Will a Photon Inside a Perfectly Reflecting Box Eventually be Detected?

[Dmitry67]

I have a sphere or a box with ideally reflecting sufraces (inside). I open a cover, catch 1 photon, and close a cover. Photon is infinitely reflected back and forth inside. I can open a cover later and analyze it.

Now say I can a 'superposition' with 50% of the chance that I have a photon and 50% that I don't have it. Even photon is bounced inside in reversible manner, I see 2 problems:

1. Photon inside increase the energy stress tensor, so very sensitive device can detect extra gravitational attraction from the box, revealing 'which path' information.

2. When photon is inside the box, the box is under additional stress. As there are no absolutely rigid bodies, box becomes slightly larger. Also, it information is not elastic, then the box becomes hotter, so it is detectable from the outside.

So, even mirrors are ideal, still ofter some time we will be able to find out if photon is inside. What is a treshold?

 

[dmtr]

Nice one. But I don't think you will be able to get away with it. I'll put my money on the conservation of information, no-cloning principle, etc. Conceptually it feels somewhat similar to the Hawking radiation, so I would think you'll be able to find the corresponding temperature for that box using the similar principles.

 

[dmtr]

And my guess, that the threshold time would be the same, as the time that the black hole (with the same mass as the box, not the photon) takes to dissipate.

Of course I might be very wrong, or not even wrong.

 

[dmtr]

Nah. The mass of the box is not important, it's the radius that makes the difference.

 

[Dmitry67]

Yes, this is what I wanted to say.

 

[dmtr]

The obvious example of such a box is an atom.

 

[Demystifier]

Dmitry, I don't even understand what is the problem we are supposed to discuss in this thread.

Perhaps you are saying that the problem is that we can determine that the box catched the photon without actually detecting the photon? That's true, we can do it, but I don't see any problem with it.

 

[Dmitry67]

My question is if we did it, how long it would take for us to detect gravitationally if photon is inside or not - without opening a box?

 

[f95toli]

Why is this any different from e.g experiments where the number of photons at one frequency in a cavity is "counted" by measuring photons at another frequency (using strong non-linear coupling)?
Both are just examples of "indirect" detection of photons, it is nothing new.
Detecting it via gravity just seems like an very complicated way of doing it...

 

[Dmitry67]

You're absolutely right
But

1. It is not important if we can create such measurement device. Because decoherence is lost even if measurement device is not functioning or if the photon hit the wall we don't know where and is lost. It is importnat that in principle what-path information is dissipated somehow in the environment.

2. The difference is that you can decide to perform such indirect measurements or not. But gravity ALWAYS works and there is no way to stop it. So it can create some kind of 'upper limit' of how low we can preserve and keep the state in superposition no matter how careful are we.

 

[dmtr]

My question is if we did it, how long it would take for us to detect gravitationally if photon is inside or not - without opening a box?

So you were asking about the minimum threshold... My point was that your box would radiate, so in some time no photons would be left there for you to detect.

IMHO it does not matter how you confine energy in some volume. It can be gravity, mirrors or whatever. At the minimum you will have Hawking radiation.

 

[Dmitry67]

Radiate? Why? Why hawking radiation?

Say box is cooled to T=0.

 

[Demystifier]

My question is if we did it, how long it would take for us to detect gravitationally if photon is inside or not - without opening a box?

And why do you find this question interesting? I know that you are mostly interested in deep fundamental questions on QM (just as I am), so my problem is to figure out how answering this particular question would make your understanding of QM deeper.

 

[WaveJumper]

If the box is sufficiently small, say on the order of microns, said photon may tunnel through the box.

 

[Dmitry67]

And why do you find this question interesting? I know that you are mostly interested in deep fundamental questions on QM (just as I am), so my problem is to figure out how answering this particular question would make your understanding of QM deeper.

Why do you think Penrose suggested objective collapse based on the gravity (long time ago)?
Gravity is special

 

[hamster143]

As soon as you measure the gravitational field of the box, you become entangled with the photon.

 

[Dmitry67]

Don't all objects around the box constantly measure gravitational attraction to the box?

 

[hamster143]

They do, and they do that by exchanging quanta of gravitational field.

What we have here basically is an argument that explains why we _really_ need to quantize gravity, and we can't just, say, equate the classical Einstein tensor to the expectation value of the stress-energy tensor.

http://fds.oup.com/www.oup.com/pdf/13/9780199212521.pdf

 

[dmtr]

Don't all objects around the box constantly measure gravitational attraction to the box?

You are talking about some kind of gravity induced decoherence, right?

 

[dmtr]

Something along these lines http://arxiv.org/abs/0803.3447 ?

 

[dmtr]

Here are couple of links, which I think also relevant.
http://www.iop.org/EJ/article/1742-6596/171/1/012007/jpconf9_171_012007.pdf
http://pirsa.org/07110037/

And IMHO that box will have a temperature (and radiation) similar to the Hawking radiation of the black hole with the same surface area. If this is indeed the case, Dmitry67 - you won't be able to cool it to T = 0.

