If time is infinite, will this particular question keep coming up infinitely often, and will we see all possible answers to it?
Given infinity, is everything imaginable inevitable?
“Anything that can happen, will happen, given enough time.” – Really?
Assuming an Infinite amount of time, are all things inevitable?
Actually we have already seen all the possible answers..which just keep repeating themselves.
Something to look into is the Hartle-Hawking state.
Or, as David St. Hubbins put it…
Not really. There was no space. There was no time. The BB created space and time.
As for infinity, the numbers between 1 and 2 have a biginning and end yet there are an infinite number of them.
Also you can’t really speak of “before” the BB since time begins there.
Kind of a “Gaudere’s Law” here: Der Trihs corrected my sloppy phrasing, and then John Mace corrects his somewhat informal phrasing.
One problem on the observation that there are an infinite number of numbers between one and two is that this doesn’t have any physical representation. The same for the number pi: beyond the 700th digit or so, the ratio has no meaning, as there are no circles large enough, and no measurement scale fine enough.
There certainly aren’t an infinite number of “measured spaces” between the one-inch and two-inch marks on my ruler. Dividing it up into more than, say, 10^2000 points is an exercise in absurdity. And, again, mathematicians can sling off numbers so unutterably much larger than that without batting an eye!
The “granular” nature of space itself precludes any measure of infinity in the direction of smallness. Largeness? Well…
I think you mean “our space and time.” Our space and time begins with the BB,
not all space and all time. All space and all time is unknowable.
Our very notion of space and time come from what we can measure. Anything outside our universe is not measurable. So it doesn’t really make sense to talk about space and time outside our universe, because we have no way of knowing if such concepts can even exist there.
Consider the positive integers. This set can be formed by starting at 1 and incrementing by 1:
1, 2, 3, 4, 5, 6, etc
This set of numbers clearly has a ‘beginning’ and is also clearly infinite.
What if DeSitter (Einstein’s Dutch contemporary) was right? Infinite space, infinite time, and no discernible expansion (because of the increasing curvature of spacetime?
Ok, ok, smoke a great big bowl of weed before you read this…
Nothing is a compound word. No Thing. 
Weed comes in bowls?
I doubt that “possible event” is a well-defined notion. If it is, and by “the universe never ending” we mean an endless succession of temporal units, then I am pretty sure that the cardinality of of possible events is greater than that of an infinite number of temporal units.
Suppose we started flipping coins and each time we got a head we took one step to the left and each time we got a tail we took two steps to the right. As we run this process we will always tend to move further to the right. The likelihood that we will ever reach a point 100 steps to the left of our starting position is near zero no matter how long we run this series. This is basically the idea behind increasing entropy. As time goes on we get more and more disorder and no amount of waiting is going to get us back.
One possible outcome of flipping a coin an infinite number of times is an infinite series of heads. While this seems unlikely, it’s just as likely as any other series of outcomes. HHHHHHHHHHHHHHHHHHHH is just as likely as HTHTHTHTHTTTHTTTHTHH.
But you could also flip the coin and get an infinite number of tails. But you can’t have a universe where you get infinite heads and also get infinite tails. You could have one or the other, but not both. And so we see not everything is inevitable in an infinite amount of time. Some outcomes make alternative future outcomes impossible.
I’m not sure I can agree with this. You’re saying that the infinite series of HHHHHHHHHH… is just as likely as some other HTHTHTHHTTTHHTH… series, but that’s misleading. There is exactly one possibility to have no tales, but with an infinite number of flips, there’s an infinite number of other possibilities. It’s sort of like the does 0.999… = 1 problem. Does 1/inf have a non-zero value?
The other problem is, assuming the stated probability. Sure, if I flip a fair coin a hundred times, it might come up all heads with 0.5^100 chance and that is just as possible as any other one, though it is outside of any reasonable margin of error. But once we’re talking an infinite number of trials, I don’t think we can reasonably say that it’s a fair coin if we can now effectively say that exhaustively it will never land on tails. It’s an utterly paradoxical result. For that matter, on top of zero is there a meaning to some series with an infinite number of Heads but a finite number of Tail results?
The point is this: for this experiment the universe must have only one, countably infinite set. Whatever this result set is, prior to doing the experiment, the chance of it occurring was zero.
Such is the paradox of considering infinitesimally likely events in an infinite experiment.
I linked the Almost surely page earlier, but I recommend you specifically read the section Throwing a dart.
It seems to me that if the number of possibilities increases exponentially with time, then not all things will happen given infinite time, even ignoring heat death. But then again, perhaps all things that are possible now will happen. Though I’m not sure what that means.
And we are talking about a lot of possibilities. Consider the Dinner Party problem. Say you have 60 guests. How many possible seating arrangements are there? Something like 60! = 8.320987113 x 10^81, which exceeds the number of atoms in the universe. Any problem where you put 60 objects in 60 locations will involve this, including structures composed of 60 bricks, planks or whatever. And usually, placement is a continuous problem, not a discrete one: we don’t just consider matching person A to Seat A, but rather where in the entire room they are situated at any given time.
70! = 1.197857167e100
80! = 7.156945705e118
90! = 1.485715964e138
100! = 9.332621544e157
Another way to think of it is, if everything possible must happen in an infinite universe, a possible thing can also be considered in the negative. If getting a million heads is possible, what about NEVER getting a million heads? It’s logically possible to consider an infinite universe in which no one ever flips a coin and gets a million heads. But if it’s guaranteed that eventually someone will get a million heads, it’s guaranteed that never getting a million heads will never happen.
If everything possible is inevitable, then there are a bunch of things that can’t NOT happen. Do those count as things that could happen? Then they don’t happen, and thus not everything possible is inevitable.
Clearly the only possible answer is yes,…AND no.
The word “happen” implies a finite event; an infinite string of coin tosses can be initiated, and we can verify that the first X happen, but since it’s infinite the string can never be completed, hence it never “happens” (or at least we can never verify it happened).
So, limiting ourselves to finite events, we have to rule out cases such as “The earth will never fall into the Sun” or “The earth will always be plagued by Justin Bieber fans.” I also think we need to rule out logical contradictions like “2+2=5”, which by definition can never be true. I’m also quietly exempting cases where the language or original intent of the predicted event can be so twisted to mean anything; the event has to be something clearly defined. Finally, we have to rule out events that by their nature are restricted to occur in a specific period of time or place; this seems to go against the spirit of the question of presuming “infinite” time (and, I’m assuming, space).
So given these four conditions–that the event is finite in extent, not self-contradictory, unambiguous and one whose occurrence is not restricted by time or place–are there still event that cannot happen given infinite time?