Chronos, Good point. I agree. I never wrote a word against the possibility of an infinite number of disjointed, finite space-time continuums. Do you have a particular favorite model along these lines?Chronos said:James, Infinities of any kind in nature create problems and paradoxes. For example, most scientists consider the classical singularity of GR as unphysical and expect it will be resolved by a working version of quantum gravity. An infinite arrow of time is really not much different from a gravitational singularity which pretty much implies the same thing, just on a smaller scale. We know the observable universe is temporally finite, which appears to immunizes us residents against 'sins of the father' invoked by an infinite arrow of time. If we assume all other universes [if any] are temporally finite and causally disconnected, an infinite number of temporally finite universes does not appear to create a paradox.
Thank you. I'll take a close look Olber's paradox. Do you know of any other examples?Chronos said:I'm not partial to any vast / infinite number of 'universes' model, but, nearly all of them, AFAIK, at least imply they are causally disconnected - which means we can, at best, only infer any of them actually exist. I've always felt that places the whole idea on equal footing with creationism, which I find unappealing.
And yes, I agree you did not rule out the possibility of causally disconnected universes. What you assert, IMO, is a paradox that arises in any universe that is infinitely old. In my mind this has already been done - e.g., Olber's paradox. This problem does not arise in a temporally finite universe.
Chronos, I took a second look at this and disagree that most multiverse models imply causal disconnection. For example, most multiverse models of inflation imply that there was no first inflation event or first vacuum fluctuation. And a cyclic universe by definition implies that there has been an infinite number of past cycles. Some of the papers on twenty-first century cyclic models include a side note that there might have been a beginning (which means it is not a true cyclic model) and make no attempt to explain the beginning, but these papers need to insist that an infinite past sequence of expansions and crunches is imposable for reasons that have been known since the sixth century while there had to be a beginning. I have no doubts of the possibility of infinite past sequences in geometry but not in nature.Chronos said:I'm not partial to any vast / infinite number of 'universes' model, but, nearly all of them, AFAIK, at least imply they are causally disconnected - which means we can, at best, only infer any of them actually exist.
james.goetz said:Chronos, I took a second look at this and disagree that most multiverse models imply causal disconnection. For example, most multiverse models of inflation imply that there was no first inflation event or first vacuum fluctuation.
Hi Mark, My objection in this thread has no qualms with multiverse hypothesis with a first vacuum inflation. Do you agree with me that all mutliverse hypotheses with an infinite past chronology of vacuum fluctuations and all genuinely cyclic universe hypotheses are impossible?Mark M said:James, this is not true. The concept of a multiverse arising from inflation is based off of the fact that the doubling time of the space occupied by the inflaton field is larger than the half-life of the inflaton field. Some models of inflation imply that the universe has been inflating forever, but there are many that allow for a first vacuum fluctuation/inflation event, and still give rise to a multiverse. Eternal inflation's predictions of the fluctuation level in the CMB have been precisely confirmed by WMAP.
james.goetz said:Hi Mark, My objection in this thread has no qualms with multiverse hypothesis with a first vacuum inflation. Do you agree with me that all mutliverse hypotheses with an infinite past chronology of vacuum fluctuations and all genuinely cyclic universe hypotheses are impossible?
Mark,Mark M said:James,
Mostly, yes. The obvious problem of any cyclic model is entropy - considering it must always increase towards the future (unless it is maximized, of course) a cyclic model must dance around this, and many do it unconvincingly. I wouldn't go as far as to say impossible, considering we do not yet have a theory of quantum gravity to analyze such situations. But I personally do not prefer the cyclic models.
Instead, I prefer the model advocated by cosmologists such as Sean Carroll that a perfectly symmetrical de Sitter space, with a chaotic, high state of energy, can be a point of beginning.
Yes, I would recommend it. It is an interesting book.james.goetz said:Mark,
I have yet to read Carroll's from Eternity to Here, but it is on my list.
