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David S

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The BGV Theorem
« on: March 03, 2015, 08:03:28 PM »
From what I've read and heard, in light of the evidence, the universe had an absolute beginning. The Borde Guth Vilenkin Theorem seems to be another strong justification for the second premise. In the past, even Vilenkin himself has said to Dr. Craig, "I think you represented what I wrote about the BGV theorem in my papers and to you personally very accurately." Furthermore, at Stephen Hawking's birthday party, Vilenkin said, "All the evidence we have says that the universe had a beginning." And in his book, Vilenkin says, "With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe." Therefore, I was devastated to hear Alan Guth, another author of the BGV theorem, say in the Craig-Carroll debate, that the universe is "very likely eternal." How can this be? How can two cosmologists who made the same theorem have such radically different views? Does the BGV theorem really imply a beginning? I've been trying to find the answers everywhere. Please help.

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ParaclitosLogos

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Re: The BGV Theorem
« Reply #1 on: March 06, 2015, 04:14:51 AM »
I answered your other post.

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David S

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Re: The BGV Theorem
« Reply #2 on: March 06, 2015, 04:23:12 PM »
Yeah, I put it in two forums to make sure a lot of people saw it :)

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Re: The BGV Theorem
« Reply #3 on: March 10, 2015, 01:26:38 PM »
The BGV theorem attempts to show geodesic incompleteness into the past according to a particular set of conditions it assumes correspond to eternal inflation. It's results are consistent with the notion of eternal inflation emerging from a "primordial singularity" but they are also equally consistent with eternal inflation being grafted upon some eternal spacetime region that is not eternally inflating. This is exactly what physicists Anthony Aquirre and Stephen Gratton showed in their 2003 paper entitled "Inflation without a beginning: a null boundary proposal" http://arxiv.org/abs/gr-qc/0301042. The results demonstrated in this paper are consistent with both the BGV theorem and the notion of an eternal universe.

It's important to note, however, that no result derived solely on the basis of classical general relativity can be used to derive anything truly fundamental concerning the nature of the cosmos or its total history. This is because classical GR fails to adequately describe the universe on the smallest of scales (a regime which is of primary importance when discussing matters pertaining to the earliest moments of the Big Bang). Since the BVG singularity theorem is purely classical in its conception, it's usefulness stems from its ability to denote exactly where classical GR breaks down when describing the universe on the planck scale. In order to derive a complete picture of the universe on this scale we must move beyond classical GR and quantize gravity. Only with a complete theory of quantum gravity can we, with any measure confidence, begin to speak meaningfully concerning the ultimate origins of the universe. It is no surprise then that both Alan Guth and Alexander Vilenkin have shown the appropriate degree of reticence when addressing the implications of the BGV theorem. Apologists would do well to mirror their caution.



« Last Edit: March 10, 2015, 05:21:29 PM by Ionian_Tradition »

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ParaclitosLogos

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Re: The BGV Theorem
« Reply #4 on: March 10, 2015, 02:31:06 PM »


If I got it right, I think, In the Aguirre Gratton we have several volumes inflating from a null boundary region at which an arrow of time reversal  occurs. Vilenkin argued that this null boundary requires a series of initial conditions being put by hand, and, this amounts to a beginning. Also, each arrow of time, going away from the null boundary surface, on each volume is independent of the other arrow of times on other expanding volumes, basically it can not be said that any segment of any of the expanding volumes is in the past, present or future of any other segment of any other expanding volume, which supports Vilenkin´s argument, that such null boundary is a beginning.


As far as I remember, Geodesic incompleteness does not necessarily mean that the theory brakes or fails, it just can not continue expanding the manifold, and it is arguable that it is evidence, even if tentative, that the universe has a limit in the past direction, as this is what exactly the model is describing, in such cases, namely a limit, when we apply the VGB theorem.

It could turn out that the correct quantum cosmological model of our universe shows the same result, this last affirmation, is what we really don´t know, but, we know that many of our GR inflationary models show they have limits into the past, that they can not go on, into the past.

Also, it could turn out that the universe, contrary to everyone´s expectations, never gets to the planck phase, and then we don´t need quantum cosmology, I am not saying this is the most probable outcome, just that what it is  that we don´t know is what quantum cosmology will show, rather it is a presumption, but, we do know what our non quantum cosmological models show.
« Last Edit: March 10, 2015, 02:52:17 PM by ontologicalme »

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Re: The BGV Theorem
« Reply #5 on: March 10, 2015, 05:13:38 PM »


If I got it right, I think, In the Aguirre Gratton we have several volumes inflating from a null boundary region at which an arrow of time reversal  occurs. Vilenkin argued that this null boundary requires a series of initial conditions being put by hand, and, this amounts to a beginning. Also, each arrow of time, going away from the null boundary surface, on each volume is independent of the other arrow of times on other expanding volumes, basically it can not be said that any segment of any of the expanding volumes is in the past, present or future of any other segment of any other expanding volume, which supports Vilenkin´s argument, that such null boundary is a beginning.

It's not clear to me how the Aguirre/Gratton model necessitates a beginning in the sense implied by the KCA. The model posits an infinite null hypersurface in which an inflation field with a "double well" potential exists everywhere in the false vacuum on the null surface. All classical fields are zero or in minima of their potentials on this field. From this eternal state, semi-classical nucleation events can occur forming inflationary bubbles from which the process of eternal inflation can emerge. Note that this is not an absolute beginning in any meaningful sense of the term, nor does it require divine intervention in the form of "creatio ex nihilo" in order to begin. The process of bubble nucleation events occurring on the null surface is effectively eternal.

As far as I remember, Geodesic incompleteness does not necessarily mean that the theory brakes or fails, it just can not continue expanding the manifold, and it is arguable that it is evidence, even if tentative, that the universe has a limit in the past direction, as this is what exactly the model is describing, in such cases, namely a limit, when we apply the VGB theorem.

Any model which produces singularities will provide a strong indication that the physical/mathematical paradigm used to describe a given phenomenon is no longer equal to the task of providing a description which is either robust or complete. In this respect, the model has effectively broken down. Now it is certainly the case that a singularity may allude to deeper physics which entail an absolute beginning of some kind, but it could also allude to deeper physics which entail the exact opposite. As such, geodesic incompleteness is more or less an indication that our current physics is not yet sufficiently developed. It should not be construed as truly compelling evidence that the universe had an absolute beginning.

It could turn out that the correct quantum cosmological model of our universe shows the same result, this last affirmation, is what we really don´t know, but, we know that many of our GR inflationary models show they have limits into the past, that they can not go on, into the past.

