I feel pretty confident that clocks and calendars are going to continue moving forward at more or less the same rate they have been since time became the abstraction it is. The Earth will continue orbiting the Sun at the same speed, while keeping on its same steady rotation. Microwave frequencies, the measuring stick used by atomic clocks, will keep on as they always have. The world might end in an endless number of ways but, in most of them, time keeps marching forward.
Unless it doesn't. What if instead of a bang or whimper, the universe simply grinds to a halt? It's a real if highly speculative idea. It might not even be that much more unlikely than all of the other end-times scenarios you've heard about: grey goo, asteroid collision, AI overthrow. Better hope you're not doing anything embarassing when the Big Stop goes down.
See, we have a neat set of physical laws, OK? Setting aside our endless battle for a Grand Unified Theory, they're still laws and should describe everything. But there's a problem with that in the endless Universe. In an endless Universe, everything necessarily happens. Duplicate Earths, for example. When everything happens an infinite number of times, as would have to happen in an endless Universe, then it becomes impossible to apply probabilities to anything.
Without probability, we lose the physics that enable something like time to exist. A group of doom-nerds (Vladimir Rosenhausa et al) at the University of California, Berkeley described this in a 2010 paper: time will cease to exist at a certain point. Specifically, they have it that there's a 50-percent chance that time will end within the next 3.7 billion years. We don't know how it will happen and, likely, we are just plain unable to know how it will happen.
The very basic idea, from the paper: "Probabilities are fundamentally defined in terms of the relative abundance of events and histories in the subset. Then the fact that spacetime is extendible is itself a physical feature that can become part of an observer's history. Time can end."
Hmmmm, OK. "If infinitely many observers throughout the universe win the lottery," Rosenhausa writes, "on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infinitely many observers who do not win, but in what sense are there more of them? In local experiments such as playing the lottery, we have clear rules for making predictions and testing theories. But if the universe is eternally inflating, we no longer know why these rules work."
In theories of the endless universe, this is known as the "measure problem." How do we know for sure what, say, the mass of the Higgs boson is if it could have an endless number of different masses in an infinite universe? Putting a limit on them would be putting a limit on the universe's offerings and, thus, the universe. The same goes for the physics that makes time what it is.
There are many problems with their theory, but we can start with a common view that the universe might be endless, but have finite energy. That is, everything in the Universe will just start blinking out at a certain point and exist in eternity as a cold, dark, and very dead place. In this endless universe, there are still finite probabilities, so time should stay safe--or however safe time can stay in a dead universe with no observers.
What our sun could look like in a few billion years: the Cat's Eye Nebula via Hubble (NASA/ESA)
It's also worth noting that there's another idea that has time draining out of the Universe, slowing everything down more and more until time just stops and the universe freezes.
So, this other theory has to do with dark matter/energy and how it's the supposed cause of the expanding Universe. What if there was actually no dark stuff at all? And the Universe is not expanding, but only appears that way because time itself is slowing down. (The theory is based on one particular variant of superstring theory, in which our universe is confined to the surface of a membrane floating in a higher-dimensional space, known as the "bulk.")
Wrap your head around this: our equations that predict the expanding Universe are always staying the same, right? And the solutions to those equations are what say the Universe is expanding. If an ecstatic version of time were placed into those static equations, well, it might look very much like the Universe is expanding. It's just a matter of looking at things in a different way, chucking out certain assumptions, like the idea that time is constant.
"Our calculations show that we would think that the expansion of the universe is accelerating," Professor José Senovilla of the University of the Basque Country, Bilbao, told the New Scientist. "Then everything will be frozen, like a snapshot of one instant, forever." (Suggest instants you would like to be frozen at in the comments, and, please make it more creative than "boning" or "complaining about Facebook.")
Hopefully, by the time that any of these scenarios actually happen, we will have figured most of this out. We'll also likely have engineered a host of other awful and more realistic doomsday threats. But also, by then our sun will have long since exploded.
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