The Minkowski relationship is an important aspect of special relativity.(adsbygoogle = window.adsbygoogle || []).push({});

(c.t)^2 - x^2 = k

For two points in spacetime, observers moving at different speeds observe different time and space differences between them. Neither is constant but the above relationship is. It is the minus sign that implies space time has a hyperbolic structure.

However if we use the other expressions from special relativity, as an observer moves, clocks slow by the factor gamma so the measured time difference increases by 1/gamma. Similarly rulers shrink by the factor gamma, so measured distances increase by 1/gamma. But if we put these into the above relationship we would get

(c.t)^2 - x^2 = (1/gamma)^2.k

Since gamma is not a constant, this is not the Minkowski relationship. What am I missing?

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# Problem with relativity

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