# quantizing relativity

AFAIK, there is no viable theory of quantum gravity.
True, there is Superstring theory ( relativity extended to 11-25
dimensions), but that exists only on paper: no quantum effects
have been observed.

Relativity is a continuum mechanics theory. Space, time, and mass
are assumed to be continuous: from infinitely large to infinitely
small.

Why can’t we simply quantize the continuae? Convert the
variables of space, time, and mass as functions of Planck Distance,
Planck Interval, and Planck Mass, repectively.

If only it were that easy.

Quantization is not simply changing your units to those based from fundamental quantities. Quantization comes about by solving the relevant equations with appropriate boundary conditions, and then finding that certain quantities can only have specific values.

The trick is coming up with a formulation that is consistent with the rest of physics. Many very smart physicists have spent years of their lives trying to do just that with gravitation.

Well, I knew I had read the other day that Physicists had dectected quantum effects of gravity recently. Amazing enough I remembered where.

http://www.sciam.com/news/011702/2.html

So, while we don’t have a viable quantum gravity theory… gravity appearently does come in quantized units. This is probably very reassuring to the theorists.

Well, at the very least I thought it was interesting.

This is a little different from “quantum effects of gravity”. The effects referred to in the cite do not require a fully quantum theory of gravity, nor are they a test of superstring theory or any other quantum theory of gravity. It is the neutron that is displaying quantum behavior, not the gravitational field itself.

The way I read it was that while it was the neutron displaying the quantum effects, it implied that they gravity was imparting the changes in energy in quantum units. Thus, implying that gravity also had a quantum nature.

I will admit it isn’t entirely clear to me, but interesting.

**Space, time, and mass are assumed to be continuous: from infinitely large to infinitely small.
**
That has only been the case because there was really no evidence to show that space & time are quantized. A recent Nature article discusses a paper that argues that we do have evidence for the non-continuity of space and time.

http://www.nature.com/nsu/020304/020304-5.html

You can find the preprint of the actual paper here: http://xxx.lanl.gov/pdf/astro-ph/0202443

The recent work with neutrons isn’t even particularly new. I’ve seen descriptions of similar experiments in decades-old textbooks. We really aren’t seeing quantum effects of gravity there, just quantum neutrons, and we’ve known that neutrons are quantum-mechanical for quite a while now.

Part of the reason that we can’t just switch everything to fundamental units and be done with it is that we don’t know yet what those fundamental units would be. We have a hunch that if space turns out to be quantized, for instance, the quantum of space will be somewhere in the vicinity of the Planck length. But it would surprise nobody if it turned out to be half the Planck length, or pi times it, or some other number in that vicinity, and for all we know, it might be nowhere near the Planck length: That’s just a SWAG. We need the theory to get the quantum, not the other way around.

As for the paper rsa links, believe it or not, that’s not the most far-fetched explanation I’ve heard seriously put forward to explain the UHECR problem (Ultra High-Energy Cosmic Rays). The most plausible answer seems to be that there’s some nearby source or sources which we can’t detect any other way, but nobody’s too sure about any of the explanations at this stage of the game.

Chronos, I get your point about UHECRs, but what is the alternative explanation for very-high-energy gamma rays from “blazers”? I gather in this case we can identify a source for the gamma rays which would rule out some closer source.

I’m not sure what the best explanation is for blazers… Note that I said that “unknown source” was the best available explanation for UHECRs, not that it was a good explanation. We don’t have any really good explanations yet, just some that are less bad than others.

In Chronos’s post on a different thread, he said that the
Kaluza-Klein theory…an extension of General Relativity describing
Electromagnetism by adding a fifth dimension to four dimensional
gravity…is not quantizable.

If Quantum Electro-Dynamics is quantizable, and describes the
same phenomenae as Kaluza Klein, Why not just make the
equasions equal to each other? After all, KK is 5D General
Relativity, while QED is Special Relativity*Quantum Dynamics.

Bump

K-K and QED don’t exactly describe the same phenomena: They only agree in the middle, so to speak. Things like the magnetic moment of the electron aren’t touched on at all by K-K, whereas QED can predict the value to something like 20 decimal places. The same methods used for QED have been tried for gravity, but fail horrendously. In quantum field theories, you end up with inconvenient infinities showing up in the equations, but with the other three forces, you can always “sweep them under the rug”, so to speak, in a process called renormilization. It turns out, though, that gravity is not renormalizable, which means that the infinities which show up can’t be ignored. I’m pretty sure that this is due to the non-linearity of gravity: The gravitational field contains energy, but that energy itself must create a gravitational field. Electric fields don’t have a charge, so QED does not have this problem.

I’ve heard about the non-renormalizationality of gravity and may
have an explanation of sorts:
The higher dimensions associated with electromagnetism, weak,
and strong nuclear forces are believed to be “Curled up” into a
space as small as the Planck Length, while the four dimensions
of spacetime extend to infinity. If spacetime were shrunk to the
order of the Planck Length…like within the vicinity of a quantum
singularity…quantum gravitational effects would be observed.