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

by james.goetz
Tags: arrow, impossible, incompatible, infinite, scientific, theory, time
 P: 3 I guess in someways my view doesn't allow for infinity if the "time's arrow" ends, and a new big bang begins where the laws of physics have broken down, than it will not be infinite cycles, but a different event, where the previous event ceased to exist. :) Oh that is just so funny to think about.
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 Quote by zhermes Throughout the course of the last 15 posts, you have yet to offer a response to a single one of my responses, critiques, or complaints. Changing every term from "time's arrow" to "lapse of time" is negligible. If you're simply looking for a place to publish your musings, PhysicsForums is not it.
Sorry, I never saw you address my primary point that an infinitely long lapse of time can never pass, but you described (1) geometric concepts of unbounded time independent of empirically observable sequential events and (2) various paradoxes of infinity that say nothing about the sequential counting of an infinite number of real numbers. But since I better understand you and you say that I never responded to one of your responses, then I will review your first response:
 Quote by zhermes No. This is false. Its basically the same idea as Hilbert's verdical Paradox (of the 'Grand Hotel'); and similarly analogous to Zeno's Dichotomy (verdical) Paradox. Both of these are resolved with calculus. The concept of confined infinites is very tricky, and completely non-intuitive. I think the underlying problem is a linguistic association between the mathematical concept of 'infinity' and an idea of 'insurmountability' --- which is not accurate. Anyway, there are an infinite number of real-numbers between 0 and 1, yet 2 can be reached :) Consider choosing a random number between 0 and 2. There are an infinite number of choices between 0 and 1, but the probability of choosing one of those numbers is finite (only a half).
I agree that there is an infinite number of real numbers between 0 and 1, between 0 and .1, between 0 and .01, and ad infinitum. And if I count .1, .2, .3, .4, .5, .6, .7, .8, .9, 1, then my counting included an infinite number of infinite numbers, but that says nothing about sequential counting of a countable infinite set. And that says nothing about identifying say the first three real numbers after 0 or after .1 or so on. And the probability of randomly picking an infinitely improbable number from an infinite set says nothing about an infinite lapse of time. In sum, I see you say nothing [directly] relevant about the passage of an infinitely long sequence of events.
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 Quote by james.goetz Sorry, I never saw you address my primary point that an infinitely long lapse of time can never pass
This was your main point. I showed that the only reason you presented for it was wrong. Once again, you suggested that if every future time is of a finite-age, time cannot be infinite. Over the entire course of this post, that is the only reasoning you have done. And it is plainly, manifestly false.
 Quote by james.goetz In sum, I see you say nothing [directly] relevant about the passage of an infinitely long sequence of events.
That is the point I have repeated responded to---and thus have responded to the body of your argument, and your post.

 Quote by james.goetz you described (1) geometric concepts of unbounded time independent of empirically observable sequential events and (2) various paradoxes of infinity that say nothing about the sequential counting of an infinite number of real numbers.
Observations show that the universe is flat, and accelerating in expansion---suggesting it will expand indefinitely, and there will be infinite time. Those are the 'empirical observations'. The verdical paradoxes I presented deal with exactly that issue---the basis of your argument.

 Quote by james.goetz I agree that there is an infinite number of real numbers between 0 and 1, between 0 and .1, between 0 and .01, and ad infinitum. And if I count .1, .2, .3, .4, .5, .6, .7, .8, .9, 1, then my counting included an infinite number of infinite numbers, but that says nothing about sequential counting of a countable infinite set. And that says nothing about identifying say the first three real numbers after 0 or after .1 or so on. And the probability of randomly picking an infinitely improbable number from an infinite set says nothing about an infinite lapse of time.
You're right. These couple of concepts, out of the many I've presented, do not directly refute your point. They were meant to help elucidate the nature of 'finite vs. infinite' and how countability is a separate issue. Both of these points you still seem to struggle with.
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 Quote by Dan81 I have found this conversation very interesting and insightful. :)
Excellent, and thanks for joining in!

