BGV theorem

[Mountain Man]

Our physical existence is potentially infinite...

Potentially, yes, as an abstract mental exercise (notice that your source deals with numbers), but in actuality, an infinite number of past causes is literally impossible.

[Roy]

Potentially, yes, as an abstract mental exercise (notice that your source deals with numbers), but in actuality, an infinite number of past causes is literally impossible.

Perhaps you could grace us with your argument or proof of the above by way of a Xmas present to TWeb? I'd like to see if it applies equally well (or badly) to an infinite number of future effects.

[shunyadragon]

Potentially, yes, as an abstract mental exercise (notice that your source deals with numbers), but in actuality, an infinite number of past causes is literally impossible.

The potential of past infinity cannot be defined by numbers nor sets of numbers. There are no numbers on the nature of our physical existence. This is a human construct of actual infinities which are conceptual math sets from the human perspective, and cannot describe nor limit the nature of our physical existence. Math sets regardless of whether they they are sets of infinities or finite sets cannot define nor limit anything beyond the set.

[JimL]

Potentially, yes, as an abstract mental exercise (notice that your source deals with numbers), but in actuality, an infinite number of past causes is literally impossible.

You contradict your own belief. For instance, your notion of god is infinite, correct? So then, what practical difference is there between our universe being created from out of an infinite Cosmos or by an infinite god? There is no difference!

[shunyadragon]

So, an infinite regress of universes? But that is what the BGV theorem addresses.

Blessings,
Lee

No it does not. None of the scientists involved even remotely mentioned actual infinite regress. Nonetheless it was mentioned that there may be infinite sets of universes in the greater cosmos. Of course, the greater cosmos that contains all universes is potentially infinite.

[shunyadragon]

Potentially, yes, as an abstract mental exercise (notice that your source deals with numbers), but in actuality, an infinite number of past causes is literally impossible.

No . . . the actual infinities only apply to sets, and sets of actual infinities cannot by definition define anything else outside the given set. Your grasp of math is bogus.

There is no evidence that our physical existence can be defined as limited to an actual infinite set of universes.

[shunyadragon]

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

Contradiction, the theorem is not accepted by all. Yes, this includes the assumptions and conditions are in dispute.

And where in the theorem does it say that?

The conclusions of authors of the bgv theorem.

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

Blessings,
Lee

Yes in their view, the universe in a multiverse has a life span in a multiverse hypothesis. In cyclic universes no.

[shunyadragon]

And where in the theorem does it say that?

Singularity theorems of Hawking & Ellis (1973) cited by Vilenkin

[lee_merrill]

Contradiction, the theorem is not accepted by all.

Who does not accept the theorem? According to Vilenkin, the theorem is not in dispute.

... the assumptions and conditions are in dispute.

Agreed.

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

Yes in their view, the universe in a multiverse has a life span in a multiverse hypothesis. In cyclic universes no.

Maybe I should rephrase my question, how has the ever-increasing expansion of the universe been shown to stop?

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

Singularity theorems of Hawking & Ellis (1973) cited by Vilenkin

Searching for Ellis in the paper shows no results, though.

Blessings,
Lee

[shunyadragon]

Who does not accept the theorem? According to Vilenkin, the theorem is not in dispute.

Agreed.

No theorem is not in dispute. Steinhardt for one offers an alternative. IF as you agree the assumptions and conditions are in dispute, therefore the theorem is in dispute.

Maybe I should rephrase my question, how has the ever-increasing expansion of the universe been shown to stop?

Neither the infinite expansion of the universe nor the stop and contraction have been shown They at present both represent alternate hypothesis

Searching for Ellis in the paper shows no results, though.

Blessings,
Lee

I will provide another reference,but nonetheless Vilenkin acknowledged the singularity theorem in relation to the bgv theorem. Simply do a search bgv theorem singularity theorem.

[shunyadragon]

Who does not accept the theorem? According to Vilenkin, the theorem is not in dispute.


Agreed.


Maybe I should rephrase my question, how has the ever-increasing expansion of the universe been shown to stop?


Searching for Ellis in the paper shows no results, though.

Blessings,
Lee

I apologize,second hand reference and I may have got it wrong. The following reference should clear itup.

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

Inflationary spacetimes are not past-complete

Arvind Borde, Alan H. Guth, Alexander Vilenkin
(Submitted on 1 Oct 2001 (v1), last revised 14 Jan 2003 (this version, v2))

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.

