I Photon emission, power output (and black holes)

[PeterDonis]

So, for that short period, although we haven't perhaps changed the metric tensor very much, we did meet the required rate of energy dissipation. So did we achieve our goal over that short period, or not?

I have no idea, since at this point you're just making up a criterion and yet professing to not understand what it says. You can make the answer be anything you want by defining the criterion appropriately, and you're the one that made up the criterion, so why are you asking me what it is telling you?

my whole confusion is really how you connect the continuity of GR (and continuous rates of change) with the discrete world of QM.

And I've already repeatedly explained how you do that: continuity is an approximation. I don't know what more I can say. It looks to me like you are insisting on beating yourself over the head with something that's irrelevant.

It might be that the question you really want to ask is, if continuity is only an approximation, how can you apply a criterion that requires continuity to be exact? And the answer to that should be obvious: you can't. So either you're misunderstanding the criterion (maybe Muller didn't intend for his rate to be an exact continuous rate valid at any single instant), or the person who made up the criterion didn't think it through (maybe Muller didn't stop to consider that the criterion he was proposing can't actually be applied). But no amount of discussion here will address that issue; you'd have to ask Muller what he meant.

 

[asimov42]

@PeterDonis - thanks for the assistance. I've clearly annoyed you, so my apologies. I'm not doing a good job of explaining the issue I'm wondering about, which is my fault. The intent above was not to make up arbitrary criteria and then ask what they're telling me...

I'm sure Muller has at least a reasonable idea of what he's doing - he would not mention black hole evaporation and the corresponding energy dissipation for nothing.

Re-reading Muller's paper, and just thinking about GR, it seems that the key is that the metric tensor for a region of spacetime changes continuously, and it must (as mass/energy moves around) - this is what links the quantum nature of black hole evaporation with his 'rate of creation' of new space/time' in Muller's eyes... there has to be a tie in between the continuous and the discrete (until we get to quantum gravity perhaps). So, you're right - "either you're misunderstanding the criterion (maybe Muller didn't intend for his rate to be an exact continuous rate valid at any single instant)." This is exactly the case.

I'd welcome any further discussion of Muller's work, as I find it quite interesting - but I'll be sure to move any further questions over to Beyond the Standard Model.

 

[PeterDonis]

I've clearly annoyed you, so my apologies.

No need to apologize, I'm not annoyed. It just seemed like you were struggling to squeeze out the window when the door was wide open, so to speak.

(maybe Muller didn't intend for his rate to be an exact continuous rate valid at any single instant)." This is exactly the case.

That would be my interpretation of Muller's intent, yes.

 

[asimov42]

Thanks @PeterDonis and all! Just as a last, short question - am I correct in understanding that the metric tensor for a region of spacetime changes continuously as mass and energy move around? If so, then the tensor (curvature) in a region will continue to change as energy radiates away.

(Just making sure I understand the smooth manifold structure of spacetime).

 

[PeterDonis]

am I correct in understanding that the metric tensor for a region of spacetime changes continuously as mass and energy move around?

A better way of putting it is that the metric tensor can have different values at different events in spacetime. Remember that spacetime already includes time; it doesn't "change", it just is, but the "is" includes descriptions of everything that an observer following a particular worldline would observe to "change" with respect to his own proper time.

 

[asimov42]

Ok, one final, final question (sorry @PeterDonis!) - going back to 'changes' in the metric tensor (i.e., variations along the time axis);

I just wanted to go back to my asking about QM involving discrete events, and the idea of sufficient QM events within a given time interval - if the metric tensor changes smoothly and continuously in an ongoing way as quanta are dissipated (radiated away from a dense source), as viewed with respect to an observer's proper time. (Or perhaps this should be the curvature tensor?)

This is (hopefully) the link I was trying to get at between dissipating 1 billion Watts in 1 second, and, say, 500,000 Watts in 1/2 a second (see post #30). For the first half second, the average rates of dissipation are the same... that's fine. But obviously the overall change to the tensor will be different (after 1 second).

Dipping back to Muller (and ignoring the plausibility of his argument - sorry, it's the best example I have) - in his view, time is expanding at a certain continuous rate, and to counteract this you must have a certain dissipation in energy within a given time. So both the amount matters and the duration matters. The only way I can imagine this is if the metric tensor varies continuously as mass/energy moves around? The, both the amount of mass/energy, and the time over which the dissipation occurs, matter (and hence the need for a black hole).

So the final questions is: does the metric tensor changes smoothly and continuously in an ongoing way along the time axis as quanta are dissipated (radiated away from a dense source)? (Possibly as viewed with respect to an observer's proper time.) E.g. since a photon is radiated away from its source at the speed of light, I would expect the metric tensor (and curvature) to change as the photon moves farther from its source.

Thanks to @PeterDonis in particular for putting up with all these questions...

