Why does quantum mechanics believe that gravity is a field?

[Michael Barry]

TL;DR Summary

General relativity states that gravity is a side-effect of the geometry of space-time. So why does quantum mechanics state that gravity is a field. Surely this violates general relativity.

According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape (bend it slightly) of the 2D hologram the virtual 3D voxels that represent the actual 3D voxels appear to move relative to each other. The real 2D distance is constant yet the virtual 3D distance is dynamic and relative and appears to morph as you bend the 2D plane. This means that gravity is a holographic illusion and not an actual force field (at least this is how I interpret it). So why does quantum mechanics state that gravity is a field, thus contravening general mechanics definition of gravity?

Does quantum mechanics take into account the geometry of space? After all space must exist, even at the quantum level, and ought to follow the same geometric principles. If two quantum particles are gravitating toward each other, why can't QM simply say that the particles are bending space-time just like the planets in space do.

I realize that it's most likely my interpretation that is lacking and I'm simply trying to understand what is actually going on here.

 

[PeterDonis]

why does quantum mechanics state that gravity is a field

QM doesn't actually "state" this, because we don't have a good theory of quantum gravity.

One hypothesis about what a theory of quantum gravity will look like is that it will be a quantum field theory, at least somewhat similar to the quantum field theories we already have for other interactions. In a theory like this, classical General Relativity, including its modeling of spacetime as a geometric object, would be emergent from the underlying quantum field. In fact, a theory like this was studied in the 1960s and 1970s: it is simply the quantum field theory of a massless, spin-2 field (as quantum electrodynamics is the quantum field theory of a massless, spin-1 field). This theory actually does have General Relativity as an appropriate classical limit; however, it has a number of issues (such as not being renormalizable) that, in the judgment of physicists, disqualify it as the true theory of quantum gravity (although it could still appear as an approximation in certain regimes in a true theory of quantum gravity).

Does quantum mechanics take into account the geometry of space?

Ordinary non-relativistic QM assumes a Newtonian view of space and time.

Relativistic QM without a quantum theory of gravity, i.e., quantum field theory as we currently have it, assumes a fixed background spacetime geometry (normally flat Minkowski spacetime although other geometries are sometimes used). This is a reasonable approximation in cases where the effect of the quantum fields on the spacetime geometry is expected to be negligible--for example, when studying particle accelerator experiments, a common application of QFT as we currently have it. However, it obviously cannot handle any interaction between the spacetime geometry and matter, as classical General Relativity does. Closing this gap is one of the main motivations for searching for a quantum theory of gravity.

space must exist, even at quantum level

You should be very careful about making such claims. In at least one approach to quantum gravity, loop quantum gravity, this statement is false since in this approach "space" (and more generally spacetime) does not exist at the fundamental quantum level. Spacetime itself (not just its specific geometry but the very concept of spacetime) is emergent in this model.

If two quantum particles are gravitating toward each other, why can't QM simply say that the particles are bending space-time just like the planets in space do.

Because that would mean there could be quantum superpositions of different spacetime geometries (since the quantum particles could be in superpositions of different states that would bend spacetime in different ways), and we do not have a quantum theory of gravity that tells us how to handle that.

 

[Michael Barry]

Thank you. You've given me food for thought and that was a fast and detailed response. Much obliged.

Because that would mean there could be quantum superpositions of different spacetime geometries (since the quantum particles could be in superpositions of different states that would bend spacetime in different ways), and we do not have a quantum theory of gravity that tells us how to handle that.

Ah, I took this for granted, but I think I'm getting mixed ideas between QM and Klee Irwins quantum gravity theory. Thank you for clearing this up

 

[PeterDonis]

Thank you. You've given me food for thought and that was a fast and detailed response. Much obliged.

You're welcome! Also, I see you're a new member, so welcome to PF!

Klee Irwins quantum gravity theory

This Klee Irwin?

https://www.quantumgravityresearch.org/klee-irwin
If so, you should be aware that his ideas about quantum gravity are definitely not mainstream.

 

[Michael Barry]

You're welcome! Also, I see you're a new member, so welcome to PF!

Thank you once again :)

This Klee Irwin?

Yes, this is who I was referring to

https://www.quantumgravityresearch.org/klee-irwin

If so, you should be aware that his ideas about quantum gravity are definitely not mainstream.

There is something to be said about the path less worn. His theories are not yet complete and I sincerely hope that once finished it will be experimentally provable (or disprovable, either works for me). I think that perhaps I'm drawn to his theories from a philosophical stand point. Something just feels right about it - but that's a topic for another forum :)

 

[Vanadium 50]

If so, you should be aware that his ideas about quantum gravity are definitely not mainstream.

