The laws of physics only work in a finite universe, but we likely live in an infinite multiverse. Resolving this discrepancy could mean a 50-50 chance time will end in 3.7 billion years. Yeah, this one's going to get weird.
The problem starts with eternal inflation, an offshoot of the inflationary universe model used to explain the Big Bang. In the original inflation model, the early universe very quickly and exponentially expanded in volume, pushing apart different sectors of the universe into causally disconnected patches. That means you could leave one patch traveling at the speed of light forever and never reach any of the others, because the ongoing expansion of the universe makes them too far apart.
In this model, the entire observable universe is just one of these disconnected patches, and there are many more - perhaps infinitely many - out there that are forever beyond our purview. We need inflation because it explains the overall shape of our universe, which is flat and homogeneous when the physics of the Big Bang suggest it should actually be curved and heterogeneous. In this understanding, the much larger overall universe fits that Big Bang shape, and our observable universe is just one tiny part of it.
That, believe it or not, was the easy part. Now for the slightly more difficult bit (we'll get to the really insane part in a moment). Eternal inflation is a subclass of the inflation theory, and it essentially states that the universe - not just our observable universe, but the entire inflated universe - is really a multiverse, with infinitely many bubble universes separated by vacuum. Different parts of the multiverse can suddenly undergo this massive inflation at any moment, splitting them off into separate universes with different physical law. This process is thought to happen an infinite amount of times and go on forever, which leads to an infinite, eternal multiverse. (For a more detailed overview of eternal inflation, check out this paper by Alan H. Guth.)
All that might seem purely academic, but the problem comes when trying to fit finite probabilities into an infinite multiverse. There are some probabilities we take for granted in our finite universe - to use the example put forward by the authors of this new paper, we know it's incredibly unlikely that you will win the lottery. But, in an infinite multiverse, all events must occur, and in fact they all must occur infinite times. That means an infinite number of people win any given lottery, and an infinite number of people lose the lottery. On a finite level, we can see the difference. But on an infinite level, how can we really say one infinitely common event is more likely than another infinitely common event?
Obviously, physicists don't usually have to calculate lottery odds on a multiversal scale, but the same probability issue affects any attempt to calculate the probabilities of the universe. Obviously, we have figured out what the laws of physics are on the finite scale of our universe, but, as the authors point out, "if the universe is eternally inflating, we no longer know why these rules work."
This becomes vitally important for certain cosmological experiments, where we need to know how probable a given phenomenon is in our universe relative to the rest of the eternal, infinite spacetime. And, more generally, it's an issue that we can ignore in our daily lives, but the fact is that our laws of physics break down in an infinite multiverse. That's the "measure problem" in a nutshell.
To get around this problem, physicists slice off a vast but finite portion of space-time and use the many universes within that region to calculate probabilities. The physics of all this are obviously pretty involved, but all we need to know is that physicists know about how much space and time they have include in their sample to arrive at finite probabilities that make sense based on what we observe in our universe.
Here's where we get to the end of time. According to UC Berkeley physicist Raphael Bousso and his team, the statistical cut-off introduced by physicists to get manageable probabilities behaves like an actual structure of the multiverse. So what does that mean? Basically, it means that the universe must end for the laws of physics to have any meaning, and since the statistical cut-off to the size of space-time already allows us to get the right values for our universe, then that cut-off might actually be a very real boundary to the universe, beyond which further expansion is impossible.
Now, if that theory is correct, we shouldn't have any problem with the space part of that equation. But it's the time part that's a concern. According to Bousso and company's projections, there's a 50-50 chance that the universe will end sometime in the next 3.7 billion years, because we will have crossed over the time part of that space-time cutoff.
3.7 billion years might sound like forever - and, on a human scale, it obviously is - but there are lots of things that are older than that. Earth is older than 3.7 billion years, and the Sun still has another five billion years before it runs out of fuel. And this is going to mean some serious retconning for at least four different Doctor Who episodes, and that's just the new series.
Now, what does it mean for the universe to end? Whatever the ending is, it will take the form of a physical catastrophe, but it's unlikely we will ever see it coming. We shouldn't be able to see the catastrophe happen elsewhere, as that means we would be causally ahead of it, which the physicists say is unlikely. More likely, the entire thing will unfold at the speed of light (or, maybe, in some weird way, simultaneously across the entire universe), meaning our descendants will never have to watch the universe burn.
Dr. Bousso explains what this means for physics, and wants to make it clear he's not simply predicting the apocalypse:
"It's very important to understand that we are not saying that we are certain of the conclusion that time will end (though we cannot rule out that it may be correct). In science, this kind of reasoning is often valuable: you realize that your reasonable-seeming theory predicts something that sounds crazy, so you have to come to grips with that. Either you have to abandon the theory, or you have to understand why the crazy-sounding thing may not actually be so crazy."
So, should you believe this? Unless you're willing (and, perhaps more importantly, able - I know I'm not) to dive into their math, the main question to consider is a philosophical one. Their theory hinges on the belief that the universe must be explicable, that it's not enough for the laws of physics to exist - we also have to be able to explain why they exist. That's a more aesthetically pleasing view, but it's just as possible that the laws of physics just sort of are, and they need no further explanation.
Dr. Charles Lineweaver of the Australian National University argues that this theory is really just turning a statistical trick into the end of the universe:
"Because the problem won't go away in their calculations, they conclude the universe must really end. Bousso's average life of a universe is a set time, only because that's what happens when you introduce a cut off point to get a reasonable probability. It's a statistical technique being taken probably too seriously."
But Bousso wants to make it clear that he's not simply arguing the universe will definitely (or at least 50-50 definitely) end. Instead, he and his fellow researchers are trying to point out a hole in physics that needs to be addressed, whether it's with the end of time or something else:
"These cutoffs have been used by many leading physicists for years. We merely pointed out that it's not such an innocent thing to do. The cutoff on time is inevitably physical and hence requires a physical justification. It cannot be considered a mere mathematical trick."