<p>In relativity you can think of a single conservation law that unites conservation of energy and momentum -- conservation of <a href="https://en.wikipedia.org/wiki/Four-momentum#Conservation_of_4-momentum" rel="nofollow noreferrer">four-momentum</a>. 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.</p>

<p>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.</p>

CC BY-SA 3.0
2016-11-24T17:47:31.733Z
2016-11-24T17:47:31.733Z
ProfRob
<p>The energy-momentum relation,</p>

<p>$$E^2 = m^2c^4 +p^2c^2,$$</p>

<p>lets us derive the momentum of a massless particle:</p>

<p>$$p = \frac{E}{c} = \frac{h\nu}{c}$$</p>

<p>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?</p>

CC BY-SA 3.0
2016-11-24T16:33:38.687Z
Is this a different question to http://astronomy.stackexchange.com/questions/18613/where-does-the-energy-of-light-go-when-it-red-shifts?rq=1 ?
ProfRob
CC BY-SA 3.0
2016-11-24T16:35:31.857Z
@RobJeffries Yes, because as far as I know, conservation of energy does not hold in GR. I'm asking about momentum.
Sir Cumference
CC BY-SA 3.0
2016-11-26T16:00:45.813Z
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.
Wayfaring Stranger
<light><cosmology><general-relativity><expansion><redshift>
Does the redshifting of photons from the Universe's expansion violate conservation of momentum?
Sir Cumference
# Does the redshifting of photons from the Universe's expansion violate conservation of momentum?

(Asked by: username_0 on 2016-11-24)

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?

**Tags:** light, cosmology, general-relativity, expansion, redshift
> **Comments:**
> **username_1**: Is this a different question to http://astronomy.stackexchange.com/questions/18613/where-does-the-energy-of-light-go-when-it-red-shifts?rq=1 ?  
> **username_0**: @RobJeffries Yes, because as far as I know, conservation of energy does not hold in GR. I'm asking about momentum.  
> **username_2**: 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.  

---

## 1 answers

### Answer by username_1 on 2016-11-24. Score: 5 | Accepted answer

In relativity you can think of a single conservation law that unites conservation of energy and momentum -- conservation of [four-momentum](https://en.wikipedia.org/wiki/Four-momentum#Conservation_of_4-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.


---

