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

james.goetz

Anthony Aquirre and Steven Gratton in 2003 developed a speculative physics hypothesis that includes a timeless generation of time. [1] However, Aquirre in 2007 argued against his 2003 hypothesis of timeless origins while hypothesizing the notion of a past infinite time's arrow. [2] This post briefly examines the possibility of an infinite time's arrow and concludes that an infinite time's arrow is impossible, which was first proposed in the sixth century AD by John Philoponus [3]. Similarly, an infinite time's arrow is incompatible with scientific theory.

The conundrum of time's beginning involves the controversial notion of infinity because an infinite sequence of events would never end in at least one direction. For example, assuming the observed spacetime continuum began fourteen billion years ago and the continuum never ends with a Big Crunch or Big Rip, [4] then the continuum always continues with an ever-increasing finite age.

Similarly, there could not have been an infinite past time's arrow. For example, if there was infinite past time, then an infinite past time would precede every point in continuum history while an infinite sequence could never pass for any point in history to exist. Likewise, there was no (1) infinite past sequence of vacuum fluctuations or (2) infinite past cycles in a cyclic universe.

Some scholars stated to me in personal communication that infinite past time is possible because of different theories of time. For example, various philosophers challenge all empirical observations of cause and effect while proposing that all appearance of such sequences is essentially an illusion in an eternalist/block universe. Such eternalist theories ultimately propose radical simultaneousness of all supposedly past, present and future events while denying all distinction between the past, present, and future. [5] This rejection of sequences disputes the proposed impossibility of infinite past time, but at the expense of rejecting the notion of time's arrow. Also, rejecting the notion of time's arrow incidentally disputes every theory involving cause and effect, which includes all scientific theory. In this case, nobody can possibly disprove that the universe is an eternal block while the appearance of time is merely an illusion, but such philosophical theories are incompatible with the notion of science.

1. Aquirre, Anthony, and Steven Gratton. 2003. "Inflation without a beginning: a null boundary proposal." http://arxiv.org/abs/gr-qc/0301042.
2. Aquirre, Anthony. 2007. "Eternal Inflation, past and future." http://arxiv.org/abs/0712.0571.
3. Wildberg, Christian. 2007. "John Philoponus." Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/philoponus/.
4. See Big Crunch and Big Rip in Caldwell, Robert R., Marc Kamionkowski and Nevin N. Weinberg. 2003. "Phantom Energy and Cosmic Doomsday." http://arxiv.org/abs/astro-ph/0302506.
5. See Markosian, Ned. 2008. "Time." Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/time/.

zhermes

Welcome to PhysicsForums james.goetz; very provocative title, and excellent post!

Why do you call this controversial?

You haven't established any reason why there can't be future infinite time.

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).

james.goetz

Thank you, zhermes.
I now see I was unclear. I tried to say that the concept of infinity is controversial. But that might not be needed in that paragraph. Here is a better way to recast that paragraph:

"The conundrum of time's arrow is comparable to a never-ending clock. For example, assuming the observed spacetime continuum began fourteen billion years ago and the continuum never ends with a Big Crunch or Big Rip, [4] then the continuum always continues with an ever-increasing finite age."
Before I can go farther with this, I need to know the following. Do you agree or disagree with the above recast?

zhermes

Okay, yeah. But I still don't really see where you're going.
But yeah, big-bang, finite-time ago, goes on indefinitely, always at a finite age.

Side-note, "time's arrow" per se refers specifically to the unwavering unidirectionality of time's passage---just want to make sure we aren't/don't stumble upon that semantic issue.

Imax

When you say an Infinite Time's Arrow is Impossible, are you saying that time can’t be an independent variable and can’t range from – infinity to + infinity?

bobsmith76

James,

You are so on target.

james.goetz

Hi zhermes, I'm glad that we clarified these details. You said in post #2:These semantics could be tricky. For example, my revised second paragraph established that no spacetime continuum with a finite beginning and an expansion that never ceases will never have an infinitely long time's arrow. Given that I established that the observed universe could expand forever with a finite time's arrow, do you agree or disagree with my proposal that an infinite time's arrow is impossible?

james.goetz

Hi Imax, I apologize because I'm unsure of what you mean by "are you saying that time can’t be an independent variable and can’t range from – infinity to + infinity?" But I'll clarify that I'm specifically talking about time's arrow and that there could never be an infinite lapse of time's arrow, past or future.

james.goetz

Thank you bobsmith76.

zhermes

Okay. I think i follow what you're saying. The problem is in your premise of what infinity is. Given a start-time of the universe, any future point in time will have a finite age. That doesn't mean this makes time finite. Something is infinite if it is unbounded. For any given time in the future, it has a finite-time (this means its a 'countable set', but the future time dimension is still unbounded, and thus infinite.

You should revisit my link about Hilbert's grand-hotel paradox---it might clarify how countability is not mutually exclusive with infinity.

And again, its not 'time's arrow' in this context, its just time.

james.goetz

You are evading the context of my argument, which is time's arrow. Could we please stick to the subject of my argument that is clearly stated in the title?

zhermes

Except for my final comment, in my last response, that's exactly what I was responding to. You're argument, as I understand it, can be summarized as follows: because every future time will be separated from the big-bang by a finite time, time is not infinite.

