Did the Universe Begin from a Singularity?

by Luke Muehlhauser on March 13, 2010 in Kalam Argument,Science

Part 10 of my Mapping the Kalam series.

singularity

Last time, I finished discussing the philosophical problems with the notion of an infinite past, problems which “are now being recognized in scientific papers by leading cosmologists and philosophers of science.” The example given by Craig is a 2003 paper by Ellis, Kirchner, and Stoeger, who write that:

…a realized past infinity in time is not considered possible [because] it involves an infinite set of completed events or moments.

…The arguments against an infinite past time are strong – it’s simply not constructible in terms of events or instants of time, besides being conceptually indefinite.

Now, we turn to Craig & Sinclair’s scientific arguments in defense of premise 2 of the Kalam Cosmological Argument: “The universe began to exist.”

The Big Picture

Nearly all cosmologists now agree – on the basis of good evidence – that the universe is expanding. They also agree that this expansion began about 13.7 billion years ago, at which time everything in the universe was condensed into a space smaller than a speck of dust.

One interpretation of Big Bang theory is that the spacetime began from a singularity. Craig & Sinclair quote P.C.W. Davies:

If we extrapolate [back into the past], we reach a point where all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe… For this reason most cosmologists think of the initial singularity as the beginning of the universe. On this view the big bang represents the creation event; the creation not only of all the matter and energy in the universe, but also of spacetime itself.1

But other cosmologists disagree that the evidence suggests a singularity, and Craig & Sinclair survey their arguments and theorems over the course of 50 pages.2 Unfortunately, this discussion is far too technical for non-physicists to judge, much less understand.

The short story is that Craig & Sinclair defend two major works that ‘prove’ an initial singularity: the Penrose-Hawking singularity theorems and also a 2003 paper by Borde, Guth, and Vilenkin. I will save the conversation about what cosmologists think about the force of these works for a later time, except to mention that Hawking has now repudiated his position on the initial singularity, and now spends his time “trying to convince other physicists that there was in fact no singularity at the beginning of the universe.”

Until then, we follow Craig & Sinclair’s logic:

Our survey shows that contemporary cosmology is quite supportive of the second premise of the kalam cosmological argument…

It seems that the field of cosmology, therefore, yields good evidence that the universe began to exist.

This concludes our discussion of Craig & Sinclair’s defense of premise 2 of the Kalam Cosmological Argument:

(2) The universe began to exist.

Next, we consider their defense of the first premise:

(1) Everything that begins to exist has a cause.

Stay tuned.

  1. “Spacetime singularities in cosmology” in J.T. Fraser (ed.), The Study of Time III, pages 78-79. []
  2. The Blackwell Companion to Natural Theology, pages 132-182. []

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{ 60 comments… read them below or add one }

NAL March 13, 2010 at 7:46 am

If we extrapolate [back into the past], we reach a point where all distances in the universe have shrunk to zero.

This assumes that distances can be infinitely subdivided, so as to approach zero. If spacetime exists in discrete units, quanta of spacetime, then this assumption is invalid.

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ImagingGeek March 13, 2010 at 8:17 am

There is a fundamental problem with using arguments like those of Craig & Sinclair’s in philosophical debates such as these – there are multiple interpretations of what the big bang could have been (singularity, quantum fluctuation, etc), and there is no way with current scientific knowledge to say which model (or even which family of models) is correct.

As such, any debate centered around big bang models will be inherently flawed, since had an other model been chosen the entire underlying assumptions of the debate would be changed.

Plus, there are some inherent issues with the way this argument has already been prefaced; NAL nailed one on the head – we have no idea if space-time is infinitely divisible, or if space-time itself is quantized. This may seem like a minor issue, but if space is quantified many of the big bang models (including that of Craig & Sinclair) are wrong. If space is quantified the very nature of singularities change; from an infinitely small, infinitely dense point, to a defined space of non-infinite density.

Another issue that I’ve noticed is the treatment of time as a separate entity from space; this is wrong (hence why it is called space-time). Time is as mutable a variable as is space. In many ways “before” the big bang is a non sequitur; “before” the big bang there was no time; and if there is no time there can be no before.

For an alternate model of the big bag – and one which I believe has a greater degree of evidentiary verification than Craig & Sinclair’s model, you can watch the following video. It is long, but in it Lawrence Krauss takes us through the evidence and explains, from an evidentiary point-of-view, how the universe could literally have formed from nothing.

http://www.youtube.com/watch?v=7ImvlS8PLIo

PS: I would also like to point out that in some models of the big bang, we are IN the singularity, rather than being a product of it.

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piero March 13, 2010 at 8:30 am

Good points by NAL and ImagingGeek. I’d only add a question: can the notion of “beginning” be reconciled with the absence of time? I find the notion of “time beginning to exist” unintelligible, but maybe my two neurons are just not up to the task.

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Briang March 13, 2010 at 8:50 am

ImagingGeek,

I watched the video with Lawrence Krauss not too long ago. I found it really interesting. However, I fail to see how he makes a case against God. He tells us that the universe came from nothing, but he also says that “nothing isn’t really nothing.”

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ImagingGeek March 13, 2010 at 9:06 am

I’d only add a question: can the notion of “beginning” be reconciled with the absence of time?

Sure; the beginning is when time begun. Literally t=o, for the entirety of our universe.

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ImagingGeek March 13, 2010 at 9:19 am

I watched the video with Lawrence Krauss not too long ago.I found it really interesting.However, I fail to see how he makes a case against God.He tells us that the universe came from nothing, but he also says that “nothing isn’t really nothing.

Using science to disprove god(s) is an impossibility; god(s) if they exist, inherently must lie outside of physical reality (otherwise, they would be obvious). Since science deals specifically with the physical world, anything (if anything) that lies outside of it is unprovable by science.

However, science can answer religious claims about the physical world – be it the age of the earth, the existence of global flooding, whether geocentrism is correct, etc. In the case of Krauss, he demolishes one of the most often made claims as proof of god(s) – that something (i.e. our universe) cannot come from nothing, and ergo there must be a creator (i.e. god[s]).

What Krauss shows is that, based on current scientific evidence, the universe can arise from nothing. Indeed, it can ONLY have arisen from nothing, as had it arisen from something there would have to be an inherent curvature to space-time.

