# World's Fastest DerivationS of the Lorentz Transformation?

1. Jun 6, 2006

### robphy

Still the "World's Fastest Derivation of the Lorentz Transformation"
http://arxiv.org/abs/physics/0606046

...apparently in response to
A faster than "World fastest derivation of the Lorentz transformation"
http://arxiv.org/abs/physics/0602153 ,

...which is apparently a challenge to
"World's Fastest Derivation of the Lorentz Transformation"
http://faculty.luther.edu/~macdonal/LorentzT.pdf ,
which in turn is an improvement over
"Derivation of the Lorentz transformation"
http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=AJPIAS&CURRENT=NO&ONLINE=YES&smode=strresults&sort=rel&maxdisp=25&threshold=0&pjournals=AJPIAS&pyears=2001%2C2000%2C1999&possible1=macdonald&possible1zone=article&SMODE=strsearch&OUTLOG=NO&viewabs=AJPIAS&key=DISPLAY&docID=17&page=1&chapter=0 [Broken]

Last edited by a moderator: May 2, 2017
2. Jun 11, 2006

### bernhard.rothenstein

State
(A) The velocity of light is the same in all inertial reference fraemes.
(B). A rod is at rest in I' where its proper length is (x'-0). Measured in I its length is (x-0). We suppose that (x-0)=G(x'-0) where G is a function of the relative velocity V.
Consider the relative position of the frames I and I' as detected from I at a given time t and an event E(x,0,t) in I and E'(x,0,t') in K'. I' moves with constant velocity V in the positive dirfection of the common OX(O'X') axes. We have obviously
x=Vt+Gx' (1)
in Iand
x'=Gx-Vt' (2)
in I'..
Taking into account that in both frames Einstein clock synchronization took place (1) and (2) lead to
t=Vt/c+Gt' (3)
t'=Gt-Vt'/c (4)
Combining (3) and (4) we obtain
G=sqr(1-VV/cc)
and the Lorentz-Einstein transformations are in our hands.
Please have a critical look at the derivations presented above and tell me if you know a shorter one.

Last edited by a moderator: May 2, 2017
3. Jun 11, 2006

### clj4

Who cares? Speed of derivation is something that is irrelevant for practical purposes.
For pedagogical reasons correctness and clarity is what counts .

Last edited by a moderator: May 2, 2017
4. Jun 11, 2006

### robphy

One point of the above papers is to identify what minimal set, or possibly more attractive set, of assumptions is needed to obtain the Lorentz Transformations (in 1+1). I think those authors are hoping that the terseness of the derivation will lead to an improvement in pedagogy. Certainly, there are "correct" but [arguably] drawn out approaches.... clarity is subjective as well. (For example, should one use an experimental result, or a mathematical requirement.)

I would agree that "for practical purposes", who cares? But for foundational purposes and for seeking alternative pedagogical approaches, I think they are worthy of some attention.

To me, the Bondi-Milne k-calculus approach (using the Doppler effect), which relates two periods via a light ray, is pedagogically more attractive than an approach which relates two time-intervals which are simultaneous in an inertial system or two lengths measured in a given inertial system. (Mathematically, the k-calculus exploits the eigenvectors and eigenvalues of the Lorentz Transformation... which are the natural structures for it.)

What would be more appealing is an approach that clearly distinguishes the Galilean case from the Lorentzian case. Along these lines, there are a bunch of "Lorentz Transformations without the Speed of Light" approaches, which usually end up with a free parameter (the maximal speed of signal propagation) in a velocity-composition formula. In some sense, this isn't so suprising since velocity-composition can be given a projective-geometric interpretation....without explicit specification of a metric.

5. Jun 11, 2006

### clj4

Yes, I agree. For me, the original 1905 presentation , cleaned up a little is still the one that I prefer for pedagogical reasons. It has several very attractive features:

1. The historical aspect (this is how Einstein got things started)

2. It includes a complete explanation of the clock synchronization method

3. It includes a large spectrum of applications of the newly derived theory. I happen to find this point the most attractive. While it has no effect on papers that try to rederive the Lorentz transforms, it has a huge effect on people trying to write "alternative" theories. For example, look at the famous Mansouri-Sexl theory: the authors derive an "alternative" set of transforms (that are super ugly, but this is a different story), then they proceed with a kinematic section, then they promise a dynamic section at some later time (which they never deliver) and they do absulutely nothing about the elctromagnetic section. Contrast this with Einstein's paper.....

6. Jun 12, 2006

### Meir Achuz

Amen!
For some reason I need 10 characters in search of an answer.

7. Jun 12, 2006

### bernhard.rothenstein

I admired my instructors who were able to teach us without using mnemonic aids. I tried to follow their way of teaching.
Do you think that some of the traditional ways of deriving the Lorentz-Einstein transformations or the transformation equations of relativistic dynamics (Tolman's way) could be tought without mnemonic aids?
The short derivations which do not violate the postulates, show clearly that the LET relate the space-time coordinates of the same event and underline the part played by Einstein's clock synchronization procedure are good teaching tools and good relativity exercises.
Sine ira et studio

8. Jun 12, 2006

### clj4

I am sorry, I do not understand your post, can you try again using shorter sentences? I do not understand the reference to mnemonics since I never use them.

9. Jun 12, 2006

### bernhard.rothenstein

mnemonic: a word, short poem or sentence that is intended to help you remember things such as scientific rules. i extended it to a lecture hold without using written material in order to support your memory.

10. Jun 12, 2006

### clj4

I know what a mnemonic is, I don't use them.