Why doesn't gravity cause double-slit decoherence?

[oknow]

A double-slit experiment can be run and get similar results using either photons or small particles that have mass, such as molecules. Why doesn't the gravitational field of molecules in the experiment reveal which-way information to the surrounding environment, and trigger decoherence and loss of interference?

 

[Reggid]

Do the maths.

A "detector" to reveal the which-way-information via gravitational forces could be a test particle, let's call it D for detector, placed between the two slits. If the other particle passes through slit 1, because of gravitational interaction D gets some momentum in the direction of slit 1, if the other particle passes through slit 2 D gets some momentum in the direction of slit 2.
I guess it was something like this that you had in mind.

First do a rough order-of-magnitude estimation of how large this momentum kick due to gravity will be.

Then make yourself clear that your detector particle D has to be placed between the two slits on order to make it work as described above. This means that its position uncertainty should not be larger than the distance of the slits.

Then calculate what this means for the momentum uncertainty and compare it to your estimate for the momentum.

Then it should become clear.

 

[oknow]

In this thought experiment, there is no need to add a gravitational field detector because the question is why the lab and the experimenter standing adjacent (the environment) do not serve as such.

After all, if we place a 10 kg lead ball at one corner of the lab, the gravitational field effect of that ball on the lab and experimenter will be different than if we place that lead ball at an opposite corner. That field reveals the location of the ball. I would expect the same to hold true for a molecule of lead at different lab locations, though the field would be weaker. Yet, when the experiment is actually performed with molecules sent through the double slit, molecule location information is apparently not revealed, as is suggested by coherence being maintained. Why not?

I imagine potentially that the gravitational field of a molecule is too weak to trigger quantum decoherence via the environment. If that is the case, what is the largest mass for which that could remain true? Up to Planck mass?

I also imagine that from the environment's point of view, a molecule's gravitational field might be the same regardless of which path it takes through the double-slit apparatus. If that is true, no which-way information would be exposed during operation of the experiment, which would permit coherence to be maintained.

 

[PeterDonis]

In this thought experiment, there is no need to add a gravitational field detector because the question is why the lab and the experimenter standing adjacent (the environment) do not serve as such.

This is not correct. The lab and the experimenter do not exhibit any observable response to the molecule's gravitational field. So they can't count as a molecule gravitational field detector.

if we place a 10 kg lead ball at one corner of the lab, the gravitational field effect of that ball on the lab and experimenter will be different than if we place that lead ball at an opposite corner. That field reveals the location of the ball.

Does it? Has this experiment been done? Can experimenters use lab equipment to find a hidden 10 kg lead ball using only its gravitational field?

More pertinent to this discussion, has an experiment been done in which a lead ball is in a superposition of being at one end of the lab and the other, to see if the lab and the experimenter will decohere the ball? Of course the answer to that question is no.

I imagine potentially that the gravitational field of a molecule is too weak to trigger quantum decoherence via the environment.

That is what the experimental results indicate, yes. It is also the point of @Reggid's response to you in post #2.

If that is the case, what is the largest mass for which that could remain true? Up to Planck mass?

We don't have a theoretical answer to this question because we don't have a theory of quantum gravity.

We don't have an experimental answer to this question because we are unable to run double slit experiments, or anything like them, with quantum systems larger than, IIRC, buckyballs (60 carbon atoms), which still show interference patterns.

 

[oknow]

I'd done the math and still did not see why decoherence does not happen. Afraid I do not understand how such a why question can be "wrong."

Thanks for the other explanations. Sounds like gravity in relation to quantum effects is still poorly understood. I find it interesting that coherence is tenuous in other applications, such as quantum computing, but is not as tenuous when it comes to the effects of small gravitational fields on the environment.

Re finding gravitational effects of large balls of lead, I had assumed Cavendish-style experiments were well known at the "undergrad level" I'd marked this topic. Should I mark posts of this sort at a higher level?

 

[Vanadium 50]

I'd done the math

What did you calculate and what number did you get?

 

[oknow]

Did the math during my undergrad days, too long ago to recall specifics. Wouldn't help even if I still had my notebooks since what I'm seeing here is quantum and gravty interplay is not yet well understood.

It did occur to me that we can put a large ball of lead into a superposition, certainly via thought experiment, and maybe in an actual experiment as well. Modify Schrödinger's cat to position a massive ball somewhere within a larger box depending on a radioactive decay. Does the ball's gravitational field outside the box trigger decoherence and end the superposition?

 

[Nugatory]

Modify Schrödinger's cat....

You may not have understood that Schrodinger introduced his cat thought experiment as an argument that any line of thinking based on such macroscopic superpositions could not be right.

If you have not read Schrodinger's paper "The present situation in quantum mechanics" (here "present" is 1935 when it was published) then everything you think you know about this thought experiment is wrong and must be unlearned.

 

[PeterDonis]

Did the math during my undergrad days, too long ago to recall specifics.

Then you will need to redo the math and show it to us in order to back up your claim, or else find a reference that supports it.

 

[PeterDonis]

Sounds like gravity in relation to quantum effects is still poorly understood.

In the sense that we don't have a good theory of quantum gravity, yes, this is true.

I find it interesting that coherence is tenuous in other applications, such as quantum computing, but is not as tenuous when it comes to the effects of small gravitational fields on the environment.

Not sure what you mean by this. Can you elaborate?

Re finding gravitational effects of large balls of lead, I had assumed Cavendish-style experiments were well known at the "undergrad level" I'd marked this topic.

Sure, Cavendish experiments can be done, but that doesn't mean you can use a Cavendish apparatus at one corner of your lab to detect a lead ball at the opposite corner. Much less that you can expect to detect quantum interference effects.

 

[physika]

It did occur to me that we can put a large ball of lead into a superposition, certainly via thought experiment, and maybe in an actual experiment.

Not even near...

 

[DrChinese]

A double-slit experiment can be run and get similar results using either photons or small particles that have mass, such as molecules. Why doesn't the gravitational field of molecules in the experiment reveal which-way information to the surrounding environment, and trigger decoherence and loss of interference?

As several have already pointed out, we don't have a quantum theory of gravity to guide us on this point. More importantly: there is absolutely no requirement that our current theory of gravity - General Relativity - needs to be updated to be a quantum theory.

There have been papers on the subject attempting to determine if gravity might induce decoherence. Here is a recent one just so you can get the idea, but so far no one has anything close to a smoking gun on the subject.

Testing whether gravity acts as a quantum entity when measured