A photon and a neutrino go into a bar

[Subluminal]

During the trip from their supernova, they passed through expanding space together. The photon says to the neutrino, "I think I've been redshifted."

What happened to the neutrino?

 

[BillSaltLake]

Redshifted also, by the same ratio. (Some of the redshift is due to climbing away from the SN).

 

[marcus]

Roughly equivalent loss of momentum. That is also why dark matter has been able to cool and gradually collect in clouds. Dark matter particles would have started out with relativistic momenta. Expansion drained them of so much of their kinetic energy (as seen by an observer at rest relative to CMB) that we now call them *Cold* Dark Matter.

EDIT: didn't see Bill SL answer. I didn't need to post, he said what needed saying.

 

[bcrowell]

Wait, I was assuming this was a joke, and we were supposed to guess the punchline...?

As in:

Two atoms are walking down the street, and one turns the other and says, "Hey, I think I've just lost an electron!"

"Are you sure?"

"Yeah, I'm positive!"

 

[DaveC426913]

Two neutrinos pass through a bar...

 

[khemist]

Two neutrinos pass through a bar...

Great one liner.

 

[BillSaltLake]

The neutrino said, "Redshifted ?? I got a serious case of the munchies!" (He had passed thru Amsterdam, whereas the photon had bounced off Beijing).

 

[BillSaltLake]

Guess I could have said the neutrino was blueshifted from its experience, but that's a little more esoteric.

 

[Subluminal]

Wait, I was assuming this was a joke, and we were supposed to guess the punchline...?

How about:

The photon, a bit of an insecure wife, turns to her neutrino husband and asks, "Does this dress make me look redshifted?"

To Bill's answer, I think of the photon crossing a bit of space during the local time she takes to oscillate from one wavelength peak to the next. So for the neutrino, he crosses his own interval of distance while taking local time to oscillate between his various flavors. Also, you note that gravity has a redshift effect as the couple climbs away from the SN. I would think there would be a time dilation effect there, that gravity was having an effect on their local time they need to oscillate normally and we interpret that as a redshift.

Does expanding extragalactic space have a time dilation effect on them?

marcus, are you saying neutrinos slow down as they lose energy?

 

[marcus]

There is a paper on the arxiv about this which refers to a math derivation of it in Steven Weinberg's book Cosmology

Roughly equivalent loss of momentum. That is also why dark matter has been able to cool and gradually collect in clouds. Dark matter particles would have started out with relativistic momenta. Expansion drained them of so much of their kinetic energy (as seen by an observer at rest relative to CMB) that we now call them *Cold* Dark Matter.
...

The neutrinos from the "big bang" have been drained (by expansion) of slightly larger fraction of their momentum than the CMB photons have been drained of their momentum. Because they started earlier. So there has been more expansion while they have been traveling.

I'll see if I can retrieve the paper.
Yes. I got it!
http://arxiv.org/abs/0808.1552
Note on the thermal history of decoupled massive particles
Hongbao Zhang
4 pages, to appear in CQG
(Submitted on 11 Aug 2008)
"This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in [Weinberg's Cosmology], the strategies employed here are simpler, and the results obtained here are more general."

 

[Subluminal]

There is a paper on the arxiv about this which refers to a math derivation of it in Steven Weinberg's book Cosmology

There are many references to Cosmology throughout the threads here. Having just peeked at some pages made available on retail sites I now recognize why that is. The answers I am looking for appear to be encoded in that book, with much decoding going on here and many links to arxiv. I simply did not know how much there is available to know, and feel dumb knowing so little of it. You have all been helpful, but ultimately the information I needed was the author and title of a book!

I got a late start - I heard a podcast about Paul Dirac a few months ago (from Scientific American I think it was) and was fascinated how the positron would be used in medical imaging decades after he predicted its existence. My own work is related to magnetic resonance imaging, where photons in an oscillating magnetic field harmlessly illuminate physical structures inside the body. I believe in 50 years there will be $1000 MRI machines for the home, where we will check for and correct vascular irregularities each morning as we might today use a mirror to check out a zit. MRI machines are $10⁶ today. Computers were $10⁶ 50 years ago. Imagine what $10⁶ pieces of equipment doctors will examine us with in 50 years?

Steven Weinberg is already a legend in his own time, as Dirac was. I'm sure the knowledge he has shared will directly enable many advancements so, needless to say, I have ordered my copy of Cosmology. It's probably biting off more than I can chew, but I still have all my calc and diff eq texts, and can get others I'll need to follow the high math without getting too googly-eyed. It will be a slow process. I'm 42 now, so I have some time - maybe 50 years.