Perhaps, but given that the correct quantum cosmological model currently eludes us, and given the fact that viable inflationary models do exist which suggest a cosmos which is eternal, we would do well to suspend judgement and await further evidence.

Also, it could turn out that the universe, contrary to everyone´s expectations, never gets to the planck phase, and then we don´t need quantum cosmology, I am not saying this is the most probable outcome, just that what it is  that we don´t know is what quantum cosmology will show, rather it is a presumption, but, we do know what our non quantum cosmological models show.

I must admit this does not seem like a sufficiently likely outcome. It seems rather evident that any robust description of the universe will, in some way, entail quantum elements.

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ParaclitosLogos

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Re: The BGV Theorem
« Reply #6 on: March 10, 2015, 06:18:07 PM »


If I got it right, I think, In the Aguirre Gratton we have several volumes inflating from a null boundary region at which an arrow of time reversal  occurs. Vilenkin argued that this null boundary requires a series of initial conditions being put by hand, and, this amounts to a beginning. Also, each arrow of time, going away from the null boundary surface, on each volume is independent of the other arrow of times on other expanding volumes, basically it can not be said that any segment of any of the expanding volumes is in the past, present or future of any other segment of any other expanding volume, which supports Vilenkin´s argument, that such null boundary is a beginning.

It's not clear to me how the Aguirre/Gratton model necessitates a beginning in the sense implied by the KCA. The model posits an infinite null hypersurface in which an inflation field with a "double well" potential exists everywhere in the false vacuum on the null surface. All classical fields are zero or in minima of their potentials on this field. From this eternal state, semi-classical nucleation events can occur forming inflationary bubbles from which the process of eternal inflation can emerge. Note that this is not an absolute beginning in any meaningful sense of the term, nor does it require divine intervention in the form of "creatio ex nihilo" in order to begin. The process of bubble nucleation events occurring on the null surface is effectively eternal.


(ignoring the fact that neither Aguirre nor Gratton state that such model is a model of our universe) We would live in one bubble and no bubble is located on the past of that one bubble (neither is the null surface), and, the bubble is not eternal, that´s all that is needed for the KCA, there is no sense in which anything is located in the past of such bubble. And, this goes for all bubbles.

The charge that the model does not require divine intervention is a presumption: Equations do not make things happen.

In fact, the use of boundary condition models based on physical laws, imply that these laws are something over and above the physical, and obviously none physical, which leaves the question, what grounds the explanatory power of these abstract laws and equations open, not to mention, what makes things be the way these laws describe.

Also, one has to keep in mind that the notion of reversal of arrow of time is rather an implausible conjecture. 


As far as I remember, Geodesic incompleteness does not necessarily mean that the theory brakes or fails, it just can not continue expanding the manifold, and it is arguable that it is evidence, even if tentative, that the universe has a limit in the past direction, as this is what exactly the model is describing, in such cases, namely a limit, when we apply the VGB theorem.

Quote
Any model which produces singularities will provide a strong indication that the physical/mathematical paradigm used to describe a given phenomenon is no longer equal to the task of providing a description which is either robust or complete. In this respect, the model has effectively broken down. Now it is certainly the case that a singularity may allude to deeper physics which entail an absolute beginning of some kind, but it could also allude to deeper physics which entail the exact opposite. As such, geodesic incompleteness is more or less an indication that our current physics is not yet sufficiently developed. It should not be construed as truly compelling evidence that the universe had an absolute beginning.

No need to construe them as truly compelling evidence, merely as evidence that it is probable.

Let me put it this way, if there was no geodesic incompleteness into the past of the expanding volume, the probability that the space time had a beginning would be lower, which is one of the main basic definitions of evidence.

If new physics will be needed will depend on a host of other matters, not only the geodesic incompleteness. 


It could turn out that the correct quantum cosmological model of our universe shows the same result, this last affirmation, is what we really don´t know, but, we know that many of our GR inflationary models show they have limits into the past, that they can not go on, into the past.

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Perhaps, but given that the correct quantum cosmological model currently eludes us, and given the fact that viable inflationary models do exist which suggest a cosmos which is eternal, we would do well to suspend judgement and await further evidence.

Viable with respect to what? they are not accepted, nor corroborated experimentally. Nor are they what would be called our main models of our universe, today.

I consider time arrow reversal anything but viable.

Concocting elaborate schemes  and internally consistent but imaginary models (that not even their authors are positing as true models our our universe, but mainly as conceptual probes ) should hold very little weight on any direction.

Also, it could turn out that the universe, contrary to everyone´s expectations, never gets to the planck phase, and then we don´t need quantum cosmology, I am not saying this is the most probable outcome, just that what it is  that we don´t know is what quantum cosmology will show, rather it is a presumption, but, we do know what our non quantum cosmological models show.

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I must admit this does not seem like a sufficiently likely outcome. It seems rather evident that any robust description of the universe will, in some way, entail quantum elements.

Sure, it does not seem likely. But my point is not that it is, just that we know what we know (what our GR models and main BB inflationary model show), and, what we don´t know we don´t know (the promised quantum cosmological model that will solved everything), it is fallacious to take a position based on what we don´t know, while foregoing what we do know.

Alexander Vilenkin Says William Lane Craig is Right About the BGV Theorem

Krauss would bet the universe had a beginning
« Last Edit: March 11, 2015, 01:47:33 AM by ontologicalme »

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Re: The BGV Theorem
« Reply #7 on: March 11, 2015, 01:19:54 PM »
(ignoring the fact that neither Aguirre nor Gratton state that such model is a model of our universe) We would live in one bubble and no bubble is located on the past of that one bubble (neither is the null surface), and, the bubble is not eternal, that´s all that is needed for the KCA, there is no sense in which anything is located in the past of such bubble. And, this goes for all bubbles.

Any given bubble is not the whole of physical reality. Rather, it is the outworking of causal precursors which exist ontologically prior to it. In this respect, the bubble is in no literal sense an absolute beginning of the physical world. Some global physical reality, on this model, will always precede bubble nucleation. As such, the claim that the Aguirre/Gratton model denotes a beginning in the sense implied by the KCA is all together spurious.

The charge that the model does not require divine intervention is a presumption: Equations do not make things happen.

Not at all. The model mathematically describes a physical system which possesses all the necessary and sufficient causal conditions which would allow for inflationary expansion to occur through purely naturalistic mechanisms. Any move which would seek to posit some divine intelligence to make the model work would not only be superfluous but unparsimonious as well. That being said, though equations do not make things happen, the physical conditions these equations seek to describe, in theory, can.

