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Chapter 33: Problem 5

Time dilation is sometimes described by saying that "moving clocks run slow." In what sense is this true? In what sense does the statement violate the spirit of relativity?

Short Answer

Expert verified
In terms of time dilation in Einstein's theory of relativity, the statement 'moving clocks run slow' is true from the perspective of a stationary observer, seeing the moving observer's clock ticking at a slower rate. However, this contradicts the spirit of relativity, which states that all non-accelerating frames of reference are equivalent and there's no preferred 'stationary' frame. From the moving frame's perspective, they are stationary and the previously stationary observer is actually the one moving.

Step by step solution

01

Explaining Time Dilation

Time dilation is a difference in the elapsed time measured by two observers, due to a relative velocity between them, or to a difference in gravitational potential between their locations. If one observer is moving relative to another observer, according to the theory of relativity, the stationary observer will perceive the clock of the moving observer to be ticking slower. This is not because of any mechanical malfunctioning of the clock or human error, but due to the inherent nature of space-time itself.
02

Illustrating with an Example

Suppose an observer A stays on Earth, and an observer B takes a high-speed round trip to a star. If each carries a clock, B's clock will lag behind A's clock at the end of the trip. So, in this sense, the statement 'moving clocks run slow' is correct as observer A perceives B's clock to be ticking slower.
03

Discussing the Spirit of Relativity

However, from observer B's perspective, he remained stationary during the journey and the Earth and star were moving. According to Einstein's theory of relativity, all non-accelerating frames of reference are equivalent - there is no preferred 'stationary' frame. This is a conceptual pillar known as the 'Principle of Relativity'. Therefore, 'moving clocks run slow' contradicts this spirit because it implies a preferred frame - the stationary frame seeing the moving clock as slower.

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