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

G.S.RAMYA

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?

Mark M

Hi,

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 non-local, 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.

Chalnoth

This isn't true. It's pretty trivial, in fact, to show that it is not possible to transmit information in QM faster than light. The apparent non-local effects are just that: apparent. They are not real.

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 space-time 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 non-obvious.

D H

This isn't correct. The problem with the mathematics is that physicists don't know how to combine general relativity and quantum mechanics. There is one place where the mathematics of each can be used to compute the same quantity, the vacuum energy density. General relativity yields a tiny value while quantum mechanics yields a huge value. The two differ by a factor of about 10¹²⁰.

This, too, is incorrect. Quantum mechanics assumes spacetime is continuous. Spacetime is not quantized in quantum mechanics.

Also incorrect. Here you are talking about special relativity, not general relativity. Quantum mechanics and special relativity have been merged in quantum electrodynamics.

Chalnoth

You can't compute the vacuum energy from General Relativity. The vacuum energy is an input parameter in GR, not a computed number.

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).

Though to be fair, it is often thought likely that space-time is quantized in the true theory of quantum gravity (whatever that theory happens to be).

Mark M

Don't they also disagree on singularities? The equations of GR give infinite density, I thought QM suggested that they can have an actually size, such as the Planck Length.

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.

Thanks for correcting that, I should have said the gravitational field is continuous in GR, but it is quantized into gravitons in QM.

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.

Nabeshin

Well the story goes like this. If you imagine compressing something (a star, the universe) down and down, GR holds just fine, and QM is unimportant. At least, until you get to the planck length. The planck length is precisely the dimensionful length you would expect when gravity and quantum effects are both necessary to describe the situation. So in a sense, we can only believe our GR solution down to the point where the object has compressed down to the planck scale. Beyond that, we obviously need quantum gravity, but as far as what QG will say on the matter, nobody knows (could be there is still a singularity!).

Mark M

Thanks for clarifying that!

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.

Chalnoth

Well, the Planck length is the length at which we can be very sure that General Relativity breaks down. But I'd be very, very surprised if it didn't break down long before that in reality.

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

Nabeshin

Of course, you start getting large deviations from GR before the planck length. How nonsensical these predictions are is impossible to know without an accurate theory of QG, so all we can really say is what you say: At l_p, we're almost positive GR is not a correct description.

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.

Chronos

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.

sahmgeek

This is a point in theoretical physics that really puzzles me. Why assume that the math is wrong when it yields infinity? Just b/c infinity does not occur in nature as we experience it does not make it nonsense as it relates to the TOE. Isn't it likely that by ignoring this conclusion you may be disregarding one of the biggest pieces of the puzzle?

sahmgeek

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

dkotschessaa

I know a "guy on the internet" (who is usually a quack but sometimes makes good points) who claims that Cantor proved that "infinity is nonsense" and so dismisses any theory that yields infinities or anything in cosmology described as infinity (such as the idea that the universe might be infinite. A fact physicists usually stop short of saying.)

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

bapowell

So how should we "perceive" infinite spatial curvatures of the kind that result from metric singularities? If our physical theories no longer align with our perception of reality, then are we doing science?

dkotschessaa

Of course. If science was about perception then we'd still be living in a geocentric model on a flat earth on the backs of turtles (ok maybe not the turtles, I haven't seen them). Don't you think? or did you mean something else?

-DaveK

bapowell

No, I don't. I actually have no idea what you mean.

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.