In fact, the use of boundary condition models based on physical laws, imply that these laws are something over and above the physical, and obviously none physical, which leaves the question, what grounds the explanatory power of these abstract laws and equations open, not to mention, what makes things be the way these laws describe.

You're assuming physical laws are abstract metaphysical prescripts as opposed to an approximate description of the way the universe and its constituents are observed to behave. I see no reason to prefer the former depiction over the latter. Moreover, it's not evident to me that the way certain things are, in and of themselves, is something which, in all cases, requires an explanation. To assume the contrary is to presume brute facts do not exist, or are metaphysically impossible. This assumption seems to me to beg the question.

Also, one has to keep in mind that the notion of reversal of arrow of time is rather an implausible conjecture. 

On what grounds do you make this assertion? Have you the requisite knowledge concerning the nature of the cosmos at large to even begin assessing the plausibility of AOT reversal? If so, state your evidence.

As far as I remember, Geodesic incompleteness does not necessarily mean that the theory brakes or fails, it just can not continue expanding the manifold, and it is arguable that it is evidence, even if tentative, that the universe has a limit in the past direction, as this is what exactly the model is describing, in such cases, namely a limit, when we apply the VGB theorem.

Quote
Any model which produces singularities will provide a strong indication that the physical/mathematical paradigm used to describe a given phenomenon is no longer equal to the task of providing a description which is either robust or complete. In this respect, the model has effectively broken down. Now it is certainly the case that a singularity may allude to deeper physics which entail an absolute beginning of some kind, but it could also allude to deeper physics which entail the exact opposite. As such, geodesic incompleteness is more or less an indication that our current physics is not yet sufficiently developed. It should not be construed as truly compelling evidence that the universe had an absolute beginning.

No need to construe them as truly compelling evidence, merely as evidence that it is probable.

"Possible" perhaps, but "probable"? The fact that a thoroughly classical model happens to show itself ill equipped to describe what the early universe was doing prior to the planck epoch (which is a thoroughly quantum regime) does not therefore suggest that an absolute beginning is probable, or at the very least more probable than an eternal cosmos.

Let me put it this way, if there was no geodesic incompleteness into the past of the expanding volume, the probability that the space time had a beginning would be lower, which is one of the main basic definitions of evidence.

Again, geodesic incompleteness only shows that, if classical rules hold, our description of the early universe will necessarily reduce to a mathematical paradox known as a "singularity". This does not intrinsically raise the probability that the universe had a beginning. It does, however, raise the probability that our classical description of reality is fundamentally incomplete, and therefore requires further development. An all together incomplete model simply cannot tell us anything truly fundamental about the nature of the cosmos or its origins.

 


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Perhaps, but given that the correct quantum cosmological model currently eludes us, and given the fact that viable inflationary models do exist which suggest a cosmos which is eternal, we would do well to suspend judgement and await further evidence.

Viable with respect to what? they are not accepted, nor corroborated experimentally. Nor are they what would be called our main models of our universe, today.

They are models of the universe which comport with the known laws of physics. They show that the idea of an eternal cosmos is viable by virtue of the fact that a cosmos in which eternal inflation is operative can be past eternal in some literal sense. Whether or not our particular universe is in fact consistent with these or other models of a similar kind will depend upon what future research happens to reveal. At the very least, these models show that an eternal universe is not intrinsically ruled out by our current cosmology.





I consider time arrow reversal anything but viable.

This seems to be a personal bias. There is nothing in current physics which suggests that this is not possible, or even implausible..



Concocting elaborate schemes  and internally consistent but imaginary models (that not even their authors are positing as true models our our universe, but mainly as conceptual probes ) should hold very little weight on any direction.

Nor should a fundamentally incomplete classical depiction of cosmic evolution (i.e. the BGV theorem) carry similar weight in swaying us toward a universe with a finite beginning. Since certain models which entail both a cosmic beginning and cosmic eternality are each theoretically consistent with our current physics, we should suspend judgement and wait to see what the universe has to tell us about the way it actually is, and which models most accurately describe it. It would be dishonest in the extreme to espouse that the BGV theorem has in any way definitively shown that the universe had a beginning in the sense implied by the KCA.



Also, it could turn out that the universe, contrary to everyone´s expectations, never gets to the planck phase, and then we don´t need quantum cosmology, I am not saying this is the most probable outcome, just that what it is  that we don´t know is what quantum cosmology will show, rather it is a presumption, but, we do know what our non quantum cosmological models show.

Quote
I must admit this does not seem like a sufficiently likely outcome. It seems rather evident that any robust description of the universe will, in some way, entail quantum elements.

Sure, it does not seem likely. But my point is not that it is, just that we know what we know (what our GR models and main BB inflationary model show), and, what we don´t know we don´t know (the promised quantum cosmological model that will solved everything), it is fallacious to take a position based on what we don´t know, while foregoing what we do know.

What we do know is that our current understanding of the cosmos, and its origin, is fundamentally incomplete. It would be fallacious therefore to rely on this knowledge alone to provide us with answers it fundamentally cannot give.



Alexander Vilenkin Says William Lane Craig is Right About the BGV Theorem

Krauss would bet the universe had a beginning

Firstly, a thorough reading of Krauss suggests that his notion of a beginning is quite different from that which Craig often refers to. In fact Craig has often pointed out that Krauss's version of "nothing" is in fact "something" when considered in detail. The primordial physical reality (quantum vacuum) from which Krauss thinks the universe evolved is effectively eternal and thus the cosmos at large, on Krauss's view, has no true beginning which necessitates a creator.

That being said, Krauss's opinion on the matter is largely irrelevant to the discussion at hand. I could easily cite Alan Guth's (another author of the BGV theorem) belief (referenced during the Craig/Carroll debate) that the universe is "probably" eternal, but this would do little to show that the universe is, in fact, most likely eternal. Our attention is surely better spent attempting to better understand the science as opposed to quote mining this or that physicist. If we're honest, the science will reveal that the question concerning whether or not the universe had a beginning is still wide open.
« Last Edit: March 11, 2015, 01:31:52 PM by Ionian_Tradition »

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ParaclitosLogos

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Re: The BGV Theorem
« Reply #8 on: March 11, 2015, 09:04:34 PM »
Fact1: In the model we are living in one bubble, and that is what we call the universe (in this specific case).