Because quantum fluctuations respect the T symmetry, it doesn't make very much sense to ask how long it existed. For example, a electron-positron annihilation can be viewed both ways, and you would have absolutely no way of distinguishing one way from another. So, a space of only vacuum fluctuations is symmetric in any direction of time. Vacuum fluctuations would eventually allow for the formation of the inflaton field, which could then begin the inflation of a region of space. This is essentially the story given by Andrei Linde's chaotic inflation.I am unsure of your background, but could you please try to describe to me a "perfectly symmetrical de Sitter space, with a chaotic, high state of energy." For example, Did this state always exist without activity until the first vacuum fluctuation?
Hi Chronos,Chronos said:Without a renewable source of energy [e.g. steady state theory], any infinitely old universe would have already suffered heat death. We know that we do not live in such a universe. We can say with great certainty the observable universe has a finite age, and there is not a shred of evidence any 'free' energy source is powering it. I think you have fallen into an exotic version of Zeno's paradox where the causality chain is infinitely divisible. The problem with infinities is the attendant risk of getting sheer nonsence from any assumption used to make inferences. You may wish to take a look at probability and set theory to see how they handle this problem.
Let us suppose we reside in a universe that is spatially infinite and contains an infinite amount of matter. What can we say about the average energy density of such a universe - is it infinite, zero, or some specific value? Obviously, it could be anything because density is a ratio between volume and matter and when you divide infinity by infinity you can get any answer your heart desires. Since our universe has an average energy density that is not infinite, does that mean it cannot be spatially infinite? Perhaps, but, the better answer is, IMO, it must at least include regions that are causally disconnected from the part observationally accessible to us.
Mark M said:James,
Yes, I would recommend it. It is an interesting book.
Because quantum fluctuations respect the T symmetry, it doesn't make very much sense to ask how long it existed. For example, a electron-positron annihilation can be viewed both ways, and you would have absolutely no way of distinguishing one way from another. So, a space of only vacuum fluctuations is symmetric in any direction of time. Vacuum fluctuations would eventually allow for the formation of the inflaton field, which could then begin the inflation of a region of space. This is essentially the story given by Andrei Linde's chaotic inflation.
Chronos, Zeno's paradox of an infinite number of points in any finite distant has no bearing on reality because Achilles can take over the tortoise regardless of a misapplication of an infinite number of points. And Zeno's paradox will never make this universe infinitely old.Chronos said:James, here is the issue "... but I am focusing on one angle, which is rejecting the possibility that an infinite sequence could pass." This is invalid for reasons I have already detailed - it's merely a version of Zeno's paradox.
Remember, in the universe today, there aren't just vacuum fluctuations. Macroscopic objects can perform thermodynamically irreversible processes, which create the 'arrow of time'. In a de Sitter space with no macroscopic components, just vacuum fluctuations, the arrow of time does not exist. Remember that time is relational - a sentence without any words is not an empty sentence, it simply doesn't exist. Similarly, a universe with no thermodynamically irreversible processes doesn't have an arrow of time - until one occurs.james.goetz said:I understand a little about the concept of a time reversible region generating verses. But there are also quantum fluctuations in the observed universe. Is that correct? And as far as quantum fluctuations in our universe, placing them in timeline should make sense. Is that correct?
It's not that Zeno's paradoxes are unscientific, they are just flat out wrong. Zeno considered the smallest unit of time to be a 'moment', a frozen slice of time. Obviously, time measures change. So, the smallest unit of time would be the smallest unit of change. (e.g. the Planck time, the time it takes light to traverse one Planck length.) This resolves the paradox. And secondly, his paradox with Achilles is resolved with calculus.james.goetz said:Chronos, I thought of one more thing about Zeno's paradoxes. He developed them to prove that motion is an illusion, similar to the modern philosophical concepts of eternalism. When you appeal to a Zeno's paradox, do you agree with Zeno that motion is an illusion? If that is the case, then appealing to motion as an illusion includes that there is no cause and effect and therefore no basis for scientific theory, which is similar to what I said in the third paragraph of my original post. Bowing to Zeno is equivalent to rejecting empirical observation of cause and effect.
