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The Cosmic Box

Solitaire

Neoclinus blanchardi
Joined
Jul 25, 2001
Messages
3,065
"Most photons in the universe belong to the cosmic background radiation that survives from the big bang. Their total number remains almost constant. The entropy per unit (call it s) equals 4/3T times the thermal energy aT4 per unit volume, where T is temperature and a the radiation energy density constant, and s is therefore equal to 4aT3/3. Hence s/T3 is constant, and because T varies aV1/3, the total entropy S = sV in volume V stays constant during the expansion. The thermal radiation energy in V, equal to aT4V, however, decreases at the same rate as T and is proportional to 1/V1/3. The energy in the cosmic background radiation, once very large, is now quite small. Where has this energy gone? Can you think of an answer that conserves total energy? (The author has tried and failed.) Do you think the second law of thermodynamics is a better conservation principle in cosmology than the familiar conservation of energy principle?" - Edward Robert Harrison

I wonder, does the he eventually find the answer to his question or do we have to wait for the sequel to come out.

:eye-poppi
 
The energy in the cosmic background radiation, once very large, is now quite small. Where has this energy gone? Can you think of an answer that conserves total energy? (The author has tried and failed.) Do you think the second law of thermodynamics is a better conservation principle in cosmology than the familiar conservation of energy principle?"

As you may know, accelerating charges radiate. Suppose I take a heavy charged ball attached to a rope. I tie one end of the rope to a ring fixed to a post and smack the ball so it flies in a circle, tethered to the ring. Neglecting friction, it is still true that the speed and kinetic energy of rotation will decrease with time. Where did it go?

Hint - the answer is really obvious (it's not a trick question). Substitute "gravitational field" for the answer to this question, and you'll have the answer to the one posed in the quote above. It's really not very mysterious.
 
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"Most photons in the universe belong to the cosmic background radiation that survives from the big bang. Their total number remains almost constant. The entropy per unit (call it s) equals 4/3T times the thermal energy aT4 per unit volume, where T is temperature and a the radiation energy density constant, and s is therefore equal to 4aT3/3. Hence s/T3 is constant, and because T varies aV1/3, the total entropy S = sV in volume V stays constant during the expansion. The thermal radiation energy in V, equal to aT4V, however, decreases at the same rate as T and is proportional to 1/V1/3. The energy in the cosmic background radiation, once very large, is now quite small. Where has this energy gone? Can you think of an answer that conserves total energy? (The author has tried and failed.) Do you think the second law of thermodynamics is a better conservation principle in cosmology than the familiar conservation of energy principle?" - Edward Robert Harrison

I wonder, does the he eventually find the answer to his question or do we have to wait for the sequel to come out.

:eye-poppi
Don't understand a word but the numbers seem to remind me of Subrahmanyan Chandrasekhar and his work on white dwarfs (I don't mean midget tossing).
 
The energy in the cosmic background radiation, once very large, is now quite small. Where has this energy gone? Can you think of an answer that conserves total energy? (The author has tried and failed.) Do you think the second law of thermodynamics is a better conservation principle in cosmology than the familiar conservation of energy principle?"/QUOTE]

As you may know, accelerating charges radiate. Suppose I take a heavy charged ball attached to a rope. I tie one end of the rope to a ring fixed to a post and smack the ball so it flies in a circle, tethered to the ring. Neglecting friction, it is still true that the speed and kinetic energy of rotation will decrease with time. Where did it go?

Hint - the answer is really obvious (it's not a trick question). Substitute "gravitational field" for the answer to this question, and you'll have the answer to the one posed in the quote above. It's really not very mysterious.
This was another type of "where does the energy lost by redshifted light go" question????
 
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