BGV theorem

[lee_merrill]

It's a very significant caveat: Vilenkin from 1983: By "nothing" I mean a state with no classical spacetime. "Nothing" is a realm of unrestrained quantum gravity, a pre-geometric state in which all of our basic notions of space, time, energy, entropy etc., lose their meaning. (Quantum Cosmology Alexander Vilenkin Tufts Institute of Cosmology).

Yes, without space-time, the theorem does not apply.

Best wishes,
Lee

[JimL]

Says Einstein! As far as I understand him, space-time binds together space and time.

That is the time coordinate as it is understood of in our material universe. That doesn't tell us anything about anything outside of this universe.

And this is important for the BGV theorem, because it only applies when the universe is describable as space-time.

Correct, we have no empirical evidence concerning anything, including time, outside of this spacetime.

[shunyadragon]

I meant there is a proof, a theorem in this area of discussion.

This is not like a math theorem that is a theorem that has a proof. The BGV theorem is a hypothesis subject to falsification that is not subject to proof, and is subject to interpretation, and NOT universally accepted among scientists..

I'm not sure what you mean here.

Exactly what I posted. The BGV theorem applies in this interpretation if universes begin as time space began as a singularity from preexisting energy. Cyclic and Bllack Hole universes do not necessarily have a beginning.

Yes, though the one universe we know of is expanding without limit.

We do not 'know' that. Cyclic models say no.

Well, again, the BGV theorem provides a restriction on possible universe scenarios, it is not in itself a scenario.

Blessings,
Lee

Well again, again and again the BGV theorem is a hypothesis subject to falsification, interpretation, and NOT universally supported by physicists and cosmologists.

[Tassman]

Yes, without space-time, the theorem does not apply.

Again, as Vilenkin says: "Nothing" is a realm of unrestrained quantum gravity, a pre-geometric state in which all of our basic notions of space, time, energy, entropy etc., lose their meaning". In short, the BGV theorem begins in time space as a singularity from "nothing", i.e. "a realm of unrestrained quantum gravity".

[Roy]

And again, if the BGV assumption of on-average expansion is not satisfied, then the theorem does not apply. But if the universes on-average do expand, then any worldline under consideration cannot be infinite in the past.

Yes, without space-time, the theorem does not apply.

That's quite a retreat from your initial announcement that

Apparently even a succession of universes has to have a beginning!

[shunyadragon]

Yes, without space-time, the theorem does not apply.

Best wishes,
Lee

This a confusing statement. The BGV theorem does accept the time-space likely only exists in our universe and all possible universes beginning with the expansion of the universe from a singularity and not in the Quantum world outside the universes.

Pretty much all the different theorems of hypothesis for the cosmology of our universe and all possible universes are in agreement for accepting that space-time and expansion is an inherent nature of the universe.

[lee_merrill]

This is not like a math theorem that is a theorem that has a proof. The BGV theorem is a hypothesis subject to falsification that is not subject to proof, and is subject to interpretation, and NOT universally accepted among scientists.

Well, the theorem is accepted, the assumptions and conditions of the theorem are in dispute.

The BGV theorem applies in this interpretation if universes begin as time space began as a singularity from preexisting energy.

And where in the theorem does it say that?

We do not 'know' that. Cyclic models say no.

Though the expansion rate is increasing, what model says the expansion will someday stop?

Blessings,
Lee

[lee_merrill]

That's quite a retreat from your initial announcement ...

I don't know, I tried to express some caution by saying "Apparently..." The BGV theorem has minimal assumptions and conditions.

Blessings,
Lee

[shunyadragon]

Well, the theorem is accepted, the assumptions and conditions of the theorem are in dispute.

I do not believe the BGV theorem is not universally accepted, and yes it is obvious if the theorem is not universally accepted the assumptions and conditions of the theorem are in dispute.

Source: https://now.tufts.edu/articles/beginning-was-beginning

Does your theorem have any detractors?