 

[twofish-quant]

During the trip from their supernova, they passed through expanding space together. The photon says to the neutrino, "I think I've been redshifted."

What happened to the neutrino?

Also red shifted.

However it's a bit more complicated because the part of the supernova that is generating the neutrinos is expanding so you should see some very strong blue shifting when you see the neutrinos come toward you.

 

[twofish-quant]

Redshifted also, by the same ratio. (Some of the redshift is due to climbing away from the SN).

The wrinkle in this is that the neutrinos are coming from a very different part of the star than the photons. The photons are coming from the outer layers, whereas the neutrinos are coming from the inner core.

 

[BillSaltLake]

Also if the neutrinos have mass, they will have generally lost a larger fraction of their momentum (than did the photons) when climbing away from the SN.

 

[Jack21222]

Roughly equivalent loss of momentum. That is also why dark matter has been able to cool and gradually collect in clouds. Dark matter particles would have started out with relativistic momenta. Expansion drained them of so much of their kinetic energy (as seen by an observer at rest relative to CMB) that we now call them *Cold* Dark Matter.

EDIT: didn't see Bill SL answer. I didn't need to post, he said what needed saying.

Have the first neutrinos really slowed down to the point they're considered CDM? I thought those neutrinos were still considered "hot" even after the expansion.

 

[cepheid]

Have the first neutrinos really slowed down to the point they're considered CDM? I thought those neutrinos were still considered "hot" even after the expansion.

Neutrinos are not the favoured candidate particle for cold dark matter, in part due to this problem. [STRIKE]Given the upper limits on their mass, I think that they would still be very much relativistic today.[/STRIKE]

EDIT: Scratched that last statement, since it is a lie. But neutrinos would have been relativistic "hot dark matter" at times in the past, and that would be problematic for models of structure formation.

 

[Flatland]

Two neutrinos pass through a bar...

...of solid iron.

 

[Jack21222]

...of solid iron.

... a light year thick

 

[marcus]

Have the first neutrinos really slowed down to the point they're considered CDM?...

Cepheid is right. I didn't mean to suggest that neutrinos are a candidate for dark matter.
What was on my mind was that CDM is another example where expansion does the cooling.

My guess is that the temperature of the primordial neutrinos is about 2 Kelvin. Somebody here probably knows the more precise estimate. It would be similar to the CMB temperature but a little cooler.

Because of their low mass, as someone pointed out, the neutrinos can be 2 Kelvin and still going fast.

But CDM particle, if it is subtantially more massive, at the same average temperature would be going more slowly. I think the idea is that because DM particles cannot radiate or interact (except gravitationally) they have no way of cooling except by expansion. But expansion in the long run is effective. So they are cool enough to collect in clouds and help ordinary matter cluster and acquire structure. Hopefully someone more knowledgeable can correct or amplify this.

Expansion cooling is kind of interesting. We have Subluminal to thank for bringing it up.

 

[twofish-quant]

Also when people talk about cold and hot, don't mean the temperature of the particle, but whether or not it's traveling relativistically.

Neutrinos are light so if you just put a tiny bit of energy in them and they are zipping around near the speed of light. Once you have something that is zipping around near or at the speed of light, it's hard to from clumps from them which means that it's hard to get huge galactic structures.

 

[cepheid]

My guess is that the temperature of the primordial neutrinos is about 2 Kelvin. Somebody here probably knows the more precise estimate. It would be similar to the CMB temperature but a little cooler.

Yup. Photons and relativistic particles (including neutrinos) cooled together at the same rate until neutrino decoupling happened. Shortly after that, electron-positron annihilation occurred (presumably at a temperature of around 0.511 keV, the electron mass, but correct me if I am wrong), which caused a boost in the photon temperature that was not propagated to neutrinos, since they were decoupled. (Decoupling just means that expansion lowers the density to the point that the timescale for the interactions that were keeping those particles in thermal equilibrium becomes too long to do so -- longer than the expansion age of the universe).

If memory serves, you can multiply the radiation temperature by a factor of (4/11)^1/3 to get the neutrino temperature. This just comes from the quantity g_*sa³ being constant (s is the entropy density, and a is the scale factor). Edit: g_* is a characteristic degeneracy factor for relativistic species that depends on which ones are present.