 

[PeterDonis]

if the metric tensor changes smoothly and continuously in an ongoing way as quanta are dissipated (radiated away from a dense source), as viewed with respect to an observer's proper time.

As I've already said, continuity is an approximation. The issue when we're talking about gravity is that we don't have a quantum theory of gravity, so we don't know what more accurate model should replace the approximation of continuity when we're talking about the metric tensor. The best model we have is to treat the metric as continuous, and to use appropriate averages of quantum observables to determine the effective stress-energy tensor that determines the metric. This amounts to assuming that the time scale on which the spacetime geometry changes is much slower than the time scale on which the quantum radiation processes happen, so that any corrections due to the actual change in spacetime geometry not being continuous are small enough not to matter.

 

[asimov42]

Right - I'm comfortable with taking the continuity of GR as a given (for now). So let's treat the metric (and curvature) as continuous. The question was more about the photon moving away...

Here's a thought experiment in 2D+time... again using simple number to make it easy. To affect the spacetime geometry in a way I desire (a la Muller), let's say I conclude that I must dissipate two joules of energy from my source (a clump of warm uranium atoms say, because they're heavy - ignoring their radioactivity).

So if I were to draw this situation from the 'side', I'd draw the simple 'ball weighing the sheet down' model (in 2D) to represent the spatial geometry at a slice in time, with the time axis sticking into the page.

Now:

Case 1: the uranium atoms emit one joule of photons out towards the left (or whichever direction) within 0.5 seconds. Then nothing else happens for the next 0.5 seconds. Hence, one joule in one second.

Case 2: the uranium atoms emit one joule of photons out towards the left (or whichever direction) within 0.5 seconds. And then emits one joule of photons in the other direction (to the right, or whichever way you wish). Ergo, two joules in one second.

Now, for the first 0.5 seconds the two systems are essentially indistinguishable (in terms of output). If I must wait 1 full second to evaluate how much energy has been released, then (correct me if I'm wrong) it's the geometry of spacetime that's going to be my bookkeeper - that is, as the photons released in the first 0.5 seconds continue to propagate farther from the source (the uranium atoms), looking along the time axis, the spacetime geometry must continue to change (as the one joule of photons move farther from the source, the 'indentation' of the uranium atoms on the sheet decreases). And the same in second case.

If the above were not true, then I'd have to say the both systems met my desired output per unit time, at least over a short period. But only the second system, relying on the geometry of spacetime to track to how much energy is actually moving where when, would satisfy my desired goal (for the amount of energy dissipated).

Back to Muller (sorry @PeterDonis, I'll have to send you a beer for putting up with this ): This is why 1 trillion joules in one second makes the cut for time reversal (say), but 500 billion joules in a half a second does not - because the spacetime geometry varies continuously as all of the emitted energy moves away from the source. Correct?

Apologies all - my confusion is something I feel i could explain by drawing on a whiteboard for 2 minutes... but it's hard to express in text.

 

[PeterDonis]

I'm comfortable with taking the continuity of GR as a given (for now).

You shouldn't be. That's where the issue is. The continuity of GR is an approximation. I've said this so many times now I've lost count. You need to read that statement again and again until it sinks in.

So let's treat the metric (and curvature) as continuous.

You can't if you want to resolve the issue that's bothering you. The only way to resolve the issue that's bothering you is to figure out how to not treat the metric and curvature as continuous--to figure out how to model spacetime geometry as a quantum thing, the same way the photon is modeled. But we don't know how to do that because we don't have a theory of quantum gravity. So we can't resolve the issue that's bothering you in the only way that it appears you will accept--by having a model that properly treats both the spacetime geometry and the photon emission process, with no approximations. Nobody knows how to build such a model.

I don't see the point of responding to the rest of your post since it is trying to construct a model that will never work. You can't have a model where spacetime geometry is continuous and the photon emission process is discrete. That's self-contradictory: it's impossible for both to be true.

The only other alternative, besides finding a theory of quantum gravity, would be to approximate the quantum emission process as continuous, by averaging the discrete emission events. But for some reason you seem unable to accept such a model as resolving your problem. So I don't know what else to say.

 

[PeterDonis]

the spacetime geometry must continue to change (as the one joule of photons move farther from the source, the 'indentation' of the uranium atoms on the sheet decreases

The "indentation" you mention is a feature of space geometry, not spacetime geometry. The "rubber sheet" analogy does not describe spacetime. It describes space, in a particular set of coordinates, at one instant of time.

That said, if one joule of photons is emitted in 0.5 second, the mass of the uranium atom (which is basically what causes the "indentation") will decrease by 1 joule divided by $c^2$. But if no more photon are emitted after that, the mass of the uranium atom won't decrease any further. That should be obvious since an atom that is emitting no energy can't change its mass.

