Is there an equivalent "redshift" for cosmic rays due to expansion?

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Discussion Overview

The discussion centers around the concept of whether there is an equivalent "redshift" for cosmic rays due to the expansion of the universe. Participants explore the implications of cosmic expansion on the energy and momentum of cosmic rays, comparing it to the redshift observed in electromagnetic radiation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question how cosmic rays, being non-electromagnetic particles, could experience a redshift similar to that of light due to cosmic expansion.
  • It is proposed that in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe, the product of the scale factor and momentum is conserved, leading to a decrease in momentum as the scale factor increases.
  • Some argue that energy is not conserved in an expanding universe, suggesting that cosmic rays lose energy as they travel through expanding space.
  • A participant provides a mathematical synopsis, indicating that the energy of cosmic rays can be interpreted through local frames and that the concept of energy loss may not be physically meaningful.
  • There is a discussion about whether all massive particles experience similar effects in an expanding universe, with some asserting that they join the local Hubble flow.
  • Concerns are raised about the possibility of recovering energy lost by cosmic rays and whether any forms of energy remain unaffected by redshift during expansion.
  • Participants discuss the conservation of angular momentum in relation to cosmic rays and whether it is affected by cosmic expansion.
  • Questions are posed regarding the intrinsic angular momentum of cosmic rays and the implications of high-energy processes in the universe.
  • It is noted that in highly bound systems, such as matter accreting into black holes, the effects of cosmic expansion may be negligible.

Areas of Agreement / Disagreement

Participants express differing views on the implications of cosmic expansion for cosmic rays, with no consensus reached on whether cosmic rays experience a redshift equivalent to that of light or how energy and momentum are affected in this context.

Contextual Notes

Discussions include various interpretations of energy conservation in an expanding universe, the dependence of energy on local frames, and the complexities surrounding angular momentum in relation to cosmic rays.

Suekdccia
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TL;DR
Is there an equivalent "redshift" for cosmic rays due to cosmological expansion?
I've found this discussion (https://astronomy.stackexchange.com...alent-of-the-red-shift-effect-for-cosmic-rays) where it is said that there is an equivalent redshift of cosmic rays due to the cosmic expansion

However, how can this be? Cosmic rays are not EM particles, so their wavelength should not be affected by the expansion of spacetime... And if it is affected by it, how does the expansion of the universe "steal" energy from cosmic rays? Does this then happen for all massive particles?
 
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Suekdccia said:
However, how can this be?
In a FLRW universe, the quantity ##a(t) p## is conserved for a test particle. When the scale factor grows, the momentum ##p## decreases.

Suekdccia said:
Cosmic rays are not EM particles, so their wavelength should not be affected by the expansion of spacetime...
Yes they should.

Suekdccia said:
And if it is affected by it, how does the expansion of the universe "steal" energy from cosmic rays?
Energy simply is not conserved in an expanding universe.

Suekdccia said:
Does this then happen for all massive particles?
Yes.
 
I can give you a synopsis of the math. How you interpret it is up to you - "expansion of space" is an interpretation, not tied to any mathematical object of GR.

Consider the generation of the cosmic ray far away, in the past light cone of 'us'. It is generated by some unknown "local" process, which as described in a local comoving inertial frame, gives energy E to the cosmic ray. Now parallel transport a tetrad representing that local frame along the cosmic ray path to us. This is local frame near us where the cosmic ray has energy E. However, our local frame will have a large velocity relative to this transported frame, so that we will measure a much lower energy for the cosmic ray.

Note that cosmological redshift can be derived with an essentially identical procedure.

There is no stealing of energy or stretching of light in this derivation.
 
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Orodruin said:
In a FLRW universe, the quantity ##a(t) p## is conserved for a test particle. When the scale factor grows, the momentum ##p## decreases.


Yes they should.


Energy simply is not conserved in an expanding universe.


Yes.
So do all massive particles tend to rest in an expanding universe? And does this occur in a universe with Λ=0?
 
Suekdccia said:
So do all massive particles tend to rest in an expanding universe? And does this occur in a universe with Λ=0?
Yes, to both. All such massive particles join the local Hubble flow. The Davis and Lineweaver paper on the tethered galaxy problem includes some analysis of this.
It's important to stress that this is not due to some force acting to brake the mass, but as a result of arriving in a region where its erstwhile local velocity begins to match the recession velocity.
 
Bandersnatch said:
It's important to stress that this is not due to some force acting to brake the mass, but as a result of arriving in a region where its erstwhile local velocity begins to match the recession velocity
But the particles lose energy arriving at that state. Can they recover it? Or as photons it is lost forever? Is there any form of energy that is not "redshifted" as spacetime expands?
 
Suekdccia said:
But the particles lose energy arriving at that state.
The energy of a particle is a local frame dependent concept, not a global one. Saying that the particles lose energy is not really physically meaningful.

Suekdccia said:
Can they recover it?
See above.

Suekdccia said:
Or as photons it is lost forever? Is there any form of energy that is not "redshifted" as spacetime expands?
See above.
 
Orodruin said:
In a FLRW universe, the quantity a(t)p is conserved for a test particle. When the scale factor grows, the momentum p decreases.
Does angular momentum also decrease?
 
Suekdccia said:
Does angular momentum also decrease?
The magnitude of angular momentum is invariant like mass of a particle. Neither gets red shifted.
 
  • #10
PAllen said:
The magnitude of angular momentum is invariant like mass of a particle. Neither gets red shifted.
Do cosmic rays have angular momentum? Are there processes with a very high/energetic angular momentum in the universe?

Also, when matter is accreted by a black hole, it loses angular momentum to fall from the orbit closer to the black hole, but the orbiting speed of the particles would be higher. Would these velocities also be redshifted by expansion? Or being a local and bound system, expansion does not have any effects?
 
  • #11
Suekdccia said:
Do cosmic rays have angular momentum?
Anything that isn't moving directly towards or away from you has angular momentum around your location.
 
  • #12
Ibix said:
Anything that isn't moving directly towards or away from you has angular momentum around your location.
Yes, but I was thinking of spin angular momentum rather than orbital. The latter is frame dependent, the former is not ( in magnitude - it is in direction, obviously). Cosmic rays being primarily fermions would have intrinsic angular momentum. A spinning pulsar with huge peculiar velocity would also have a spin angular momentum that does not redshift.
 
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  • #13
Suekdccia said:
Also, when matter is accreted by a black hole, it loses angular momentum to fall from the orbit closer to the black hole, but the orbiting speed of the particles would be higher. Would these velocities also be redshifted by expansion? Or being a local and bound system, expansion does not have any effects?
This would be a highly bound system, so expansion would be irrelevant.
 
  • #14
PAllen said:
A spinning pulsar with huge peculiar velocity would also have a spin angular momentum that does not redshift.
And the peculiar velocity would be the one redshifted correct?
 
  • #15
Suekdccia said:
And the peculiar velocity would be the one redshifted correct?
Yes, when it reached us it would have much lower peculiar velocity than it had when it was ejected somehow from a galaxy (for example).

Note, this is exactly what @Bandersnatch explained in post: post #5
 
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