# Do particles and objects trend toward 0 velocity.

## Main Question or Discussion Point

Light traveling long distances through the universe will red-shift due to cosmic expansion. Particles like electrons also have a wavelength described by the equation λ=h/ρ. If an electron were traveling through the universe undisturbed would it's wavelength also be stretched by cosmic expansion resulting the loss of momentum? If so, would the same logic also apply to macroscopic object meaning that over cosmic distances and time scales all objects would trend toward 0 velocity with respect to the Hubble flow?

In the early universe when "cosmic time scales and distances" were tiny, could this be the mechanism that selected 1 particular frame of reference that we now observe as being at rest with respect to the CMB?

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Simon Bridge
Homework Helper
Light traveling long distances through the universe will red-shift due to cosmic expansion. Particles like electrons also have a wavelength described by the equation λ=h/ρ. If an electron were traveling through the universe undisturbed would it's wavelength also be stretched by cosmic expansion resulting the loss of momentum?
Sort of ... if the electron is emmitted from a body with a relative speed away from the observer, then it's relative momentum will be modified to account for that in the usual way. This changes the wavelength in the deBroglie relayion - a red-shift since reducing momentum lengthens wavelength. However, this will not affect the rest mass.

I think you are confusing classical waves with quantum particles.
I also suspect you are imagining that someone standing close to an very red-shifted object sees that object as very red.

If so, would the same logic also apply to macroscopic object meaning that over cosmic distances and time scales all objects would trend toward 0 velocity with respect to the Hubble flow?
Distant objects actually tend towards an infinite velocity ... though, once they pass the speed of light, we don't see them.
In the early universe when "cosmic time scales and distances" were tiny, could this be the mechanism that selected 1 particular frame of reference that we now observe as being at rest with respect to the CMB?
No. It is the same mechanism that allows us to see ourselves to be in a particular reference frame which is at rest ... or anything else for that matter.

K^2
Red shift in Hubble's Law is due to relative velocities of gallaxies, not directly due to expansion. Photon is emitted already red-shifted relative to us, not becoming more and more red-shifted as time goes on. So your analysis is flawed right there.

If an electron were traveling through the universe undisturbed would it's wavelength also be stretched by cosmic expansion resulting the loss of momentum? If so, would the same logic also apply to macroscopic object meaning that over cosmic distances and time scales all objects would trend toward 0 velocity with respect to the Hubble flow?
YES!!!! I believe you hit the nail squarely on the head. The following is inconsistent with the prior two posts...I'm noit sure what they mean..... But 'expansion' and 'redshift' are slippery concepts and have been discussed/dissected/debated in these forums in detail.

'Expansion' and Hubble flow are a result of the FRW metric, in particular a(t), and 'Redshift' is a measured [and unambiguous] shift in received frequency versus emitted frequency. [But exactly what such a shift represents is subject to interpretation.] In other metrics [cosmological models] there may not be superluminal expansion.

PeterDonis and Chalnoth have, I believe, agreed on this, from a Chalnoth post:

" … You get some total redshift for faraway objects due to cosmological expansion. How much of that redshift is due to the Doppler shift and how much is due to the expansion between us and the far away object is completely arbitrary."
Here is how Tamara Davis [of Lineweaver and Davis] explains a closely related phenomena:

Photons traveling in an expanding universe appear to lose energy via cosmological redshift. What about matter: You find that the de Broglie wavelength of particles increases by exactly the same proportion as a photon’s wavelength does! Thus light and matter seem to behave in exactly the same way.
[Not a precise quote, edited and abbreviated some, but close enough]

Photons do not lose energy in expansion.

If we fire a rocket into space at some significant fraction of the speed of light (say 0.1c) and then switch off the engines and let it cruise indefinitely, will it appear to accelerate away from us and in effect be carried along by the Hubble flow. Given a million or a billion years would it eventually appear to be receding at greater than the speed of light in the same way that distant galaxies appear to recede?
Answer in brief: [yes] It eventually recedes at the Hubble flow or the ‘distance expansion’ of the metric.

Marcus: "expansion causes things to lose momentum relative to the CMB."

So if you send a rocket off at .1c (relative to ancient light) it will eventually slow down (relative to ancient light)…. Expansion bleeds momentum from a flash of light as well. It keeps going the same speed but its wavelength lengthens, which means its momentum is drained also.

My comment: from Tamara Davis:
In an expanding distance, a matter particle exhibits the same proportional redshift as a photon.

