[Physics] a layman explanation for why the wavelength of light increases when space itself expands

Question

I understand that the universe is generally agreed to be expanding based on observations. What I have read is that space itself is expanding. My question is why does this expansion of space affect the spectra of light itself?

It has been observed countless time since Hubble that light from distant galaxies arrive to us with spectra shifted to longer wavelengths (red-shifted). If a wavelength of light is defined with a metric of spatial distance, then what is the significance of spatial distance itself increasing? Would not the expansion of space where our instruments of observing light also matter?

To add to my confusion on red-shifts, here is the Planck-Einstein relation:

$\lambda = \frac{hc}{E_{photon}}$

Wavelength is a function of $c$, but would this constant (distance over time metric) be affected if space dilates? The same rationale goes for time, but I have heard that time at a fixed location would not be affected by the expansion of space, but I am uncertain how time for moving objects are affected.

Answer 1

Here is simple explanation:

• Suppose a light source and a observer are in an expanding space.
• Now think of two subsequent crests of wave emitted by the lightsource.
• The second crest is emitted slightly later than the first one, hence the space has expanded slightly in the meantime.
• Consequently, the second crest has to travel further to reach the observer, taking more time.*
• Hence, the time between the arrivals of the crests at the observer is longer than the time between their emission at the source.
• This is the same thing as saying that frequency of the wave is lower, or (since the speed of light is the same) that the wavelength is longer.

*(And since it is taking longer, space expands more while its travelling increasing its travel time a bit more.)