Fact2: when we say that the universe had a beginning, in the KCA, we can mean that one bubble.

Fact3: There is nothing that lies at the past of that bubble.

Fact4: The universe/bubble had a beginning.

Fact5: This can be said about any other universe/bubble.

Fact6: Vilenkin argues that the low-entropy boundary conditions are imposed (by hand) at the bounce, which is different from other models where such boundary conditions naturally arise from quantum cosmology of the model (example Hartle-Hawking model) wave function of the universe. The AG model bounce hypersurface breaks de Sitter invariance (the laws are no longer invariant in the region) and this represents the beginning of the universe in this said model.

In other words:  the mirror universe on the other side of the boundary in no sense represents a past out of which our current universe evolved, nor vice versa, and,  our universe (this one bubble) began-to-exist

Thus, our universe (and any other universe) had a cause I will comment on the cause, later on.

Fact 7: The model offers no additional predictions.

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On laws and initial condition status:

The common use of the concept of physical laws is called , by some, Governability model:

2 views:

1. Laws govern, because a governor breaths fire into them. 

2. Laws are primitives, that have the power to govern.

*** on 2, given an A theory of time, one has to ask laws are primitives of what??

When I say that it is a presumption, it is in fact a philosophical presumption; one either chooses 1 or 2 (both, philosophical presumptions).
Historically, this view was developed by Francis Bacon, then, echoed by Decartes, Newton and others, on the basis of God as a law giver (view no. 1) .
3 philosophical accounts of physical Laws
In this video a 3rd option is presented, but, the Governability (which is the one basically currently in use, in physics) account is also commented. Enjoy.
Tim Mudlin is a very recognized philosopher of science who defends the Governability account No. 2.
Quote from: Mudlin
The direction of time is embedded so deeply into our language and concepts that it is impossible to expunge. Most verbs are time-directed: the difference between a rock falling and the rock rising is determined by which direction of time is toward the future and which toward the past. The words “to” and “from” have their usual application by reference to time: processes run from earlier states to later ones. We remember the past and anticipate the future. Our present actions can influence the course of the future but are impotent to influence the past. To say that the past-to-future direction of time is intrinsically different from the future-to -past direction is not the same as saying that the future must be qualitatively different from the past. The physicist Fred Hoyle once proposed a “steady state” theory of the universe: the universe as a whole is and always has been expanding, with galaxies moving ever farther apart from one another. But in Hoyle's theory, the average density of matter in the universe does not go down: new matter is created in the empty spaces at just the right rate to keep the density constant. In this model, all times— future, present, and past —are qualitatively the same: hence “steady state.” But there is still a fundamental direction of time, in virtue of which it is correct to say that the universe is expanding and new matter being created, rather than contracting with matter being destroyed. Our world is filled with processes that have an evident time direction. Ice cubes in hot water, isolated from outside influence, melt and produce lukewarm water. Lukewarm water, isolated from outside influence, never spontaneously segregates into ice cubes and hot water. But the laws of physics seem to allow the latter process just as much as the former. Once again, our very description of the two processes presupposes a time direction: the only difference between melting and freezing is the direction of time. Similarly, our description of a black hole in figure 27 presupposes a direction of time: it is because the direction to the future is represented by up on the diagram rather than down that we say things fall into and never escape the event horizon rather than are ejected from and cannot remain within it. Just as the fundamental laws seem to allow both the melting and spontaneous freezing of ice, so General Relativity allows for both black holes and their time reverses. And just as ice often melts but never spontaneously forms in lukewarm water, so there seem to be many black holes in the universe but no time-reverses of them. There are, then, two distinct questions to ask about the direction of time. One is why there seem to be processes that never occur even though their time-reverses regularly occur. When asked in terms of, say, spontaneous melting and spontaneous freezing, this question presupposes that there is a fundamental difference between the past-to-future and future-to-past direction. The question of the de facto directionality of processes— why ice cubes spontaneously melt in hot water but lukewarm water does not spontaneously segregate itself into ice cubes and hot water— is addressed by statistical physics. The idea that time has no intrinsic directionality at all is harder to evaluate . One could be lulled into this idea by an unreflective use of space-time diagrams, which are purely spatial objects with no intrinsic directionality. The past-to-future direction represented by such a diagram must be indicated by some extra convention, since the medium of the representation itself has no such asymmetry. But equally, the difference between the representation of space-like and time-like directions on the diagram must be indicated by a convention. Similarly, purely mathematical representations of space-time require many conventions, such as whether time-like Intervals are to be represented by real or imaginary numbers, or whether a time coordinate increases or decreases in the past-to-future direction. None of this even vaguely suggests that the two time directions are not fundamentally different, any more than it suggests that time-like directions do not differ intrinsically from space-like directions.
Maudlin, Tim (2012-07-22). Philosophy of Physics: Space and Time (Princeton Foundations of Contemporary Philosophy) (p. 166). Princeton University Press.
According to Barry Leower, Mudling argues, and he agrees, that, a Governing version of Laws implies an intrinsic direction of time.
Furthermore, the question was the plausibility of a reversal of the arrow of time.
Plausibility , philosophically speaking, is  roughly understood as being worthy of belief.  Above Maudlin explains how embedded is the arrow of time, in our lives, at all levels, in our models, etc.
It is everyone´s prerogative and within their capacity to elucidate a judgment as to how plausible is that everything we seem to know about the world, including our scientific knowledge of the world which includes statistical physics and the more.
Another reason or evidence to consider it implausible is that Aguirre and Gratton inserted the conditions at the null surface by hand, inducing the reversal, it does not come out of the equations by itself.
This is different than it would come out of the equations, and a far cry from accepting it due to real experimental evidence in favor of a reversal of the arrow of time, or, deductive argument to that conclusion, for instance.



No other motivation was given. Calling it a boundary does not change the fact that it is a set of initial conditions, a non generic low entropy condition, put there by hand
See from min1 to 1:44

Even more, the model is not accompanied by any experimentally verifiable predictions.

============
Assuming brute facts are possible go even against the practice of science, which you purport to use.
I copy here an argument that I find quite reasonable against such view , and words things much better than I could.
“Robert Koons (1997): Start with the observation that once we admit that some contingent states of affairs have no explanations, a completely new skeptical scenario becomes possible: No demon is deceiving you, but your perceptual states are occurring for no reason at all, with no prior causes.
Moreover, objective probabilities are tied to laws of nature or objective tendencies, and so if an objective probability attaches to some contingent fact, then that situation can be given an explanation in terms of laws of nature or objective tendencies. Hence, if the PSR is false of some contingent fact, no objective probability attaches to the fact.
Thus we cannot even say that violations of the PSR are improbable if the PSR is false. Consequently, someone who does not affirm the PSR cannot say that the skeptical scenario is objectively improbable. It may be taken to follow from this that if the PSR were false or maybe even not known a priori, we wouldn't know any empirical truths. But we do know empirical truths. Hence, the PSR is true, and maybe even known a priori.”

