Is Time Dilation in space and Doppler effect one and the same phenomenon?

Answer 1

No. Time dilation is a relativistic effect. It is very tiny except near the speed of light. The Doppler shift operates at any speed. Consider the sound of a truck or train moving past you.

Answer 2

The question is good, and the answer is no: time dilation is unrelated to Doppler effect, although the concepts are somewhat similar.


The Doppler effect, like red shift and blue shift, is *directional*.

If something emitting waves is coming towards you, then the waves are compressed and the frequency goes higher. If it's going away from you, the waves are stretched and the frequency goes lower.

The amount by which the waves compress or stretch varies linearly according to the difference between the speed of sound and the magnitude of the velocity towards or away from the observer.

For sound, here's the formula for observed Doppler frequency:
|--: F = F0 / (1 ± v/S)
(S = speed of sound; v = velocity; F0=emitted frequency)

Here's the formula for observed red/blue-shift frequency:
|--: F = F0 * (1 ± v/S)
(S = speed of light; v = velocity; F0 = emitted frequency)

In both of the above cases, S depends on the medium transmitting the waves.


Time dilation on the other hand, is nondirectional. The amount of time dilation compared to base time measurement, T0, varies in the following fashion:
|--: T = T0 / √(1-v²/c²)
(c = speed of light in a vacuum; v = velocity; T0 = base timelength)
In the above, c is an absolute. It does not depend on the medium of transmission


A thought experiment that might be helpful.

Suppose you are communicating with two other observers in non-inertial frames: in other words, all three of you feel yourselves to be at rest. And let's suppose you're all fairly close together -- within the same solar system, for example.

You agree on a distant pulsar as your shared "wristwatch". The rate at which it ticks tells you how quickly you are traveling with respect to the pulsar. The three of you can use it to determine your relative speeds without knowing anything about direction. The observer who clocks the slowest ticking is the one moving most slowly with respect to the pulsar.

As an added bonus to this thought experiment, you could also all three independently measure the Doppler shift of the pulsar's spectrum, to learn how much of your velocities' directions were towards or away from the pulsar. If all three of you were in different orbits around the Sun, the directional components would change over time but the relative speed would not change.

Answer 3

I don't think so. The Doppler effect is used to describe how a wave (of sound or light) will change its relative appearance depending on if you are travelling towards or away from it.

That's why when a car drives past you, its engine has a high pitch as it approaches and a low pitch as it moves away.

Time Dilation has (I think) nothing to do with your movement towards or away from anything.

Answer 4

They are different effects, although there is a relativistic Doppler effect that is in addition to the classical Doppler effect. It only become significant at speeds near that of light though.