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Moving Clocks - Implications

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• Transverse Distances
• The Photon Clock
• Time Dilation Formula
• Proper-time Formula

Moving Clocks

If distances perpendicular to the direction of an object's motion depend on the object's velocity, then the same physical laws will lead different observers to make contradictory predictions.

Transverse distance must not depend on velocity.

Implications --- Example: --- Question:

If a clock ticks at a rate determined by light travel-time over a known distance, then

• all other kinds of clocks must agree with it (or else measure the wrong speed of light)
• all observers will agree on its rate in its own rest-frame (because they agree on the speed of light).

Implications --- Example: --- Question:

Apply the constancy of the speed of light to the photon clock:

For T = time interval between two events in a moving frame,
and t = interval between the same two events in the rest frame,

Implications ---Otherwise: --- Example: --- Question:

Suppose that two events are separated by a time interval t and a distance interval x in some inertial reference frame.

If a clock moves at constant speed between the two events, then the elapsed time T on that clock is given by (c=1 units):

The time T is the proper time interval between the events.

Implications ---Otherwise: --- Example: --- Question: