The Lorentz transformation is derived from a simple thought experiment by using a vector formula from elementary geometry. The result is used to obtain general velocity and acceleration transformation equations.

1.
Kenneth
Krane
,
Modern Physics
(
Wiley
,
New York
,
1983
), p.
23
.
2.
W. N.
Mathews
, Jr.
, “
Relativistic velocity and acceleration transformations from thought experiments
,”
Am. J. Phys.
73
,
45
51
(
2005
).
3.

For the sake of completeness, it must be mentioned that the LT can be derived by using the sole relativity principle (first Einstein postulate) and dispensing with the second (invariance of the speed of light). This derivation demands more abstract work, which is what we are trying to avoid here, having in mind beginning students. See, for example, Ref. 5, p. 57.

4.
David
Park
, “
Derivation of the Lorentz transformations from gedanken experiments
,”
Am. J. Phys.
42
,
909
910
(
1974
).
5.
Wolfgang
Rindler
,
Relativity, Special, General and Cosmological
(
Oxford U. P.
,
New York
,
2001
), p.
5
.
6.

The word particle is used to designate a pointlike object. Application of Eq. (29) to an extended body raises interesting issues that are beyond the scope of this article.

7.
See, for example, Ref. 5, p.
100
.
8.
There are much quicker derivations than the one presented here. See, for example,
Alan
Macdonald
, “
Derivation of the Lorentz transformation
,”
Am. J. Phys.
49
,
493
(
1981
). Our purpose here is to be simple and to go beyond the “standard configuration.”
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