An Infinite Time's Arrow is Impossible and Incompatible with Scientific Theory

In summary, zhermes argues that the concept of infinity is controversial and that there is no reason why future infinite time cannot exist. However, he does not provide any evidence to support this claim.
  • #36
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.
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?
 
Space news on Phys.org
  • #37
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?

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.
 
  • #38
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.
 
  • #39
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.
Mark,

I want to clarify that I'm not looking at the possibility if a cyclic model can regenerate low entropy, but that an infinite past chronology of cycles could never pass. For example, if one of the hypotheses for regeneration of low entropy in cyclic universe is correct, then it still would be impossible on the grounds that an infinite sequence can never pass.

I have yet to read Carroll's from Eternity to Here, but it is on my list. 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?
 
  • #40
James,
james.goetz said:
Mark,
I have yet to read Carroll's from Eternity to Here, but it is on my list.
Yes, I would recommend it. It is an interesting book.
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?
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.
 
  • #41
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.
Hi Chronos,

I am unsure that I am following you. I reject a past infinite causality chain. I guess I do [not] see how that could translate into me falling into an exotic version of an infinitely divisible causality chain. Or are you merely saying that I am rejecting such a causality chain? And I will clarify that I understand that there are various other reasons in physics that support a finite space-time universe or multiverse, but I am focusing on one angle, which is rejecting the possibility that an infinite sequence could pass regardless if for example there is a reasonable proposal for the renewal of low entropy. This should eliminate the possibility of all hypotheses of a literally infinitely old multiverse or literally infinitely old cyclic universe without needing to address their approach to low entropy.
 
Last edited:
  • #42
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.

Please work with me as I try to understand some of these details. I looked at Linde's reversible time, which is foundational to the first article I cited in this thread, Aguirre, Anthony, and Steven Gratton. 2003. "Inflation without a beginning: a null boundary proposal." http://arxiv.org/abs/gr-qc/0301042.

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?
 
  • #43
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.
 
  • #44
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.
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.

I'm curious, if I said "but I am focusing on one angle, which is rejecting the possibility that an infinite sequence [of event] could pass," then would you still have quoted Zeno's paradox?

Or if I said, "but I am focusing on one angle, which is rejecting the possibility that infinite time could pass," then would you still have quoted Zeno's paradox?

Consider this, Zeno's paradox tries to make an infinite number of infinite points look insurmountable while a point is nothing in dimension, which makes Zeno's paradox a trick about infinite nothingness and nothing more.
 
  • #45
Chronos, Could you at least explain how that my primary point is an exotic version of Zeno's paradox? I say this especially since it is not at all clear to me after restudying Zeno's paradoxes and since observation indicates that an ever expanding universe will always be a finite universe. If I'm wrong about any of this, then please help me to see it.
 
  • #46
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.
 
  • #47
James,
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?
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:
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.
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.
 
  • #48
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.
 
  • #49
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.
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?

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?

Also, the occurrence of vacuum fluctuations indicates or suggests the possibility that the natural laws cause the expansion of the space. This suggests the possibility that this region of space had a finite origin.

As I think this out, I suppose that I have been misinterpreting the Aguirre and Gratton 2003 article. Perhaps they proposed merely for a singularity at the beginning of each bubble verse while the region generating these verses is expanding space itself because the generation of vacuum fluctuations requires vacuum energy, and as far as I know, vacuum energy exists only in expanding space.

I'll also take a closer look at Guth 2007 "Eternal inflation and its implications" (http://arxiv.org/pdf/hep-th/0702178v1.pdf) insisting that infinite past inflation is impossible.

In any case, I ordered FROM ETERNITY TO HERE for a mere $9.97 that included shipping and taxes, so I'll start to take a fresh look at these concepts in about a week. I'll incorporate what I learn from Carroll's book and the thread to revise my brief opening article in the original post of this thread.

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.

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.

Another way to look at the Achilles paradox is that the he makes the mistake of aiming to catch up to the tortoise and always approaches the speed of tortoise, which causes a constant decline of Achilles' speed. He constantly slows down and is never as slow as the tortoise and never catches the tortoise.
 
  • #50
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?
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.
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?
Not necessarily. The point is that you can have vacuum fluctuations 'from nothing' that could produce a universe.
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.
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.
 
  • #51
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.

We agree on 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 heard differently but cannot do the calculations by myself. This could make an interesting question for the forum, which probably has been addressed previously:

"Do theories of quantum gravity require that spacetime is a lattice instead of a continuum?"
 
  • #52
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?
 
  • #53
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 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?
 
  • #54
Travis, I see I missed the four question in your quick question.
QA1. yes
QA2. not sure what you're asking about the wall yet
QA3. no
QA4. no
 
  • #55
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.
Hi Chronos,

I see a huge difference. Zeno looked at a finite length such as a cubit and said that it is infinitely divisible and therefore nobody can travel a cubit, while in fact observation clearly indicates that uncountable animals have traveled a cubit. 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. Your comparison of Zeno's paradox and my observation is a false analogy.
 
  • #56
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.

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).
 
  • #57
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).
Hi thorium1010: Yes, that is what I meant by "always."
 
  • #58
  • #59
Semantics. Time is merely the measurement (calibration) of change. No change, no time. The issue isn't whether time is infinite, but whether change is infinite.

The "arrow of time" is a misleading borrowing of a spatial term. Does change have an arrow? If you consider trillions of quantum particles all doing their own thing a "direction" - I guess it might.

www.thisistime.co.uk
 
Back
Top