How Is the Original Energy of CMBR Photons Affected by Universal Expansion?

[jnorman]

the photons emitted during the big bang, now detected as the CMBR, have been red-shifted by a very large degree due to the expansion of the universe since the BB, resulting in much lower photon energy now than when the photons were first emitted. (i hope i have that correct.)

since there is a law of conservation of energy, where did the original energy of the CMBR photons go?

 

[Khashishi]

This is a fairly common question. Here's one answer. http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

 

[Chronos]

The usual answer is global energy conservation is not required by GR, which is technically correct, but, rather unsatisfying. An adventurerous soul might suggest the missing energy goes into the gravitational field, which is plausible, but, rather confusing. GR is tricky because it really has no firm definition of energy - or even mass for that matter.

 

[Whovian]

Or a really adventurous soul (namely me) might suggest that that energy is known as Dark Energy. :)

 

[mathman]

Or a really adventurous soul (namely me) might suggest that that energy is known as Dark Energy. :)

Very unlikely.

 

[Whovian]

Exactly why I used "really adventurous." I doubt it, too.

 

[mrspeedybob]

This is a fairly common question. Here's one answer. http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Thanks. That was a good read.

 

[haruspex]

I'm not sure it's that complicated.
Consider a light source receding from you rapidly. You see it red-shifted.
You also see the light source accelerating away from you (conservation of momentum).
So the photons appear to you to have done work accelerating the source.

 

[Whovian]

I'm not sure it's that complicated.
Consider a light source receding from you rapidly. You see it red-shifted.
You also see the light source accelerating away from you (conservation of momentum).
So the photons appear to you to have done work accelerating the source.

But that relies on the two energies being EXACTLY the same. Say two objects are the same distance away from you. One's a couple billion times as bright as a GRB (just as a reference, i doubt such things exist), and the other hardly emits or reflects light at all. By your argument, the star should shoot away from you, and the other object should verrrrrrrrrrrrrrrrrrrrrry slowly.

Also note that the objects are not truly moving away from us in a way that requires conservation of energy to give some sort of energy supply to allow them to move away, it's simply the space between us and them is expanding.

 

[haruspex]

But that relies on the two energies being EXACTLY the same. Say two objects are the same distance away from you. One's a couple billion times as bright as a GRB (just as a reference, i doubt such things exist), and the other hardly emits or reflects light at all. By your argument, the star should shoot away from you, and the other object should verrrrrrrrrrrrrrrrrrrrrry slowly.

Also note that the objects are not truly moving away from us in a way that requires conservation of energy to give some sort of energy supply to allow them to move away, it's simply the space between us and them is expanding.

You're reading far too much into what I wrote. I'm not claiming the photons' momenta are responsible for the whole or even much of the object's speed. Indeed, a star is likely sending similar flux in all directions.

Let's take a simple model. A mirror mass m is moving away at from you speed v and you bounce a photon off it. The photon had frequency f when it left you, momentum p.
Impulse on mirror = 2p (well, slightly less because the mirror sees it as redshifted, but it'll do for now). Δv = 2p/m.
Mirror's KE, as seen by you, is approx. mv^2/2. (These need not be relativistic speeds, so I'll leave the exact calculation to you ;-). Increase in KE = mvΔv = 2pv.
Returning photon's redshift z = 2v/c = Δf/f.
Change in photon energy = hΔf = 2vhf/c = 2pv.

So in this case the loss of energy in the photon matches the gain in KE of the mirror.