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Quote from: IonianT
“Again, geodesic incompleteness only shows that, if classical rules hold, our description of the early universe will necessarily reduce to a mathematical paradox known as a "singularity". This does not intrinsically raise the probability that the universe had a beginning. It does, however, raise the probability that our classical description of reality is fundamentally incomplete, and therefore requires further development. An altogether incomplete model simply cannot tell us anything truly fundamental about the nature of the cosmos or its origins.”
Quote from: Antony Aguirre
On the PH, BV and BVG singularity theorems: “… Singularity theorems, certainly, don´t tell you that there is a singularity, they tell that you there is geodesic incompleteness over the space time regions over which the theorem assumptions hold…singularity theorems tell you there is a finite geodesic, or an incomplete geodesic. “ (Anthony Aguirre)


Quote from: IonianT
"Possible" perhaps, but "probable"? The fact that a thoroughly classical model happens to show itself ill equipped to describe what the early universe was doing prior to the planck epoch (which is a thoroughly quantum regime) does not therefore suggest that an absolute beginning is probable, or at the very least more probable than an eternal cosmos.
I find strange your interpretation, If that was all there was to it, Aguirre, Gratton, Carroll, Chen, would not be have spent their efforts in circumventing the assumptions.

Aguirre, for instance, thinks that the theorems don´t show that the universe had a beginning (not necessarily), not because he thinks the models are ill equipped, but, because he thinks he can circumvent the assumptions of the theorems.

=====================
The AG model does not make predictions, which just goes to under write its character as a conceptual probe, and, not as a serious model of the world.
Putting credence over such probe models , above the main stream models, seems unwarranted.

A couple of things more, one can argue for the existence of brute facts, but, that is truly inconsistent, with the practice of science, in its very core (see Popper´s The logic of scientific discovery).

another thing, nobody is arguing that eternal universe are  ruled out, much less intrinsically (what ever that amounts to) by our current cosmology, merely that given the evidence and analysis, it appears to be less probable that those are the correct models of our universe, so far.

I think you mentioned something to the effect that our current models are incomplete, or, something on those lines. Scientific physical models by their own nature will never be complete models of our universe. Let me give you some examples.

Some quantum loop theories still use the same Newton constant, with out ever showing where it comes from.
The infamous Carroll´s quantum eternity theorem is hoax, must quantum cosmologists think the energy of the universe is zero, while Carroll passed that one under the table, saying that if the universe had a non zero energy, the universe would then be infinite to the past and future. Even more, that the energy is zero, under one of the most accepted interpretations just means that the dynamic equations that govern the universe, are rather arbitrary. etc etc etc.


there will never be such a thing as a complete model of the universe, and, that is fine.

Guth beliefs the universe might be eternal based on certain criteria by which he prefers eternal models, according to Carroll ( read it from his blog ), not because he analysed and gave arguments in favor of such conclusion, like Vilenkin and Mithanis have done.  Carroll´s showing of his pictures on screen is nothing more that a fallacious appeal to authority, since no arguments nor analysis of the models was put forward, in behalf of Guth.

I am probably wrong, after all, I am no one (since you asked), but in principle Guth´s , Carroll´s , Aguirre´s argument of the eternality of the universe is missguided. Using Penrose diagrams where the models of the universe are compressed from t=-oo to t=oo , for example, sort of makes people forget that such t=oo is an ever increasing time, not an actual infinite. As George Ellis argues, (very broadly) paraphrasing: one can substitute the "oo" by a very large number, to get a more physical picture of what is going on.  And in the cases one gets something like an actual infinite one should reject the implications.

On a side note: there is as far as I know zero experimental corroboration that the universe reaches planck density, into the past. I am not saying it does not, just that we are all presuming it does.


Thanks for the exchange.




« Last Edit: March 12, 2015, 06:57:01 AM by ontologicalme »

9
Re: The BGV Theorem
« Reply #9 on: March 12, 2015, 06:10:33 PM »
Fact1: In the model we are living in one bubble, and that is what we call the universe (in this specific case).

Any given bubble is not the "global" universe. It is merely a local pocket of inflationary expansion. In this respect, our bubble universe is best described as a constituent of a much larger physical reality which does not begin to exist in the sense implied by the KCA.

Fact2: when we say that the universe had a beginning, in the KCA, we can mean that one bubble.


Fact3: There is nothing that lies at the past of that bubble.

Fact4: The universe/bubble had a beginning.

Fact5: This can be said about any other universe/bubble.


Bubbles begin to form via nucleation but the global physical state from which these bubbles emerge, on this model, does not begin to exist. In this respect, the "universe writ large" is eternal. A useful analogy would be that of the Steady State model. Per the steady state model, the physical universe doesn't begin to exist, never the less material objects still coalesce and take form within it. Though these material structures do, in some local sense, begin to exist, the global universe from which these structures emerge does not. In principle, the same would apply to the model posited by Aquirre/Gratton. The underlying physical state form which bubble nucleation event emerge is both eternal and ontologically prior to all bubble universes.

Fact6: Vilenkin argues that the low-entropy boundary conditions are imposed (by hand) at the bounce, which is different from other models where such boundary conditions naturally arise from quantum cosmology of the model (example Hartle-Hawking model) wave function of the universe. The AG model bounce hypersurface breaks de Sitter invariance (the laws are no longer invariant in the region) and this represents the beginning of the universe in this said model.

In other words:  the mirror universe on the other side of the boundary in no sense represents a past out of which our current universe evolved, nor vice versa, and,  our universe (this one bubble) began-to-exist

Thus, our universe (and any other universe) had a cause I will comment on the cause, later on.

Again, I think you're missing the bigger picture. While it may be the case, that bubble nucleation, in some sense "begins", this is not a true beginning of the "universe writ large". To argue that the emergence of a bubble (on this model) necessitates an absolute beginning of physical reality (which is certainly the type of beginning Dr. Craig implies when employing the KCA)  would be equivalent to arguing that the emergence of a bubble in an eternally boiling pot of water necessitates an absolute beginning of the pot.

