# Objective collapse almost

1. Dec 14, 2009

### 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 dont 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?

2. Dec 14, 2009

### 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.

Last edited: Dec 14, 2009
3. Dec 14, 2009

### 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.

4. Dec 14, 2009

### dmtr

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

5. Dec 14, 2009

### Dmitry67

Yes, this is what I wanted to say.

6. Dec 14, 2009

### dmtr

The obvious example of such a box is an atom.

7. Dec 14, 2009

### 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.

8. Dec 14, 2009

### 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?

9. Dec 14, 2009

### 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...

10. Dec 14, 2009

### 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 dont 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.

11. Dec 14, 2009

### dmtr

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.

12. Dec 14, 2009

### Dmitry67

Say box is cooled to T=0.

13. Dec 14, 2009

### Demystifier

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.

14. Dec 14, 2009

### WaveJumper

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

15. Dec 14, 2009

### Dmitry67

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

16. Dec 14, 2009

### hamster143

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

17. Dec 14, 2009

### Dmitry67

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

18. Dec 14, 2009

### 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 [Broken]

Last edited by a moderator: May 4, 2017
19. Dec 14, 2009

### dmtr

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

20. Dec 14, 2009