Could someone please explain, in layman's terms, yet very accurately, why quantum mechanics and general relativity are not compatible?
Could someone please explain, in layman's terms, yet very accurately, why quantum mechanics and general relativity are not compatible?
The moment an instant lasted forever, we were destined for the leading edge of eternity.
The basic problem is that general relativity is a theory that works on a smooth spacetime that allows you to talk about the (x,t) of an event, as if events could occur at a specific place and time. But in quantum mechanics, x is an observable, treated in the theory as an operator, while t is a parameter of the theory, such that observations come out differently at different t. What's more, neither x nor t take on exact values, because they cannot be measured exactly, and efforts to do so would change the outcomes of the measurement because any attempt to get x and/or t exactly would require introducing a huge amount of energy into the system. So the two theories have very different philosophies and languages, but they are still generally compatible at most scales. You just use GR to understand the nature of the spacetime (in particular, it's local curvature), and then you do QM on that spacetime, by which I mean, you decide how you are interpreting the t parameter, and then you use the spatial information left over from GR as a kind of input or boundary condition on your QM calculation. In this way, you can actually use QM and GR to obtain Kepler's laws of planetary motion, even though anyone in their right mind would use Galilean relativity with Newtonian gravity to do that.
Where you really run into a problem, though, is on the "Planck scale." That means, you want to understand what is happening when two point particles approach to within a "Planck length" of each other, let's say. GR has no difficulty describing that behavior, but QM says that to be able to talk meaningfully about two particles being so close together, you'll need enough energy present to create a gravity that would cause the spacetime to close on itself and become a black hole. So the spacetime cannot be meaningfully talked about on scales of the Planck length or smaller. You could just avoid those scales, and "coarse-grain" the GR by smoothing over larger scales, but then the spacetime doesn't behave quite the way GR says it does. I don't know that one cannot find ways around this problem, but QM expects the gravitational interaction to be mediated by spin-2 particles called "gravitons", and GR expects gravity to be a geometric effect on the spacetime. On the Planck scale, the two would work very differently, and no theory of gravitons has been worked out that actually functions correctly.
If I throw a ball up vertically it gets so far then comes back along the same path. A general relativitist says it is following a geodesic! Both ways! Ah well, they beleive if I learned all the mathematics of the subject I would see the beauty of it all and not ask impertinent questions. But someone did invent gravitons on a wet tuesday afternoon so the story may not be complete yet
In my mind there is a clear distinction between gravity being a geometric function of spacetime (as described in GR) and gravity being a force originating from particles "gravitons" (as described by QM) Which is correct and if both are correct, which is how I'm interpreting your explanation, how can they ever be reconciled?
As a layman, here is my ultra-simple understanding. This is from reading Brian Greene's The Elegant Universe. I book I highly recommend if you like (pop-)science without the calculus.
GR is a field theory, which means it is a smooth, continuous property - there is a value for g at every point in space, even points infinitesimally close together.
QM is based upon Heisenberg's Uncertainty Principle, which in essence states that as the position of a point (or two points) approaches zero, its momentum (energy) approaches infinity. In QM, space is essentially a quantum foam, full of hills and bumps and loops of vacuum energy (see image below). Because of HUP, the closer two hills are, the bigger they will be.
So, if we try to apply QM to GR, we have hills that can be infinitesimally close together, meaning their energy approaches infinity.
You essentially get transfers of infinite energy over an infinitely short distance.
(I've fumbled some of the technical terms such as 'momentum'. Been a decade or two since I read it. Perhaps someone could follow up with the correct terms.)
Google Image 'quantum foam'.
Last edited by DaveC426913; 2018-Apr-28 at 05:39 AM.
If we had a quantum theory of gravity based on gravitons, then it would have to be in agreement with GR because GR is consistent with observations (in the domains where GR is still applicable). So in that sense they would both be correct (and Newtonian gravity would still be correct within its domain).
This is why (most) philosophers of science (and some scientists ) agree that physics is not telling us what reality is, just describing how it behaves.
As for how they would be reconciled ... we don't know (yet) is the answer to that, I suppose.
Copernicus,
General relativity predicts black holes whenever the mass/radius ratio is too big, reaching approx c^2/G. The radius when this happens, the Schwarzschild radius is r=2GM/c^2
Black holes have singularities, a place of infinite density and traditionally in physics, infinities in equations have been a sign that something is going wrong with the theory, when applied to that domain. Usually in cosmology black holes are thought to occur at galactic centres etc... i.e places where the m term is large.
But in circumstances where the r term is very small, the m/r problem occurs again. This could happen on the quantum scale, as it deals with point particles.
It seems that nobody has a proper answer, maybe GR should be amended when m/r is large, maybe QM too in some way.
"...when you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes
My bold. I would not say wrong so much as incomplete. GR is in good agreement with observations under conditions where the quantum complications are negligible. As I think I understand it, some of our top physicists are mentally busting a gut in a quest to unify it with quantum mechanics in domains far removed from the domain in which it was derived. I wish them well.