An Infinite Lapse of Time is Impossible and Unscientific

james.goetz

Hi Chalnoth, you do not understand infinity. For example, a flat universe with an incomplete past will never age an infinite number of Planck times. For example, after the elapse of a googolplex raised to the googolplexth power of Planck times, then the universe would not be close to an age of an infinite number of Planck times.

Chalnoth

I understand infinity just fine. If there's an infinite future, then there will be an infinite elapsed time. End of story. It will take an infinite amount of time to get there, but that is of no consequence. It still destroys your argument, even if no observer within our universe can be around to witness it.

jobigoud

I'll have a try at it.

elapsed time = t₁ - t₀

If t₁ is +∞, then elapsed time is also +∞, even if t₀ is an actual value instead of -∞.

james.goetz

Hi Haelfix,

You appear to have missed a major point in my original point or neglected to mention it above. I start with an example of observation. A flat universe with an incomplete will infinitely expand and never have an infinite age. For example, the observed universe will have an age of an infinite number of Planck times. Then I apply the observation on elapsed time in a flat universe to past elapsed.

And yes, I read the interesting papers by Vilenkin and Susskink. I wrote a response at PhilPapers http://philpapers.org/archive/GOETIO-3.1.pdf:

Note
Observation indicates that a flat universe begins, endlessly expands, and forever develops a finite age. Nothing ever stops the aging of a flat universe while it endlessly develops a finite age. Despite an infinite number of time coordinates independent of phenomena, an infinite number of Planck times will never elapse in a single lineage. Likewise, an infinite number of Planck times have never elapsed in a single lineage. The universe could not have been past-eternal.

Imagining a scenario of apparently unlimited time travel in a universe with an eternal past also helps to explain the impossibility of infinitely elapsed time. For example, if a time traveler could survive in a scenario where a two-minute journey in a wormhole could travel to any event in the past, then the time traveler would find that an infinite number of Planck times precede all past events. The time traveler with no apparent limits could never travel an infinite number of Planck times.

This observation excludes the possibility of all cosmology models with a past infinite elapse of Planck time. For example, Mithani and Vilenkin [1] recently refuted three categories of models with an eternal past: (1) past eternal inflation, (2) cyclic evolution, and (3) emergence from static seed. Apart from all reasons supported by Mithani and Vilenkin, those models also fail on the grounds that infinitely elapsed time is impossible.

However, Leonard Susskind [2] replied to Mithani and Vilenkin in a note and argued that the universe is past-eternal. Susskind concluded his argument with saying, "we may conclude that there is a beginning, but in any kind of inflating cosmology the odds strongly (infinitely) favor the beginning to be so far in the past that it is effectively at minus infinity." This expresses a major misunderstanding of infinity. For example, any finite number of Planck times such as googolplex raised to the googolplexth power is infinitely smaller than an infinite number on Planck times. Nothing is remotely close to an infinite number of Planck times except an infinite number Planck times.

In sum, any scientific model of cosmology must have an incomplete past: that is, a beginning. And all apparent merits in cosmology models that include an infinite elapse of time are futile unless the merits are transferable to models with an incomplete past.

References
[1] A. Mithani and A. Vilenkin, "Did the universe have a beginning?," arXiv:1204.4658 [hep-th]
[2] Leonard Susskind, "Was there a beginning?," arXiv:1204.5385 [hep-th].

james.goetz

An infinite expansion never ends and there is no final time coordinate. You possibly sound as if you treat infinity as if it were a real number that could be used as a coordinate. For example, there is a countable set with an infinite number of positive integers and infinity is not a real number.

james.goetz

Hi jobigoud,
+∞ and -∞ are not real numbers and time coordinates are real numbers.

james.goetz

Hi Impaler:

I am not making any suggestions of some ultimate time. But ticks on a clock are not geometric time coordinates. Here are time coordinates t1 and t2:
t1 = 2012/05/02 23:59:00 GMT and t2 = 2012/05/03 00:00:00 GMT

As of the time of this post, t1 and t2 have no phenomena. The time coordinates exist in a geometric sense while those periods of time do not exist. When those periods of time exist, then they will be associated with phenomena. And a clock ticking from t1 to t2 will represent the elapse of time from t1 to t2. And before t1, there will be no elapse of time from t1 to t2.

