Using general relativity to violate the uncertainty principle

[Souma]

Hello everyone,
Heisenberg's uncertainty principle tells us that we cannot measure the position and the momentum of a particle to infinite accuracy. My question is, can we use general relativity to overcome this difficulty?
From what I know, any mass can curve spacetime even if it was small, and this must be true for electrons (for example). Can we measure the momentum of the particle to great accuracy, while determining the position of it by looking at the changes in the spacetime curvature?

 

[anuttarasammyak]

Contrary to your expectation historically Niels Bohr made use of GR to show uncertainty relation in a debate with Albert Einstein.

 

[PeroK]

Hello everyone,
Heisenberg's uncertainty principle tells us that we cannot measure the position and the momentum of a particle to infinite accuracy. My question is, can we use general relativity to overcome this difficulty?
From what I know, any mass can curve spacetime even if it was small, and this must be true for electrons (for example). Can we measure the momentum of the particle to great accuracy, while determining the position of it by looking at the changes in the spacetime curvature?

Trying to measure the gravitational effects of the electron would be a challenge! If you try to measure the position of an electron by its spacetime curvature, then you would have to measure the position of another particle, subject to and moving according to the electron's gravity, even more accurately. The uncertainty principle would get you on that.

In any case, there is no quantum theory of gravity to describe gravitational effects on that scale.

In principle you can use the electromagentic force to locate an electron, but the electromagnetic interaction on that scale must be modeled quantum mechanically and the uncertainty principle cannot be avoided.

 

[EPR]

An electron curves spacetime roughly as much as me sneezing in Amesterdam affects the Pacific ocean typhoon season.

 

[phinds]

An electron curves spacetime roughly as much as me sneezing in Amesterdam affects the Pacific ocean typhoon season.

And probably not even that much.

@Souma you seem to think that the HUP is a measurement problem. It's not. It's an inherent characteristic of nature.

Rather than look at it, as you have, as an attempt to measure a single particle's complementary characteristics simultaneously with infinite precision, look at it this way: The HUP says that it is not physically possible to start with EXACTLY the same starting setup, produce particles or send them on their way or whatever, and then measure their characteristics and get the same results. Even if you COULD measure two complementary characteristics to infinite precision it wouldn't invalidate the HUP because you wouldn't get the same results the next time. You always get a probabilistic distribution. THAT'S what the HUP really says.

Classical physics says that if you start with EXACTLY the same starting conditions you will always get the same result. That's the difference between the classical world and the quantum world (which is the real world at the quantum level).

 

[Souma]

Contrary to your expectation historically Niels Bohr made use of GR to show uncertainty relation in a debate with Albert Einstein.

Do you have a link to it? I would like to see this.

 

[Souma]

Trying to measure the gravitational effects of the electron would be a challenge! If you try to measure the position of an electron by its spa

And probably not even that much.

@Souma you seem to think that the HUP is a measurement problem. It's not. It's an inherent characteristic of nature.

Rather than look at it, as you have, as an attempt to measure a single particle's complementary characteristics simultaneously with infinite precision, look at it this way: The HUP says that it is not physically possible to start with EXACTLY the same starting setup, produce particles or send them on their way or whatever, and then measure their characteristics and get the same results. Even if you COULD measure two complementary characteristics to infinite precision it wouldn't invalidate the HUP because you wouldn't get the same results the next time. You always get a probabilistic distribution. THAT'S what the HUP really says.

Classical physics says that if you start with EXACTLY the same starting conditions you will always get the same result. That's the difference between the classical world and the quantum world (which is the real world at the quantum level).

cetime curvature, then you would have to measure the position of another particle, subject to and moving according to the electron's gravity, even more accurately. The uncertainty principle would get you on that.

In any case, there is no quantum theory of gravity to describe gravitational effects on that scale.

In principle you can use the electromagentic force to locate an electron, but the electromagnetic interaction on that scale must be modeled quantum mechanically and the uncertainty principle cannot be avoided.

I see, so whatever we do, it always ends up considering the uncertainty principle. But, the thing that made me ask this question is how spacetime "sense" the mass of the particle. I don't get a picture in which spacetime itself doesn't know where the mass is. I thought we could use this as a tool for getting the measurement, but it seems not possible.

 

[PeroK]

I see, so whatever we do, it always ends up considering the uncertainty principle. But, the thing that made me ask this question is how spacetime "sense" the mass of the particle. I don't get a picture in which spacetime itself doesn't know where the mass is. I thought we could use this as a tool for getting the measurement, but it seems not possible.

Except the model of spacetime you are using (General Relativity) is not compatible with observed quantum mechanical phenomena. An appropriate theory of quantum gravity (if and when one is found) will have to be comaptible with QM and the uncertainty principle.

 

[atyy]

Do you have a link to it? I would like to see this.

Here is an account of the Bohr-Einstein debates by Jørgen Veisdal which @anuttarasammyak referred to.

 

[vanhees71]

https://en.wikipedia.org/wiki/Bohr–Einstein_debates#Post-revolution:_First_stage

 

[Vanadium 50]

There are many misconceptions in the OP, and I suspect that responses will be confusing because there are so many different places one can try and shine a light on.

I would back up. The OP doesn't understand what the HUP says, so we should drop GR and focus on that.

The HUP does not say you can't measure x and p as accurately as you like. It says you cannot prepare a state so that if you measure position you always get the value x, and if you measure momentum you always get the value p. That includes looking at the same system multiple times, or preparing multiple systems in the same state.

 

[phinds]

The HUP does not say you can't measure x and p as accurately as you like. It says you cannot prepare a state so that if you measure position you always get the value x, and if you measure momentum you always get the value p. That includes looking at the same system multiple times, or preparing multiple systems in the same state.

I thought that's what I said in post #5, no?

 

[Vanadium 50]

It adds the idea of "prepare a state". Or that's` what I wanted, anyway.

 

[phinds]

It adds the idea of "prepare a state". Or that's` what I wanted, anyway.

Fair enough. That's a more formal/precise way of what I was attempting to explain.

 

[Demystifier]

Contrary to your expectation historically Niels Bohr made use of GR to show uncertainty relation in a debate with Albert Einstein.

But I have shown that this argument was wrong.
http://de.arxiv.org/abs/1203.1139