Re: [math-fun] What if Turing/Shannon/Bekenstein were wrong?
I did a Google search on "photon conservation" & came up with nothing (there were discussions of _preserving_ as many photons as possible in detectors, but that was completely different). If there is such a notion of photon conservation, that would be a valuable insight. Do you have any links or references? At 11:14 AM 4/9/2014, Eugene Salamin wrote:
As the universe expands, the number of photons is conserved, and the wavelength of each photon lengthens proportionally to the expansion.
On 4/10/2014 7:06 AM, Henry Baker wrote:
I did a Google search on "photon conservation" & came up with nothing (there were discussions of _preserving_ as many photons as possible in detectors, but that was completely different).
If there is such a notion of photon conservation, that would be a valuable insight.
Of course photon number isn't conserved; they're created in charged particle collisions for example. But in the expansion of the universe example they are not interacting with anything - they're just following a null geodesic in spacetime. Brent
Do you have any links or references?
At 11:14 AM 4/9/2014, Eugene Salamin wrote:
As the universe expands, the number of photons is conserved, and the wavelength of each photon lengthens proportionally to the expansion.
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On Apr 10, 2014, at 10:06 AM, Henry Baker <hbaker1@pipeline.com> wrote:
If there is such a notion of photon conservation, that would be a valuable insight.
Photon number conservation is an example of an adiabatic invariant: something that is constant only in the limit where a parameter in the system is changing very slowly. The strict conservation laws, that do not involve a slow limit, are based on symmetries. Examples of these are momentum, energy, and charge. The simplest mechanical example of an adiabatic invariant I know of is a particle bouncing elastically between two parallel walls, when the walls are moved slowly. The change in the particle energy is easy to work out in the limit where the walls are infinitely massive and their speed is small compared to the speed of the particle. Although the particle energy is not conserved, in the slow-wall limit the action of the particle is. The action is the integral of p dx around one period of the motion. Action corresponds to the number of quanta in quantum mechanics. So if we think of the two walls as representing the finite universe, and the particle as a wave in that universe, then adiabatic invariance in mechanics corresponds to preserving the number of quanta as the universe changes its size. -Veit
Speaking of photons, there was a recent article in Discover magazine about how some physicists were able to get two photons to "stick together" in some sense, but causing them to collide. How they did that, I do not understand from the description given. On Apr 10, 2014, at 12:58 PM, Veit Elser <ve10@cornell.edu> wrote:
On Apr 10, 2014, at 10:06 AM, Henry Baker <hbaker1@pipeline.com> wrote:
If there is such a notion of photon conservation, that would be a valuable insight.
Photon number conservation is an example of an adiabatic invariant: something that is constant only in the limit where a parameter in the system is changing very slowly.
The strict conservation laws, that do not involve a slow limit, are based on symmetries. Examples of these are momentum, energy, and charge.
The simplest mechanical example of an adiabatic invariant I know of is a particle bouncing elastically between two parallel walls, when the walls are moved slowly. The change in the particle energy is easy to work out in the limit where the walls are infinitely massive and their speed is small compared to the speed of the particle. Although the particle energy is not conserved, in the slow-wall limit the action of the particle is. The action is the integral of p dx around one period of the motion.
Action corresponds to the number of quanta in quantum mechanics. So if we think of the two walls as representing the finite universe, and the particle as a wave in that universe, then adiabatic invariance in mechanics corresponds to preserving the number of quanta as the universe changes its size.
-Veit _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
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Dan Asimov -
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Veit Elser