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What is the conflict between General theory of relativity and Quantum theory? 
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#1
Mar1812, 04:25 AM

P: 3

General relativity and Quantum theory are two pillars of physics... The unified theory concept trying to combine 4 basic forces of nature. I don't know what is the actual conflict between gravitational force and other 3 forces?



#2
Mar1812, 08:47 AM

P: 526

There are many problems when trying to combine them, I'll explain a few. First of all, there's the mathematics. When trying to combine the formulas of GR and QM to calculate something, the same answer is always yielded: infinity, which is nonsense. Next there is the issue of spacetime curvature. In GR, spacetime is continuous and flat like a placid lake. But in QM, the Heisenberg Uncertainty Principle says nothing can have an absolute value. This also includes the gravitational field. Since the gravitational field is determined by the curvature of spacetime, that would mean on small scales, space would not be continuous and smooth, but rather would be violently curved and fluctuating up and down. Then, there is the problem of quantization. In QM everything can be broken down to basic particles, such as the quark, the photon, the gluon, etc. But in GR, spacetime isn't broken down into discrete packets, like QM claims. In QM, the universe is nonlocal, so events can effect each other instantaneously, even if they are light years apart. But GR says, like in classical physics, you must traverse the space in between to have an effect on an event. Also, in the standard model, particles are zero dimensional. Therefore, the moment and place the collisions between particles, say, and electron and positron, must be agreed on by every observer. But it is an important fact of relativity that certain events can be disagreed on by different frames of reference. 


#3
Mar1912, 04:48 AM

Sci Advisor
P: 4,782

Anyway, I thought I'd just list two other ways: 1. In quantum mechanics, time and space are a fixed background. The various quantum mechanical particles all interact with one another, but do not impact the behavior of the background. General Relativity describes the interaction between this background spacetime and matter. Taking this into effect, then, requires, at the very least, a massive rewriting of quantum mechanics, as it could no longer treat space and time as fixed parameters. Attempts to do this so far have largely failed (though loop quantum gravity and string theory are two candidate attempts). 2. In quantum mechanics, objects can exist in a superposition of states. General Relativity has no sense of superpositions. For example, a hydrogen atom may be in a superposition of the n=0 (ground) state and n=1 (first excited) states. These states have different energy. So if the atom is in a superposition of these two energy states, what is the gravitational field? Trying to put the gravitational field into a similar superposition of states doesn't work, at least not in the simple manner of doing this. So the answer is, at the very least, incredibly nonobvious. 


#4
Mar1912, 06:13 AM

Mentor
P: 15,067

What is the conflict between General theory of relativity and Quantum theory?



#5
Mar1912, 06:36 AM

Sci Advisor
P: 4,782

That said, yes, it is correct that the problem is that the combination of the two is ambiguous (such as the superposition of states situation I mentioned earlier). 


#6
Mar1912, 11:55 AM

P: 526

Also, trying to fit gravitons into general relativity also leads to ultraviolet divergences, without any way of renormalizing(except a theory of quantum gravity, of course.) For example, trying to use two gravitons in a Feynman diagram leads to infinite, nonsensical answers. Though, what I was trying to get at was that fact that at distances shorter than the Planck Length, the idea of smooth space vanishes in favor of violently curved quantum foam. 


#7
Mar1912, 12:15 PM

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#8
Mar1912, 01:42 PM

P: 526

Though, what I was trying to say was that standard QM (electromagnetic force, weak nuclear force, and strong nuclear force, no gravity) fails to renormalize GR's infinities in a singularity, because, like you said, at the planck length gravitons would be required, and standard QM can't handle graviton interactions. 


#9
Mar1912, 03:33 PM

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P: 4,782

Also, I don't think a singularity is physically possible, as a singularity is nonsensical. 


#10
Mar1912, 07:20 PM

Sci Advisor
P: 2,193

With regards to singularities, I agree that such a physical object is nonsense, but that's not what I said. Whatever theory of QG could still predict such a mathematical beast, just as GR did (assuming such a theory of QG is not some kind of 'ultimate theory of everything', but whatever that means is a long tangent). If the cosmic censorship hypothesis is correct, it could be reasonable that a physical description of such objects can never be made concrete, since they are doomed to remain forever within event horizons. On the other hand, of course (and this is more likely IMO), the theory could predict some other as of yet unknown behavior for the objects. 


#11
Mar2012, 05:39 AM

Sci Advisor
PF Gold
P: 9,387

In mathematical terms, a singularity is the value or range of values of a function for which a derivative does not exist. In more common usage a singularity is the point at which our models cease to be predictive. Most scientists view a singularity as a defect in the model as opposed to something tangibly infinite in some respect. One of the great successes of quantum theory was development of renormalization techniques that resolved the infinities that formerly plagued quantum field theory. Unfortunately, we have not figured out how to renormalize gravity.



#12
Mar2012, 06:51 AM

P: 65




#13
Mar2012, 06:56 AM

P: 65

Disregarding as accurate that which you can't understand, even after it's been shown to you, is like a dog chasing his tail.



#14
Mar2012, 08:05 AM

P: 598

I am familiar with Cantor's work on infinity, but I'm not sure that this is quite what he was getting at. He proved that there are different types or degrees of infinity, but I don't think this is the same as saying "infinity is nonsense." I'm also not sure of the relevance of his work to physics, though I have heard of "Cantorian space time." (No idea what it is) Lots of cool stuff to be explored here though I think. I'd be interested to hear what people think. Dave K 


#15
Mar2012, 08:56 AM

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#16
Mar2012, 09:39 AM

P: 598

DaveK 


#17
Mar2012, 09:43 AM

Sci Advisor
P: 1,676

EDIT: Sorry, that response was curt and unhelpful. What I mean to say is that science uses empiricism to form a representation of reality. You seem to be suggesting that we should suspend this correspondence in the face of mathematical singularities. 


#18
Mar2012, 10:13 AM

P: 65




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