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Bandersnatch
Red shift in Hubble's Law is due to relative velocities of gallaxies, not directly due to expansion. Photon is emitted already red-shifted relative to us, not becoming more and more red-shifted as time goes on. So your analysis is flawed right there.
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
(Page 9, specifically)
suggests that yours is a common misconception about the expansion of the universe.

Simon Bridge
Homework Helper
That would be p43.
Or, even, wikipedia:
http://en.wikipedia.org/wiki/Hubble's_law#Redshift_velocity
... agrees well with the idea of a linear doppler shift due to relative motion of distance objects.

However - I still think there are many possible confusions evident in the question to be able to answer clearly at this point. We need to hear back from OP before making too many assumptions.

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K^2
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
(Page 9, specifically)
suggests that yours is a common misconception about the expansion of the universe.
The writer of that article is very much confused about accelerated coordinate systems and associated red shift.

How do I explain this in simple terms? Well, lets say I put a whole bunch of equidistant observers between Earth and the distant galaxy. Lets say I ask them to measure the wavelength of a single pulse of light emitted at said galaxy towards earth as it passes them by. What will they observe? Well, naturally, each observer will report a more and more red-shifted beam as they get further from the galaxy and closer to Earth. Hey, that seems consistent with what that article says! But wait, why is this happening? Are we sure the light's wavelength actually changes? Each observer is located in different part of space separated by some distance. Due to expansion, all these observers are moving away from each other. Each observer's coordinate system is moving with respect to other observer's coordinate systems. When you go from one coordinate system to the other, where they are not at rest with respect to each other, you will end up with corresponding red/blue shifts.

So the disagreement between observers is still accounted for by simple Doppler shift. What gives? Well, this is actually very interesting. Metric that allows for uniform expansion of space actually requires all points in space to be moving apart from each other. The red shift due to the metric is absolutely equivalent to Doppler shift due to resultant motion. And it would point to a major flaw in GR if this was not the case.

Now here is the fine point which the author of the article doesn't appear to understand. Light's wavelength in any inertial frame does not change. It behaving otherwise would require light to age, which is impossible since light is massless. The apparent expansion of light as it travels arises from light's wavelength being measured in different coordinate systems at different points along the journey. The coordinate system in the right panel of that page is an accelerated one. Will light red/blue shift in an accelerated frame? Well, yeah.

But let us take a frame of reference that is not accelerating. For example, I can take the reference frame tied to the galaxy itself. In that frame, light is never red shifted. (I am ignoring gravitational red shift here.) From that frame of reference, the wavelength does not change all the way until it reaches Earth, which appears to be moving away. On the other hand, I can consider Earth as my inertial coordinate system. In that coordinate system, light doesn't change wavelength throughout the journey either. No acceleration. But in that coordinate system, the galaxy is moving away, so light became red shifted when it was emitted.

So again. Relative to us light got emitted already red shifted. It did not get red shifted in journey.

If you are comfortable with tensor calculus required for General Relativity, I can show you derivation of this effects using an actual simple example of an expanding space-time metric. It's fairly straight forward, but you do need to have some rudimentary understanding of GR to follow.

Starting with the premise that space expands, it seems inescapable that the wavelength of light should expand also. If the wavelength of a given photon is 1000 nm and the space it is in expands at a rate if 1/140% per million years then after 1 billion years it should have a wavelength of 1074 nm. The fact that it's moving is irrelevant since every nm of space that it moves through is expanding uniformly. K^2 (or anyone else who shares his view), where is this reasoning flawed?

K^2
In that space isn't a fixed grid. If it was, you'd have a concept of absolute velocity. But velocity is relative. Wavelength of light is entirely determined by the observer. So talking about what happens to wavelength of light without establishing a coordinate system is silly.

The coordinate system in which wavelength is gradually expanding is an accelerated one. In an inertial frame, it is not changing. It's that simple.

K^2 posts:

So talking about what happens to wavelength of light without establishing a coordinate system is silly.

The coordinate system in which wavelength is gradually expanding is an accelerated one. In an inertial frame, it is not changing. It's that simple.
this is the very subtle point I referred to above:

But 'expansion' and 'redshift' are slippery concepts and have been discussed/dissected/debated in these forums in detail........

