General Relativity and Heisenberg Uncertainty

[rubenvb]

First, I'm not sure where this fits (here or Quantum Mechanics), because it's completely in-between the two...

Is there a way to account for the fundamental uncertainty in quantum mechanics through a modification of general relativity? I have very limited experience in Quantum mechanics, and only a notion of what general relativity is.

What I'm after is this: I have a proton (point particle), which curves space-time due to it's charge and to a lesser extent, it's mass. I now shoot an electron past the proton, which should follow its geodete of the curved space-time. If you try to describe this process with eg the Schrödinger/Dirac equation and time evolution, you would make the electron into a (gaussian) wave packet that would dilute throughout the whole process and generate a probability distribution of where the electron could be after the interaction. General relativity in contrast has exactly one point in space-time where the electron should be. Is there a modification to general relativity that could account for the different (experimentally measured) probability distributions?

If I'm thinking about this in the wrong way, please enlighten me, I'm eager to learn. If my example of proton and electron is incorrect, think about the two-slit Young experiment, which would equally well generate a quantum mechanical probability/intensity distribution, whereas (as far as I can deduce) general relativity would not.

 

[arkajad]

Nothin prevents you from writing Schrodinger's equation in a given gravitational background - provided it is not too crazy. On the other hand, if you are not scared of somewhat heretical views, you can read this for start:

http://www2.warwick.ac.uk/fac/sci/physics/staff/academic/mhadley/explanation/"

 

[Dale]

Is there a way to account for the fundamental uncertainty in quantum mechanics through a modification of general relativity?

There is currently no accepted quantum theory of gravity, although there is a large effort to devise one.

 

[rubenvb]

Nothin prevents you from writing Schrodinger's equation in a given gravitational background

I had the impression it wasn't so easy?

There is currently no accepted quantum theory of gravity, although there is a large effort to devise one.

I know, and stuff like string theory comes to mind, but I'm trying to look at it the other way around: a general relativistic theory of quantum mechanics, to express it in mildly confusing terminology.

What about my example then? How does this fit into the picture?

 

[arkajad]

I had the impression it wasn't so easy?

For a starter:

N. D. Birrell, P.C.W. Davies, "Quantum fields in Curved Space", Cambridge (1982)

Stephen Fulling, "Aspects of Quantum Field Theory in Curved Space-Time", Cambridge (1989)

 

[JustinLevy]

I know, and stuff like string theory comes to mind, but I'm trying to look at it the other way around: a general relativistic theory of quantum mechanics, to express it in mildly confusing terminology.

What about my example then? How does this fit into the picture?

So you want to use the "extra variables" of the state of spacetime itself to somehow provide a "hidden variables" solution to quantum mechanics?

GR is a classical and local theory. And local realism hidden variable theories have been experimentally ruled out for quantum mechanics. So this won't work unfortunately. There's no way to get rid of the "uncertainty" in quantum mechanics by saying it is just unknown classical laws.

 

[Passionflower]

I now shoot an electron past the proton, which should follow its geodete of the curved space-time.

I think the problem is that there is no classical worldline as the electron's time and space are probabilistic when not measured.

 

[arkajad]

GR is a classical and local theory.

But GR does not have to be such. For instance to GR is attached the manifold of null geodesics. And points of this manifold are non-local is space-time.

 

[Rebound]

Sadly, this is more or less what Einstein worked on unsuccessfully for most of the latter part of his career.

 

[arkajad]

Sadly, this is more or less what Einstein worked on unsuccessfully for most of the latter part of his career.

The reason for his lack of success could be related to his personality, to his immediate environment, and to his philosophical and metaphysical prejudices, not necessarily to an objective impossibility. These elements are inseparable, and they influence our science. Metaphysical believes influenced many scientists in the past, for instance Newton. Sometimes for good, sometimes for not so good.

 

[Rebound]

Possibly. But I think it is more likely that is not possible to describe the universe at the smallest scales within the framework of General Relativity. It is cannot take into account the various aspects of quantum weirdness in a self-consistent manner. For example, a major problem with classical physics in general is that gravity no longer has any apparent meaning at that scale.

 

[arkajad]

It is cannot take into account the various aspects of quantum weirdness in a self-consistent manner.

But quantum theory also cannot take into account its own quantum weirdness in a self-consistent manner.

 

[Rebound]

But quantum theory also cannot take into account its own quantum weirdness in a self-consistent manner.

Precisely. Hence the plethora of theories intended to provide a completely new framework, e.g. Loop Quantum Gravity and String Theory.

 

[georgir]

I now shoot an electron past the proton, which should follow its geodete of the curved space-time. If you try to describe this process with eg the Schrödinger/Dirac equation and time evolution, you would make the electron into a (gaussian) wave packet that would dilute throughout the whole process and generate a probability distribution of where the electron could be after the interaction. General relativity in contrast has exactly one point in space-time where the electron should be. Is there a modification to general relativity that could account for the different (experimentally measured) probability distributions?

The most straightforward way to include the uncertainty principle in that scenario seems to be this: since you shouln't be 100% certain about the position and velocity of the electron that you "shoot" initially, you repeat the experiment many times and shoot many slightly differing electrons. Now you have many possible answers instead of "exactly one point in space-time where the electron should be".

 

[rubenvb]

The most straightforward way to include the uncertainty principle in that scenario seems to be this: since you shouln't be 100% certain about the position and velocity of the electron that you "shoot" initially, you repeat the experiment many times and shoot many slightly differing electrons. Now you have many possible answers instead of "exactly one point in space-time where the electron should be".

Well, that's what I had in mind in my badly explained example. Why not let the wave-function diffuse when its moving in a GR curved space-time. Why not make the inherently "perfectly smooth" curved spacetime (as I think it is for many simple problems: a smooth curvature without bumps) a bit "rougher", thus less probabilistic and "more quantum-mechanical". I would find this quite logical that there would be indeterministic disturbances in space-time.