# How can light coming from the receding galaxies be stretched like matter?

Edwin Hubble discovered in 1929 that the universe in expanding and the light from the receding galaxies are red-shifted; their wavelengths become longer. How can light which is an electromagnetic wave be stretched or compressed like matter ? We observe the Doppler effect in sound waves, with the pitch increasing when the source and listener are approaching, and a decrease in pitch when they are moving away from each other. But at least in case of sound waves, a physical medium is there. But light waves require no such medium and can travel in the vacuum of space as well as through air or any transparent medium. How can it be subject to stretching or compressing, though its an electromagnetic wave which do not even need a medium for its propagation ?

The sound Doppler effect is due to the emitter moving relative to the medium at the time of emission, and/or to the receiver moving relative to the medium at the time of reception. The frequency doesn't change as the sound propagates from emitter to receiver.

The situation with light is far more ambiguous because there's no medium with a definite state of motion. But you can consistently think of its Doppler effect as working in the same way as sound's, if you want to.

In special relativity, you can pick any inertial frame and treat light as though it's a sound propagating through a medium that's at rest in that inertial frame and in which the speed of sound is $$c$$. You then get a Doppler effect for light for essentially the same reason that you got one for sound. The equivalence of inertial frames means that you'll get the same value for the Doppler shift factor no matter which frame you pick.

In general relativity, you can't always choose a global inertial frame, but you can always put inertial coordinates on a narrow strip of spacetime that includes the emitter and the receiver and the path of the light between them, which is the only part of the spacetime that actually matters to the Doppler effect calculation. Then the analysis is the same as in the special-relativistic case.

When talking about redshift from cosmological expansion, it's more popular to think of the light as changing wavelength en route from emitter to receiver due to "stretching of space". There are many people who believe that that's the only correct way to think of it, but it isn't. The sound-wave-like model and the space-stretching model are descriptions of the same physical phenomenon with respect to different coordinate systems (inertial in the first case, noninertial in the second).

You are right in that light requires no medium. But that is not important to whether or not redshift occurs. The fact is that light is a wave and that is sufficient for redshift (or blueshift) to occur.

Consider a source of light like a star. As this source recedes, each peak in the waveform it produces is emitted from a position which is continually moving farther and farther away. You can then visualise this as a wave getting stretched. Because of this, the wavelength shifts and the frequency at which peaks arrive at the observer will be changed or redshifted. And when you ask “how can they be stretched like matter”, it is very important to note that it is the space that is expanding or “stretching”.

To visualise this even more think about if you drew two points on a half-inflated balloon. Let one point be the observer and the other be the source. In between these two points draw a squiggly line representing a light wave joining the two points, and then proceed to fully inflate the balloon. This inflation is analogous to the expansion of space-time. If you have done this thought experiment (or you actually did it!) correctly, you would notice that peaks in the wave are further apart.