Electromagnetic waves and space expansion: myths versus reality
Question: Do electromagnetic waves stretch with the expansion of space?
From the point of view of physics, this is not entirely true. However, the truth is that observers in numerical thought experiments will see "stretched" (i.e. with a redshift) light located in cosmologically different "points" of space (which also exist only in the form of mathematical numbers, not physically).
This conclusion indicates that something is happening to the light on its way.
But first, about the logic: we see a combination of two things. Firstly, observers who are "travelling" (i.e. observers who are at rest in their reference frames relative to the bulk of matter at one point) move relative to each other. The distance between them increases. Consequently, a velocity-dependent Doppler redshift is created.
However, for really distant observers, a different effect occurs. Light takes a very long time to travel from one observer to another. Meanwhile, the average density of the Universe decreases significantly, changing the average background gravitational field. This leads to gravitational time dilation, which also affects the observed frequency and hence the wavelength of the received light.
Victor Toth, Ohio University, proposes the following experiment: you travel at a speed close to the speed of light. Almost as fast as a photon. You start a detector, and a split second later you follow it, and then you shoot a photon towards that detector.
Because you're travelling at almost the speed of light relative to the rest of the universe, for most people it will take billions of years before your photon reaches the detector, although in your frame of reference it will only take a fraction of a second.
And when you do detect the photon, its frequency and wavelength will be the same as they were "at the time" of its launch. Nothing has stretched it, nothing has changed it. And the cosmological redshift (relative to competing observers)? The main thing is that they did not move with you. The physical properties of electromagnetic radiation depend solely on the observer.
A fundamental lesson of relativity is that redshift is a measure of the connection between a source and a detector. Nothing happens to the electromagnetic wave. It's just that the source and detector are in different frames of reference, and this difference relates to both motion and gravitational potential.