Take two: This post evaluates the concept of an infinite lapse/passage of time and concludes that an infinite lapse of time is impossible, which was proposed in the sixth century AD by John Philoponus. Likewise, models of cosmology that require infinitely lapsed time such as models of a genuinely cyclic universe or a multiverse with past eternal vacuum energy are impossible and unscientific. Modern day observation of a flat universe indicates that a flat universe endlessly ages and always has a finite age. For example, a flat universe has a potential infinite age and a continuously increasing finite age. Nothing ever stops the aging of the universe while the universe endlessly has a finite age. Despite a potential infinite age, an actual infinite age never occurs. The observed impossibility of an infinite lapse of time indicates the impossibility of infinitely lapsed time. Likewise, all scientific hypotheses of cosmology should exclude the possibility of infinitely lapsed time. For example, the technical definition of a "cyclic universe" implies an infinite number of past cycles. This indicates that the concept of a cyclic universe is unscientific, regardless of widely published papers in scientific journals about cyclic models. Other concepts widely published in scientific journals that require an unscientific infinitely lapsed time include "eternal inflation" with no beginning. Some scholars skirt around the impossibility of infinitely lapsed time and propose the philosophical concept of eternalism, which holds that future phenomena already exist. For example, the universe is uncaused with absolutely no distinction between the past, present, and future while all appearance of lapsed time and sequential events are an illusion. This concept of radical simultaneousness for all supposedly past, present, and future events disputes the impossibility of an apparent infinite lapse of time but at the expense of rejecting the concept of lapsed time. Also, rejecting the concept of lapsed time disputes every theory involving cause and effect, which includes the concept of scientific theory. In this case, perhaps nobody can disprove eternalism while the appearance of lapsed time is merely an illusion, but such philosophical theories are incompatible with the concept of science. My argument about the impossibility of infinitely lapsed time sometimes prompts debate about Zeno's fifth century BC paradoxes of infinity. Zeno pointed out problems with the concept of infinity while attempting to support the nonexistence of motion and change, which is still in vogue today with the philosophical eternalism mentioned above. For example, Zeno said that all apparently finite lengths such as a cubit are infinitely divisible and likewise nothing has actually traveled the length of a cubit. But this amusing paradox never explains observations of objects that travel a cubit. In sum, this post holds that the science of cosmology excludes impossible concepts such as infinitely lapsed time and limits itself to inference based on scientific observation.
I thought this was addressed already that the universe as per current observations will continue to expand infinitely that means infinite time.
Except it doesn't. It all depends upon the model. There is a time before which we can't say what occurred. But that doesn't mean that nothing occurred before then.
Hi Chalnoth, I never said that nothing happened before the big bang, but that there is no infinitely lapsed time. Likewise, models that require infinitely lapsed time such as eternal inflation with no beginning, a cyclic universe, [or] a non-zero Hamiltonian should not be considered scientific hypotheses. For example, this does not refute the concept of a multiverse with a beginning, which my original post never excluded.
James, I don't think I see the point of your argument. Just because an individual clock will never record an infinite time, does not mean an infinite past/future is impossible. For example, the concept of a spatially infinite universe is one that is considered, and I doubt too many people would say it is 'unscientific' or impossible. In an infinite universe, no measuring tape would be able to ever reach an infinite length, but that does not change the fact that the universe would be spatially infinite. So, if you want to totally reject the possibility of an infinite past/future on the basis that clocks always measure a finite time, you would also need to reject a spatially infinite universe. Also, if I began to count off numbers, I will always have counted a finite amount of numbers. But, this does not change the fact that there is an infinite amount of real numbers.
Hi Mark, A key to understanding this is to understand the difference of "actual" and "potential" that I noted in the third paragraph of the original post. For example, you understand that an individual clock will never tick and infinite number of ticks in a case where nothing ever bounds the ticking process. I understand that a flat universe will always expand and always be a finite universe, except for the possibility of a Big Rip that would keep the age of the universe finite but make the space infinite. My argument has no objection to a Big Rip making space infinite, but my argument objects to continuous expansion turning into infinite space. We agree on this. I never challenged the concept that there is an infinite amount of real numbers.
