Sputnick wrote:'Anything divided by infinity is 0' is a phrase I came across in 'Origins' by Neil de Grasse Tyson and Donald Goldsmith, published 2004. In the same book it says the currently accepted model of the universe says it will expand infinitely .. resulting in a cold, dark, dead void.
the first supposition I make is that time cannot be infinite, because time divided by infinity would be zero time .. but there is time .. and because time is not infinite, it will end.
the second supposition I make, since time is not infinite, with the universe expanding in time as well as space, is that the universe can not expand infinitely because time will end.
Any comments?
We run into trouble constructing mathematics when we treat infinity like a number, so doing so is strictly avoided by mathematicians doing logic and proof. "Divided by" is arithmetic. Arithmetic only applies to numbers. "Infinity" is not a number. As a mathematician or a layman trying to think and talk as one, I must go no further.
Likewise, while a measure of time or a segment of time might be a number, "time" itself is not a number. So any use of "divided by" in this case is not in the usual mathematical sense.
So I'm not going to grant you any mathematical backup for the "cannot" in your phrase "time cannot be infinite". And I'm not going to grant your logic that uses the mathematical backup to conclude that "time cannot be infinite". But don't worry, I'll address the simpler question of
whether time is infinite without the troublesome "cannot".
Is Time Infinite?
Sputnick presents the supposition that time is not infinite.
If time is not infinite, it will end, or so says Sputnick. Sounds possible to me. If a beginning of time sounds possible, why not an end? But what if it reverses? It wouldn't be infinite, but it wouldn't end either, or at least it wouldn't end going forward. Hey, it wasn't my idea. A bunch of noted physicists made it up.
If time is not infinite and will end, the expansion of the universe will end with it, or so says Sputnick. Sounds logical to me.
As far as I know, "we" still generally think the way they did in the 1930s that we don't know whether the universe will end (1) in a
big crunch (reversal of expansion, time along with it according to a few), in (2) a
big rip (continued expansion forever - the "cold, dark, dead void" you mention), or (3) a
heat death (eventual dissolution of matter in place, localized or on a grand scale, irretrievably into energy - entropy death). I haven't heard anything about the "end of time" in (2) or (3), and I have only heard it in (1) with regard to the time reversal already mentioned.
But who knows?
I personally see time as infinite going forward, no matter what the fate of the contents of the universe. But that might just be my bias talking, based on my personal experience that time started when I first became aware and has continued ever since. There may be more things going on out there than an analogy to my personal experience can suggest.