Photon's History: Quantum Expression for Energy Loss with Scale Factor Increase

[anorlunda]

I know that QM and GR have not net been combined, so perhaps this is a foolish question, but I'll try anyhow.

A photon traveling in the vacuum, has energy h/λ. That energy is fixed. It never varies in any circumstances (true?) except one. That one is the expansion of space time; i.e. the scale factor. That is why high energy primordial photons appear low energy today (CMB 3 degrees K).

The only way I can think of that loss of energy is when the wavelength λ increases with the scale factor a. We could express λ in giga light years instead of meters as a reminder that we are talking about cosmological scale distances.

What I would like to find is a quantum expression for the energy of a photon to decrease by one increment as the result of scale factor increasing. A non-energy conserving quantum event. If such exists, where might I go to study it?

 

[Drakkith]

A photon traveling in the vacuum, has energy h/λ. That energy is fixed. It never varies in any circumstances (true?) except one. That one is the expansion of space time; i.e. the scale factor. That is why high energy primordial photons appear low energy today (CMB 3 degrees K).

The energy of the photon can also differ depending on if the frame of reference with respect to the emitting object is moving. AKA doppler shift.

What I would like to find is a quantum expression for the energy of a photon to decrease by one increment as the result of scale factor increasing. A non-energy conserving quantum event. If such exists, where might I go to study it?

What do you mean by "one increment"?

 

[Nugatory]

A photon traveling in the vacuum, has energy h/λ. That energy is fixed. It never varies in any circumstances (true?)

Not true. The frequency, energy, and wavelength are all frame-dependent and different for different observers moving at different velocities relative to one another. There's not even any way of defining them as properties of a photon unless and until the electromagnetic radiation interacts with one of these observers.

 

[anorlunda]

Wow, thank you Nugatory. I never thought about it that way but you must be right. In the vacuum there is no observor, and thus no observable.

Now I have to go away and rethink Feynman diagrams where I thought that the photon must carry away a defined energy to make the energy-mass of the reaction balance. As you say, the energies of all the inputs and outputs of particle interactions are frame dependent..

I know that we're not suppose to try to visualize many of these things, but who can resist?

 

[Torbjorn_L]

I know that QM and GR have not net been combined

In the interest to pick nits (SIWOTI syndrome http://xkcd.com/386/ ), this isn't correct.

QM and GR has been combined, if not unified, with semiclassical physics. That means having quantum field theories on a background of weak gravity, meaning low energy on large scales, so little curvature. Examples would be cosmological red shift, inflationary cosmology et cetera.

I would assume such circumstances means one can treat GR as roughly linear. But regardless, there is another combination that goes deeper in such a case. One can quantize gravity and predict the existence of gravitons, without string theory:

"It’s often said that it is difficult to reconcile quantum mechanics (quantum field theory) and general relativity. That is wrong. We have what is, for many purposes, a perfectly good effective field theory description of quantum gravity. It is governed by a Lagrangian

S= [ ... ]

This is a theory with an infinite number of coupling constants (the ci and, all-importantly, the couplings in Lmatter). Nonetheless, at low energies, i.e., for ε ≡ E²/M²_pl ≪ 1, we have a controllable expansion in powers of ε. To any finite order in that expansion, only a finite number of couplings contribute to the amplitude for some physical process. We have a finite number of experiments to do, to measure the values of those couplings. After that, everything else is a prediction.

In other words, as an effective field theory, gravity is no worse, nor better, than any other of the effective field theories we know and love.

The trouble is that all hell breaks loose for ε∼1. Then all of these infinite number of coupling become equally important, and we lose control, both computationally and conceptually. [Goes on to discuss how (electro)weak quantum field theory is similarly effective and eventually breaks down at higher energies too. Perhaps at much lower energies than the effective theory of gravity at that?]"

[ https://golem.ph.utexas.edu/~distler/blog/archives/000639.html ; my bold]

 

[Chronos]

A photon has no history, the point is irrelevant.

 

[Clayjay]

A photon has no history, the point is irrelevant.

A photon has no history because____________
Your declaration leaves the reader guessing. Do you mind filling in the blank____?

A photon traveling at C is in a reference frame where time stops passing so the concept of history is irrelevant. Is this interpretation accurate or relevant to your statement?

 

[Chronos]

Yes, GR suggests time dilation and length contraction are infinite for a photon, meaning it has no valid inertial reference frame, or history.

 

[phinds]

... In the vacuum there is no observor, and thus no observable...

That is irrelevant. The actions of a photon do not depend on an observer

 

[jjalexand]

A closely related question: Re photons affected by gravity, as photon p passes particle m there is a mutual g force f1 on approach due to energy of p and mass of m (fact), and there is a mutual retarding force f2 on leaving (supposition s1). They move together slightly on passing due to gravitational attraction? (s2). So as p leaves this embrace, the m is slightly nearer to p than it was on approach of p, on average? (s2). So the retarding g effect is slightly greater than the attracting g effect? (s3). So on average the energy of the photon is reduced slightly by this differential acceleration? (s4). So some of the photon red shift we detect is caused by this effect? (s5). Question q1: are all the suppositions s1 to s5 correct? q2: If so, what approximate percentage of total average photon red shift per light-year is due to this effect (hard)?