Faced with the contradiction between classical mechanics and electromagnetism, at the end of the 19th century one could in principle formulate three distinct hypotheses. Each saves two of the three claims at stake — the validity of the Galilean transformations, the correctness of Maxwell’s equations, the independence of Maxwell’s equations from the reference frame — and sacrifices the third.
| Galilean transf. valid | Maxwell’s eq. correct | Maxwell indep. of the IRF | |
|---|---|---|---|
| Hypothesis I | ✓ | ✓ | ✗ |
| Hypothesis II | ✓ | ✗ | ✓ |
| Hypothesis III | ✗ | ✓ | ✓ |
- Hypothesis I: there exists a privileged reference frame (the ether) in which Maxwell’s equations hold; in other frames the Galilean transformations hold, and Maxwell’s equations are “deformed”.
- Hypothesis II: Maxwell’s equations, as we know them, are valid only in a certain frame; in others (reachable via Galilean transformations) they take different forms.
- Hypothesis III: the Galilean transformations are not correct. If we want Maxwell’s equations to hold in every IRF, we must change the law of transformation between reference frames.
The first two hypotheses share a common trait: both accept that the Galilean transformations remain the correct law for passing from one reference frame to another, and for this reason they must postulate a special frame in which light really does travel at speed . The third is the most radical — and the most uncomfortable for intuition — because it calls into question the very way we combine space and time between observers.
Note
What decided which of the three would survive was not an argument, but a measurement: the Michelson-Morley experiment. And it was Einstein, in 1905, who drew out its full consequences.
Links
Topics: Special relativity Concepts: Einstein’s postulates Skills: Changing reference frame
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