There was a lot of debate about this. Most recently, Leonard Susskind of Stanford posted a paper to arXiv in which he said, even though the theorem is mathematically correct, if eternal inflation goes on forever, how likely is it that we are living right near the beginning? If inflation is eternal to the future, we are most likely to be very, very far from the beginning. And if we live very, very far in the future from the beginning, then almost all traces of the beginning are erased from our surroundings. So, says Susskind, we cannot really detect anything about the universe’s origins observationally.

Since then, we had some discussions, and he [Susskind] posted a second note to arXive saying, actually, not all information about the beginning of the universe is erased. There are some indications that, in principle, evidence about the beginning could be observed.

© Copyright Original Source

And where in the theorem does it say that?

First, the BGV theorem makes no assumption of an absolute beginning.

Second,

Source: https://arxiv.org/pdf/gr-qc/0110012.pdf

Inflationary spacetimes are not past-complete
Arvind Borde,1, 2 Alan H. Guth,1, 3 and Alexander Vilenkin


What can lie beyond this boundary? Several possibilities
have been discussed, one being that the boundary
of the inflating region corresponds to the beginning of
the Universe in a quantum nucleation event [12]. The
boundary is then a closed spacelike hypersurface which
can be determined from the appropriate instanton.
Whatever the possibilities for the boundary, it is clear
that unless the averaged expansion condition can somehow
be avoided for all past-directed geodesics, inflation
alone is not sufficient to provide a complete description of
the Universe, and some new physics is necessary in order
to determine the correct conditions at the boundary [20].
This is the chief result of our paper. The result depends
on just one assumption: the Hubble parameter H has a
positive value when averaged over the affine parameter
of a past-directed null or noncomoving timelike geodesic.
The class of cosmologies satisfying this assumption is
not limited to inflating universes. Of particular interest is
the recycling scenario [14], in which each comoving region
goes through a succession of inflationary and thermalized
epochs. Since this scenario requires a positive true vacuum
energy ρv, the expansion rate will be bounded by
Hmin =p

8πGρv/3 for locally flat or open equal-time
slicings, and the conditions of our theorem may be satisfied.
One must look carefully, however, at the possibility
of discontinuities where the inflationary and thermalized
regions meet. This issue requires further analysis.
Our argument can be straightforwardly extended to
cosmology in higher dimensions. For example, in the
model of Ref. [15] brane worlds are created in collisions
of bubbles nucleating in an inflating higher-dimensional
bulk spacetime. Our analysis implies that the inflating
bulk cannot be past-complete.

© Copyright Original Source

Though the expansion rate is increasing, what model says the expansion will someday stop?

Blessings,
Lee

The cyclic model of our universe and all possible universes. https://www.accessscience.com/conten...heory/YB090037

[shunyadragon]

And where in the theorem does it say that?

To add the referenced article in the previous post does not describe an alternative to a greater cosmos without preexisting energy that would begin from absolute nothing.

[lee_merrill]

Source: https://now.tufts.edu/articles/beginning-was-beginning

Does your theorem have any detractors?

...

Since then, we had some discussions, and he [Susskind] posted a second note to arXive saying, actually, not all information about the beginning of the universe is erased. There are some indications that, in principle, evidence about the beginning could be observed.

© Copyright Original Source

This seems to indicate that Susskind is retracting his initial protest.

First, the BGV theorem makes no assumption of an absolute beginning.

Yes, agreed.

Source: https://arxiv.org/pdf/gr-qc/0110012.pdf

Inflationary spacetimes are not past-complete
Arvind Borde,1, 2 Alan H. Guth,1, 3 and Alexander Vilenkin

Whatever the possibilities for the boundary, it is clear
that unless the averaged expansion condition can somehow
be avoided for all past-directed geodesics, inflation
alone is not sufficient to provide a complete description of
the Universe, and some new physics is necessary in order
to determine the correct conditions at the boundary [20].
This is the chief result of our paper.

© Copyright Original Source

That's different than I had understood.

