Muller's 'Now and the Flow of Time' - what's up?

[asimov42]

I recently re-read an article by Muller (https://arxiv.org/pdf/1606.07975.pdf) about the flow of time, and the possibility of time reversal given sufficient energy dissipation (basically during black hole evaporation, he concludes). Although the paper is on arXiv and not peer reviewed, Muller has written a book on the topic. I posted quite a long thread in the Quantum Physics forum, but there were still a number of unresolved issues...

Regardless of whether you buy Muller's argument or not - I have a fundamental question about the relationship between GR and QM. Muller defines the expansion of time just like the expansion of space (actually due the Hubble constant in fact) - i.e., as a continuous process in time. His bound on energy dissipation is also continuous (6e11 Watts or some such). Now, my body dissipates, maybe 200 Watts, on average...

So, similar to what I posted before (and thanks to @PeterDonis and @vanhees71 for chiming in - would love to hear from Arnold Neumaier ): in a much more mundane sense, let's consider the emission of a single photon from an excited hydrogen atom...

If photon emission is instantaneous, then one could say that the power output (energy dissipation rate) is infinite (finite energy photon emitted in zero time). I don't think this is what Muller is getting at... but in any quantized system (e.g., a blackbody radiator), the energy emission (power output) will vary, just by virtue of energy coming out in 'chunks'. So if Muller's correct, did my electron also go back in time?

I had two thoughts:

1) Photon emission is a continuous time process, then a bound on the emission rate could be true bound. No clear response on this from the community so far (@vanhees71 was looking at this...)

2) As @PeterDonis said, GR and QM can't be reconciled in this case - but this still leaves me with the question: every so often does some benign even (a energetic photon emitted in a femtosecond) actually cause time reversal in Muller's model?

In the second case, it would seem that Muller's idea could be tested without looking at black holes, but he specifically states that small evaporating black holes are the only objects that radiate sufficiently.

I'm totally confused about how to square the idea of continuous radiation output with the nature of a quantized systems. As @PeterDonis pointed out, he's not aware of any other physical systems (QM) that require an emission rate in continuous time... but then this is the clash between GR and QM exactly.

Any insights at all would be most helpful or even places to look. The best current answer is the QM one, that a specific number of quantum events must occur in a specific time - but this does not address the issue of my lonely electron at all ...

Thanks all.

 

[jedishrfu]

Calling @A. Neumaier

 

[asimov42]

Even if sometime could comment on the time of photon emission or absorption, that would be very helpful. (@vanhees71 ?)

 

[asimov42]

Or perhaps a better way I could phase the question?

 

[asimov42]

Maybe starting with a different question: are there any quantum processes that depend on a rate per unit time? (essentially a derivative) Or is that a fundamentally a no-go for systems at the quantum level?

 

[ohwilleke]

It isn't really clear what you are asking, so I'll make a couple of observations (none of which involve beyond the Standard Model and General Relativity physics, by the way).

Infinities In Photon Emission

Photon emission and most other quantum mechanics functions operate in probability amplitude space which consists of a field of probabilities superimposed on local space-time. The functions you use tell you the probabilities of certain events happening at particular places in space-time under certain well defined circumstances. The calculations are applied to the probability functions rather than the events themselves, and the discreteness that is the nominative characteristic of quantum mechanics comes in only after the probabilities are calculated and you "roll the dice" so to speak by observing the system and collapsing the wave function. This is how you get rid of the infinities associate with an "instantaneous" process as a practical matter. (The probability of a particle emitting a photon or absorbing a photon arises from a function in probability amplitude space that depends upon the particle's electromagnetic charge.)

The most common interpretation of quantum mechanics is that these probability amplitudes aren't "real" and are merely a tool used to calculate the probability of observable phenomena.

This lack of reality is actually pretty important because probability amplitudes, unlike observables, don't have to obey the laws of physics that apply to "real" things which can be observed.

For example, in a path integral calculation for the propagator of a photon, some of the paths considered have the photon moving at more than, or less than, the speed of light, which is prohibited by special relativity, for things that are "real" (the potential paths of particles do advance at finite rates, however, not instantaneously, and the average speed of massless particles in all of the observables is the speed of light).

Similarly, in quantum mechanics you can have "virtual" or "off shell" particles that aren't "real" as intermediate steps in a path to an observable outcome that violate conservation of mass-energy, even though the end state will never violate conservation of mass-energy.

Properties of these equations like unitarity (i.e. probabilities add up to 100%) and various conservation laws (which have more loopholes than classical physics such as quantum tunneling) prevent what naively seem like infinities associated with "instantaneous" processes from getting out of hand or violating any actual laws of physics.

Time Reversal

One way to interpret an electron-positron annihilation into two photons is as an electron moving forward in time and colliding with a photon moving backward in time. The collision sends the photon forward in time and sends the electron backward in time. An electron moving backward in time is called a positron, and in general, antiparticles are mathematically equivalent to ordinary particles of the same type moving backward in time.

Some people don't like this interpretation, since it sacrifices causality in favor of treating space dimensions and time dimensions interchangeably. For example, many quantum gravity theories make causality one of their bedrock axioms.

But, this interpretation is mathematically consistent with the more conventional interpretation of two matter particles transforming into pure electromagnetic energy in the form of photons in an annihilation event. In general, the time and space axes of a Feynman diagram can be rotated without changing the calculations of probabilities implied by it. A rotation merely changes the description of the event by an observer in space-time as opposed to having a "God's eye view".

Further Reading

One of the best ways to grasp these concepts in a short book readable by a layman (maybe 176 pages of easy reading with little difficult math) is to read the book "QED" by Richard Feynman which is a collection of four lectures he gave in New Zealand on this topic, transcribed and cleaned up for print in 1988. Essentially everything but some slight details in the last few pages of the last chapter is perfectly accurate and accepted today, and the parts that might become outdated are clearly identified.