Concern about Spacetime Invariance

Asked Mar 08 '18 at 01:50

Active Mar 08 '18 at 03:42

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The space-time invariance principle states that:

$(c^2)(\Delta t^2) - l^2 = \rm invariant$ for any inertial frame.

Consider two events that occur at the same time in inertial frame $S$, and frame $S_1$ moves with translational speed $v$ relative to $S$. It seems that by the length contraction, the distance between these events should be shorter in $S_1$ because the events are moving, yet since these events do not happen simultaneously in frame $S_1$, then $(c^2)(\Delta t^2) - l^2$ for frame $S_1$ is larger than for $S$, which is a contradiction. Can someone please explain the issue in this contradiction (without using Minkowski diagrams)?

edited Mar 08 '18 at 03:42

Chris

17,189

asked Mar 08 '18 at 01:50

A. Remorov

2

Possible duplicate of Spacelike interval and length contraction – Mike Mar 08 '18 at 02:20
2

The answer to that other question is correct. The basic point is that the contracted length that the moving observer measures is not the distance between the two events you're talking about. – Mike Mar 08 '18 at 02:26
Possible duplicate of “Reality” of length contraction in SR – John Rennie Mar 08 '18 at 05:50
See also How do I derive the Lorentz contraction from the invariant interval? – John Rennie Mar 08 '18 at 05:51

Concern about Spacetime Invariance

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