'Expansion' and Hubble flow are a result of the FRW metric, in particular a(t), and 'Redshift' is a measured [and unambiguous] shift in received frequency versus emitted frequency. [But exactly what such a shift represents is subject to interpretation.] In other metrics [cosmological models] there may not be superluminal expansion.

K^2:
The writer of that article is very much confused about accelerated coordinate systems and associated red shift.
I believe Lineweaver and Davis are precisely correct.....
Would you quote what you believe is in error?? Such a discussion would likely be of benefit to Mrspeedy....maybe me too!!

In that space isn't a fixed grid. If it was, you'd have a concept of absolute velocity. But velocity is relative. Wavelength of light is entirely determined by the observer. So talking about what happens to wavelength of light without establishing a coordinate system is silly.

The coordinate system in which wavelength is gradually expanding is an accelerated one. In an inertial frame, it is not changing. It's that simple.
We can agree on that.

For cosmic scale problems I find it convenient to use a reference frame in which "at rest" means at rest with respect to the CMB. Since any 2 objects at rest with respect to the CMB will be accelerating away from each other this is 1 type of accelerating coordinate system. Please revisit the original question with the understanding that all measurements are relative to the CMB.

Mr speedy: I continue to agree with your original premise....relative to the CMB...

A few descriptions from experts in these forums I saved to clarify several perspectives:

PALLEN:
The Doppler effect is completely determined by the relative velocity of source and target. Both of these velocities are frame dependent, but the relative velocity between emitter at event of emission and receiver at event of detection is frame invariant. Thus all observers agree on the Doppler measured by a given detector from a given source.

Redshift is a measured shift in received frequency versus emitted frequency. Doppler [shift] refers to one of two formulas (pre-relativistic; relativistic) for relating redshift to velocity. Doppler shift is a particular explanation of redshift, with a particular formula. It is not a measure of redshift.

Mathematically, relative speed is defined by parallel transport of 4-velocity from one event to another (in SR, this is path independent, thus unique), then dot product of transported source 4-velocity with unit 4-vector 4-orthogonal to target 4-velocity. Dot products are invariant - period. (In a standard inertial frame in SR, parallel transport leaves a vector unchanged).
PAllen:

Cosmological redshift is typically considered distinct from Doppler redshift because it is a relation between distance and redshift rather than speed and redshift, under the assumption that both source and target are motionless relative to center of mass of the local matter (here, local is quite large - galaxy or galaxy cluster).
Marcus:

Don’t think of the redshift as a Doppler [relative velocity] effect. It is not the result of some particular speed. The formula involves the entire [varying] factor by which distances have been expanded during the whole time the light has been traveling.
PeterDonis:

The law governing the relationship of emitted to observed photon energies (or frequencies) is general and applies in any spacetime. The 4-momentum of the photon gets determined at the emitter; then it gets parallel transported along the photon's worldline from emitter to observer; then you contract that 4-momentum with the observer's 4-velocity to get the observed energy (or frequency if you throw in a factor of Planck's constant). That "parallel transport" process is actually where the "redshift" occurs in an expanding universe; the expansion alters the 4-momentum of the photon as it travels (or at least that's one way of looking at it), whereas in a static universe the photon's 4-momentum would "stay the same" as it traveled.

The red shift due to the metric is absolutely equivalent to Doppler shift due to resultant motion.
We have a disagreement, I think:..Lineweaver and Davis [and to my understanding this is consistent with PAllens description posted above] :

The cosmological redshift is not a normal Doppler shift. Astronomers frequently refer to it as such, and in doing so they have done their students a serious disservice. The Doppler redshift and the cosmological redshift are governed by two distinct formulas. Doppler redshift comes from special relativity, which does not take into account the expansion of space, and the second comes from general relativity, which does. The two formulas are nearly the same for nearby galaxies but diverge for distant galaxies. According to the usual Doppler formula, objects whose velocity through space approaches light speed have redshifts that approach infinity. Their wavelengths become too long to observe. If that were true for galaxies, the most distant visible objects in the sky would be receding at velocities just shy of the speed of light. But the cosmological redshift formula leads to a different concllusion. In the current standard model of cosmology, galaxies with a redshift of about 1.5--that is, whose light has a wavelength 150 percent longer than the laboratory reference value--are receding at the speed of light.
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Mr speedy...I'd reply to K^2's post #3

Red shift in Hubble's Law is due to relative velocities of gallaxies, not directly due to expansion. Photon is emitted already red-shifted relative to us, not becoming more and more red-shifted as time goes on.
as follows: