It can’t have already happened, though. It would still be unwinding (all the time required to get to the present, that is) and it would be done–never. Why? Because it’s an infinite amount of time. So, if time moves in one direction, in the linear fashion that we perceive it to, then an infinite regress is an impossibility.
Seriously, how much time will need to have elapsed before our universe arrives at the present if there is an infinite past? By definition, the universe will arrive at the present moment (or any moment) after an infinite amount of time passes. That is, never. And yet, here we are.
The problem with your logic is that it’s assuming there’s a beginning point called “negative infinity” or something like that. That’s not how it would work, presumably – there wouldn’t be any beginning point at all.
So you can easily calculate how many years elapsed from year -1,000,000 to today, or from -1,000,000,000 to today, etc.
Stratocaster, why does time have to “start” anywhere? Why would time have to have elapsed since “the beginning” if there is no beginning? Saying that infinite time has elapsed is not the same as saying that it never happened.
Try this: You say that infinite time would have had to have elapsed in order for us to be here, now. But…elapsed since when?
Really? I don’t think they are different at all. Zeno’s paradox is sort of the mirror image of your argument… Here’s your argument, broken into every individual piece:
A. Suppose the past extends to infinity.
B. Suppose now also an observer is positioned at the “beginning” of time, and counts each second that goes by. (This is your “how many seconds have gone by?” refrain)
C. Associate a unique second to each moment in time which defines a unique ordering (this is the universal assumption that time moves in one direction uniquely). We shall only say a moment in time has “occurred” if the counting observer counts that moment’s associated second.
D. Note that the number of moments preceding any given moment is infinite, since it is the length of an interval from negative infinity to x - always infinite.
E. Pick any particular moment in time. The number of seconds which must be counted before it is infinite, which is uncountably enormous, so that moment cannot have occurred.
F. However, the present is occurring. Contradiction, completing the proof.
This has many errors in reasoning. Many posters above argue that your demands for someone to count “how much time will need to have elapsed before our universe arrives at the present?” (ie point C) are nonsensical.
I think the bigger issue is that you are assuming that all intervals of time must be measurable, including the interval from the present to the beginning of time. There’s just no justification for that - you define that the present only occurs when a finite amount of time has passed between it and the past, and then say “But the infinite past means an infinite amount of time. See? Impossible!”
Why should we say that the present only occurs if a finite amount of time has passed?
But that’s exactly the point. It’s a non sequitur, because an infinite past assumes that time NEVER starts–it goes back…forever. Don’t worry about a beginning point, because there is no beginning point, by definition. Time is sequential and linear (as we perceive it, at least). You can’t get to any point on the time-line until you’ve proceeded through all the prior points on the time-line. When will we arrive at the present if there is an infinite past? The only logical answer is “never.” And yet, here we are.
spenczar, that’s the answer to your question, too: “Why should we say that the present only occurs if a finite amount of time has passed?” Because if the past is infinite, it is never exhausted. It goes on infinitely, by definition, if you start with an assumption of an infinite past (the question posed by the OP). You’re hypothesizing about the beginning of time when there is no beginning of time, not if the past is infinite. An infinite past assumes some level of measurement. And that measurement has concluded a length of time: infinite.
Really, you’re handwaving away something that is self-evident (if time has the properties we perceive it to): If the past is infinite, then the amount of time that needs to pass before we get to the present? An infinite amount. We would never reach any point in time, not just the present. Last Tuesday is right out, and so is next Wednesday. That’s what makes an infinite past nonsensical, a non sequitur.
Because those time segments are finite. But I’m not assuming any beginning point for the past in total, since an infinite past has none, by definition. That’s the insurmountable logical conundrum in positing an infinite past (again, unless time doesn’t have the properties we perceive it to, that it is somehow an illusion).
In addition to the embedded contradiction already pointed out in the notion of “elapsed time”, I believe that there is a fundamental problem with the idea of identifying “this particular cycle”. In fact, if the past is infinite, then there will already have been an infinite number of states that are indistinguishable from the current one.
Snark aside, I’m serious - it’s not very complicated calculus that shows that infinite intervals can yield finite answers to lots of questions. What’s the problem here?
I’m pointing out that there is no starting point, by definition, in an infinite past. There can be no “start point” between the present and the “beginning” of an infinite time-line. Cause there isn’t one. So, how much time needs to have passed before we’d reach the present, assuming an infinite past? Infinity.
You’re trying to force an infinite past into a finite time-line context, and in doing so, you’re acknowledging the logical problem with an infinite past (even if you don’t realize it). Doesn’t make sense, right?
Then show your math. I’m asserting that an infinite time span is, in fact, impossible to traverse. No matter how much time you dedicate to traversing that span, you ain’t even remotely close. Explain what’s wrong with that logic.
Sure. Let x(t) denote position on a semi-infinite interval R := [-∞, a] where a is some finite value. dx/dt is then velocity and d²x/dt² is acceleration. The task is to prove that we can find a function x(t) for which the integral
Time to span = ∫(x(t))dt over R
converges (ie, is finite).
It is immediately clear that x(t) = e^t satisfies. See for yourself:
Antiderivative of e^t = e^t. Evaluate at the boundaries to get
Semi-infinite doesn’t mean at all what you think it means. It means an interval with endpoint “at infinity” and the other endpoint at some finite point. That is exactly what time is in this conception, isn’t it?
But if you don’t like that, there are many functions that also evaluate to a finite quantity over an infinite interval:
Let R:= [-∞, ∞]
Let R1 be the subinterval of R [-∞, 0] and R2 the subinterval [0, ∞]
Time to span = ∫(x(t))dt over R
Time to span = ∫(x(t))dt over R1 + ∫(x(t))dt over R2
Choose x(t) = e^-|t| where |t| means the absolute value of t.
Time to span = ∫e^-|t| dt over R1 + ∫e^-|t| dt over R2
=∫e^t dt over R1 + ∫e^-t dt over R2
=( e^t evaluated from t=-∞ to t=0 ) + ( -e^-t evaluated from t=0 to t=∞ )
=(e^0 - e^-∞) + (-e^-∞ - -e^0)
=2
which is finite.
But I would stress that the OP’s question is over a semifinite interval, so this is all besides the point. In either case, its perfectly possible to traverse an infinite interval in finite time.
spenczar, sorry, I’m not dusting off my calculus textbooks to decipher your proofs. I will rest comfortable in my wild assertion that a finite amount of time will NEVER traverse an infinite span of time. Let me show you my math:
Finite < Infinite
I worked on that for a couple of hours, but I’m going to refine my hypothesis this evening. If I have any new math, I’ll let you know.
How much time needs to have passed between what two time points? You have indicated one time point - the present. However, you haven’t indicated what the other time point is (clearly not “the beginning” since we are assuming there isn’t one). Without two time points for there to be an interval between, it is meaningless to talk about how much time has passed.
All assuming an infinite past (which I do) implies is that for any finite x regardless of how large x is it is meaningful to talk about an event occurring x number of seconds ago. Since there was no beginning you can’t talk about how many seconds have occurred since the beginning because there wasn’t one!
