Answerer

Guys, are there any good reasons that spacetime must be quantized? Because it seems to me that if the spacetime is quantized, it must have a wavefunction as well.

Beer God

Yes there is indeed a "quantum foam theory" and it is different to what people mean by quantum foam, it deals with emergent universes being connected, if I remember correctly.

Certainly the apparent lack of quantum foam will also go along way to dispel that contingent of scientists who still believe in black holes.

fando

Yes, plenty. Gravitons, the quanta of gravity, are quantum ripples in spacetime. There's your wavefunction. Also, string theory and loop quantum gravity predict a quantized spacetime. There is even evidence under some theories that spacetime is quantized. In particular, quantized space time would result in neutrinos having mass, something that has been experimentally verified. (Well, there's an upper bound to the mass.) Here's a paper on that. (arXive rocks!)

That's news to me. The stuff I'm talking about is more of a pertubation thing than outright metaphysics. It could be better described as "Planck Scale Phenomenology" as the papers put it. I'll adopt that terminology from now on to reduce confusion. Could you provide a reference to the theory you're referring to?

Are you suggesting that black holes don't exist?

Beer God

The beginning of the universe

There should be better sites, but this was the first I came across.

And while many, including myself, believe in the theory of black holes and the maths behind it to be rather silly, there is still a contingent, albeit one that is getting smaller, that think black holes do exist. For an interesting, but dull read on the topic of black holes and quantum foam, I suggest:

Geons, Black Holes, & Quantum Foam: A Life in Physics
by John Archibald Wheeler Kenneth Ford

theyeti

My understanding is that strings, since their size is the planck length, are large enough not to be affected by the quantum foam. Since strings are fundamental, and all particles and force charges are derived from their vibrational patterns, the foam is simply irrelevant. So you wouldn't expect to see the foam affecting anything if string theory is true.

theyeti

Jesse

I had thought that string theory assumed a continuous flat background space-time just like other quantum field theories, and that this is one of the things that advocates of other approaches to quantum gravity sometimes criticize about it. But it's also my understanding that because of all the mathematical subtleties in string theory/M-theory, it's not impossible that it could turn out to be compatible with a discrete space-time after all. As for quantum foam, I'm not sure if it assumes discrete space-time or if it assumes continuous but curved space-time.

Answerer

Yeah but why( I mean the math's part)?

Demosthenes

The simplest answer is because the equations describing black holes have singularities in it. To be more specific, those signularities exist because the general relativity equations blow up at the center of the black holes. Yes, very massive objects with properties matching the mathematical black holes exist in the universe but to believe that they actually are identical to the idealized black holes is rather silly.

The so called singularity is where the mass and the energy become infinite, but that's simply absurd. Where did the infinite mass and energy come from? The reason why infinities pop up is because we lack a comprehensive theory with a set of equations allowing us to describe what goes on within a event horizon. The best we can do right now is to describe external features that can be experimentally verified.

Jesse

I believe you're wrong about this--the density of mass and energy may become infinite at a singularity (along with the curvature of spacetime) but the mass and energy themselves do not, as far as I know. I'm not sure if it makes sense to talk about "the mass of a singularity", but if it does then I suspect it would be the same as the mass of the object that collapsed to form a black hole, in which case there's no need to worry about where any extra mass "came from".

If one believes that spacetime is continuous and can contain features at arbitrarily small magnitudes (as those who postulate a 'quantum foam' may in fact believe), I don't see why one should necessarily think there is something impossible or pathological about singularities. If one thinks spacetime will turn out to be discrete in our final theory of quantum gravity, though, that would be a good reason to be doubtful about the existence of singularities.

NumberTenOx

If your model of a lepton or a quark is an infinitely small point, then at some radius, as you get closer and closer, the gravitational effects become large and your particle becomes a black hole all by its tiny self.

Clearly our theory of gravity does not work well at very small distances. Apparently attempts to make a QM theory of gravity are underway. String theory gives particles a minimum radius, so this problem disappears.

When we understand how particles keep from being singularities, we might know more about the singularities in the middle of massive black holes.