dorsal/arxiv
View SchemaLorentz transformations: Einstein's derivation simplified
| Authors | Bernhard Rothenstein, Stefan Popescu |
|---|---|
| Categories | |
| ArXiv ID | physics/0702157 |
| URL | https://arxiv.org/abs/physics/0702157 |
Abstract
We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the linear character of the Lorentz transformations we guess that the transformation equation for the space coordinate has the form x=ax'+cbt'. Imposing the condition that it accounts for the time dilation relativistic effect and taking into account the fact that due to the clock synchronization a la Einstein the space-time coordinates of the same event in the two frames are related by x=ct and x'=ct', we find out expressions for a and b. Dividing the transformation equation for the space coordinate by c we obtain the transformation equation for the time coordinate t=at'+b/cx'. Combining the two transformation equations we obtain directly the inverse Lorentz transformations.
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"date_created": "2026-03-02T18:01:17.709000Z",
"date_modified": "2026-03-02T18:01:17.709000Z",
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"abstract": "We show that the Lorentz transformations for the space-time coordinates of\nthe same event are a direct consequence of the principle of relativity and of\nEinstein\u0027s distant clocks synchronization procedure. In our approach, imposing\nthe linear character of the Lorentz transformations we guess that the\ntransformation equation for the space coordinate has the form x=ax\u0027+cbt\u0027.\nImposing the condition that it accounts for the time dilation relativistic\neffect and taking into account the fact that due to the clock synchronization a\nla Einstein the space-time coordinates of the same event in the two frames are\nrelated by x=ct and x\u0027=ct\u0027, we find out expressions for a and b. Dividing the\ntransformation equation for the space coordinate by c we obtain the\ntransformation equation for the time coordinate t=at\u0027+b/cx\u0027. Combining the two\ntransformation equations we obtain directly the inverse Lorentz\ntransformations.",
"arxiv_id": "physics/0702157",
"authors": [
"Bernhard Rothenstein",
"Stefan Popescu"
],
"categories": [
"physics.gen-ph"
],
"title": "Lorentz transformations: Einstein\u0027s derivation simplified",
"url": "https://arxiv.org/abs/physics/0702157"
},
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"execution_id": "b49beccd-938c-42f2-9aad-0c215cff1ce7",
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