This evidence specifically disproves the “something cannot come from nothing” proof of god(s). So while it does not disprove the existence of god(s) in absolutus, it does disprove one of the stronger evidences used as an argument for the existence of god(s).

As for the “nothing isn’t really nothing”I believe (its been a while since I read the video) that true nothingness doesn’t really exist, given quantum fluctuations.

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Zeb March 13, 2010 at 9:28 am

It seems to me this argument boils down to the contingency argument. The scientific and logical arguments for limits on all four axes of space-time are strong; the universe almost certainly does not extend infinitely physically in any direction. It’s not as though there was singularity sitting around doing nothing that somehow suddenly exploded, or an empty space into which suddenly appeared a singularity that instantly exploded. The universe can be thought of as a (at least) 4 dimensional object consisting of a certain amount of space-time and energy/matter in a certain arrangement, which at time-0 is in the shape of a singularity about to explode. All events have a time value greater than that of the singularity, and relate to it via the physical laws. And is that not just what ‘causation’ means, in the sense of one thing making another thing happen?

I think the outstanding question is not, “What knocked over the first domino which is the singularity->big bang?” but rather, “What determines the content and arrangement of the universe at any or all points of time?” The KCA notices a boundary on the universe called a “beginning,” and claims it is a special kind of boundary that requires a special kind of determiner. But outside of our material/space-time bound existence, don’t all the boundaries look the same? Aren’t they all equally demanding of explanation, or not, depending on what you think about contingency?

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Robert Oerter March 13, 2010 at 9:52 am

ImagingGeek: There is a fundamental problem with using arguments like those of Craig & Sinclair’s in philosophical debates such as these – there are multiple interpretations of what the big bang could have been (singularity, quantum fluctuation, etc), and there is no way with current scientific knowledge to say which model (or even which family of models) is correct.As such, any debate centered around big bang models will be inherently flawed, since had an other model been chosen the entire underlying assumptions of the debate would be changed.

This is exactly right. ALL of those cosmologies are completely speculative at this point, having little or no basis in the observable evidence. So for Sinclair&Craig to claim that cosmology is “supportive” of a beginning to the universe is complete garbage.

Plus, there are some inherent issues with the way this argument has already been prefaced; NAL nailed one on the head – we have no idea if space-time is infinitely divisible, or if space-time itself is quantized.This may seem like a minor issue, but if space is quantified many of the big bang models (including that of Craig & Sinclair) are wrong.If space is quantified the very nature of singularities change; from an infinitely small, infinitely dense point, to a defined space of non-infinite density.

Not only this, but Craig’s argument that an actual infinity cannot exist REQUIRES spacetime to be quantized. Because, if spacetime is infinitely divisible, than any interval of space (or time) contains an actual infinity.

So Craig’s “no infinities” argument defeats his “universe begins” argument.

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Briang March 13, 2010 at 10:12 am

ImagingGeek,

Showing that the universe came out of a zero energy state hardly proves that the universe pop into existence uncaused out of nothing. At best it shows that there is no pre-existing material out of which the universe was made. I think this fits nicely with the doctrine of Creation out of nothing. Since according to the doctrine, God didn’t make the world out of pre-existing material.

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Briang March 13, 2010 at 10:31 am

Robert Oerter,

Craig’s argument doesn’t depend on whether the time is infinitely divisible. When he argues for a finite past, his isn’t saying there are infinite moments (where moments are point-like). He saying that if you take some finite non-zero interval, there are only finite many intervals in the past. So he’s arguing that there are only finitely many seconds in the universe ( or minutes or hours or days).

I don’t see how an argument that says that there is a finite number of seconds, is committed to saying that you cannot potentially divide a second into smaller and smaller units. I think the arguments against an infinite past would require the commitment to the view that one could not complete the division of a second into a an infinite number of divisions (and perhaps perform some task in each moment.) For example if one could divide a second into an infinite number of point-like moments, one could build one room of a hotel in each point-like moment of a second and one could finish Hilbert’s hotel in a second. I think a person who accepts the arguments against an actual infinity, would have to also say that this is impossible. Yet, I don’t think one must be committed to the view that seconds are not potentially infinitely divisible.

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NAL March 13, 2010 at 10:35 am

Robert Oerter:
Not only this, but Craig’s argument that an actual infinity cannot exist REQUIRES spacetime to be quantized. Because, if spacetime is infinitely divisible, than any interval of space (or time) contains an actual infinity.

So Craig’s “no infinities” argument defeats his “universe begins” argument.  

While I agree that Craig’s argument requires spacetime to be quantized, I don’t see how this defeats his argument for a beginning of the universe. Time could still start at t=0 and the next instance of time would be t=quanta-of-time.

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ImagingGeek March 13, 2010 at 11:06 am

Showing that the universe came out of a zero energy state hardly proves that the universe pop into existence uncaused out of nothing.

You’ve already started with a logical fallacy here; the assumption of causality. Krauss’s video pretty much addresses that very point; there is no need for a “cause” to the universe, all you “need” is run-of-the-mill vacuum fluctuations. In other words the “creation” of our universe was not causative, but rather probabilistic.

At best it shows that there is no pre-existing material out of which the universe was made.

No, it actually shows quite a bit more than that. It both eliminates the need for a “cause” of the big bang, and instead describes it (and our resulting universe) as a probabilistic event no different than other quantum probabilistic event. Its important to note that quantum systems are generally considered to be free of deterministic causality; the very property you are assuming is required for the creation of our universe.

The fact that the quantum fluctuation is of zero energy is very informative; its important to note that the energy involved affects more than matter. The energy of the event dictates the structure of the universe, as well as its physics (i.e. the relative size and strength of the cosmological constant vs. gravity is directly determined by the initial energy state).

The initial energy state also tells us if our universe arose as a result of an outside (causative) or intrinsic (probabilistic) event. Zero-sum quantum events can only occur under one condition; that being a zero-energy (probabilistic) starting condition. Causative events lead to quantum decoherance (sometimes called waveform collapse). This only produces non-zero quantum states.

Ergo, if something caused our universe, our universe would have a non-zero quantum state.

