# Vilenkin's proposal

#### agnostictheist

Hi all,

I have a question according to Vilenkin's proposal using GR one borrows the notion that geomerty is not fixed can be distorted, he then goes on to argue that one of the sets or distortions of geomerty is empty thus no geomerty (absolute nothingness) is that truely possible? I thought that geomerty defines structure and i assume it does this via points and relationships between points (eg lines) if what i say is true then how can one have a geomertry of compele nothing ??!!! surely something is required for geomerty, even a hole what can be considered nothing, as a boundary which has something and thus has some difinative shape.

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#### hellfire

I am not going to answer your question because I am also confused with that. There is a paper in which Vilenkin explains his proposal in a very simple way: http://arxiv.org/gr-qc/9812027 [Broken].

Take a look to equation (8). May be you know what the path integral is. You can compute probabilites for quantum processes summing over all possible paths which go from the initial to the final state. For example, in the double slit experiment one must consider both possible paths of the electron through both slits. If one adds a new slit, a new path must be considered between the initial an the final state. It seams that this technique is used for quantum gravity also, and one calculates transition probabilities between different three-geometries. As far as I know, this follows from a hamiltonian formulation of general relativity. The dynamic variable is not the four-dimensional metric but the spatial three-dimensional metric because one splits spacetime in non-intersecting spatial hypersurfaces for each value of time. Well, this whole thing is above my level and I am also not sure to understand what (8) actually means.

But coming back to your question. It seams that Vilenkin writes in eq. (8) a path integral for the transition between the state he calls "nothing" and a state with a definite three-geometry. The state "nothing" is defined as g = 0. The question is what g = 0 actually means. If g would be the four-dimensional metric (let's differentiate between guv and gik for four and three dimensions) this would make no sense, because, as far as I know, guv = 0 has no physical meaning. You cannot have guv = 0 in general relativity because other quantities in the theory would not be well defined. However, the question is what gik = 0 means... May be this is a question for the quantum gravity forum.

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#### agnostictheist

re

hi Hellfire:

fristly I think I better say a bit more -in the least whats confusing me the question in my veiw, is what is or what accounts for a geometery!? I personally don't see how a geomeretry can be deviod of all, even surfaces are something, and i dare say surfaces are constructed with points, conectors eg lines and boundarys. thats hardly nothing. even if by emty set of geomertry he meant nothing on it, would thismean there is no energy matter? etc...and in fact he seems to suggest from what i have reAD ( I will read the link later) in this empty geometery there are not even points there is utterly nothing!!. - i am far from mathmatically minded so HELP!

you say:

"For example, in the double slit experiment one must consider both possible paths of the electron through both slits. If one adds a new slit, a new path must be considered between the initial an the final state"

from as far as i can tell intergals are merely the sum over histories, and how things evolve from A to B.

I've read that path integrals are forumlated in 4 spatial demensions and then one can convert one of those into time. (imginary time)

which reminds me can anyone help me in ways of thinking about instantions!? they apparentaly do not arise in spacetime, and thus they are spontanous. would it be right to thus say they simply are there? or that they are in a sense an effect that is simultanous? - do they poses energy? (from what i can tell thats yes to the last question)

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