Neither are his ideas on crystals, health supplements, mathematics, etc...

There is something to be said about the path less worn.

Yes, but it's not what you think it is. If the appeal of an idea decreases with increasing knowledge, that's seldom the right direction.

 

[gtorassa]

Summary: General relativity states that gravity is a side-effect of the geometry of space-time. So why does quantum mechanics state that gravity is a field. Surely this violates general relativity.

According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape (bend it slightly) of the 2D hologram the virtual 3D voxels that represent the actual 3D voxels appear to move relative to each other. The real 2D distance is constant yet the virtual 3D distance is dynamic and relative and appears to morph as you bend the 2D plane. This means that gravity is a holographic illusion and not an actual force field (at least this is how I interpret it). So why does quantum mechanics state that gravity is a field, thus contravening general mechanics definition of gravity?

Does quantum mechanics take into account the geometry of space? After all space must exist, even at the quantum level, and ought to follow the same geometric principles. If two quantum particles are gravitating toward each other, why can't QM simply say that the particles are bending space-time just like the planets in space do.

I realize that it's most likely my interpretation that is lacking and I'm simply trying to understand what is actually going on here.

You say "After all space must exist". But in the fantastic world of particles, you can't say "must" for anything. Particles appear from nowhere, photons go through two holes at the same time, measurements on a particle influence the measurement on another distant particle.
In Quantum Mechanics you have to be open to any possibility ;-)

 

[DrChinese]

There is something to be said about the path less worn. ...

There are many speculative theories from so many places - from well-established physicists in the field, or physicists straying from their primary field, or from gifted skeptics whose assertions generally far exceed any credible connection to experiment. There is no shortage for paths that are "less worn"! The problem is that they are NOT useful paths, meaning: they either don't make a prediction that is experimentally verifiable, or the experimental verification/falsification is not feasible for some reason.

Whenever someone trumps new theory speculation, it needs to solve some open mystery to be of much interest. In other words: what is its benefit? If I assume little X, then it solves big Y - something like that. The only thing I see like that with Klee's team is to explain the value of 1 or more fundamental constants*. That would be good, but it is also the objective of perhaps 1000 other researchers in LQG and related quantum gravitation theories.

But the elephant in the room for such research is that there is essentially no experimental support for any theory past General Relativity (which is not quantum) at this time.

Klee's team is also "targeting is a non-local and non-deterministic quantum mechanical hidden variables theory explicitly allowed by Bell’s theorem." OK, that is huge endeavor, as everyone who pushes such theories (there are a few on the table) already knows. At least they are following Bell, which is what I use as a quick check for novel ideas.

I say good luck to them, and let us know when you've got something useful to look at (as opposed to "being promising"). *On their web site, the Klee team claims the experimental value of Planck's constant is disputed in the 5th decimal place. Yet it appears to be well tested to over 7 decimal places as of 2019, and is currently defined as 6.62607015×10-34. Kind of an odd point for them to in disagreement with the rest of the community, unless their research is pointing to a different number.

 

[DrChinese]

If two quantum particles are gravitating toward each other, why can't QM simply say that the particles are bending space-time just like the planets in space do?

That would more or less be the generally accepted perspective right now (i.e. General Relativity). Although as PeterDonis correctly points out, that leaves GR not unified with QM. There is no single specific requirement that these 2 cannot co-exist separately.

Keep in mind that one of the effects of gravity is to slow time in the presence of mass (such as the Earth, as opposed to open space). And quantum processes are shown to respect that (for example: the rate of radioactive decay varies under gravity).

 

[PeterDonis]

That would more or less be the generally accepted perspective right now (i.e. General Relativity).

The generally accepted perspective right now is to use the expectation value of the stress-energy tensor due to the particle as the effective stress-energy tensor in the Einstein Field Equation. But every QM interpretation (except the thermal interpretation of @A. Neumaier, discussed in other PF threads) says that's the wrong answer. Under a collapse interpretation, it should be just one of the terms in the superposition (whichever one corresponds to an observed measurement result); under a many worlds type interpretation, spacetime itself should be in a superposition of different curvatures, but GR can't do that since it's a classical theory. So while this method works empirically, at least so far, theoretically it clearly leaves open issues.

 

[A. Neumaier]

General relativity states that gravity is a side-effect of the geometry of space-time. So why does quantum mechanics state that gravity is a field. Surely this violates general relativity.

Already in classical general relativity, gravity is described by a field, defining the geometry of space-time. This is likely to remain valid in quantum gravity, although there are proposals that suggest that geometry itself would emerge only in the classical limit.