I apologize for the confusing nature of the above statements – I lack the ability to clearly enunciate quantum dynamics. I understand it (philosophically, anyways); but I have a hell of a time describing it.

I think this fits nicely with the doctrine of Creation out of nothing.Since according to the doctrine, God didn’t make the world out of pre-existing material.

Even ignoring your mistakes about what the zero energy state tells us, even the above claim doesn’t hold water. Keep in mind that Kruass (nor I) claimed to disprove god(s) in absolutus, but rather were addressing a specific claim often made (that something cannot come from nothing). Krauss demolished this claim – both by showing that something (our universe) could in fact come from literally nothing (a quantum fluctuation of zero energy) AND also showed that the universe itself did not – indeed could not – have arisen through a causative process.

Shifting the goal posts (which is what you did above, by changing the claim under scrutiny) does not make Krauss’s argument incorrect.

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ImagingGeek March 13, 2010 at 11:32 am

While I agree that Craig’s argument requires spacetime to be quantized, I don’t see how this defeats his argument for a beginning of the universe. Time could still start at t=0 and the next instance of time would be t=quanta-of-time.

It also doesn’t stand up to the scrutiny of general relativity. GR tells us that time, like space, is mutable. It also tells us how it is mutable. If you run the clock backwards the curvature of space-time increases. As curvature increases, time slows. Get close enough to the big bang and the curvature approaches infinity; ergo time slows to “infinity”.

So there is, in fact, an infinite (or at least undefinable) amount of time between the big bang and now; or at least there is if space-time is not quantified and our understanding of GR is correct.

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Robert Oerter March 13, 2010 at 11:36 am

Briang:

I don’t follow you. If infinite divisibility of time is possible, what is to prevent me carrying out some task in each interval of time? Then I will have successfully completed an infinite number of tasks – and in a finite time, no less!

More fundamentally, if time and/or space is infinitely divisible, then time and/or space is a counterexample to Craig’s claim that an actual infinite cannot exist.

NAL:

As ImagingGeek said, quantized space-time would make many big bang models false. Specifically, quantized space-time would prevent a singularity from forming (or so it is generally believed), circumventing the singularity theorems that Craig loves to cite. If no singularity, then no need for an initial time for which there is no preceding time. That is, we expect a quantum gravity theory to allow us to extend the model back before the “t = 0″ moment to some predecessor state/universe. The various possibilities for the predecessor state are (1) infinite in past time, (2) finite in past time, or (3) timeless. Only (2) would support Craig’s argument; but there is no reason to expect (2) to be the “winner” according to this as-yet-unknown theory.

I should clarify that quantized space-time defeats the SCIENTIFIC part of Craig’s argument for a beginning to time. It doesn’t affect his other arguments for no-past-infinity. (I have dealt with those other arguments, in part, here: http://earlychristianreligion.org/forum/viewtopic.php?f=3&t=64 )

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Robert Oerter March 13, 2010 at 11:41 am

If you run the clock backwards the curvature of space-time increases.As curvature increases, time slows.Get close enough to the big bang and the curvature approaches infinity; ergo time slows to “infinity”.So there is, in fact, an infinite (or at least undefinable) amount of time between the big bang and now; or at least there is if space-time is not quantified and our understanding of GR is correct.  

Sorry, this is incorrect. In the usual big bang models there is a finite amount of past time. (Even though the curvature approaches infinity at t = 0 the proper time can be integrated to obtain a finite value.)

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ImagingGeek March 13, 2010 at 11:44 am

Specifically, quantized space-time would prevent a singularity from forming (or so it is generally believed)

To be accurate, it would change what we consider a singularity to be. You would not get an infinitely dense/small point, but rather a finite volume of finite density. This, however, would not eliminate the general characteristics we expect of singularities – i.e. space-time curvature greater than that allowing light to escape, etc.

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ImagingGeek March 13, 2010 at 11:55 am

Sorry, this is incorrect. In the usual big bang models there is a finite amount of past time. (Even though the curvature approaches infinity at t = 0 the proper time can be integrated to obtain a finite value.)

Hence why it was predicated with the statement “or at least there is if space-time is not quantified and our understanding of GR is correct”

As you say time must be integrated to make the math work – GR itself breaks down once the universe is smaller than its Schwarzschild radius. So we cannot describe (as discrete events) events before this time. You correctly point out we integrate multiple events to account for the events occurring before the Schwarzschild radius is reached, but what that means is we are using approximations to account for events we cannot describe with currently available physics.

In its strictest interpretation (i.e. not integrating events, but treating them as discrete entities), GR gives us infinite time from the big bang itself to when the Schwarzschild radius is reached. The use of integration is simply a mathematical trick to get around the obvious issue that infinite (or more accurately, undefinable) time gives us.

It all comes back to the original point I tried to make in my first post. We currently cannot describe the big bang nor the earliest events with modern science. Hence, any philosophical debates based on them are going to be deficient.

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manicstreetpreacher March 13, 2010 at 12:13 pm

The KCA is yet another example of Craig quote-mining atheist scientific authorities to support his position.

Penrose and Hawking have recanted their earlier thesis when they said that the universe began with the Big Bang singularity. However, hacks like Craig and Dinesh D’Souza mine extracts from Hawking’s A Brief History of Time and The Nature of Space & Time to make it appear that Hawking still believes that the universe began with the Big Bang singularity.

Hawking acknowledges in Brief History “So in the end our [Hawking and Penrose] work became generally accepted and nowadays nearly everyone assumes that the universe started with a Big Bang singularity.” However, the very next sentence Hawking writes, “It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe – as we shall see later, it can disappear once quantum effects are taken into account.” (p. 50)

In The New Atheism physicist Victor Stenger clarifies:

D’Souza has glanced at A Brief History of Time, mining quotations that seem to confirm his preconceived ideas. He quotes Hawking as saying, ‘There must have been a Big Bang singularity.’ D’Souza has lifted it out of context and given it precisely the opposite meaning of what Hawking intended… Hawking was referring to the calculation he published with Penrose in 1970, and D’Souza cut off the quotation. This act of editorship makes it look like Hawking is confirming that the Big Bang actually happened when in fact the full quote reveals just the opposite.

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manicstreetpreacher March 13, 2010 at 12:14 pm

@All those commenters wondering why there is “something” rather than “nothing”:

From Vic Stenger’s first rebuttal in his 2003 debate against WLC:

Why is there something rather than nothing?