Hi HallsofIvy, I rarely if ever use the adjective "unbounded" in a mathematical sentence, but that might work. However, I used the adverb "infinitely" and I see no adverb for "unbounded." I guess since I have not used "unbounded" in many sentences I needed to consider it in a few. For example, Are the two following phrases the same? 1. "an infinite number of ticks on a clock? 2. "an unbounded number of ticks on a clock"
James, A flat universe does not necessarily have to finite, it can go either way. I wasn't trying to argue about the size of the universe - I was trying to make the point that since you state that the fact a clock will never measure an infinite amount of seconds is an argument against a universe with an infinite past, we also apply this to say 'Since a measuring device will never measure an infinite amount of feet, an infinite distance is impossible, and hence a spatially infinite universe is impossible'. So, your argument requires you to reject the possibility of an infinite universe, too. I wasn't trying to prove there is an infinite amount of real numbers - that is obvious. The point I am trying to show is that even though only a finite quantity of numbers can be counted, there is truly an infinite amount of numbers. Similarly, although an infinite amount of time can never be elapsed by a clock, an infinite time can exist. I understand the basis of your argument - since no observer can measure an infinite amount of time, there can not exist an infinite past. But here's my problem with that reasoning - a clock must beging ticking at some point - but in a universe with an infinite past, there is no beginning to count from. If we had a clock that ticked off time in reverse (it traveled back through time) it would coninue to measure more and more time, and similar to the way you said that an infinite future is possible via 'potential infinity', we could say the universe is 'potentially infinite' in the past.
Hi Mark, This analogy is problematic. For example, I do not object to an infinite number of time coordinates or an infinite number of space coordinates. But I am specifically referring to elapsed time and I unsure of what in space compares to elapsed time. The closest comparison that I can think of is gradually expanding space. If that is the comparison, then finite space will never gradually grow into infinite space. But an instantaneous Big Rip into infinite space sounds interesting to explore. I agree that if a clock could tick in reverse then "the universe is 'potentially infinite' in the past just as elapsed time in the observed universe is potentially infinite in the future. I also understand your problem that an actual infinite past chronology would have no starting point, but that is part of my point. If that were the case, then no matter how far back we would go in that time, then there always would be infinite past chronology. You apparently indicate that if time travel were possible then a time traveler could never travel an infinite chronology of time. I suppose that such time could exist only if the entire infinite timeline always existed, which would mean that all future phenomena has always existed and makes observation of cause and effect meaningless.
So, your opposition is to an infinitely long chain of causality, because it would require that time always existed. Correct?
Hi Mark, No, I never argued against an infinite chain of causality in the case of a finite elapse of time in a continuum, if that were possible. My argument refutes the possibility of an infinite chain of causality in a time lattice but possibly not in a finite time continuum. Zeno would never let me get away with that one.
It sounds to me that all you have established james is that a universe infinite/unbounded in time must be cyclical and their will be a time 'horizon' in the past beyond which nothing can be known to inhabitants of that universe. While I agree this has many of the outward appearances of finite time it is not quite the same thing. Again changing to a spacial infinity is a useful analogy, in infinite space their must inevitably be an infinite number of exact copies of ourselves as all possible configurations of matter and energy are repeated. Move far enough and space appears to loop back like the Arcade game Asteroids, but you might also describe it as repeating forever like wall-paper both interpretations are equally valid and in truth are BOTH correct as nothing could ever distinguish between them.
Hi Impaler, I am not looking at merely time coordinates but elapsed time. These are two different things. I agree with you that there are no limits to time coordinates that are independent of phenomena.
And what qualifies time as "elapsed"? Because I'm pretty sure that even if the current elapsed time is finite, the indefinite future of our universe would lead to an infinite elapsed time.
The OP does not contain an argument at all, instead each sentence basically asserts using different words, that 'the universe can't be past eternal'. Not very convincing! Now, there is a debate in academic circles whether this is true or not (see recent papers by Vilenkin and Susskind), but its actually a relatively nontrivial question to answer.
Please elaborate on the distinction between time coordinates and elapsed time. It sounds to me like your making a distinction between 'ticks' on a clock (time coordinates) and some kind of more 'true' time that can be said to have an elapsed period greater then what the clock can measure? If this is the case then I disagree with the existence of the latter. Time is what we can measure with a clock (mechanical or biological) and a clock has a finite number of degrees-of-freedom aka bits of data it can hold which means it can only measure a finite amount of time before it rolls over establishing a finite past time-horizon measurement/history. This change in the degrees-of-freedom of a system IS time in my interpretation, and if done in such a way as to create a history of that change then by definition we have a clock. Their can't be any view of time from outside of time, just as their can be no view of space from outside of space.
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.
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.
I'll have a try at it. elapsed time = t_{1} - t_{0} If t_{1} is +∞, then elapsed time is also +∞, even if t_{0} is an actual value instead of -∞.