So even aside from the issue I raised in my previous post, I think you are confused about how the process you are trying to model would actually affect the spacetime geometry. My advice would be to forget all the quantum stuff and just try to understand classical emission of radiation in a curved spacetime, where everything is modeled as continuous. If you don't have a good handle on that, trying to add quantum complications on top of it is not going to be productive.

 

[asimov42]

Thanks @PeterDonis. My understanding was that QFT is currently built on continuous spacetime geometry (albeit fixed, perhaps).

Ok really the last go at this promise - let's instead go with everything being classical and continuous - and pop back to Muller (sorry). His paper suggests modifications for the GR metric tensor (so classical). And then he comes out with a rate at which 'new time' is created. He then calculates (somehow, using what I would assume are continuous curves for Hawking radiation) that a hole with a mass less than 2.4e10 kg would dissipate energy at the required rate (something like 6e11 Watts) to in fact cause time reversal.

Now we're back to rates, because we're talking entirely about continuous processes here. So let's just say that we scale way down, and talk about nanoseconds ... there are lasers here now that will meet the above power requirement for short time durations. So who needs a black hole? Shouldn't my nice nanosecond laser pulse at 3 Joules reverse time (slightly) just as well as that very massive black hole? What gives?

It makes no sense to me how the two cases above can be any different, unless there is a requirement for some aggregate change in mass/energy, connected with geometry. But that's not what the paper suggests...

 

[PeterDonis]

My understanding was that QFT is currently built on continuous spacetime geometry (albeit fixed, perhaps).

Yes, it is. In most cases, the spacetime geometry is treated as fixed (almost always it's flat Minkowski spacetime, but in the treatment of Hawking radiation, for example, it's curved Schwarzschild spacetime).

There have been some attempts to model "back reaction" of the quantum field on the spacetime geometry; all of them use the averaging method I described--they define an effective stress-energy tensor for the quantum field by suitable averages of the QFT operators, which means they are approximating the quantum processes as continuous for purposes of modeling their effect on the spacetime geometry.

pop back to Muller (sorry)

As I've said before, I can't usefully comment on Muller's paper since I'm highly skeptical of his whole idea, so I don't see much point in trying to figure out whether particular sub-ideas under it make any sense.

 

[asimov42]

As I've said before, I can't usefully comment on Muller's paper since I'm highly skeptical of his whole idea, so I don't see much point in trying to figure out whether particular sub-ideas under it make any sense.

You could actually remove most everything about Muller from my post above - I have a continuous-time process that can only be reversed by dissipating energy at a given rate. I'm told I need a black hole to do this... but then I find a nice laser on Earth that will generate the required dissipation for short durations - if everything is continuous, why do I need to do this over 1 second, or 10 seconds... if everything involves continuous rates, my nice little laser should do just fine intermittently, no?

If all I care about (apparently) in the classical case is rate to achieve a given effect, then the time involved should not matter...

I am sure there must be other physical processes that also fall into the above category...

 

[PeterDonis]

I am sure there must be other physical processes that also fall into the above category...

I'm not. I'm not aware of any process that only depends on a rate. There has to be some threshold of total energy transferred, not just a rate of energy transfer.

 

[asimov42]

Oh! Interesting - could you give an example of one or two such processes @PeterDonis?

 

[PeterDonis]

could you give an example of one or two such processes

You mean processes where there is a threshold of energy transferred? One example would be the photoelectric effect.

However, the burden of finding processes is really on you, since you were the one who claimed that there should be ones that depend only on a rate.

 

[asimov42]

I mean I can certainly think of processes that are continuous - the expansion of the universe for example. But I'm assuming you'll say that this will turn out to discontinuous, once we have a theory of quantum gravity.

@PeterDonis, I know you discount the Muller paper - but that makes it very difficult to ask any related question. If fact, he's even got testable consequences - so that's something. The only thing I'm not clear on is why a black hole is required (but we already know that from the long discussion above), ... when he says 'rapid' dissipation, that to me implies a rate.

I'd pay cold hard cash (to @PeterDonis or someone, no joke) to look at what Muller's written and discern (even just hazard a guess) on how time reversal might be based on a threshold on total energy transferred. i really don't think the work should be dismissed outright..

Maybe i should move to Beyond the Standard Model and ask there?

 

[PeterDonis]

I can certainly think of processes that are continuous - the expansion of the universe for example. But I'm assuming you'll say that this will turn out to discontinuous, once we have a theory of quantum gravity.

It might, yes. I don't think we'll know for sure until we have the theory; but what you describe certainly seems to be the most common expectation among physicists who are working on the issue.

I know you discount the Muller paper - but that makes it very difficult to ask any related question

You can ask about it, but not here. It belongs in the Beyond the Standard Model forum, as I think I've said before.

Maybe i should move to Beyond the Standard Model and ask there?

Yes. But don't be surprised if other responders there are highly skeptical as well. My sense is that Muller is making a fundamental conceptual error; I don't think his concept of "time reversal" will even turn out to make sense when examined more closely.