Dr Craig also asks why is there “something” rather than “nothing”, why does the universe exist rather than “nothing”?

Well, why should “nothing” be a more natural state than “something”? Why would you expect “nothing” rather than “something”? In fact, how could “nothing” even exist? If it existed, wouldn’t it be “something”?

And finally, why is there God rather than “nothing”? Dr Craig doesn’t answer those questions.

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Briang March 13, 2010 at 12:48 pm

Robert Oerter: Briang:I don’t follow you. If infinite divisibility of time is possible, what is to prevent me carrying out some task in each interval of time? Then I will have successfully completed an infinite number of tasks – and in a finite time, no less!
More fundamentally, if time and/or space is infinitely divisible, then time and/or space is a counterexample to Craig’s claim that an actual infinite cannot exist.

I think the crucial difference is between a potential infinity and an actual infinity. Because their are infinity many natural number, a person could count potentially to infinity. Meaning that he could start at zero and always add another number. But this doesn’t imply that he could finish counting to infinity (aleph-0). The same can be said with division of time. Just because because one could potentially divide time into smaller and smaller units, doesn’t mean that a person can finish dividing time into an infinite number of units (aleph-1).

Also, check out Pruss’ Grim Reaper argument.

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lukeprog March 13, 2010 at 12:51 pm

Robert,

I love your site, by the way.

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lukeprog March 13, 2010 at 12:59 pm

Thanks for the quote, manicstreetpreacher.

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John D March 13, 2010 at 1:08 pm

Briang: I think the crucial difference is between a potential infinity and an actual infinity.

I’m not sure that works in this instance. I’m not entirely comfortable with making pronouncements in this area but it seems to me that physical models are supposed to represent reality. And the debate is whether the correct model says that spacetime is infinitely divisible or is quantized.

If the model says spacetime is infinitely divisible, then we are not simply talking about a possible or potential infinity, we are talking about an actual, metaphysically instantiated infinity.

Maybe the physicists can speak to this.

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ImagingGeek March 13, 2010 at 1:41 pm

John D:
I’m not sure that works in this instance. I’m not entirely comfortable with making pronouncements in this area but it seems to me that physical models are supposed to represent reality. And the debate is whether the correct model says that spacetime is infinitely divisible or is quantized.
If the model says spacetime is infinitely divisible, then we are not simply talking about a possible or potential infinity, we are talking about an actual, metaphysically instantiated infinity.Maybe the physicists can speak to this.  

I hope I am not putting words into Briang’s mouth, but I think much of this “argument” comes from the fact that most people think of infinity as some sort of number; which it is not. Infinity is not a value you can count to, given enough time, but rather is a mathematical convention used to describe what are generally impossible situations.

Take, for example, what an infinitely short period of time would be – zero time. If you could divide time into an infinitely small piece, that piece would have no time (if n were the units of time (t)”, n/t is infinite only when t is 0). The same is true of any other infinite value – density is only infinite if you have some non-zero amount of mass in zero volume.

So when Briang refers to “potential” verses “real” infinites I suspect (s)he is referring to potential infinites (i.e. something you could potentially keep dividing into smaller and smaller pieces without any end to the degree of smallness you get to) vs. a real infinite, where you end up with something contained in zero.

To be clear, if space were potentially infinitely divisible, no matter how many times you divided your space it smaller spaces, you would always be able to divide it smaller (i.e. your volume could always get closer to zero, but would never actually get there). That would be different that an real infinitely divided volume, where the volume of the subspaces” is zero.

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Chris Hallquist March 13, 2010 at 2:44 pm

I don’t think the Vilenkin et al 2003 paper shows what Craig claims it shows. He wants it to be a proof that any conceivable model of cosmology will require the past is finite, but I’ve read the paper, and I can’t see where it says this, though it does say many models (including the ones Vilenkin is betting on being right) will have a finite past. But Craig seems to be illegitimately trying to ignore the fact that we don’t really know what model of cosmology is right, and the right one might turn out to have a finite past. And no one seems to be saying Vilenkin’s models require a singularity–a singularity and a finite past are different things.

P.S. Awesome graphic–where’d you get it?

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Thomas Reid March 13, 2010 at 2:52 pm

A general question: which cosmological models account for:

(1) Discretized space-time, and
(2) The inflationary period

ImagingGreek:

It all comes back to the original point I tried to make in my first post. We currently cannot describe the big bang nor the earliest events with modern science.

This is all entirely consistent with the idea that space-time expanded from a singularity, no? Or in other words, this is not an objection to the scientific evidence.

Hence, any philosophical debates based on them are going to be deficient.

The scientific evidence points to a singularity approximately 13.7 billion years ago. Another way of saying this is that our scientific methods of inquiry stop there. That seems like very reasonable scientific evidence that space-time began to exist.

Anyway, if by deficient you mean “possibly wrong”, then I would agree. That doesn’t mean the premises are unreasonable, however.

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Conor Gilliland March 13, 2010 at 3:46 pm

where did you get the graphic?

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John D March 13, 2010 at 3:49 pm

Imaging Geek,

Thanks for the explanation. One comment, not addressed at anyone in particular but arising from this:

ImagingGeek: The same is true of any other infinite value – density is only infinite if you have some non-zero amount of mass in zero volume.

Isn’t that what a singularity is supposed to be, i.e. a point with non-zero mass in zero volume?

So if we accept the existence of such singularities, aren’t we accepting the existence of an actual infinite? Which is something Craig says we cannot accept.

All of which makes me wonder: why are Craig and Sinclair so keen on singularities?

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Thomas Reid March 13, 2010 at 4:48 pm

John D:
Isn’t that what a singularity is supposed to be, i.e. a point with non-zero mass in zero volume?

So if we accept the existence of such singularities, aren’t we accepting the existence of an actual infinite? Which is something Craig says we cannot accept.

All of which makes me wonder: why are Craig and Sinclair so keen on singularities?  

Ah, that’s an interesting observation. But the situation is not analogous. In the case of the cosmological singularity, the mass is finite, but the volume is zero. The limit of this ratio as you approach zero volume is infinity, of the “lazy eight” variety. The strict approach to division by zero is to say that it is not possible, therefore not permitted mathematically. Otherwise, obvious fallacies would result.

This is quite distinct from the concept of a set whose cardinality is aleph-naught, ie, a set that contains an actually infinite number of items.

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lukeprog March 13, 2010 at 5:37 pm

Chris,

Google images. :)

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Zeb March 13, 2010 at 5:38 pm

Robert- “If infinite divisibility of time is possible, what is to prevent me carrying out some task in each interval of time? Then I will have successfully completed an infinite number of tasks – and in a finite time, no less!”

But only if, as ImaginingGreek implied, your tasks each took 0 units of time to complete, which is a physical impossibility. No matter how infinitesimal your interval of time, you could always double your number of tasks by halving the time each takes, but you could never reach an infinite number of tasks completed.

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Supernova March 13, 2010 at 7:35 pm

William Lane Craig notes any universe, which has, on average, been expanding can’t be infinite in the past…

“Arvin Borde, Alan Guth, and Alexander Vilenkin, were able to prove that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.” – William Lane Craig

Alexander Vilenkin notes cosmologists can no longer hide behind the possibility of a past-eternal universe…

“It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning.” – (Many Worlds in One [New York: Hill and Wang, 2006]). – Alexander Vilenkin

Luke, you quote Stephen Hawking in his, 1996, book ‘The Illustrated Brief History of Time, Updated and Expanded Edition’…

“trying to convince other physicists that there was in fact no singularity at the beginning of the universe.” – Stephen Hawking

However, when Hawking uses his no-boundary proposal he is using imaginary numbers, and simply doesn’t convert back to real numbers. Once we convert back to real numbers, presto, the singularity returns.

“I still believe the universe has a beginning in real time, at the big bang. But there’s another kind of time, imaginary time, at right angles to real time, in which the universe has no beginning or end.” – (Hawking, S., (1994). Black Holes and Baby Universes and Other Essays. Oxford Oxfordshire: Oxford University Press.)

I know this quote comes two years before from his, 1996, book ‘The Illustrated Brief History of Time, Updated and Expanded Edition’, but the fact remains the same. That when he uses the no-boundary proposal he simply doesn’t convert back to real time. He keeps the imaginary time intact, and therefore the singularity is no longer there. He also notes this in his, 1996, book ‘The Illustrated Brief History of Time, Updated and Expanded Edition’. It would’ve took me much longer to hunt it down and find it, so, please, forgive me on being lazy. LOL

Also, I think it’s important to add that the Kalam Cosmological Argument doesn’t hinge on the singularity, rather the beginning of the universe. The 2nd premise isn’t contingent on a singularity, but the beginning of the universe itself. Even on the no-boundary proposal when Hawking doesn’t convert back to real time to get back the singularity, he still says the universe is finite and began to exist, so the 2nd premise is still valid on this scenario.

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lukeprog March 13, 2010 at 8:20 pm

Thanks, Supernova!

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Rhys Wilkins March 13, 2010 at 9:37 pm

When Quentin Smith talks about the singularity in his physics articles and debates on religion, he always stresses the importance of recognizing that the singularity is an ideal mathematical limit to a series, i.e. it is something which can be approached ad infinitum but never actually reached.

It’s very nature is mathematically and logically contradictory. For example it says that mass and energy must exist in zero dimensions, which is totally and utterly impossible. It can be compared with trying to imagine a real, tangible married bachelor holding a round triangle, or a twelve sided square etc.

The history of the universe can be expressed in a number line. At t=0 it is open ended. This means there is no exact instant in time which constitutes the absolute origin of the universe. There is literally no limit to how close we can go to t=0, but we can never hit actually it.

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Hermes March 14, 2010 at 1:21 pm

Craig & Sinclair quoting Davies: On this view the big bang represents the creation event; the creation not only of all the matter and energy in the universe, but also of spacetime itself.

That’s not correct, though, since this instance of the universe did not ‘create’ matter and energy at that point any more than I ‘create’ garbage by dropping a wine glass on a rock. Did I ‘create’ garbage? Yes, but I doubt that is what Craig and Sinclair are promoting.

Craig, by quoting Davies, is probably leaving out some critically important detail such as the ‘creation event’ being short hand for Davies acknowledging that to us there is no difference at this time because we currently lack knowledge and are not arrogantly asserting that we know the answers.

The same thing happens with Einstein’s ‘God doesn’t play dice’ quote.

If anyone can provide insight and details on what Davies actually intended and his reasons for it, that would be great.

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Cecilia March 14, 2010 at 1:23 pm

I am very much out of my league here, not being mathematically inclined in the least. But I have been pulled into this KCA series and find it v. interesting. Please bear with me,this is probably a v. stupid question.

Regarding Hilbert’s Hotel which I really can’t get my head around because I keep obsessing on this question:why does the manager need to move any guests to accommodate new guests? The poor schmo who is in Room #1 has to move to Room #2, Room #2 has to move to Room #3, etc, etc, etc, all so the manager can move the new guest into Room #1. And, then the manager decides that everyone in even # rooms (or odd, I forget) has to move out and new guests move into their vacated rooms. Huh? Why all this disruption? What is the point? Why not just move new guys into Room # “infinity + 1… + 2… +3, etc, etc, etc” and leave all the other guys in peace? I am quite serious about this question because I don’t understand all this unnecessary moving about of the guests in this thought experiment. Consequently, I can’t wrap my mind around the idea that it “proves” that an actual infinite is impossible or paradoxical or whatever it is.

Hope someone can help because I haven’t found much to make me understand on “the Google.” I did see something on this at the Philosophy of Religion website about infinity: “If there exists an infinite past, then if we were to assign a number to each past moment then every real number (i.e. every positive integer) would be assigned to some moment. There would therefore be no unassigned number to be assigned to the present moment as it passes into the past.” Why? Why would there be no unassigned number to be assigned to the present? If infinity is infinite then why not? Wouldn’t there be an unlimited number to assign to past, present and future?

Anyway, I will be interested to see where you end up with analysis of the KCA. I am not clear though why this is necessarily an argument for God versus an argument for something we simply do not understand at this point in the development of human scientific understanding? Why does an uncaused, first cause necessarily = God? And, as you point out, it certainly does not point to any specific brand of god……. But I am not convinced about the “uncaused, first cause” thing yet…..

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Hermes March 14, 2010 at 1:46 pm

Briang: ImagingGeek,Showing that the universe came out of a zero energy state hardly proves that the universe pop into existence uncaused out of nothing.At best it shows that there is no pre-existing material out of which the universe was made.I think this fits nicely with the doctrine of Creation out of nothing.Since according to the doctrine, God didn’t make the world out of pre-existing material.  

That’s *not* what Krauss said and I don’t know of *any* current cosmologist who makes that claim.

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Haukur March 14, 2010 at 2:15 pm

Cecilia: What is the point? Why not just move new guys into Room # “infinity + 1… + 2… +3, etc, etc, etc” and leave all the other guys in peace?

Because there is no such number as ‘infinity’ and the hotel is full. What does “the hotel is full” mean? It means that if you ask “is room x full?” the answer will be “yes” for any ‘x’ you can think of. So the only way to make room for new guests is to move the existing guests. Admittedly, it seems horribly inefficient to move infinitely many guests just to make room for one new guest but that’s the way the cookie crumbles.

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cecilia March 14, 2010 at 3:45 pm

@Haukur:

Okay, so, there is “no such number as ‘infinity’”….what, then, is infinity? I mean, I know it is a concept but I don’t know what it is for. And, isn’t asking if room x is full different from asking if there are any rooms available? I understand that room x is not available but since there are an infinite number of rooms than rooms clearly are available. Also, is “infinity” the same concept as “an infinite number of [something]?

As hard as it is for me to wrap my mind around infinity, I am just not following Hilbert’s Hotel thought experiment as a way to show that the actual infinite is not possible or produces absurd paradoxes. Is it my legal training which produces a different way of thinking about problems (not only that but the types of problems we deal with are totally different from mathematical, etc-type problems)??

Just as an aside, the two biggest mind blowers for me have always been both the concept of “infinity” and the concept of “nothing” or “nothingness.” Both seem impossible!

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Thomas Reid March 14, 2010 at 6:58 pm

cecilia:
As hard as it is for me to wrap my mind around infinity, I am just not following Hilbert’s Hotel thought experiment as a way to show that the actual infinite is not possible or produces absurd paradoxes.

You just added an infinite number of people to Hilbert’s Hotel, which was previously occupied by… an infinite number of people. Now ask yourself, how many people are in the Hotel after that huge (!) addition of guests? Why, the exact same number of people occupy it now as did previously. But, that’s impossible, you protest! Look at all the people that just checked in! You have just demonstrated to yourself the absurdity of an actual infinite number of things existing in reality.

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Sharkey March 14, 2010 at 7:14 pm

cecilia:

Okay, so, there is “no such number as ‘infinity’”….what, then, is infinity?

The only reason we can talk about “infinity” as a well-defined mathematical concept is entirely due to the work of Georg Cantor.

There’s too much to describe in a simple blog comment post, so I’ll have to direct you to a text on set theory; however, if you’ve got the time, this documentary was pretty good, looking at Cantor (and others) from a personality perspective: http://video.google.com/videoplay?docid=-5122859998068380459

The short answer is: a countably infinite set is any set that can be put into correspondence with the natural numbers. That is, if you can label a list with the numbers 1,2,3,… ad infinitum, then that list is countably infinite. With this definition, you can find some interesting results, such as (a) you can label the integers (both negative and positive numbers) using the natural numbers (1,2,3…), (b) you can label the rational numbers (a/b for any integer a and b), and (c ) you _can’t_ label the reals this way.

That final point was the most shocking. There are different “sizes” of infinity! In fact, certain questions about infinity are not knowable using “traditional” mathematics; see the Continuum Hypothesis.

Hilbert’s hotel is just a metaphor for the first labeling. In essence, you can label 0,1,2,3,4,… using the numbers 1,2,3…, creating space for a new guest (guest 0). By continuing this process, you can make space for guest -1, -2, -3, etc.

Just as an aside, the two biggest mind blowers for me have always been both the concept of “infinity” and the concept of “nothing” or “nothingness.” Both seem impossible!

The nice thing about math is that it formalizes and creates rigor for these types of questions. But yes, both concepts blow minds :) Some of the most interesting results of the 20th century were “nothingness” results: there are certain things that can’t be known or created, like a consistent and complete first-order predicate logic (Godel), a computer program to tell if another program is buggy (Turing), or how often a computer program halts (Chaitin).

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TaiChi March 14, 2010 at 7:37 pm

Cecilia: I am not clear though why this is necessarily an argument for God versus an argument for something we simply do not understand at this point in the development of human scientific understanding? Why does an uncaused, first cause necessarily = God?

It’s not even an argument for a first cause, strictly speaking. Just an argument for a cause.

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Yair March 15, 2010 at 2:42 am

Virtually any physicist believes that GR is an approximation for an underlying quantum theory (there are some notable exceptions, of course). No quantum theory would allow a true singularity. Arguing for a singularity seems to me to be anachronistic. For example,
http://arxiv.org/abs/0810.0514

Most of the attempts to contemplate quantum gravity imply that there is some sort of multiverse that our universe, seen as a space-time block or “bubble”, is only a part of. This makes the question of the finitude of the universe’s time obsolete – even if the time within the space-time bubble we call our universe has a beginning, this is but a part of a greater existence (which exists atemporally, in relation to that time). As we lack a good understanding of quantum gravity, no option can currently be ruled out, but the weight of the evidence seems to suggest that there is a multiverse that has no single time axis, and with areas without a time axis at all. For example,
http://arxiv.org/abs/0908.0721

That weight is still too weak to form a solid opinion, so that the assumption that “The universe [i.e. existence] has a finite past” is still plausible, albeit unlikely.

In short, the scientific evidence for “(2) The universe began to exist” (interpreting “began” as a noun, as in “Highway 65 begins at Northampton…” – not as a verb) is rather weak, but this hypothesis cannot (yet?) be ruled out.

The philosophical case for this proposition is pure metaphysical rubbish; it’s an empirical question, not a philosophical one.

The proposition that existence began to exist as a verb, however, is philosophical rubbish. Even Parmenides knew time cannot flow.

