Monday, January 10, 2005

The Emergence of Time, What Lies Beneath?

The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated.

Taken in context of how supersymmetrical levels could have ever been reached, is really a wonderful thnng to consider. If singularities were to be devised in methods that would experiementally bring forth blackholes at the microstates. Then what value is derived from learning about high energy and the levels we must go through to speak about these singularities?

From classical discritpion of GR to the understanding that supergravity could have ever been devised as a method to live in supersymmetrical worlds, would have been a challenge indeed, and we might ask where would time would begin, and what was below time?

The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation. The no boundary hypothesis also predicts that the universe will eventually collapse again. However, the contracting phase, will not have the opposite arrow of time, to the expanding phase. So we will keep on getting older, and we won't return to our youth. Because time is not going to go backwards, I think I better stop now.
by Stephen Hawking

It becomes very difficult then for anyone to accept that Robert Laughlin might have "wondered" about about condensed matter physics to have wonder what the building blocks shall be at such levels? That he might have wanted to stay to discrete structures for explanations as far as he could tell experimentally?:)

Likewise, if the very fabric of the Universe is in a quantum-critical state, then the stuff that underlies reality is totally irrelevant-it could be anything, says Laughlin. Even if the string theorists show that strings can give rise to the matter and natural laws we know, they won't have proved that strings are the answer-merely one of the infinite number of possible answers. It could as well be pool balls or Lego bricks or drunk sergeant majors

You see this is okay. That one can direct their attention to such infrastructures to ask, what the ultimate building block shall be, that we constantly refocus our mind to the finer things(abstract mathematical forays into these fine building blocks), only to find, we have progress well into the cosmological view, of such microstates?

"The path integral is taken over metrics of all possible topologies, that fit in between the surfaces. There is the trivial topology, the initial surface, cross the time interval. Then there are the non trivial topologies, all the other possible topologies. The trivial topology can be foliated by a family of surfaces of constant time. The path integral over all metrics with trivial topology, can be treated canonically by time slicing. In other words, the time evolution
(including gravity) will be generated by a Hamiltonian. This will give a unitary mapping from the initial surface, to the final.

But to follow is this what Peter Woit thinks?

Peter Woit said--?His argument is in Euclidean quantum gravity, which he describes as "the only sane way to do quantum gravity non-perturbatively", something which some might disagree with. What he seems to be arguing is that, while it is true you get information loss in the path integral over metrics on a fixed non-trivial black hole topology, you really need to sum over all topologies. When you do this you get unitary evolution from the trivial (no black hole) topology and the non-trivial topologies give contributions that are independent of the initial state and don't contribute to the initial-final state amplitude.

I guess what this means is that he is claiming that, sure, if you knew you really had a black hole, then there would be a problem with unitarity, but in quantum gravity you don't ever really know that you have a black hole, you also have to take into account the amplitude for not actually having one and when you properly do this the unitarity problem goes away.

You must accept my humble apologies, but to have been given these directions(quotes analogies in reference links and statements, from both Lubos Motl and Peter Woit, I wonder about the difference in their interpretations of the mathematics they are using? Are they so fundamntally at odds with each other, that they do not realize that they are working very close in their idealizations?

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