Quantum gravity is a gauge theory with the gauge symmetry spacetime diffeomorphisms. Presumably the quantum state of our universe is invariant under spacetime diffeomorphisms, including timelike diffeomorphisms. But I believe that these diffeomorphisms need not affect the conformal boundaries of spacetime.

The anthropic principle is a form of postselection on a quantum state, and postselection criteria have to be gauge invariant, otherwise, we end up with a quantum state which isn't gauge invariant. If anthropic postselection occurs in the "finite" "bulk" of spacetime, can that be made invariant under timelike diffeomorphisms?

If not, postselection can only occur at the conformal boundaries. If this post-selection doesn't happen at the big bang (which seems to moot the entire point of postselection--- selecting on current observations), does this mean that the only consistent post-selection is on a state defined on the future conformal boundary?

As far as I can see, the only form of the anthropic principle consistent with that is the final anthropic principle of Tipler and Barrow. This makes claims that intelligent life has to last forever, and other seemingly strange predictions. Is this type of post-selection required by diffeomorphism invariance?

  • $\begingroup$ GR can be formulated as a gauge theory with diffeomorphism invariance, however it is not at all clear that quantising this theory is the correct way to formulate quantum gravity. $\endgroup$ – John Rennie Jun 29 '12 at 10:56
  • $\begingroup$ The first sentence is a bit vacuous. As you are only talking about an approach to a problem, I'm afraid the sentence "We all know the moon is described to be made out of cheese" is an equally valid statement. $\endgroup$ – Nikolaj-K Jun 29 '12 at 12:13
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    $\begingroup$ I edited the question to remove "or is this disputed?" after every sentence, replacing it with "I think" where appropriate. I also tried to make the question clearer. I think it's a good question, but please roll back something if I misrepresented the idea. $\endgroup$ – Ron Maimon Jun 30 '12 at 2:53
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    $\begingroup$ This is a legitimate physics question... $\endgroup$ – Dilaton Sep 9 '12 at 22:30

This question confuses postselection as a conceptual act and postselection as a physical process.

Postselection as a conceptual act means that you are filtering a model or a computation in some way. Maybe you simulate the climate a thousand times and only keep those runs which behave plausibly. Maybe you calculate some probabilities and then condition them on something that you want to be true. Either way, postselection is just a computational step in extracting predictions from a model.

But in quantum computing, postselection has come to mean pruning a superposition by measuring it. You project the state of the quantum computer onto the subspace in which the postselection criterion is true. So here, uniquely, "postselection" has a physical meaning and not just a computational one.

"Anthropic postselection" could only be postselection in the first sense. For example, you might derive a probability distribution for possible values of the cosmological constant, and then you might condition that distribution on the existence of molecules, assuming that to be a prerequisite for the existence of "observers". The point is that there was no physical process which pruned the wavefunction of the universe, there was just a stage in your calculation in which you excluded from further consideration all the uninhabited possible states of the universe.

As for the remarks about diffeomorphism invariance and the conformal boundary... The usual argument is that there are no gauge-invariant local observables in quantum gravity, because of diffeomorphism invariance. We also have two examples - perturbative string theory in flat space, and string theory in anti de Sitter space - where there are local observables defined on the conformal boundary. In flat space, these are the properties of the asymptotic "in" and "out" states of the S-matrix; and in anti de Sitter space, they are the observables in the holographic dual, which is a field theory defined on the boundary. For asymptotically de Sitter space, there may be a dual theory defined on the future conformal boundary, but how to make that work is still an open problem.

Very occasionally this is taken to mean that the bulk space-time is not entirely real, and that only the boundary, infinitely far away from us here in the bulk, is truly real. I'd say that is definitely an interpretive mistake, and what one needs to do is to identify observables and states on the boundary which correspond respectively to definite properties of the bulk and definite histories of the bulk. The bulk is where we live and what we see around us, so if theory makes it seem less than real, that just means that our theoretical understanding is deficient. And there's plenty of work already on constructing approximately local bulk observables from nonlocal combinations of boundary observables, so we'll figure it out eventually.

The question wasn't saying that the boundary is more real than the bulk, but it was arguing that a certain type of physical process could only happen at the boundary, using the same argument about diffeomorphism invariance. So the counterargument also applies - this is a wrong interpretation of the relation between bulk and boundary.

  • $\begingroup$ This doesn't answer the question--- his question is how you find the map from bulk to boundary not to define things as "real" (whatever that means) but to even make a statement of the form "the universe has to be so and so big in order for life to evolve". $\endgroup$ – Ron Maimon Jul 30 '12 at 15:21

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