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ImagingGekk March 15, 2010 at 5:57 am

I feel as though I dropped the ball – posted for a day and disappeared. In my defence I was stuck at an airport.

@John D “Isn’t that what a singularity is supposed to be, i.e. a point with non-zero mass in zero volume?”

It is, if space-time isn’t quantised. If space-time is quantised than a singularity would be very different.

@Hermes “That’s *not* what Krauss said and I don’t know of *any* current cosmologist who makes that claim”

If our universe came from a zero-energy quantum fluctuation, than by definition we did not come from any pre-existing matter. If we did then our quantum fluctuation would have a non-zero energy balance. Obviously, that assumes any “pre-universe” works on rules the same as ours.

Hence his statement “we literally came from nothing”

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Robert Oerter March 15, 2010 at 6:43 am

Supernova: William Lane Craig notes any universe, which has, on average, been expanding can’t be infinite in the past…“Arvin Borde, Alan Guth, and Alexander Vilenkin, were able to prove that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.” – William Lane Craig

Alexander Vilenkin notes cosmologists can no longer hide behind the possibility of a past-eternal universe…“It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning.” – (Many Worlds in One [New York: Hill and Wang, 2006]). – Alexander Vilenkin

But, as Chris has already noted, the theorem doesn’t actually say what Vilenkin says it says. Borde has mentioned this (can’t find the article right now): the theorem only says that SOME worldlines cannot be extended infinitely into the past. It is still possible that OTHER worldlines DO have an infinite past.

A deeper problem is that the theorem still relies on GR being true. If, as physicists today usually assume, GR breaks down at the Planck scale, then the conclusions of the theorem break down too.

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Hermes March 15, 2010 at 7:51 am

Yair: The philosophical case for this proposition is pure metaphysical rubbish; it’s an empirical question, not a philosophical one.

The proposition that existence began to exist as a verb, however, is philosophical rubbish. Even Parmenides knew time cannot flow.

Yair, good comments.

I find it strange that many people who engage in philosophical conversations — even people who should know better — completely ignore the core of what they discuss, or even what the words they use actually mean.

ImagingGekk, I agree. Thank for you for your more through treatment. I was only commenting on Craig and Sinclair’s (& Briang’s) use of an argument for ‘creation’ being ‘nothing’ then ‘poof!’ (thus, must be Yahweh) which is not supported or proposed by any cosmologist.

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Hermes March 15, 2010 at 8:00 am

A clarification: My mocking caricature of Craig/Sinclair (& Briang’s) position in strict philosophical terms is not correct. It is correct in intent, though. I have no doubt that they would assert that their deity Yahweh has no creation moment, and that when Yahweh initiated the universe that we are in now their deity did so rapidly if not instantly regardless of how long that point of initiation took to get to the moments we exist in now for this conversation.

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Briang March 15, 2010 at 9:18 am

Hermes:
That’s *not* what Krauss said and I don’t know of *any* current cosmologist who makes that claim.  

Well it may be that I misunderstood Krauss, however, I think this may be because he didn’t clearly articulate an argument about how the universe came from nothing. If you’d like to clarify what he meant, I’m certainly open to trying to understand it.

I find this to be a frustrating pattern emerging from atheist conferences I’ve watched. I’m told that my religious beliefs are silly, ignorant, unscientific, etc. Then, I’m told that science is the true way to discover knowledge. Then I’m given some discussion of some scientific findings given in a context of religion and atheism. While given no explicit argument, I’m left with the impression that I’m supposed to find the evidence problematic for religion somehow.

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Hermes March 15, 2010 at 10:04 am

Briang, he did specify what he meant. Others here have filled in quite a few gaps here in the replies that have gone back and forth — many answers were well beyond what I am currently able to provide.

So, you have plenty of very good summaries, and an informed group of people that will probably be willing to address any actual questions you have.

What do you do next? Do you already have the answers and need nobody to offer any contrary comments, or do you have some that you do not know and are actually curious about?

You can check any answers people give you if you want later, as long as you are careful with the source you use to check them.

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Supernova March 15, 2010 at 10:39 am

Robert Oerter:
But, as Chris has already noted, the theorem doesn’t actually say what Vilenkin says it says. Borde has mentioned this (can’t find the article right now): the theorem only says that SOME worldlines cannot be extended infinitely into the past. It is still possible that OTHER worldlines DO have an infinite past.A deeper problem is that the theorem still relies on GR being true. If, as physicists today usually assume, GR breaks down at the Planck scale, then the conclusions of the theorem break down too.  

Yes, General Relativity, a classical theory, predicts its own demise at singularities.

However, Alan Guth says it is not controversial to say our universe or as he says our local universe had a beginning for the science, as he believes, helps back this up. The more controversial thing, b/c it’s quite speculative, is inflation or the pre-history. Alan Guth is the founder of inflation and says even on this theory that it, too, has a beginning. He says one can’t extrapolate infinitely into the past even on this theory.

Reference:
http://www.closertotruth.com/video-profile/Did-Our-Universe-have-a-Beginning-Alan-Guth-/856

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Robert Oerter March 16, 2010 at 6:04 am

Supernova:
Yes, General Relativity, a classical theory, predicts its own demise at singularities.However, Alan Guth says it is not controversial to say our universe or as he says our local universe had a beginning for the science, as he believes, helps back this up. The more controversial thing, b/c it’s quite speculative, is inflation or the pre-history. Alan Guth is the founder of inflation and says even on this theory that it, too, has a beginning. He says one can’t extrapolate infinitely into the past even on this theory.Reference:
http://www.closertotruth.com/video-profile/Did-Our-Universe-have-a-Beginning-Alan-Guth-/856  

Inflation is not separate from GR – it relies on it. So when I say GR breaks down, that goes for inflation, too.

That our local universe had a beginning, in Guth’s sense, is not at all what Craig is talking about. Guth means merely that whatever came before was a very different state than our current universe. And no one (not even Guth) knows what that previous state was like.

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Hermes March 16, 2010 at 6:50 am

Robert Oerter: And no one (not even Guth) knows what that previous state was like.