Jack Smart

Can I suggest that instead of using the word "time" you use the word "change". Then you need not concern yourself about infinite time (which is irrelevant as time is merely a measurement of change), instead you can consider infinite change. What causes change...

Chalnoth

I think that just makes it worse, because change is even more nebulous than time. The goal should be to nail down the definition, make it specific. Not make it more nebulous.

Jack Smart

Time measures (including calibrating & indexing) change (which means events, duration, interval ). That is it. It might be that change is nebulous (though I'm not sure that's necessarily so), but that doesn't alter time being a very simple concept ... though its simplicity is usually missed.

www.thisistime.co.uk

Chronos

James, you're still playing a restated version of Zeno's paradox. By your logic, the planck clock should never have started ticking in the first place.

james.goetz

Chronos, You're still playing a false analogy.
Apr28-12, 11:06 AM
http://www.physicsforums.com/showpos...7&postcount=55

Perchie

Surely, infinity is purely a concept ?

If infinity and dimensionality are mutually exclusive within the same domain, then infinity cannot exist within our dimensional universe ... ergo, infinity is simply a human construct.

If there is a limit to the divisibility of matter and to the size of the universe, then the physical universe is composed of a finite number of indivisible particles, which means that any calculation involving quantities greater than that totality of particles cannot be applied to the physical universe.

Lino

James, can I ask if you are saying that a future time slice (please forgive the clumsy language) does not currently exist, or that because a future time slice does not currently exist, one can not have infinite time?

Also, in relation to Zeno's cubit, would you agree that there is no limit to the length of road that I can measure (past), and that there is no limit to the length of road that I can plan to measure (future)? If I think of a clock in the same fashion, then there is no limit to the amount of time (past or future) that I could measure (and so can be infinite), but anything that I do measure is constrained witin a physical start/end point (and so can not be infinite). Therefore the difference, just like infinity, is a philosophical one between 'could' and 'can'. I'm not sure that this agrues for or against what you are saying, but I'm also not sure that the difference is material.

(By the way, personally, I like Jack Smart's description and agree with his comments on simplisity.)

Regards,

Noel.

andrewkirk

To James Goetz.
In this thread you repeatedly refer to your argument that an 'infinite elapsed time' is impossible but as haelfix pointed out on pages 1, you have not presented an argument. All you have done is restate the same assertion in different ways and dance around the issue.

An argument consists of premises and conclusions connected by logically valid steps. You have not presented any premises, nor any logical steps.

You will also need to define what you mean by an 'infinite elapsed time'.

Note to the moderators: This thread should be moved to the philosophy subforum because it is not physics.

andrewkirk

Follow-on to my previous post. I see you made this reply to haelfix. Yet you still did not present an argument, only a thought experiment. Even assuming this thought experiment enables you to conclude that your first sentence quoted above is true, the second sentence is a non sequiteur, an utterly unfounded leap. There is no reason at all to suppose that it follows from the first sentence. But, as noted above, it requires definition of what is a cosmology model 'with a past infinite elapse of Planck time'. Without such a definition, the leap is not even wrong.

SpaceTiger

I'd say the point is largely irrelevant to the scientific process, since any of the current cosmological models could simply turn out to be local approximations. Even if the models formally project to infinity, there is no way we could distinguish between a universe that is truly infinite in time and one that very slowly transitions into something else at very late times. A similar argument could be made for just about any infinity you find in scientific models.

It's really more of a philosophical debate, I think. As long as a model continues to fit the data, there's no scientific benefit to introducing an ad hoc tweak to make it finite.