 Quote by Dan81 I feel like you both have valid points, but neither one has the true answer, which is that "times arrow" must have a beginning and an end, but it is infinite in the amount of cycles that occur.
This is an interesting proposition, and it is not only appealing but the basis for many theories in cosmology. None-the-less, there is nothing either theoretical or observational to negate the possibility that time is infinite.

 Quote by Tanelorn My view is that being mathematical concepts only, infinite and infinitessimal are equally impossible in the real world.
I think I might agree with you Tanelorn; but the problem is that such an idea could be entirely founded on our day-to-day experiences in which such a proposition seems appealing, if not obvious. It might be that not only are particles/energy/etc quantized, but also space-time itself---creating a minimum size-scale of the universe, and thus no true 'infinitesimal'. It could similarly be true that the universe is bounded and finite in all respects, and thus there is no true 'infinite'. But again, none-the-less, this need not be the case.
 P: 49 If infinite past time is impossible, then why would infinite space at your left or right side be possible? The current model of the universe is a universe of infinite size. If you are going to argue that it would be impossible to arrive in the now if there is an infinite amount of preceding time, than I wonder why it would be possible to arrive in the here if there's an infinite amount of space left or right of us. I've heard about the idea of the direction of time being defined by the direction in which entropy increases. If the universe truly is infinite in size, then there ought to be places in the universe where the entropy is steadily decreasing and the beings living there would consider it as a factor they could depend on.
 PF Patron Sci Advisor P: 8,883 The observable universe is temporally finite, I trust we all agree on that point. We know nothing about the unobservable parts of the universe, and probably never will. This renders the argument unfalsifiable, which is a polite way of saying it is unscientific.
 P: 49 I'm fully aware of that, but I'm not trying to prove anything based on that. I'd like to carry the model of the universe which is based on the observable universe a little further and see what it implies about our universe beyond the borders which we are able to observe. It may lead to insights which might be testable and help us get a better understanding of the world we live in. Whoever came up with the idea of a Calabi-Yau manifold must be fully aware of the fact that is, at least for the moment, absolutely unfalsifiable. Still it does not stop physicists from talking about the idea and wandering about what that means about the world we live in.
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 Quote by zhermes This was your main point. I showed that the only reason you presented for it was wrong. Once again, you suggested that if every future time is of a finite-age, time cannot be infinite. Over the entire course of this post, that is the only reasoning you have done. And it is plainly, manifestly false. That is the point I have repeated responded to---and thus have responded to the body of your argument, and your post. Observations show that the universe is flat, and accelerating in expansion---suggesting it will expand indefinitely, and there will be infinite time. Those are the 'empirical observations'. The verdical paradoxes I presented deal with exactly that issue---the basis of your argument. You're right. These couple of concepts, out of the many I've presented, do not directly refute your point. They were meant to help elucidate the nature of 'finite vs. infinite' and how countability is a separate issue. Both of these points you still seem to struggle with.
Hi zhermes, I needed to break for another project.

One main problem that I see is that you could brush up on your informal logic and avoid fallacies. For example, we both provide anecdotal examples of surmountable infinities. However, it's a logical fallacy to insist that since some infinities are surmountable then all infinities must be surmountable.

Also, my original post clearly described the observed universe with unlimited expansion. And here you tell me that the observed universe is flat with indefinite expansion as if I was unaware of that. And then you completely contradicted a previous statement of yours because you earlier agreed with me that the spacetime continuum will always expand and will always be finite.

I'll clarify that I'm not objecting to the existence of infinite past and future time independent of sequential events.
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 Quote by luitzen If infinite past time is impossible, then why would infinite space at your left or right side be possible? The current model of the universe is a universe of infinite size. If you are going to argue that it would be impossible to arrive in the now if there is an infinite amount of preceding time, than I wonder why it would be possible to arrive in the here if there's an infinite amount of space left or right of us. I've heard about the idea of the direction of time being defined by the direction in which entropy increases. If the universe truly is infinite in size, then there ought to be places in the universe where the entropy is steadily decreasing and the beings living there would consider it as a factor they could depend on.
Hi luitzen, there is a difference between unlimited potential expansion and current infinite size. The entire idea of science saying that space with physical laws is expanding indicates that space is finite. And I have no doubts about infinite nothingness (no physical laws) beyond the observed universe.
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 Quote by james.goetz we both provide anecdotal examples of surmountable infinities. However, it's a logical fallacy to insist that since some infinities are surmountable then all infinities must be surmountable.
I made no such claim. And once again, to draw you back to Hilbert's Hotel---the entire point of that 'paradox' is establishing that there are degrees of infinite, some larger than others---and thus some which contain contain the others.

