What Does It Mean That Quantum Gravity Has No Symmetry? | Hacker News Reader

What Does It Mean That Quantum Gravity Has No Symmetry?

forbes.com

56 pointsespeed14 comments

For those that did not read to the end of the article, there is an important update due to feedback from one of the authors. The result only applies to global symmetries but the article talks mostly about gauge symmetries - which are not really symmetries to begin with. More specifically in the standard model it only applies to the difference of the lepton and baryon numbers.

Side note / question to real physicists: I am curious, for example, why general relativity does not break conservation of momentum in 3D, given that it seems like warped space time (to my lay perspective) violates 3D translational symmetry. For example, how do wormholes or the Alcubierre drive not violate conservation of momentum?

Edit: Removed my own confused interpretation of the article’s confused interpretation and correction footnote.

Energy and momentum are in general _not_ conserved in general relativity. This is a well-known feature of the theory, not a mistake made by the article's author.

In field theories like GR, energy is generator of time translations. It's conserved if time translations leave the system invariant, but this only occurs in very special cases in general relativity (static spacetimes). So in general, in Gr, energy is not conserved. Same thing goes for momentum, which generates spatial translations.

Thank you!

Another question on a tangentially related topic: Could you perhaps shed more light on why there so much pessimistic skepticism towards any claims of working reaction-less propulsion drives (violating conservation of momentum), for example?

I understand the experience-based reasons for skepticism (since there have been many claims that don’t replicate), but why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work, according to current physics theory?

I’m referring for example to skepticism about things like “EMDrive” from a theoretical perspective (e.g. the posts from physicists here: https://www.reddit.com/r/EmDrive/) as opposed to focusing on experimental failures to replicate.

I'm not an expert in these things. But my recollection is that the solutions of general relativity that behave like warp drives all violate various energy conditions and hence are only possible in the presence of what physicists politely refer to as "exotic matter". The Alcubierre drive, for example, requires matter with a negative energy density. We're reasonably certain that the class of quantum field theories we use to describe matter (QED, QCD, the Standard Model itself,..) are not compatible with these requirements.

why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work

Because it would violate conservation of momentum. Now wait a minute, you might think, haven't we just learned that such conservation laws don't hold in GR?

It's more complicated than that.

An analogy would be doing mechanics in a rotating reference frame. To make this work out, you have to account for things like centrifugal forces, with energy contributions that come 'out of nowhere' - as in, if you go to the non-rotating, inertial frame, they vanish: There's no real physical source providing that energy.

Something similar happens in general relativity, where you can get conservation laws via Noether's second theorem even if your spacetime is not static (or rather stationary, to be pedantic). You will generally get a contribution from the gravitational field, which cannot be localized, but also - in contrast to the previous example - cannot be made to vanish because global inertial frames do not exist in general.

One should perhaps also mention that reactionless motion supposedly is possible in classical physics: It's been claimed that a body can change its position without ejecting any propulsive mass through a series of deformations in an inhomogeneous gravitational field. There's a cute name for this, 'swimming in spacetime'.

That's only if you view the metric separate from the rest of the physics though, when you include it the resulting (classical) field theory is invariant under time translations (see Hilbert-Einstein equations).

The fact that energy isn't conserved for a fixed metric is basically just what makes flybys capable of increasing the kinetic energy of a projectile.

http://archive.is/wo3JL

When you fall... you might not land on both feet at the same time...

I'm very happy that quantum gravity doesn't work.

Quantum describes matter and gravity as we know from GR is just shape of the spacetime. It would be horrible if same math ruled two so different things.

Math is abstract, which means it 'rules' many different things by its very nature. You can describe the geometry of space-time with vectors just as well as you can describe quantum state transitions. It's hard to make sense of what your objection could be here; the world works the way it does, and it is not good or bad whether we can describe it using unified mathematical frameworks or not.

> You can describe the geometry of space-time with vectors just as well as you can describe quantum state transitions.

I don't think that's true. Quantum description of gravity that has any aspirations to describe real world doesn't even get the math solid with irreducible infinites popping up everywhere.

As they should.

I just don't think shape of the spacetime is something that should be possible to quantize. It's just fundamentally different for me and expectation that it should be ruled by similar equations as other forces seems misguided.

Classical physics and quantum mechanics are already unified by shared mathematical frameworks. So not only is it possible, it's already been done, which is why people expect it to work for gravity as well.

Quantum mechanics is not so much unified with classical physics as it is more precise description of part of physics that degrades to clasical physics when you adjust parameters to get less detail.

Same way GR is more precise description of ANOTHER part of classical physics that reduces to classical physics if you adjust some parameters.

There's really no reason that GR should share with quantum model much more math than the simplest mathematical operations.

Why unify GR with quantum and not for example fluid dynamics?

GR and quantum field theory for me just describe completely different parts of physics.

Sure it would be neat to know how world behaves when neither GR nor quantum is sufficient to predict what will happen but I just think it's way more likely that unified theory will be quantum model with relativistic terms not the quantum description of gravity.

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