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marcus

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In the cosmol. redshift thread (Q) asked

[[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

It is clear that a whole lot of energy has been lost by the stretching out of light over the course of billions of years and

in that thread some people were speculating that it had gone somewhere (instead of being simply lost) like into fueling the dark energy or something. I can't say just what the idea is, but I can try a rough estimate of how much energy has been lost.

(I don't think it is very much compared with the present amount of dark energy.)

Up to a factor of order one, the volumetric density of radiation at temp T is (correct me if I am mistaken) T

The temp of the CMB in absolute units is 2.0E-32

So raise that to the fourth and you get 16E-128

That is the current energy density in the space around us of the CMB (or about 2/3 that because of the order-one factor I omitted)

And the CMB is at redshift 1100. So, if the CMB had not been being redshifted all these billions of years since socalled "recombination" (estimated 300,000 years after bigbang) then its photons would each be 1100 times as energetic.

So the amount of lost energy (per unit volume of space) is about

1000 x E-127 which is E-124

But the dark energy density I have calculated a couple of times here (being 70 percent of critical) as 1.3E-123

So this redshift loss is only an order of magnitude smaller than the cosmological constant or dark energy density!

I did not realize that when I first calculated---and also made

a multiplication error I just corrected---so got a different conclusion.

Light from all the galaxies is a smaller density---it does not noticeably effect the temperature of space so I neglect it. So the energy lost from the CMB by space-expansion is (admittedly a huge huge amount of energy) is smaller but roughly comparable with Lambda, or Dark or "quintessence" whatever you call it.

(Q)'s question is provocative in that it tempts us to speculate that the energy lost by cosm. redshift as gone into something like expanding space and creating more dark energy.

I have no clue as to how that could happen and assume that the energy is simply lost.

Note that I calculated the CMB energy density in space simply by raising the temp to the fourth. (c=G=hbar=k=1) Would someone show how to calculate the joules per cubic meter of the CMB in metric terms? Probably not, but it would provide a check.

The actual CMB temp is 1.93E-32 absolute (corresponding to

2.725 kelvin) but for back-of-envelope I took it to be 2E-32.

E-32 of the Planck temperature is what corresponds roughly

in size to a kelvin, more accurately 1.4 kelvin.

[[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

It is clear that a whole lot of energy has been lost by the stretching out of light over the course of billions of years and

in that thread some people were speculating that it had gone somewhere (instead of being simply lost) like into fueling the dark energy or something. I can't say just what the idea is, but I can try a rough estimate of how much energy has been lost.

(I don't think it is very much compared with the present amount of dark energy.)

Up to a factor of order one, the volumetric density of radiation at temp T is (correct me if I am mistaken) T

^{4}times k^{4}/hbar^{3}c^{3}The temp of the CMB in absolute units is 2.0E-32

So raise that to the fourth and you get 16E-128

That is the current energy density in the space around us of the CMB (or about 2/3 that because of the order-one factor I omitted)

And the CMB is at redshift 1100. So, if the CMB had not been being redshifted all these billions of years since socalled "recombination" (estimated 300,000 years after bigbang) then its photons would each be 1100 times as energetic.

So the amount of lost energy (per unit volume of space) is about

1000 x E-127 which is E-124

But the dark energy density I have calculated a couple of times here (being 70 percent of critical) as 1.3E-123

So this redshift loss is only an order of magnitude smaller than the cosmological constant or dark energy density!

I did not realize that when I first calculated---and also made

a multiplication error I just corrected---so got a different conclusion.

Light from all the galaxies is a smaller density---it does not noticeably effect the temperature of space so I neglect it. So the energy lost from the CMB by space-expansion is (admittedly a huge huge amount of energy) is smaller but roughly comparable with Lambda, or Dark or "quintessence" whatever you call it.

(Q)'s question is provocative in that it tempts us to speculate that the energy lost by cosm. redshift as gone into something like expanding space and creating more dark energy.

I have no clue as to how that could happen and assume that the energy is simply lost.

Note that I calculated the CMB energy density in space simply by raising the temp to the fourth. (c=G=hbar=k=1) Would someone show how to calculate the joules per cubic meter of the CMB in metric terms? Probably not, but it would provide a check.

The actual CMB temp is 1.93E-32 absolute (corresponding to

2.725 kelvin) but for back-of-envelope I took it to be 2E-32.

E-32 of the Planck temperature is what corresponds roughly

in size to a kelvin, more accurately 1.4 kelvin.

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