But I might easily be wrong. Please correct me, if you have some good reasons why this might be wrong.

 

[Dmitry67]

I don't understand why Hawking radiation will be emitted by an ordinary object, not a BH

 

[dmtr]

I don't understand why Hawking radiation will be emitted by an ordinary object, not a BH

I was not saying that there is going to be Hawking radiation, only that something similar to it may show up. I thought that there was some similarity between your ideally reflecting box and the black hole. Please excuse me for bugging you with very naive and uneducated guesses.

BTW: To hamster143 - thanks for the explanations and links. To Dmitry67 - thanks for a very nice question.

 

[Dmitry67]

Radiation from a black hole is generated by the horizon. I don't see how cold body (absolutely black or reflecting - it is irrelevant) can generate any radiation.

 

[Demystifier]

Why do you think Penrose suggested objective collapse based on the gravity (long time ago)?
Gravity is special

Now I understand your motivation, thanks!
Anyway, I don't think that gravity is so special and I don't buy this Penrose suggestion at all.

 

[Dmitry67]

Gravity is special that you can decide if you want to detect or not to detect. But gravity ALWAYS works, it always slowly tries to 'measure' everything.

 

[Demystifier]

Radiation from a black hole is generated by the horizon. I don't see how cold body (absolutely black or reflecting - it is irrelevant) can generate any radiation.

The same mechanism which is responsible for Hawking radiation (created by a COLLAPSING black hole) is also responsible for radiation from ANY time-dependent gravitational field. The horizon is responsible for the thermal spectrum of the radiation, but not for the creation of radiation itself.

 

[Demystifier]

Gravity is special that you can decide if you want to detect or not to detect.

I don't get it. Why, e.g., electromagnetism does not have this property?

 

[Dmitry67]

I don't get it. Why, e.g., electromagnetism does not have this property?

Electric charges can be cancelled. We can pass electrons thru neutral material (sonsisting of e- and p+). As there is no interaction (or it is cancelled) then there is no decoherence

gravity is like having all matter positively charged and conducting experiments on the electrons.

 

[Dmitry67]

The same mechanism which is responsible for Hawking radiation (created by a COLLAPSING black hole) is also responsible for radiation from ANY time-dependent gravitational field. The horizon is responsible for the thermal spectrum of the radiation, but not for the creation of radiation itself.

Ah, I see.
Is gravitational field from the photon is contantly changing (because it is moving, bouncing back and forth) or constant (because it forms a static wavefunction in cavity)?

 

[Fra]

These are great reflections. I am also quite convinced that there is some kind of connection between gravity and information updates (collapses), but I do not share Penrose exact ideas.

He tries to explain the collapse objectively, by using gravity (somehow).

I personally find gravity to be far more "mysterious" than and information update, so for me, I think the more natural path of inference is to rather post-dict gravity, from mutual information updates. Gravity could somehow be some particular "DC-component" in an ambient chaotic HF information update. In this sense, perhaps the notion of a physical graviton in the ordinary sense is a doubtful, since ALL information carriers in a sense universally enters this abstraction. The universality of gravity, would then relate to the universality of information capacity. All information needs to be encoded in physical degrees of freedom, and the "inertia" of information update, might be related to "gravitational forces".

But I doubt the main objective of Penrose, to restore "OBJECTIVITY".

I'm curious to hear more about Dmitry's further ideas since I know we have drastically differing views of realism.

/Fredrik

 

[Demystifier]

Is gravitational field from the photon is contantly changing (because it is moving, bouncing back and forth) or constant (because it forms a static wavefunction in cavity)?

It depends on how photon interacts with the environment. If the environment destroys the coherence, then a static wave function is not formed in the cavity, in which case the gravitational field is changing.

 

[Demystifier]

Electric charges can be cancelled. We can pass electrons thru neutral material (sonsisting of e- and p+). As there is no interaction (or it is cancelled) then there is no decoherence

gravity is like having all matter positively charged and conducting experiments on the electrons.

But the difference is not so much between gravity and electromagnetism, but between the SOURCES for gravity and electromagnetism. If gravitational sources with negative energy existed (e.g., the Casimir effect is believed to represent such a source), then gravity could be killed too, at least in principle.

 

[dmtr]

Now I understand your motivation, thanks!
Anyway, I don't think that gravity is so special and I don't buy this Penrose suggestion at all.

Why?

It looks like gravity couples this photon with the environment. You can't shield from gravity. So if you let some time pass there would be some loss of information from the system. As a result instead of seeing 50/50 distribution of pure states sometimes you'll see some mixed states (i.e. you'll be able to detect the photon on both paths or not been able to detect the photon at all).

The only argument against it (that I could see, from a layman point of view!) is that the gravity is too weak, to create enough information loss/decoherence (to explain the wavefunction collapse/time arrow).

 

[Demystifier]

Dmtr, see my post #33.