# How is red shifting explained with quantum mechanics? [duplicate]

Light travels as waves through space, and since space is expanding, the light gets stretched out. This is the explanation for red shifting I learned before.

Now I know some more and that explanation isn't good enough.

• The longer wavelength light that would result from red shifting has lower energy.
• Total energy in the system must be conserved, so the amplitude of the light must be higher after red shifting.
• As per quantum mechanics, light exists as discrete photons. The loss of energy must be instant, and at the same time, more photons must be created so the total energy is conserved.

So this photon "splitting" explanation sounds okay, but it still seems problematic. Photons can split (like here), but a photon cannot split on its own in a vacuum, as far as I know.

Perhaps some assumption I made here is wrong.

What is the explanation for red shifting that agrees with quantum mechanics?

I'm not very familiar with relativity, I may have missed some phenomenon in relativity that explains all this.

• Quite similar to physics.stackexchange.com/q/428542. It would seem that your understanding of red shift is incorrect. – Jon Custer Sep 13 '18 at 20:47
• I'm reluctant to bring relativity into this since I'm not that familiar with it, but light is the same speed to all reference frames, so there shouldn't be any changes in the photon depending on the observer and source, and thus no Doppler red shift. – user183160 Sep 13 '18 at 20:55
• But relativity is indeed the point... – Jon Custer Sep 13 '18 at 20:57
• Energy is not a conserved quantity in GR. Many duplicates. – Rob Jeffries Sep 13 '18 at 21:32
• Possible duplicate of photons in expanding space: how is energy conserved? – Rob Jeffries Sep 13 '18 at 21:36

You have discovered a prediction of general relativity! The prediction is that energy is not actually conserved at a global cosmological scale. It is conserved in its motion through space-time, which we would express with the equation $\nabla_\alpha T^{\alpha\beta} =0$, but the warping of space-time itself changes the ground rules of the universe in a way that does change energies, in this case the energies of red-shifted photons when viewed from a certain perspective inside the space-time. A much more dramatic version of this holds for the general relativistic prediction of dark energy, where the dark energy density remains constant even as the volume of the boxes that contain it increase, so that the total dark energy, if viewed from this perspective, is also increasing. It is just a change that cannot be described as a flow through space-time, so it doesn't have to obey any conservation principle.