To put it succinctly, while the AG model does posit bubble nucleation resulting from a set of physical causal precursors, it does not posit a beginning of physical reality. If universe is to be defined as the whole of physical reality (which seems a reasonable definition), then on the AG model, the universe is effectively eternal.

Fact 7: The model offers no additional predictions.

Well it certainly offers the same predictions that nearly every inflationary model happens to offer (e.g. a particular distribution of galaxies suggesting scale-invariant spatial variations in energy in the early universe, temperature antisotropies in the CMB, etc.). An additional, and somewhat mathematical, prediction would be that the Weyly curvature tensor (on this model) will bear a unique dependence upon the boundary conditions of the model. If this dependence holds, it should be expected to produce a de sitter space.

But predictability was really never the point, as you're aware many of the elements pertaining to the model are beyond the realm of empirical observation. But this lack of empirical verification is no more problematic for what the model attempts to imply than a lack of empricial verifiability is problematic for the doctrine of "creatio ex nihilo" and its implications.  It must be remembered that the AG model's primary goal was simply to effectively show that certain geodesic incompleteness theorems need not necessitate a universe which is finite into the past. The model does indeed show, that there are certain conditions, consistent with the known laws of physics, which would allow not only for the existence of past directed eternities via AOT reversal, but an infinite physical state from which all nucleation events emerge. In this respect, the model fulfills its intended purpose. Since these results are fully consistent with the BGV theorem, any argument which seeks to use the theorem to show that an eternal (global) universe is fundamentally impossible, or even unlikely, will ultimately beg the question.


----------------

On laws and initial condition status:

The common use of the concept of physical laws is called , by some, Governability model:

2 views:

1. Laws govern, because a governor breaths fire into them. 

2. Laws are primitives, that have the power to govern.

*** on 2, given an A theory of time, one has to ask laws are primitives of what??

When I say that it is a presumption, it is in fact a philosophical presumption; one either chooses 1 or 2 (both, philosophical presumptions).
Historically, this view was developed by Francis Bacon, then, echoed by Decartes, Newton and others, on the basis of God as a law giver (view no. 1) .
3 philosophical accounts of physical Laws
In this video a 3rd option is presented, but, the Governability (which is the one basically currently in use, in physics) account is also commented. Enjoy.
 

There is certainly much to be said on this topic, and I will delay responding until I've given due consideration to what professors Loewer and Maudlin have to say concerning the nature of physical law. Since this aspect of our discussion appears to extend somewhat beyond the purview of the OP, it may be appropriate to have this topic moved to a new thread. I've taken the liberty of creating one here .

Furthermore, the question was the plausibility of a reversal of the arrow of time.
Plausibility , philosophically speaking, is  roughly understood as being worthy of belief.  Above Maudlin explains how embedded is the arrow of time, in our lives, at all levels, in our models, etc.
It is everyone´s prerogative and within their capacity to elucidate a judgment as to how plausible is that everything we seem to know about the world, including our scientific knowledge of the world which includes statistical physics.

It's long been known that the arrow of time can be accounted for in a purely statistical fashion. While it is true that our day to day vernacular is largely predicated upon common sense intuitions concerning the flow of time, this seems to be a poor ground in which to root an argument in favor of an intrinsic direction of time. All of the reasons cited by Maudlin for believing there exists and intrinsic arrow of time directed toward the future could be used in an analogous sense by peoples residing in a world in which the arrow of time was reversed. To them, they would believe their experience of the world suggests an intrinsic direction of time oriented toward the past. Common sense intuitions however have a rather poor track record when it comes to determining the nature of physical reality. From Aristotle to Einstein, even the brightest minds have rejected unintuitive physical paradigms which eventually showed themselves to be true. We ought be cautious then in relying on intuition and linguistic pragmatism to tell us something truly fundamental about the cosmos.


Another reason or evidence to consider it implausible is that Aguirre and Gratton inserted the conditions at the null surface by hand, inducing the reversal, it does not come out of the equations by itself.
This is different than it would come out of the equations, and a far cry from accepting it due to real experimental evidence in favor of a reversal of the arrow of time, or, deductive argument to that conclusion, for instance.

These conditions were selected because they served the underlying purpose of the model (i.e. to show that an eternal model in which eternally past/future-directed pockets of inflationary expansion formed could be shown to be consistent with the known laws of physics). While the model is certainly not sufficient to show that we inhabit such a universe, it is certainly enough to show that the BGV theorem, in particular, does not preclude the possibility. Since both a finite and an eternal cosmos are both theoretically permitted by the BGV theorem, and because the theorem constitutes an incomplete description of the cosmos, it alone cannot legitimately be employed to show in any compelling fashion that the universe most probably had a beginning.



No other motivation was given. Calling it a boundary does not change the fact that it is a set of initial conditions, a non generic low entropy condition, put there by hand
See from min1 to 1:44

As was said previously, the point of the entire endeavor was to produce a model which avoids the problem of geodesic incompleteness whilst giving rise to a local environment analogous to the one we observe. Since the model was never intended to depict states of the global universe which would not give rise our local patch, it's really no surprise that boundary conditions which fail to produce this outcome were not selected. 

That being said, the manipulation of a purely theoretical model to comport with some intended outcome is a perfectly acceptable practice, and in certain cases can lead to important discoveries. Einstein himself inserted the cosmological constant as an added term to his field equations solely for the purpose of making general relativity comport with a particular model of the universe. The result, much to Einstein's chagrin, was a term which is still of immense importance to the physics community today.


Assuming brute facts are possible go even against the practice of science, which you purport to use.
I copy here an argument that I find quite reasonable against such view , and words things much better than I could.
“Robert Koons (1997): Start with the observation that once we admit that some contingent states of affairs have no explanations, a completely new skeptical scenario becomes possible: No demon is deceiving you, but your perceptual states are occurring for no reason at all, with no prior causes.
Moreover, objective probabilities are tied to laws of nature or objective tendencies, and so if an objective probability attaches to some contingent fact, then that situation can be given an explanation in terms of laws of nature or objective tendencies. Hence, if the PSR is false of some contingent fact, no objective probability attaches to the fact.
Thus we cannot even say that violations of the PSR are improbable if the PSR is false. Consequently, someone who does not affirm the PSR cannot say that the skeptical scenario is objectively improbable. It may be taken to follow from this that if the PSR were false or maybe even not known a priori, we wouldn't know any empirical truths. But we do know empirical truths. Hence, the PSR is true, and maybe even known a priori.”

