- #1
timetraveldude
- 42
- 0
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?
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.HallsofIvy said: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?
This is not true. The Lorentz transformations only describe distance and time transformations between coordinate systems if there is a universal speed limit.Fredrik said: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.
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.timetraveldude said:This is not true. The Lorentz transformations only describe distance and time transformations between coordinate systems if there is a universal speed limit.
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.jcsd said: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.
timetraveldude said: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.
Thank you. You are the first person I have met in this thread who actually thinks.cragwolf said: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]]
Thanks. WOW! Two useful posts in a row. This is a violation of statistics.Garth said: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
Fredrik: The Lorentz tranformation is equivalent to the statement that the speed of light is the same to all inertial observers.
timetraveldude: This is not true.
timetraveldude said:It is amazing that the people who make the most useless posts are the so called mentors.
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.Tom Mattson said: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.
fixizrox said: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.
timetraveldude said: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?
fixizrox said:I derived the LT without any reference at all to light.
I think timetraveldude knows that. I think he understands that the Lorentz transformations imply the existence of a velocity that's the same to all inertial observers. What he's trying to make a big deal of here, is that there's nothing in the Lorentz transformations that explicitly mentions light. Sure, they mention the speed of light (the universal velocity), but they don't say that this is the same thing as the speed of light (photons/electromagnetic waves). That's why he won't accept that the Lorentz transformation is equivalent to the speed of light postulate.Tom Mattson said:Of course they do. As has been said repeatedly, you can derive the speed of light postulate from the LT.
Fredrik said:I agree. I just think it's interesting that even if you've never heard of Maxwell's equations, and have no idea what the speed of light is, it's still possible to realize that SR (with some universal velocity) is at least a possibility.
Fredrik,Fredrik said:Timetraveldude, if you have derived the Lorentz transformations without using light, that's not really a big deal. As I mentioned before, the most general velocity addition law that's consistent with rotational and translational invariance has been shown to be (u+v)/(1+Kuv), where K is just a constant to be determined later.
If K is not 0, we can define a constant c that has dimensions of velocity: c²=1/K. The velocity addition formula can be used to derive the Lorentz tranformations, and this will lead us to the idea of Minkowski space. Now, if we try to construct a theory of light that's consistent with the idea that Minkowski space is an accurate representation of space and time, we will eventually end up with QED, Maxwell's equations, and the identification c = the speed of light.
There are many derivations of the Lorentz transformation that do not use Einstein's second postulate. See http://www.everythingimportant.org/relativity/special.pdf for example.timetraveldude said: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?
Also see http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001 [Broken]There are many derivations of the Lorentz transformation that do not use Einstein's second postulate. See http://www.everythingimportant.org/relativity/special.pdf for example.
Hurkyl said:Just to make sure you realize, these approaches will derive the constancy of the speed of light.
timetraveldude said: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.
PatrickPowers said:[..]
The reason the Einstein interpretation is preferred is that there is no reason to prefer any particular frame over any other and the preferred frame is impossible to identify. So there is no reason to believe that it exists and it seems an unnecessary, arbitrary complication.
Fredrik said:This thread had been dead for more than 7 years. I wonder if it's a new necropost record.
The Lorentz Transformation is a mathematical formula that describes how measurements of space and time change between two frames of reference that are moving relative to each other at a constant velocity. It is a fundamental concept in the theory of special relativity.
An alternate derivation of the Lorentz Transformation is useful for gaining a deeper understanding of the concept and for verifying its validity. It also allows for different perspectives and approaches to solving problems related to special relativity.
The traditional derivation of the Lorentz Transformation is based on the principles of symmetry and invariance, while the alternate derivation uses the concept of hyperbolic geometry to derive the same equations. It also provides a more intuitive understanding of the equations.
One of the main advantages of the alternate derivation is that it does not rely on the concept of simultaneity, which can be difficult to define and measure in relativistic scenarios. It also allows for a more geometric interpretation of the equations.
While the alternate derivation provides a different perspective on the Lorentz Transformation, it still relies on the same underlying principles and assumptions. It may not be suitable for all applications and may be more complex than the traditional derivation for some individuals.