sen, "How Galileo could have derived the Special Theory of Relativity", Am. J. Phys. 62 157-162 (1994)
J.H.Field, "Space-Time Exchange Invariance: Special Relativity as a Symmetry Principle", [http://arxiv.org/physics/0012011 [Broken]]

Last edited by a moderator: May 1, 2017
13. Oct 16, 2004

### timetraveldude

Thank you. You are the first person I have met in this thread who actually thinks.

Last edited by a moderator: May 1, 2017
14. Oct 16, 2004

### Garth

Have you tried K calculus? Developed by Milne in his Kinematic cosmology in the 1930's and used by d'Inverno in "Introducing Einstein's Relativity".
Garth

15. Oct 16, 2004

### timetraveldude

Thanks. WOW! Two useful posts in a row. This is a violation of statistics.

It is amazing that the people who make the most useless posts are the so called mentors.

16. Oct 16, 2004

### Hurkyl

Staff Emeritus
Just to make sure you realize, these approaches will derive the constancy of the speed of light.

17. Oct 16, 2004

### Tom Mattson

Staff Emeritus
Yes, it is true.

Einstein started with the constant speed of light postulate and Maxwell's equations. Requiring the latter to be covariant, he derived the Lorentz transformation. But you could just as easily start from the Lorentz transformation and derive from that the speed of light postulate, and of course the covariance of Maxwell's equations.

Lose the attitude.

18. Oct 16, 2004

### Tom Mattson

Staff Emeritus
Never mind folks. Timetraveldude is just another alias for our beloved protonman and tenzin.

He won't be joining us in this thread anymore.

19. Oct 16, 2004

### fixizrox

The lorentz transformations say nothing about the speed of light being the same in all inertial reference frames. I derived the LT without any reference at all to light.

20. Oct 16, 2004

### Tom Mattson

Staff Emeritus
Of course they do. As has been said repeatedly, you can derive the speed of light postulate from the LT.

Good for you. Now use it to derive the relativistic velocity addition law, and then then Einstein's speed of light postulate.

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