2
$\begingroup$

The energy-momentum relation,

$$E^2 = m^2c^4 +p^2c^2,$$

lets us derive the momentum of a massless particle:

$$p = \frac{E}{c} = \frac{h\nu}{c}$$

However, the expansion of the Universe redshifts light. This should decrease the momentum of photons. Where would the momentum go, in order for conservation of momentum to hold?

Improve this question
$\endgroup$
3
  • $\begingroup$ Is this a different question to astronomy.stackexchange.com/questions/18613/… ? $\endgroup$
    – ProfRob
    Nov 24, 2016 at 16:33
  • 1
    $\begingroup$ @RobJeffries Yes, because as far as I know, conservation of energy does not hold in GR. I'm asking about momentum. $\endgroup$
    – Sir Cumference
    Nov 24, 2016 at 16:35
  • $\begingroup$ Light blue-shifts as it falls into super-clusters, then red-shifts a little less as it climbs out of the ever-expanding cluster's gravity well. Basically expansion causes universe to not act like a closed system energy or momentum-wise; but this is only on extremely large scales. $\endgroup$
    – Wayfaring Stranger
    Nov 26, 2016 at 16:00

1 Answer 1

Reset to default
5
$\begingroup$

In relativity you can think of a single conservation law that unites conservation of energy and momentum -- conservation of four-momentum. Energy and momentum are the zeroth and the first to third components of the four-momentum respectively. Such conservation laws arise from invariance of the Lagrangian with respect to a translation in space-time coordinates.

In General Relativity these conservation laws are local concepts that (most people think) can only be applied in local, inertial (flat) frames of reference. In particular, they cannot be applied in changing space-times and so cannot be applied to situations involving the expansion of the universe.

Improve this answer
$\endgroup$
1
  • $\begingroup$ The second paragraph is a little muddled and makes it sound as though there is a controversy among experts, when there isn't. The issue isn't whether the spacetime is "changing" or has a timelike Killing vector. That's just the condition for test particles to have a conserved energy. The issue is whether the spacetime is curved. (As a side issue, not relevant here, there is a way to make a globally conserved mass-energy in the case of asymptotically flat spacetimes.) $\endgroup$
    – user15381
    Dec 17, 2020 at 16:13

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .