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From the Book 'In Search of Schrodinger's Cat':

Coordinates in space-time represent position; causality depends on knowing precisely where things are going, essentially on knowing their momentum. Classical theories assume that you can know both at once; quantum mechanics shows us that precision in space-time coordination has to be paid for in terms of uncertainty of momentum, and therefore of causality. The general theory of relativity is a classical theory, in this sense, and cannot be regarded as the equal of quantum mechanics as a fundamental description of the universe.

Here it says that because The General Theory of Relativity is a Classical Theory, it does not completely agree with Quantum Mechanics (as QM does not agree with Classical Mechanics).

Is this true - and if so, which theory is the better of the two at explaining the universe?

Qmechanic
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zordman
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  • Related: http://physics.stackexchange.com/q/387/2451 and links therein. – Qmechanic Dec 17 '14 at 17:27
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    There are a million articles on the issues involved with reconciling GR and QM lurking out there in Googlespace just a quick search away. As it stands this is far too broad a question to be usefully answered here. If you want to do a bit of reading around this area we'd be happy to help with any technical issues. – John Rennie Dec 17 '14 at 17:28
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    GR explains the universe at large fairly well, QM explains the small stuff. Where both break down is where the small stuff becomes extremely dense. We don't have a theory for that. Period. – CuriousOne Dec 17 '14 at 17:37
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    Also related: http://physics.stackexchange.com/q/71568/. You seem to be asking a lot of questions in a hurry without even researching them on this site. Seriously, don't expect us to do your work for you. – dmckee --- ex-moderator kitten Dec 17 '14 at 17:48

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It is not true that these theories cannot coexist.

To put things in context: Ever since Newton's time we have been thinking of things taking place in locations in space and time. Special relativity (SR) showed us that these are connected, and we really should be thinking of spacetime as the theater in which we live. General relativity (GR) simply gave some subtle extra structure to spacetime, but nothing fundamentally changed.

Parallel to this, quantum mechanics (QM) is a theory of linear operators acting on states, yielding measurements. The set of states in a given situation (the ubiquitous Hilbert space) is not physical space, but is another way of organizing the universe. In fact, QM has little to do with space(time) -- we can and often do formulate physical scenarios in QM without reference to space or time. Sometimes QM makes reference to where/when things take place, but it is not beholden to spacetime.

If you do want to mix QM with some notion of space and time, you can construct a quantum field theory (QFT), where the Hilbert space consists of fields (i.e. functions defined on spacetime). Usually this is done explicitly incorporating SR rather than starting with Newton's space.

But you can go further. One can have a QFT defined on the curved spacetime of GR. The equations can be a mess, but it's certainly doable. In fact, QFT+GR is how we derive the Unruh effect, more famously known as Hawking radiation.

Ultimately, QM is about measuring physical systems, while GR provides the setting in which we like to place those systems. They are complimentary in what they seek to do, so it doesn't make sense to ask which is fundamentally better.

There is tension between the two theories, but it comes from attempts to make spacetime itself behave like a quantum field. But if you are in a regime where effects like that can be neglected (i.e. most everything we have access to in the universe), then you can have a non-quantized spacetime hosting whatever quantum effects you want.

  • The real problem is that none of this shoehorning of these two theories that describe the world in rather contradictory terms has yielded any testable results. If anything there may be indications that naive predictions about the existence of a Planck scale seem to be wrong by many orders of magnitude, at least if we put a little more weight on some cosmic x-ray and gamma-ray measurements than they probably deserve at this point. – CuriousOne Dec 17 '14 at 17:43
  • @CuriousOne: that's not true. Hawking/Unruh radiation is a testable (in principle) prediction. – John Rennie Dec 17 '14 at 17:44
  • @JohnRennie: Hawking/Unruh radiation is basically a semi-classical/thermodynamic effect. It happens at all accelerations and tells us nothing about the Planck scale or the quantum regime near a singularity. That black holes have to have a temperature follows from the third law of thermodynamics... it doesn't even take GR to guess that correctly. – CuriousOne Dec 17 '14 at 17:48