# Mathematical Proof For Lorenz Coordinate Transformation

1. Dec 14, 2006

### DrorH

Hi, I have a pretty in depth understanding of special relativity. Recently I have been searching for mathematical proof of the Lorenz transformation.
I found some information about it, but to tell the truth I didn't understand much of it.
Maybe one of you guys can shead some light on the proof or can link me to an article or a book?

Last edited: Dec 14, 2006
2. Dec 14, 2006

### robphy

What "info about it" did you find? Can you post a reference?

Can you elaborate of the "depth" of your "understanding of special relativ[it]y" so that appropriate alternative references can be offered? For example, I'll rattle off some terms in no particular order to see what you are familiar and unfamiliar with: interval, time-dilation, doppler-effect, radar-measurements, 4-velocity, rapidity, rotation, vector-space, spacetime diagram, metric, vector, tensor...

3. Dec 14, 2006

### DrorH

First, sorry for typing errors which are now fixed. Heh.

I am well familiar with space-time interval as an invariant size, time dilation as a result of Lorenz time transformation, doppler-effect relaltive formula as a result of Lorenz transformations, I am in the Israeli navy so I have a very good understanding of radars if that is what you meant, I am not familiar with the term 4- velocity, I don't know rapidity as a SR term, rotation duh, familiar with vector space, familiar with Minkowski space-time diagram, metric as in meter system?, vector duh, and I have no idea what tensor is.

Sigh! :)
I have a book which breifly describes the math behind it. Tell me if you want me to copy it to the message with much effort.

4. Dec 14, 2006

### cristo

Staff Emeritus
5. Dec 14, 2006

### DrorH

Thanks a lot.
At first glance I understand close to nothing. I'll try my best.. hehe.
I wonder if einstein found the transformations through math or did he find it intuitivly. From my knowlege he found those transformation without even knowing that they were also made by Lorenz as a technical tool to correct a "calculation error" rather then natural fact as they are used in SR. Because after all these transformations make rational sence. Their proof makes less sence though.. :)
I'll appreciate if you try to explain it with more depth on the mathematical tools used which I am obviously not familiar with. I'll understand if it is too much of a hassle.

Last edited: Dec 14, 2006
6. Dec 14, 2006

### robphy

Well... here is a transcription of Einstein's paper:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

A Lorentz Boost Transformation is analogous to a Euclidean rotation. So, if you can follow the mathematics of the derivation of a rotation, the Lorentz Boost shouldn't be too difficult... mathematically.

There is a neat (and arguably more physically motivated) mathematical proof using the (doppler-effect) k-calculus and radar measurements... but I don't have the time to write it up right now.

7. Dec 14, 2006

### DrorH

I will appreciate it if you write it up when and if you find the time.
Thanks a lot for the help.

8. Dec 14, 2006

### bernhard.rothenstein

please have a critical look at

arXiv.org > physics > physics/0607048

abstract

Following an approach proposed by Rosser for deriving the transformation equations of volume charge density and current density we derive the transformation equations for the space-time coordinates of the same event, for the mass and the momentum of the same particle and for the electric and the magnetic field generated by the same distribution of electric charges.
the best things a physicist can offer to another one are information and constructive criticism

9. Dec 15, 2006

### lalbatros

The Lorentz transformation was known already at least ten years before Einstein's special relativity.
The interpretation was a problem, as well as the reconcilition with the other part of physics, specially Newtonian mechanics.

Einstein, solved all these problems by understanding that spacetime was involved and that classical physics had to be modified. Since 1905, spacetime has to be discovered and studied experimentally just like any physical object. This led Einstein to the further steps of general relativity.

Michel

peace and freedom

Last edited: Dec 15, 2006
10. Dec 15, 2006

### bernhard.rothenstein

LET derivation: what was first the chicken or the egg?

I am glad seeing that you aggree with other ways to derive the LET, illustrating the way in which the relativistic postulates should be applied. As I see, here on the Forum, there are physicists who become angree when they here about them.
There is an old, nonsolved problem: What was first the egg or the hen? I think that the relativistic postulate is compulsory as clock synchronization and definition of the concept of same event are. The first results are time dilation and length contraction which lead to the addition law of relativistic velocities or two the LET. With them in hands and with the concept of proper physical quantity the way to all the relativistic transformaion equations in all the fields of physics is paved avoiding paradoxes. Of course hundred years of special relativity generated many derivations with other starting points. Far from me to blame them because i learned a lot from them.
sine ira et studio

11. Dec 15, 2006

### bernhard.rothenstein

help

please let me know if all parts of the course are available?

12. Dec 15, 2006

### DrorH

I found 4 articles that corespond to that number but only one of them has anything to do with math and it's about "Compactness of the solution operator to d-bar in weighted L^2 - spaces"...
Couldn't find what you were reffering to.

13. Dec 15, 2006

### bernhard.rothenstein

arxiv paper

go google and give it to look for
physics/0607048
Special relativity from a single scenario following the same strategy. If you have some problem give me an e-mail address and I will forward you the paper and some others devoted to the same problem.

14. Dec 15, 2006

### cristo

Staff Emeritus
I just googled this site- it's nothing to do with me personally! It's from a course on classical electromagnetism, and the rest of the course is here http://farside.ph.utexas.edu/teaching/em/lectures/

15. Dec 16, 2006

### DrorH

This article reveals a way of reaching the Lorenz transformation without actually using it. But it does a huge intuitive leap by incorperating the size v^2/C^2 without any mathematical analysis. You can't really reach the conclusion without being familiar with the proper Transformation. Get my drift?
From my understanding there is a mathematical way of revealing this particular size, and others, with no physical intuition. Am I wrong?

16. Dec 16, 2006

### robphy

You may recall an earlier 2005 post of mine
https://www.physicsforums.com/showpost.php?p=694535&postcount=8
which features a chart (as an attachment) from
"Spacetime and Electromagnetism" by J.R. Lucas, P.E. Hodgson (https://www.amazon.com/exec/obidos/tg...60834?v=glance ) where they try to diagram the various approaches to obtain the Lorentz Transformations.

Last edited by a moderator: May 2, 2017
17. Dec 16, 2006

### bernhard.rothenstein

Before to go further with our discussion please have a look at the paper by Asher Peres "Relativistic telemtry" published in Am.J.Phys. who made among others the big jump showing where from vv/cc arrises.
pleas do not hesitate to put further questions. i learn a lot from them.