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Whenever the Doppler effect is mentioned, it's typically in the context of sound waves or electromagnetic radiation. On the cosmological scale, red-shifting is also important because of the enormous speed of receding galaxies, thanks to the expansion of the universe.

Yet, red-shift is always discussed as the red-shifting of electromagnetic waves. Can gravitational waves be red-shifted? If so, could observations of them be used like red-shifted electromagnetic waves from distant sources are; that is, to figure out how fast an object is receding?

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Yes, gravitational waves will undergo the same red-shift as any wave that propagates at $c$. There were probably very violent gravitational waves in the very early universe. If those waves hadn't been red-shifted, they'd be ripping us apart right now.

If so, could observations of them be used like red-shifted electromagnetic waves from distant sources are - that is, to figure out how fast an object is receding?

Gravitational waves have frequencies that vary over time and that also depend on the particular physical characteristics of the emitting systems. Therefore we don't know a priori what frequency a wave should have had when emitted. This is different from electromagnetic waves in a discrete spectrum.

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    $\begingroup$ Cite: "Yes, gravitational waves will undergo the same red-shift as any wave that propagates at c." Isn't this true for all waves without respect for their speed? $\endgroup$ – arc_lupus Sep 26 '14 at 9:51
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    $\begingroup$ Re: "This is different from electromagnetic waves...": seems to me it's the same. We know more about the sources of electromagnetic waves because we've studied those sources and developed models of what they do. Study of gravitational waves hasn't progressed that far yet. $\endgroup$ – Pete Becker Sep 26 '14 at 13:08
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    $\begingroup$ Great answer. I'm glad you mentioned gravitational waves from the early universe. $\endgroup$ – HDE 226868 Sep 26 '14 at 15:19
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    $\begingroup$ @arc_lupus: Isn't this true for all waves without respect for their speed? No, it can't be. If a wave travels at some velocity v that is less than c, then v depends on the frame of reference, and the Doppler shift can't just be a function of the emitter's state of motion relative to the receiver. For example, the Doppler shift of a sound wave depends on the emitter and receiver's states of motion relative to the vibrating medium. $\endgroup$ – Ben Crowell Sep 30 '14 at 1:33
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    $\begingroup$ @arc_lupus: Cite: "Yes, gravitational waves will undergo the same red-shift as any wave that propagates at c." This is simple kinematics. It has nothing to do with the specific characteristics of the wave. For an example of how this is derived, see section 3.2 of my SR book: lightandmatter.com/sr $\endgroup$ – Ben Crowell Sep 30 '14 at 1:34

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