© Copyright Original Source

. . . and again I may not have missed it.

[shunyadragon]

Who does not accept the theorem? According to Vilenkin, the theorem is not in dispute.


Agreed.


Maybe I should rephrase my question, how has the ever-increasing expansion of the universe been shown to stop?

Lee

As far as universes having a beginning including Steinhardt's cyclic universe is not the real issue concerning 'beginnings' in the nature of our physical existence. Pretty much all the physicists, cosmologists,and related sciences do not consider the beginning of our universe any sort of absolute beginning, and we have no evidence to think this is the case. Pretty much all these scientists believe there is sufficient evidence to support the multiverse existence.

Borde, Guth and Vilenkin support the view of the multiverse cosmology.

[lee_merrill]

Neither the infinite expansion of the universe nor the stop and contraction have been shown They at present both represent alternate hypothesis

I believe dark energy has been proposed to explain the accelerating expansion, what will counteract dark energy?

I will provide another reference,but nonetheless Vilenkin acknowledged the singularity theorem in relation to the bgv theorem. Simply do a search bgv theorem singularity theorem.

Well, I did, but the matches I saw were for the BGV theorem, which is also called the singularity theorem.

Blessings,
Lee

[lee_merrill]

As far as universes having a beginning including Steinhardt's cyclic universe is not the real issue concerning 'beginnings' in the nature of our physical existence. Pretty much all the physicists, cosmologists,and related sciences do not consider the beginning of our universe any sort of absolute beginning, and we have no evidence to think this is the case. Pretty much all these scientists believe there is sufficient evidence to support the multiverse existence.

References? From what I have heard, the Big Bang is the current view: "The Big Bang theory is the prevailing cosmological model for the observable universe from the earliest known periods through its subsequent large-scale evolution."

Borde, Guth and Vilenkin support the view of the multiverse cosmology.

Citations, please?

Blessings,
Lee

[shunyadragon]

I believe dark energy has been proposed to explain the accelerating expansion, what will counteract dark energy?

Your asking the wrong person. I personally do not believe that either expansion to the Quantum nothing is possible, or contraction where the point that dark matter no longer prevents contraction. Steinhardt could better answer your question.

Hawking also believed that contraction is possible without time reversal, and explained it in the following summary:

Source: http://www.hawking.org.uk/the-beginning-of-time.html

The no boundary proposal, predicts that the universe would start at a single point, like the North Pole of the Earth. But this point wouldn't be a singularity, like the Big Bang. Instead, it would be an ordinary point of space and time, like the North Pole is an ordinary point on the Earth, or so I'm told. I have not been there myself.

According to the no boundary proposal, the universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe.

Eventually, the period of inflation would have ended, and the universe would have settled down to a stage of more moderate growth or expansion. However, inflation would have left its mark on the universe. The universe would have been almost completely smooth, but with very slight irregularities. These irregularities are so little, only one part in a hundred thousand, that for years people looked for them in vain. But in 1992, the Cosmic Background Explorer satellite, COBE, found these irregularities in the microwave background radiation. It was an historic moment. We saw back to the origin of the universe. The form of the fluctuations in the microwave background agree closely with the predictions of the no boundary proposal. These very slight irregularities in the universe would have caused some regions to have expanded less fast than others. Eventually, they would have stopped expanding, and would have collapsed in on themselves, to form stars and galaxies. Thus the no boundary proposal can explain all the rich and varied structure, of the world we live in. What does the no boundary proposal predict for the future of the universe? Because it requires that the universe is finite in space, as well as in imaginary time, it implies that the universe will re-collapse eventually. However, it will not re-collapse for a very long time, much longer than the 15 billion years it has already been expanding. So, you will have time to sell your government bonds, before the end of the universe is nigh. Quite what you invest in then, I don't know.

© Copyright Original Source

I am not sure where this is going with the problem of not being past complete, as in the beginnings of our universe, and all possible universes is no problem in cosmology. They pretty much all believe that they formed from singularities formed in the Quantum World of the multiverse. Even some like Steinhardt and Hawkins that consider cyclic nature of universes possible.

Well, I did, but the matches I saw were for the BGV theorem, which is also called the singularity theorem.

Therefore your questions are answered concerning Vilenkin and the singularity theorem. The next post will be about Hawking's work in the Penrose-Hawking singularity theorem.probably the best work demonstrating the existence of the multiverse.