This is false, for the above reasons.

james.goetz

No, that is a misunderstanding of one point in my argument. This point of my argument is summarized as follows: because every future time in the observed spacetime continuum will be separated from the "big-bang" by a finite time, then time's arrow will never be infinite.

I'll also add that time's arrow is bounded by the present. However, if somebody supposes that the future already exists, then perhaps they're an eternalist who rejects the existence of time's arrow. In case of eternalist theory, as stated in the fourth paragraph of my original post, there's no time's arrow and no sequences of events but a mere illusion of sequential events. Likewise, there would be no observations of cause and effect that are foundational to scientific observation.

zhermes

What exactly is the 'misunderstanding'? What is the difference between the bolded statements? The argument is false, for the above reasons. Read the article on countable sets (http://en.wikipedia.org/wiki/Countable_set) and Hilbert's grand hotel (http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel).

1. The philosophical concept of eternalism or presentism is subjective, speculative, and irrelevant.
2. "Time's arrow", per se is a term used to describe the unidirectionality of time. You are using that term incorrectly. The arrow of time is in no way "bounded" by the present. It behaves the same in the past, the present, and the future. If you mean just 'time', as suggested by the context of all of your posts, 'time' is still not bounded by the present, as it existed in the past, exists in the present, and will exist in the future. Time can be conceptually segmented based on the present, and time relative to observers or events can be described relative to the present.
3. For semantic reasons, the future (i.e. events yet to come) cannot "already exist". Quantum mechanics also suggests that events in the future are indeterminate. Time, per se---which is a direction of freedom---is a dimension like any other: it exists everywhere in the space, regardless of particular location (e.g. 'present').

james.goetz

I reread the articles that you cited. The misunderstanding has nothing to with any disagreement about countable sets and Hilbert's paradox. For example, those articles offer no insight about a never-ending clock that never lapses an infinite duration of time .

Perhaps, as you say, I misused the term "time's arrow." I supposed time's arrow refers to the unidirectional lapse of time, but if time's arrow does not refer to unidirectional lapse of time, then I will recast my brief article. Please see the recast below:

"An Infinite Lapse of Time is Impossible and Incompatible with Scientific Theory"

Anthony Aquirre and Steven Gratton in 2003 developed a speculative physics hypothesis that includes a timeless generation of time. [1] However, Aquirre in 2007 argued against his 2003 hypothesis of timeless origins while hypothesizing a past infinite lapse of time. [2] This post briefly examines the possibility for an infinite lapse of time and concludes that an infinite lapse of time is impossible, which was first proposed in the sixth century AD by John Philoponus [3]. Similarly, an infinite lapse of time is incompatible with scientific theory.

This conundrum of time is comparable to a never-ending clock. For example, assuming the observed spacetime continuum began fourteen billion years ago and the continuum never ends with a Big Crunch or Big Rip, [4] then the lapse of time in the continuum always continues with an ever-increasing finite age."

Similarly, there could not have been a past infinite lapse of time. For example, a past infinite lapse of time would indicate that an infinite lapse of time preceded every point in continuum history while an infinite lapse of time could never pass for any point in history to exist. Likewise, there was no (1) past infinite lapse of time with vacuum fluctuations or (2) infinite past cycles in a cyclic universe.

Alternatively, various scholars propose the philosophical concept called eternalism, which proposes a radical simultaneousness of all supposedly past, present and future events while denying all distinction between the past, present, and future. [5] This rejection of sequential events appears to dispute the impossibility of a past infinite lapse of time. But this rejection includes the expense of rejecting the possibility for a lapse of time. Also, rejecting the possibility for a lapse of time incidentally disputes every theory involving cause and effect, which includes all scientific theory. In this case, nobody can possibly disprove eternalism while the appearance of sequential events is merely an illusion, but such philosophical theories are incompatible with the notion of science.

1. Aquirre, Anthony, and Steven Gratton. 2003. "Inflation without a beginning: a null boundary proposal." http://arxiv.org/abs/gr-qc/0301042.
2. Aquirre, Anthony. 2007. "Eternal Inflation, past and future." http://arxiv.org/abs/0712.0571.
3. Wildberg, Christian. 2007. "John Philoponus." Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/philoponus/.
4. See Big Crunch and Big Rip in Caldwell, Robert R., Marc Kamionkowski and Nevin N. Weinberg. 2003. "Phantom Energy and Cosmic Doomsday." http://arxiv.org/abs/astro-ph/0302506.
5. See Markosian, Ned. 2008. "Time." Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/time/.

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.

Dan81

I have found this conversation very interesting and insightful. :)

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.

I E a big bang occurs and the universe expands along with time moving forward and continues for a finite amount of time of "infinite cycles" and once the Dark matter cannot be overcome by the expansion of the universe it starts collapsing. At the moment of collapse "times arrow" ends. Then another big bang occurs, but and here is the doozy, because the laws of physics have collapsed it can't be that time has continued, restarted, or ended, but that the "new" universe is completely different and a separate new "time's arrow" begins. The real question is will the laws of physics be the same when the next big bang occurs, and I laugh asking myself that question because the idea humors me so much.