<p>For simplicity I'll refer to the launched object as a probe and other cosmological objects as planets (one of which is Earth).</p>
<p>There's no good answer to what happens to the probe's speed relative to Earth, since there's no good way to define a notion of relative speed of very distant objects in cosmology.</p>
<p>The speed of the probe relative to the nearest planet will decrease over time. This happens simply because the planets are moving away from each other. If you imagine the planets and probe to have negligible mass so that there is no gravity (and also no cosmological constant), everything has a constant speed, and the probe will eventually pass every planet that has a lower speed, and will never pass any planet that has a higher speed, so ultimately it will end up permanently in between planets with slightly higher and slightly lower speeds, with a small speed relative to them. To put it another way, objects that initially have a high peculiar speed relative to the Hubble flow end up moving with the Hubble flow, if you wait long enough.</p>
<p>Cosmological redshift happens for the same reason. You can imagine that the light is absorbed/detected by each planet it reaches and then reemitted at the same frequency. The reemitted light will be detected by the next planet with a redshift or a blueshift depending on the relative motion of those two planets. On average, the planets are moving apart, so the longer the chain of planets, the larger the accumulated redshift.</p>
<p>The energy density of the universe in the present era is very low, so this gravityless model is pretty accurate out to distances of hundreds of millions of light years. At larger scales, you can no longer ignore spacetime curvature, but spacetime curvature doesn't fundamentally change what happens, it only deforms it a bit. It's a misconception that the loss of momentum is due to some peculiar general-relativistic property of spacetime, like curvature or intrinsic expansion. It's simply due to the fact that the planets (and stars and galaxies) are moving away from each other.</p>

CC BY-SA 4.0
2020-12-17T03:16:19.800Z
@BenCrowell I'm just saying that expansion of space is not a new physical phenomenon introduced by general relativity. Even in Newtonian physics you can transform a system of mutually gravitating planets in relative recessional motion into FLRW-like coordinates and say that the planets are stationary and the space between them expands. It's just a formal substitution of variables, and that's all it is in general relativity too.
benrg
CC BY-SA 4.0
2020-12-17T05:56:22.617Z
@BenCrowell If you have a continuous distribution of matter then you can define an expansion scalar. It's not defined in vacuum, such as between the planets. I've actually read part of [your GR textbook](http://www.lightandmatter.com/genrel/) where you make what may be a related error: you calculate a force in a FRW background, note it's equal to the Newtonian force due to the continuous matter distribution implied by the Friedmann equations, but maintain that the force is there in the real world even though the matter isn't. (cont'd)
benrg
CC BY-SA 4.0
2020-12-17T05:56:35.020Z
(cont'd) That's no more true in GR than it would be in Newtonian gravity. (I mentioned this in [another comment](https://physics.stackexchange.com/q/2110#comment1138467_37584) a year ago but I don't know if you saw it.) I think you're doing the same thing here: calculating the expansion scalar of matter that doesn't exist. The scalar can be defined approximately at large scales, where it measures the motion of the planets. It can't be defined between planets.
benrg
CC BY-SA 4.0
2020-12-17T01:17:38.317Z
2020-12-17T01:17:38.317Z
benrg
<p>As far as I know, photons' wavelengths can be considered increasing as space expands, making them lose energy and momentum. Does the same apply to physical objects? I understand a photon's speed is the same regardless of the system of reference, and the same does not hold for physical objects, but is it possible to draw any kind of analogy, for instance, would the momentum of an object launched from Earth (neglect non-cosmological effects) be steadily decreasing when looked at from Earth?</p>

<cosmology><photons><frame-of-reference>
Do objects lose momentum as space expands
Tosic
# Do objects lose momentum as space expands

(Asked by: username_0 on 2020-12-16)

As far as I know, photons' wavelengths can be considered increasing as space expands, making them lose energy and momentum. Does the same apply to physical objects? I understand a photon's speed is the same regardless of the system of reference, and the same does not hold for physical objects, but is it possible to draw any kind of analogy, for instance, would the momentum of an object launched from Earth (neglect non-cosmological effects) be steadily decreasing when looked at from Earth?

**Tags:** cosmology, photons, frame-of-reference

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## 1 answers

### Answer by username_1 on 2020-12-17. Score: 2

For simplicity I'll refer to the launched object as a probe and other cosmological objects as planets (one of which is Earth).

There's no good answer to what happens to the probe's speed relative to Earth, since there's no good way to define a notion of relative speed of very distant objects in cosmology.

The speed of the probe relative to the nearest planet will decrease over time. This happens simply because the planets are moving away from each other. If you imagine the planets and probe to have negligible mass so that there is no gravity (and also no cosmological constant), everything has a constant speed, and the probe will eventually pass every planet that has a lower speed, and will never pass any planet that has a higher speed, so ultimately it will end up permanently in between planets with slightly higher and slightly lower speeds, with a small speed relative to them. To put it another way, objects that initially have a high peculiar speed relative to the Hubble flow end up moving with the Hubble flow, if you wait long enough.

Cosmological redshift happens for the same reason. You can imagine that the light is absorbed/detected by each planet it reaches and then reemitted at the same frequency. The reemitted light will be detected by the next planet with a redshift or a blueshift depending on the relative motion of those two planets. On average, the planets are moving apart, so the longer the chain of planets, the larger the accumulated redshift.

The energy density of the universe in the present era is very low, so this gravityless model is pretty accurate out to distances of hundreds of millions of light years. At larger scales, you can no longer ignore spacetime curvature, but spacetime curvature doesn't fundamentally change what happens, it only deforms it a bit. It's a misconception that the loss of momentum is due to some peculiar general-relativistic property of spacetime, like curvature or intrinsic expansion. It's simply due to the fact that the planets (and stars and galaxies) are moving away from each other.

> **Comments:**
> **username_1**: @BenCrowell I'm just saying that expansion of space is not a new physical phenomenon introduced by general relativity. Even in Newtonian physics you can transform a system of mutually gravitating planets in relative recessional motion into FLRW-like coordinates and say that the planets are stationary and the space between them expands. It's just a formal substitution of variables, and that's all it is in general relativity too.  
> **username_1**: @BenCrowell If you have a continuous distribution of matter then you can define an expansion scalar. It's not defined in vacuum, such as between the planets. I've actually read part of [your GR textbook](http://www.lightandmatter.com/genrel/) where you make what may be a related error: you calculate a force in a FRW background, note it's equal to the Newtonian force due to the continuous matter distribution implied by the Friedmann equations, but maintain that the force is there in the real world even though the matter isn't. (cont'd)  
> **username_1**: (cont'd) That's no more true in GR than it would be in Newtonian gravity. (I mentioned this in [another comment](https://physics.stackexchange.com/q/2110#comment1138467_37584) a year ago but I don't know if you saw it.) I think you're doing the same thing here: calculating the expansion scalar of matter that doesn't exist. The scalar can be defined approximately at large scales, where it measures the motion of the planets. It can't be defined between planets.  

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