Philosopher of Religion Keith Parsons offers us reasons to be skeptical of the claim that brute facts cannot possibly exist:

Quote
The problem with any attempted metaphysical demonstration is the supposedly self-evident principle it invokes. An instance of such a supposedly self-evident principle would be the principle of sufficient reason (PSR), the claim that nothing exists unless there is a sufficient reason for its existence. However, over the history of philosophy, claims for the alleged self-evidence of metaphysical principles have been protean and elusive. What is self-evident for one philosopher will not be for another. For instance, the PSR is not self-evident for me. If you accept the PSR, you cannot hold that there are any brute facts. However, it seems self-evident to me that there could possibly be brute facts, i.e. states of affairs that are just so with no sufficient reason for their being so.

Defenders of PSR will point to its intuitive nature and the fact that, in neither our scientific or mundane lives are we content with the “explanation” of the old bumper sticker, “shit happens.” We always want to know why it happens. However, if we deny the existence of brute facts, then we either have to say that the chain of causes that we invoke to account for any phenomenon either extends ad infinitum, or it ends with something that has no further cause or explanation, in short, a brute fact. If God is the end of our explanatory chain, then God is a brute fact. Of course, some philosophers have tried to avoid this consequence by saying that God is his own sufficient reason. However, trying to make sense of this, without returning to the concept that God is logically necessary, is notoriously difficult.

Given that it is not obvious that all explanations end in logically necessary truth, and given the fact that it seems difficult to establish God (including his idiosyncratic qualities, characteristics and traits) as a viable candidate for logical necessity, the theist may yet have cause to take seriously the possibility of brute facts. Yet even if the existence of brute facts should prove untenable and the PSR should prevail, it is not at all obvious that certain features of physical existence (e.g. physical laws or primordial states) would not themselves constitute viable candidates for metaphysical necessity.



Aguirre, for instance, thinks that the theorems don´t show that the universe had a beginning (not necessarily), not because he thinks the models are ill equipped, but, because he thinks he can circumvent the assumptions of the theorems.

=====================
The AG model does not make predictions, which just goes to under write its character as a conceptual probe, and, not as a serious model of the world.
Putting credence over such probe models , above the main stream models, seems unwarranted.

Firstly, what mainstream models are you referring to which suggest an absolute cosmic beginning? Second, the model fulfills its intended purpose of showing that geodesic incompleteness need not entail an absolute beginning. In this respect, the model grants us added incentive to be skeptical of arguments which seek to posit the BGV theorem as "the definitive proof" that the universe had a beginning.



Nobody is arguing that eternal universe are  ruled out, much less intrinsically (what ever that amounts to) by our current cosmology, merely that given the evidence and analysis, it appears to be less probable that those are the correct models of our universe, so far. 

What forms of evidence are you referring to which show that our universe is probably not eternal? As far as current cosmology is concerned, an eternal universe is every bit as consistent with our present (and exceedingly limited) understanding of cosmic evolution as is a universe with a definitive beginning. Honestly, I find it somewhat ironic that an eternal universe model which at least attempts to play by the rules of physics is deemed by some to be less scientifically plausible than an appeal to something like creatio ex nihilo which, by its very nature, is a theory of cosmic origins predicated upon a host of non-scientific metaphysical assumptions which cannot, even in principle, be formalized mathematically let alone be shown to comport with modern physics. For all we know creatio ex nihilo could be right, but to assert, or even imply, that it is more scientifically founded than the AG model is, to me, a rather odd notion indeed.


« Last Edit: March 12, 2015, 06:56:46 PM by Ionian_Tradition »

10
Re: The BGV Theorem
« Reply #10 on: March 12, 2015, 06:31:00 PM »
(continued)

I think you mentioned something to the effect that our current models are incomplete, or, something on those lines. Scientific physical models by their own nature will never be complete models of our universe. Let me give you some examples.

Some quantum loop theories still use the same Newton constant, without ever showing where it comes from.

Do you have a source for this? Even if what you claim is true, should these models be ruled out simply because they make particular assumptions? Can you show these assumptions are in some way flawed? Moreover, can you show that the use of these assumptions is somehow inappropriate?


The infamous Carroll´s quantum eternity theorem is hoax, must quantum cosmologists think the energy of the universe is zero, while Carroll passed that one under the table, saying that if the universe had a non zero energy, the universe would then be infinite to the past and future. Even more, that the energy is zero, under one of the most accepted interpretations just means that the dynamic equations that govern the universe, are rather arbitrary. etc etc etc.

I must confess, this seems like a bit of a rant. I don't recall ever having brought up Carrol's appeal to the QET...Nor do I see how it's truth or falsity has any bearing on our present discussion.



Guth beliefs the universe might be eternal based on certain criteria by which he prefers eternal models, according to Carroll ( read it from his blog ), not because he analysed and gave arguments in favor of such conclusion, like Vilenkin and Mithanis have done.  Carroll´s showing of his pictures on screen is nothing more that a fallacious appeal to authority, since no arguments nor analysis of the models was put forward, in behalf of Guth.

Are you therefore asserting that Alan Guth has no scientific justification for believing the universe is probably eternal? It bears mentioning that not all appeals to authority are fallacious. Given that Guth most undoubtedly knows more about the implications of the BGV theorem than either you or I, his willingness to express sympathy towards the notion of an eternal universe (in light of the BGV theorem) should at the very least give us pause.

That being said, while I cannot speak for Mithanis (I haven’t read his work), Vilenkin's critique of the AG model was predicated upon the imprecise notion that the bubble nucleation denotes a definitive beginning (it doesn’t) and that the boundary conditions placed upon the null surface by Aguirre and Gratton were more or less arbitrary (the conditions selected were in fact appropriate given the intent of the paper…i.e. to show that geodesic incompletness does not necessarily preclude an eternal universe).


I am probably wrong, after all, I am no one (since you asked), but in principle Guth´s , Carroll´s , Aguirre´s argument of the eternality of the universe is missguided. Using Penrose diagrams where the models of the universe are compressed from t=-oo to t=oo , for example, sort of makes people forget that such t=oo is an ever increasing time, not an actual infinite. As George Ellis argues, (very broadly) paraphrasing: one can substitute the "oo" by a very large number, to get a more physical picture of what is going on.  And in the cases one gets something like an actual infinite one should reject the implications.

The AG model only posits inflationary expansion which is either eternally past or future directed. The problem of “actual infinities” is no more a problem for the model than actual infinities are a problem for a (local) universe which expands forever (which many physicist believe will be the fate of our universe).


