Hive Mind Query - General Relativity link to Quantum Physics

Serendipity

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Query - as I understand it general relativity is based on spacetime being continuous while in quantum physics it has discontinuities. Has there been any theories developed to somehow come up with a theory to cover both the continuity and discontinuities?
 

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Thanks for this - as you effectively say - this is all dependent on the massless spin-2 graviton particles existing of which I understand there is no experimental evidence as yet.
 

Stephen Palmer

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Query - as I understand it general relativity is based on spacetime being continuous while in quantum physics it has discontinuities.
I don't think discontinuities is the right word to use. Rather, QM is rooted in random chance - for instance, the chance creation of two particles, which usually then annihilate one another. Can I recommend you watch the terrific two-part series by Jim al-Khalili on QM, which was one of the best science programmes recently broadcast by the BBC!
 

tegeus-Cromis

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I don't think discontinuities is the right word to use. Rather, QM is rooted in random chance - for instance, the chance creation of two particles, which usually then annihilate one another. Can I recommend you watch the terrific two-part series by Jim al-Khalili on QM, which was one of the best science programmes recently broadcast by the BBC!
Actually, the notion of discontinuity is built into the very notion of quanta. As energy can only be an integer multiple of a quantum, it cannot be described by a continuum. You cannot have half, or say 1/π, of a photon, and an electron in an atom can only occupy certain discrete energy states. There are no in-between states, so it's discontinuous.
 

Venusian Broon

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Query - as I understand it general relativity is based on spacetime being continuous while in quantum physics it has discontinuities. Has there been any theories developed to somehow come up with a theory to cover both the continuity and discontinuities?

Assuming we are just talking about the space-time both theories use as the OP stated- this has nothing to do with the energy states of particles.

If anything General relativity is the one with 'discontinuities' because it allows things like singularities and closed time-like curves. Quantum mechanics on the other hand has a sort of 'backdrop' spacetime - a simple Euclidean 'stage' that the particles act out their interactions, so I'd say that QM space-time was actually always handled as continuous.

However it may be that you are thinking about the idea of the Planck-length spacetime, that makes a smallest 'bit' of QM spacetime because of fundamental limits at trying to measure spacetime at those levels (i.e. we end up expending so much energy that we create black holes.) Whereas GR does not have such a problem as it doesn't model the microscopic at all.

Now there are some theories that assume that is the reality - that the universe is effectively made up of these discrete bits and they are real, possibly even observable if we are in fact in tha hologram universe (but that's another story...) So then the universe is some sort of giant QM computer built from these bits. But other QM theories still assume that space-time is continuous, just that on scales below the Planck length are completely inaccessible for measurement.

However remember both theories are incomplete. General relativity breaks down on the small scale and cannot explain QM observatoins, plus it forms these singularities which my guess is, will disappear in a unified theory. Whilst Quantum mechanics can't handle the gravity force nor the large scale structure questions.

A new theory of everything will hopefully shed light on what is a better model of reality and whether space-time is continuous or discontiuous, as it should provide a new model.

EDIT: i.e. Some approaches such as Causal Dynamical Trigulations have a fascinating properties that on the extremely small scale, spacetime for quantum particles drops from fourth dimensions to two. My basic understanding is that the two 'extra' dimensions do not dissappear, btw, so it's not really a discontinuity in a 'real' sense, but more of a observational/measurement thing. Interestingly other approaches come to the same conclusions with respect to this dimensionality.
 
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Venusian Broon

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Oh I should point out (before I go out into the garden and lift weights :) ) both of these theories suffer from the problem that they have to assume that the space-time each uses just exists - they have to add it in as an axiom. Space-time does not 'drop out' of the theory as a result of more fundamental considerations. So it is probably no surprise that each theory makes versions of space-time that are incompatible with each other - given that each theory was developed with different 'scope'. Einstein in no way tried to incorporate the results that were coming out on wave-particle duality in General Relativity (and anyway didn't believe the Copenhagen interpretation), and Quantum theory was never developed to probe the large-scale structure of the universe.

Again some interesting work, like CDT above and numerous other approaches are trying to rectify this!
 

Venusian Broon

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EDIT 2. Another thought popped into my mind. Another major difference between the two theories is that with General Relativity, mass curves spacetime. And curved spacetime has an effect on mass. There isn't such a loop in classical Quantum mechanics, QM mass does not curve its spacetime!
 

Ashley R

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I recommend following Sabine Hossenfelder's blog: Back Reaction:


She's a charming commentator on all things physics from the perspective of a physicist.
 

Venusian Broon

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I recommend following Sabine Hossenfelder's blog: Back Reaction:


She's a charming commentator on all things physics from the perspective of a physicist.
Some of us are trained as physicists too ;)

EDIT Sabine is great though and I concur with your recommendation. Prefer her Youtube videos. I think it unlikely though she will come down and have a chat with us!
 
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Venusian Broon

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After discussing her, Sabine might help answer some of the issues brought up here! Here she uses the word discrete rather than discontinous, but it's the term/technicality that I think the OP was meaning. She states at the end, that a theory of quantum gravity does not necessarily mean that space and time has to be discrete. Which I agree with.


With regards to 'theories to cover both continuities and discontinuties', well the obvious solution is that if space-time is actually discrete it is discrete on such a small scale - say the Planck length of 1.6 x 10-35 metres that we can never get even close to observing this granuality, so that for all intents and purposes 'local' patches of space-time can be treated as continuous. And thus we wouldn't have to worry too much about it. Unfortunately then, it would mean that it is impossible to test discrete space-time theories as we will never be able to observe on small enough scale to prove them.

The one caveat to this I can think of, is that it might be possible to observe a discrete universe if we are a 'hologram universe', via a sensitive enough gravity wave experiment.
 

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