At no point did I even suggest that all infinities are 'surmountable' --- presuming that you mean something about countability, or a finite range containing an infinite set...

The fact is that, in theory, the span of time can be directly mapped to the real-numbers. The real-numbers are infinite in range. Thus time, can be infinite in range. Period. As I've said repeatedly, your fundamental point suggests that because every time is finite (i.e. every corresponding real number is finite), the full range of time (or real numbers) cannot be infinite. This is plainly false. And you have yet to offer a refutation, only redirections.

This isn't a debate on the validity of your arguments. I'm explaining why they're wrong - and I've thoroughly lost interest. The purpose of PhysicsForums is to learn and educate; not to share one's personal theories on the universe.

 Quote by james.goetz Also, my original post clearly described the observed universe with unlimited expansion. And here you tell me that the observed universe is flat with indefinite expansion as if I was unaware of that.
'You keep saying that word. I do not think it means what you think it means.'
You're using the terms "un-limited" and "in-definite" yet claiming the same things are NOT "in-finite". ?!

 Quote by james.goetz And then you completely contradicted a previous statement of yours because you earlier agreed with me that the spacetime continuum will always expand and will always be finite.
Again, you don't understand the language. At any given time in the future, a time may be finite, but it is possible that time is still infinite.

 Quote by james.goetz I'll clarify that I'm not objecting to the existence of infinite past and future time independent of sequential events.
Really?! To quote from the title of the thread "An Infinite Time's Arrow is Impossible".

Or from previous posts:
#7 "[the spacetime continuum] will never have an infinitely long time's arrow"
#8 "I'm specifically talking about time's arrow and that there could never be an infinite lapse of time's arrow, past or future."
#11 "Could we please stick to the subject of my argument that is clearly stated in the title?"
#13 "time's arrow will never be infinite."
#15 The restated title of your post "An Infinite Lapse of Time is Impossible"
#20 "my primary point that an infinitely long lapse of time can never pass"

And with that, I unsubscribe.
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I understand that zhermes unsubscribed from this thread, but I wish to respond to distortions in his parting comments since others might read this thread.

First, he says that my view of a finite universe is a personal view. I suppose that would be the case in the nineteenth century but not since the 1920s.

Second, he possibly assumes that unlimited potential is equivalent to unlimited actualization. I definitely mean that "unlimited" potential is not "infinite" actualization.

Third, I apparently originally miss-used the term "time's arrow" and thought that it meant the unidirectional passage/lapse of time. So my original title could look misleading. But in post #15, I responded to education from this forum and said the title should be "An Infinite Lapse of Time is Impossible and Incompatible with Scientific Theory."

Fourth, he implies that "an infinite lapse in time" is exactly the same thing as "the existence of infinite past and future time independent of sequential events." For example, in post 14, he acknowledged that future events do not yet exist. And he always refers to infinite future time. But given infinite future time and the nonexistence of future events, then logically infinite future time is independent of sequential events.

Fifth, I kept clarifying my argument, but he kept twisting my argument into a straw man and finally accused me of unwillingness to learn.
 PF Patron Sci Advisor P: 8,883 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.
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 Quote by Chronos 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.
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?
 PF Patron Sci Advisor P: 8,883 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.
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 Quote by Chronos 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.
Thank you. I'll take a close look Olber's paradox. Do you know of any other examples?
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 Quote by Chronos 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.
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.

I'm in no way opposed to inference in science, but any inference of an infinite past sequence of any type of events is impossible and likewise should be incompatible with scientific theory.

Also, per your comment on creationism, we need to clarify that this in no way supports young earth creationism. And conjectures about theism are philosophical and I already got a warning about that in this forum, so I am sticking to the limits of science here.
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 Quote by james.goetz 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.
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.
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 Quote by Mark M 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?

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