1
$\begingroup$

I watched this lecture on Lorentz transformation (https://www.youtube.com/watch?v=EhXWiAJBmzc). I'd say the tutor employed a simplistic and elegent approach to derive the transformation. But I also got these questions: How did Einstein know the transformation of an event in two frames was a Lorentz transformation which already prescribed time dilation and length contraction? How did he know it would not involve higher order relationships or other non-linear relationship? Another question: is it possible to derive length contraction and time dilation using a single reference frame and classical kinetics? Hope someone could enlighten me on this rudimentary questions.

$\endgroup$
8
  • 1
    $\begingroup$ From en.wikipedia.org/wiki/Lorentz_transformation#History Many physicists—including Woldemar Voigt, George FitzGerald, Joseph Larmor, and Hendrik Lorentz himself—had been discussing the physics implied by these equations since 1887. $\endgroup$
    – PM 2Ring
    Dec 3, 2019 at 6:33
  • $\begingroup$ hermes.ffn.ub.es/luisnavarro/nuevo_maletin/… $\endgroup$
    – Umaxo
    Dec 3, 2019 at 7:04
  • 2
    $\begingroup$ Have you read Einstein’s original 1905 paper on the subject? $\endgroup$
    – Bob D
    Dec 3, 2019 at 7:33
  • $\begingroup$ See "Chasing the Light Einstein's Most Famous Thought Experiment" by John D.Norton. "pitt.edu/~jdnorton/papers/Chasing.pdf" $\endgroup$ Dec 3, 2019 at 8:19
  • $\begingroup$ He may not have "known", he figured it out based on a couple simple principles and lot of algebra. Also, Lorentz had figured out these transforms before Einstein. $\endgroup$
    – user196418
    Dec 5, 2019 at 0:26

2 Answers 2

1
$\begingroup$

Thanks everyone for your comments. Special relativity is a theory with assumptions and verified by result of experiments.

I found the following derivatation uses least assumption and is easiest to understand:

Since space is assumed to be homogeneous, the transformation must be linear. The most general linear relationship is obtained with four constant coefficients, A, B, γ, and b:

$$x'=\gamma x + b t \;$$ $$t'=A x + B t. \,$$

https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations

$\endgroup$
1
0
$\begingroup$

One can find two different approaches from Einstein, the first in his book, "Zur Elektrodynamik Bewegter Körper von Albert Einstein, 1905", and the second in " Ueber the spezielle und allgemeine Relativitaetstheorie" . In the first he starts with the definition of time for a point at a constant distance from the origin of the moving system, "t1=0.5(t0+t2)". If you read this approach, you'd find it mathematically correct up to the point on page 13, where he multiplies the result by "a= ((c^2-v^2)^0.5)/c " . It is not clear, why can't "a" have any other value. The second approach is mathematically wrong. the most simple approach I found myself is to solve 2 equations x'=Ax+Bt (!) t'=ct+Dx (2) by applying the conditions for relative velocity and equal appearance of equal long stabs. THIS results in x'=Ax -Avt (1) t'=At-(A-1/A)x/v (2) if we put x=ct and x'=ct', you get A=gamma and you'd have LT. By A=1 one gets the Galileo transform

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.