[ Including Craig or any other religiously motivated spokesman or book. ]

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Thomas Reid March 16, 2010 at 9:35 am

Robert Oerter:
A deeper problem is that the theorem still relies on GR being true. If, as physicists today usually assume, GR breaks down at the Planck scale, then the conclusions of the theorem break down too.

GR and quantum theory need to be reconciled, for sure. But that fact does not mean that the inference to a finite past is invalid. You would need to show that GR is false to make that inference. That’s a tall order for such a well-tested theory.

Robert Oerter:
That our local universe had a beginning, in Guth’s sense, is not at all what Craig is talking about. Guth means merely that whatever came before was a very different state than our current universe. And no one (not even Guth) knows what that previous state was like.

Well, that’s all consistent with Guth’s claim that inflation cannot be extrapolated to the infinite past. It is the finitude of the past that is central to Craig’s claim, and it sure seems to me like Guth confirms it.

Guth is, by necessity if indeed there was a “local” Big Bang, making a metaphysical claim when discussing what “previous states” were like without the universe as we know it. But then, so is Craig. Metaphysical objections to the inference that God brought space-time into being are of course permitted, but let’s recognize them for what they are.

Here’s a good interview of Vilenkin doing metaphysics. He declares right up front that other universes would not be detectable (empirically, of course) since light cannot travel from here to “there”:

http://www.thoughtcast.org/science/the-end-of-our-universe-among-other-timely-topics/

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Robert Oerter March 16, 2010 at 10:09 am

Thomas Reid:
GR and quantum theory need to be reconciled, for sure.But that fact does not mean that the inference to a finite past is invalid.You would need to show that GR is false to make that inference.That’s a tall order for such a well-tested theory.

You are shifting the burden of proof, but it won’t fly. If you (or Craig) want to infer on the basis of GR that the universe had a beginning, you need to demonstrate that GR is a valid description of the universe at that time. As of right now, there is no reason to believe that GR IS good description before the Planck time, and there are good reasons to believe that it is NOT.

It is simply incorrect to claim that science “supports” the claim that the universe had a beginning.

Well, that’s all consistent with Guth’s claim that inflation cannot be extrapolated to the infinite past.It is the finitude of the past that is central to Craig’s claim, and it sure seems to me like Guth confirms it.

But Guth clearly states at beginning of the interview that what he’s saying is SPECULATION. At the end, he repeats that it is an open question. He is not talking about settled science, he is talking about a specific model of what the pre-BB state MIGHT HAVE BEEN like.

These “might have beens” cannot be used to argue that the universe had a beginning. At best, Craig could say something like, “Some cosmological models are consistent with the idea that the universe had an absolute beginning in time.” But, to be honest, he should add, “Other cosmological models are not.” Since neither sort of model has a clear upper hand, scientifically speaking, at this time, it is illegitimate to claim that science supports Craig’s view.

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Hermes March 16, 2010 at 11:00 am

Thomas Reid: GR and quantum theory need to be reconciled, for sure. But that fact does not mean that the inference to a finite past is invalid. You would need to show that GR is false to make that inference. That’s a tall order for such a well-tested theory.

Doing a slight bit of extrapolation from what Robert wrote would address your reply to him.

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Thomas Reid March 16, 2010 at 1:20 pm

Robert Oerter:
As of right now, there is no reason to believe that GR IS good description before the Planck time, and there are good reasons to believe that it is NOT.

Right, and is the Planck time finite or not? The point being, one need not simply conform GR to quantum theory. Rather, they must be reconciled. All I’m aware of is physicists speculating that a quantum theory of gravity may avoid the singularity. Well sure, that’s a pretty harmless statement, and one that doesn’t really dent the claim that the cosmological theory we do have points to a beginning.

But Guth clearly states at beginning of the interview that what he’s saying is SPECULATION. At the end, he repeats that it is an open question. He is not talking about settled science, he is talking about a specific model of what the pre-BB state MIGHT HAVE BEEN like.

I agree he is speculating. My point was, even when speculating, his theory must comport with GR such that inflation cannot be considered to extend to the infinite past.

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Hermes March 16, 2010 at 3:35 pm

Thomas Reid: Right, and is the Planck time finite or not?

Mu.

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question June 3, 2010 at 9:20 pm

how does big bang prove the infinitely dense zero volume singularity had a beginning ?

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Roger November 25, 2011 at 10:11 pm

Common sense implies that a singularity is in itself impossible, for a universe to exist. If a singularity exists, there is no universe, or space, or time, or reality, nor can there ever be. A singularity implies “infinite” gravity, or “infinitely” small which implies that if it is infinite, nothing, not even light can escape and all known reality breaks down, and a true singularity is theoretically the existence of nothing. But how can nothing “exist”? If it’s nothing, then there is no existence and therefore it can’t be something, and how can nothing become something? If something is “infinitely” small, then it isn’t “something”, then all reality is sucked in to the infinite and if it’s infinite there can be no reality or big bang either. How can there be a big bang if the gravity of a singularity is infinite and light itself can’t even escape? There will never be a big bang OUTWARD if all is “infinitely” INWARD? And on and on it goes to the infinite…Aha! There must be a God or Being, that is outside of spacetime to be the first cause of “all” things. Our finite minds cannot even beging to imagine the infinite. But we CAN still believe, even if we don’t fully understand. It takes more faith to believe that we are here by mere accident or random processes, than to believe in God as the first cause of ALL things. I Believe in God. It is the only logical conclusion, if we consider ourselves “intelectually honest”.

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Robert Oerter November 28, 2011 at 6:46 am

Roger, you have to be careful using “common sense” when you’re talking about advanced physics! :)

There is no “outward” and “inward” at the singular point: the singularity happens at EVERY point in space. However, you are right to say that this singularity cannot be considered the beginning of the universe. The singularity is a point where the laws of physics as we know them do not apply. So, it makes no sense to say the singularity is the physical cause of the whole universe (as Quentin Smith tries to do).

As far as taking things on faith, it doesn’t take any faith at all to believe the universe exists: we can SEE that it exists. Supposing that God is an explanation for it all is far more speculative than supposing everything began (for example) by tunneling from a quantum vacuum state. At least we have some reason to think that quantum mechanics describes the universe to some approximation.

Inventing an imaginary being, and then claiming that that being somehow explains the origin of the universe, does not seem like the intellectually honest approach to me.

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