On a side note: there is as far as I know zero experimental corroboration that the universe reaches planck density, into the past. I am not saying it does not, just that we are all presuming it does.

Geodesic incompleteness, and indeed all singularity generating theorems, more or less imply a universe which reaches the planck scale. To argue otherwise is to seat oneself firmly among the minority of professional physicists/cosmologist (in fact, I'm not aware of a single cosmologist or physicist of decent repute who thinks this is plausible).


Thanks for the exchange.

Thank you as well.
« Last Edit: March 12, 2015, 06:33:38 PM by Ionian_Tradition »

11

ParaclitosLogos

  • ***
  • 4902 Posts
Re: The BGV Theorem
« Reply #11 on: March 12, 2015, 06:48:27 PM »
Ok. I think we disagree, pretty much, on everything, then.Thanks.

12
Re: The BGV Theorem
« Reply #12 on: March 12, 2015, 07:03:26 PM »
Ok. I think we disagree, pretty much, on everything, then.Thanks.

Well who knows, after I find some time to watch Loewer's lecture in full, I might end up agreeing with you about the nature of physical law.

13

lfzadra

  • *
  • 2 Posts
Re: The BGV Theorem
« Reply #13 on: March 13, 2015, 10:58:17 PM »
I was devastated to hear Alan Guth, another author of the BGV theorem, say in the Craig-Carroll debate, that the universe is "very likely eternal." How can this be? How can two cosmologists who made the same theorem have such radically different views? Does the BGV theorem really imply a beginning?

The BGV theorem proves that the inflation of the universe must be past eternal, not the universe. Both claims are radically different. The beginning of inflation is not the "beginning" of the universe in the sense that the universe was non existent at one moment and later it popped into existence. This is a naive understanding of what the theorem is saying.

If you are thinking in the universe in terms of what happens after the Big Bang (inflation), then the universe begins. But if by universe you are referring to the entire set of physical reality, then no, the universe does not begin according to the BGV theorem. It merely shows inflation must be past finite. What lies beyond the point where inflation begins is unknown and outside the scope of the theorem. 

The universe, if understood as the entire set of physical things, can't "begin" in any meaningful concept of the word, but scientists use the word for the lack of a better term in the same way they use the word "nothing" when talking about the quantum vacuum.

This is the source of confusion. Of course Dr. Craig takes advantage of the limits of language and the layman use of words to suggest that the BGV theorem proves that once there was nothing and then the universe came into being.

14

ParaclitosLogos

  • ***
  • 4902 Posts
Re: The BGV Theorem
« Reply #14 on: March 14, 2015, 05:36:32 AM »
I was devastated to hear Alan Guth, another author of the BGV theorem, say in the Craig-Carroll debate, that the universe is "very likely eternal." How can this be? How can two cosmologists who made the same theorem have such radically different views? Does the BGV theorem really imply a beginning?

The BGV theorem proves that the inflation of the universe must be past eternal, not the universe. Both claims are radically different. The beginning of inflation is not the "beginning" of the universe in the sense that the universe was non existent at one moment and later it popped into existence. This is a naive understanding of what the theorem is saying.

If you are thinking in the universe in terms of what happens after the Big Bang (inflation), then the universe begins. But if by universe you are referring to the entire set of physical reality, then no, the universe does not begin according to the BGV theorem. It merely shows inflation must be past finite. What lies beyond the point where inflation begins is unknown and outside the scope of the theorem. 

The universe, if understood as the entire set of physical things, can't "begin" in any meaningful concept of the word, but scientists use the word for the lack of a better term in the same way they use the word "nothing" when talking about the quantum vacuum.

This is the source of confusion. Of course Dr. Craig takes advantage of the limits of language and the layman use of words to suggest that the BGV theorem proves that once there was nothing and then the universe came into being.

Quote
Did the universe have a beginning?

Audrey Mithani, Alexander Vilenkin
(Submitted on 20 Apr 2012)
We discuss three candidate scenarios which seem to allow the possibility that the universe could have existed forever with no initial singularity: eternal infation, cyclic evolution, and the emergent universe. The first two of these scenarios are geodesically incomplete to the past,and thus cannot describe a universe without a beginning. The third, although it is stable with respect to classical perturbations, can collapse quantum mechanically, and therefore cannot have an eternal past.

DID THE UNIVERSE HAD A BEGINNING

Quote from: Vilenking and Mithanis
3 Did the universe have a beginning?
At this point, it seems that the answer to this question is probably YES.2 Here we
have addressed three scenarios which seemed to offer a way to avoid a beginning,
and have found that none of them can actually be eternal in the past. Both
eternal inflation and cyclic universe scenarios have Hav > 0, which means that
they must be past-geodesically incomplete. We have also examined a simple
emergent universe model, and concluded that it cannot escape quantum collapse.
Even considering more general emergent universe models, there do not seem to
be any matter sources that admit solutions that are immune to collapse


Quote from: Vilenkin
Arrows of time and the beginning of the universe

Alexander Vilenkin
(Submitted on 16 May 2013 (v1), last revised 29 May 2013 (this version, v2))
I examine two cosmological scenarios in which the thermodynamic arrow of time points in opposite directions in the asymptotic past and future. The first scenario, suggested by Aguirre and Gratton, assumes that the two asymptotic regions are separated by a de Sitter-like bounce, with low-entropy boundary conditions imposed at the bounce. Such boundary conditions naturally arise from quantum cosmology with Hartle-Hawking wave function of the universe. The bounce hypersurface breaks de Sitter invariance and represents the beginning of the universe in this model. The second scenario, proposed by Carroll and Chen, assumes some generic initial conditions on an infinite spacelike Cauchy surface. They argue that the resulting spacetime will be non-singular, apart from black holes that could be formed as the initial data is evolved, and will exhibit eternal inflation in both time directions. Here I show, assuming the null convergence condition, that the Cauchy surface in a non-singular (apart from black holes) universe with two asymptotically inflating regions must necessarily be compact. I also argue that the size of the universe at the bounce between the two asymptotic regions cannot much exceed the de Sitter horizon. The spacetime structure is then very similar to that in the Aguirre-Gratton scenario and does require special boundary conditions at the bounce. If cosmological singularities are allowed, then an infinite Cauchy surface with `random' initial data will generally produce inflating regions in both time directions. These regions, however, will be surrounded by singularities and will have singularities in their past or future.

Arrows of time and the beginning of the universe
« Last Edit: March 14, 2015, 05:57:29 AM by ontologicalme »