Okay, I picture a model of space with zero mass and no time's arrow. This space has natural laws that generates vacuum fluctuations with T symmetry and some fluctuations develop into space-time bubbles. Is this all correct?Mark M said:Remember, in the universe today, there aren't just vacuum fluctuations. Macroscopic objects can perform thermodynamically irreversible processes, which create the 'arrow of time'. In a de Sitter space with no macroscopic components, just vacuum fluctuations, the arrow of time does not exist. Remember that time is relational - a sentence without any words is not an empty sentence, it simply doesn't exist. Similarly, a universe with no thermodynamically irreversible processes doesn't have an arrow of time - until one occurs.
Mark M said:It's not that Zeno's paradoxes are unscientific, they are just flat out wrong. Zeno considered the smallest unit of time to be a 'moment', a frozen slice of time. Obviously, time measures change. So, the smallest unit of time would be the smallest unit of change. (e.g. the Planck time, the time it takes light to traverse one Planck length.) This resolves the paradox. And secondly, his paradox with Achilles is resolved with calculus.
The idea is that in the wide variety of fluctuations, something along the lines of an inflaton field will be produced. This will then begin inflation in the region it exists in, and inflation takes over from there.james.goetz said:Okay, I picture a model of space with zero mass and no time's arrow. This space has natural laws that generates vacuum fluctuations with T symmetry and some fluctuations develop into space-time bubbles. Is this all correct?
Not necessarily. The point is that you can have vacuum fluctuations 'from nothing' that could produce a universe.I suppose that a lack of time's arrow and T symmetry events would not negate the events occurred within a countable sequence, regardless that each event looks the same in forward or reverse. Perhaps we disagree about this?
AFAIK, all theories of quantum gravity propose a discrete spacetime. Otherwise, calculations result in a variety of infinities. The discovery that there is fundamental limit to how much information can be contained in a region, is irreconcilable with the view of a continuous spacetime.I see space-time as a continuum, so likewise I see Planck time and Planck length as discretionary units that are infinitely divisible and points are insubstantial. But particles are indivisible and subject to annihilation while nobody can certainly identify the center point of a particle for any given point in time.
Mark M said:The idea is that in the wide variety of fluctuations, something along the lines of an inflaton field will be produced. This will then begin inflation in the region it exists in, and inflation takes over from there.
The point is that you can have vacuum fluctuations 'from nothing' that could produce a universe.
I heard differently but cannot do the calculations by myself. This could make an interesting question for the forum, which probably has been addressed previously:AFAIK, all theories of quantum gravity propose a discrete spacetime. Otherwise, calculations result in a variety of infinities. The discovery that there is fundamental limit to how much information can be contained in a region, is irreconcilable with the view of a continuous spacetime.
Hi Travis, Yes you describe an infinite road with one finite end comparable to a geometric ray. Also consider that there is an infinite number of positive natural numbers and an infinite number of negative natural numbers and an infinite numbers natural numbers in multiples of 2, 3, 4, and ad infinitum. But how does this relate to the thread?Travis_King said:Quick question:
You stand with your back against a wall and begin walking on a perfectly flat road. This road extends into spatial infinity in front of you, but that wall always remains where it is.
We would call this road infinitely long, no? As it does extend an infinite length in the direction you are walking. But what about the wall? Does the fact that the wall exists negate the "infinity-ness" of the road? Would the road be more infinite if the wall were removed and you were able to walk the road in the other direction as well?
Hi Chronos,Chronos said:Zeno's paradox is based on the idea that space is infinitely divisible and Achilles never catches the turtle because it would take infinite time to cross the infinite number of infinitesimal points separating him from the turtle. If you replace infinitely divisible space with an infinitely divisible number of causal events, you have merely restated Zeno's paradox. Even Zeno knew something was wrong with this argument, but, not how to prove it.
james.goetz said:In my case, I observe the expansion of a flat universe and say that it will always expand and always have a finite size and age.
Hi thorium1010: Yes, that is what I meant by "always."thorium1010 said:I think the bolded part is important to understand that current observations appear that the universe will continue to expand that means it will expand infinitely and that includes time, there is no finite time in the future at which the universe will stop expanding (as per current observations).