Spacetime must have an end or else probabilities are impossible to calculate. That's the reasoning being used by a few physicists wrestling with the problem of how to calculate probabilities in a universe, like ours, that appears to be eternally inflating, according to

The problem boils down to a simple philosophical dilemma. As predicted by Einstein's theory of general relativity, current empirical evidence suggests our universe is expanding at an accelerated rate and will continue to do so forever. If true, one consequence of this "eternal inflation" is that time is endless.

But if time is endless, then it poses a significant problem for anyone who relies upon calculating probabilities to predict future outcomes-- a methodology perhaps most important to science. This is because when time is infinite, any event that might occur, will occur-- eventually. In fact, even the most unlikely of events are certain to occur an infinite number of times! Thus, in an eternal universe, probabilities are impossible to calculate because every event is equally likely to happen.

In a brazen effort to save the validity of probabilistic predictions, Raphael Bousso, a physicist from the University of California at Berkeley, is one of a few scientists making the bold suggestion that, rather than throw out probabilistic predictions because they aren't consistent with the logic of an ever-expanding universe, we throw out the empirical evidence instead.

In other words, Bousso thinks we can avoid the philosophical conundrum about the validity of probabilistic predictions if we simply conclude, instead, that time does have an end.

In fact, Bousso thinks he can predict when the end will come. Using rigorous probabilistic calculations based upon a number of assumptions about allowed events, Rousso has calculated that time will most likely end somewhere between 3 and 4 billion years from now.

Bousso admits that his conclusion rests upon assumptions which can be refuted by current empirical evidence about the actual state of the universe, not to mention resting upon an extreme view about the pragmatic limits of probabilistic calculations. But his conclusion is not meant to be taken as correct, just rational.

Even so, it's worth asking: What would the end of time be like for observers around at the (for lack of a better term...) time?

"The observer will necessarily run into the cutoff before observing the demise of any other system," Bousso and his coauthors write. Or, in other words, anyone alive at the end of time wouldn't notice it happening.

One moment time would exist, and the next moment... well, there wouldn't be a next moment.

Time will end within a few billion years, say physicists
Physicists have calculated that time is likely to end within the next 4 billion years due to a catastrophe that no one alive at the time will witness.