Proper time Relativity

I was wondering about this hypothetical situation and wanted to clarify whether the following is true or not:

Consider a person playing with a slinky. The Slinky moves at relativistic speed.

The person is standing at location A and when he lets the slinky extend it reaches out to position B.

Would I be correct in saying that in the situation where the slinky is being extended to position B the time that is measured by the person playing with the slinky is not proper time, as the two events which are being measured do not happen at the same location but one at A and the other at B.

However if the person playing with the slinky were measuring the total time it took for the slinky to reach B and come back to A then he would measure proper time.

Also in the reference frame of the slinky the slinky is always measuring proper time as it feels as though it is stationary. (This statement is not truee as someone has already pointed out due to acceleration of slinky

Any help would be appreciated.

• Note that moving from A to B and then back to A is not an inertial reference frame, as it involves an acceleration to turn around. The person's frame of reference, however, is inertial. – probably_someone May 30 '17 at 10:44

1 Answer

The clock on the mobile end of the slinky records the proper time along the world line of the mobile end of the slinky.

The clock on the fixed end of the slinky records the proper time along the world line of the fixed end of the slinky.

These two times will not agree; the fixed end clock will show greater elapsed time than the mobile end clock.

This is because, though both clock's world lines pass through the same two events (mobile end starts extending towards B and mobile end returns to A), the world line of the mobile end is an accelerated world line and, according to SR, the inertial (unaccelerated) world line through two events has the largest proper time interval.

Would I be correct in saying that in the situation where the slinky is being extended to position B the time that is measured by the person playing with the slinky is not proper time, as the two events which are being measured do not happen at the same location but one at A and the other at B.

You would be correct; the elapsed time measured by two spatially separated, synchronized clocks at relative rest is not Lorentz invariant and thus not a 'proper' (invariant) quantity.