Source: arXiv

The class of cosmologies satisfying this assumption is
not limited to inflating universes. Of particular interest is
the recycling scenario [14], in which each comoving region
goes through a succession of inflationary and thermalized
epochs. Since this scenario requires a positive true vacuum
energy ρv, the expansion rate will be bounded by
Hmin =p

© Copyright Original Source

And this seems to say that cyclic universes are addressed by their theorem.

The cyclic model of our universe and all possible universes. https://www.accessscience.com/conten...heory/YB090037

So how do they get around the second law of thermodynamics? Eventually usable energy goes to zero.

The BGV theorem applies in this interpretation if universes begin as time space began as a singularity from preexisting energy.

And where in the theorem does it say that?

To add the referenced article in the previous post does not describe an alternative to a greater cosmos without preexisting energy that would begin from absolute nothing.

I'm not sure what you are saying here--as I understand it, the theorem assumes a space-time universe that is on average expanding, there is no other assumption about preexisting energy etc.

Blessings,
Lee

[shunyadragon]

This seems to indicate that Susskind is retracting his initial protest.


Yes, agreed.

Source: https://arxiv.org/pdf/gr-qc/0110012.pdf

Inflationary spacetimes are not past-complete
Arvind Borde,1, 2 Alan H. Guth,1, 3 and Alexander Vilenkin

Whatever the possibilities for the boundary, it is clear
that unless the averaged expansion condition can somehow
be avoided for all past-directed geodesics, inflation
alone is not sufficient to provide a complete description of
the Universe, and some new physics is necessary in order
to determine the correct conditions at the boundary [20].
This is the chief result of our paper.

© Copyright Original Source

That's different than I had understood.

Source: arXiv

The class of cosmologies satisfying this assumption is
not limited to inflating universes. Of particular interest is
the recycling scenario [14], in which each comoving region
goes through a succession of inflationary and thermalized
epochs. Since this scenario requires a positive true vacuum
energy ρv, the expansion rate will be bounded by
Hmin =p

© Copyright Original Source

And this seems to say that cyclic universes are addressed by their theorem.


So how do they get around the second law of thermodynamics? Eventually usable energy goes to zero.


I'm not sure what you are saying here--as I understand it, the theorem assumes a space-time universe that is on average expanding, there is no other assumption about preexisting energy etc.

Blessings,
Lee

I cited the authors conclusions. We are not talking about assumptions. I also cited the detractors, despite your selective. If you want to know how those who propose cyclic universes read their works that are published and asked them. There are still peer reviewed published proposals for cyclic universes despite your objections.

Your playing wiggle worm to justify your religious agenda.

[lee_merrill]

Well, I wanted to discuss the BGV theorem, it seems that has been done, so we can leave it at that.

Blessings,
Lee

[Mountain Man]

Apparently even a succession of universes has to have a beginning!

Of course. An infinite number of past causes leading up to the present is literally impossible.

[shunyadragon]

Of course. An infinite number of past causes leading up to the present is literally impossible.

Individual past causes whether finite or infinite (Complete [sets of infinities] or actual infinities) cannot limit potentially infinite nature of our physical existence, whether our physical existence is infinite or not. Our physical existence is potentially infinite, but it is unknown whether it was or is not. It is possible to have infinite sets of infinite causes within a potentially infinite physical existence.

Aristotle was probably the first to understand this.

Source: http://sites.middlebury.edu/fyse1229pisapati/mathematical-work/potential-infinite-v-actual-infinite/

Potential infinity - The potential infinite is a group of numbers or group of “things” that continues without terminating, going on or repeating itself over and over again with no recognizable ending point. What distinguishes the potential infinite and gives it the characteristic of being “potential” is the idea that if one were to take a sliver, or examine just one isolated portion of that infinite set of numbers, one would be able to capture or observe a finite set of numbers. The obvious example is the the grouping of natural numbers. No matter where you are while listing or counting out natural numbers, there always exists another number to proceed the one before. Also, a geometric line with a starting point could extend on without end, but could still be potentially infinite because all one would have to do is add on more length to a finite length to allow it to extend.

© Copyright Original Source