Can the wavelength of light change after it is emitted in a vacuum?

Question

Can the wavelength of light change after it is emitted in a vacuum?

As the picture below describes, is it possible for light to change wavelengths after being emitted in a vacuum (no medium).

Answer 1

This is in fact possible. Apart from the "normal" Doppler effect, there are two ways the frequency of an electromagnetic wave can change:

• Gravitational redshift: Let's say a photon is emitted from the surface of a massive object such as a planet. Due to gravitational time dilation, we can loosely speaking say that a clock A at the surface of the planet "run slower" than a clock B at a large distance from the planet. Clock B will thus measure a lower frequency of the wave when it arrives at B. This effect can also be interpreted as the photon losing energy as it "climbs up" the gravitational potential of the planet (of course, everything is also possible in reverse – if the photon is emitted from B to A, it will gain energy and its wavelength will decrease).

• Expansion of spacetime: Imagine a photon travelling through space with negligible gravity (i.e. far from any star or planet). Since space itself expands, you could imagine the wavelength of the photon being "stretched out" over time, thus getting larger.

Answer 2

This is not what is being depicted in the diagram you quote.

The middle section, showing a wave with a wavelength that slowly increases as you go along the wave from left to right,

is purely illustrative, and it is used to show graphically what the comparison is between longer wavelengths and shorter ones.

(One particular issue with this plot: it does not at all reflect the actual sizes of the wavelengths involved. In the diagram, the wavelengths on the left are bigger than the ones on the right by a factor of $10$, i.e., by one order of magnitude. The overall scheme, going from radiowaves to gamma rays, spans fifteen orders of magnitude, i.e. a factor of $10^{15}$, in the wavelengths involved.)

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That said, it is possible to have pulses of light with a waveform that looks like that. This property (a changing frequency and wavelength over the duration of the pulse) is known as chirp, and it can be introduced into a pulse of light as simply as transmitting it through a block of glass. This has important technological applications which I described in this previous Q&A.

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In any case, though, in the absence of effects coming from general relativity (i.e. any earth-bound experiment unless you're working at extremely high precision), the frequency and wavelength of light cannot change in vacuum once the radiation has been emitted.