Robert Frost famously noted that,"Some say the world will end in fire / Some say in ice." Lucky us! We're pretty sure we know the answer: it's ice. But how long do we have until the end of time, and what will it look like? In this week's "Ask a Physicist," we'll find out.

Reader Tony Phan asks:

In an article a few months ago, you said that, if the Big Rip theory is valid, the universe will undergo the rip in 80 billion years. However, you state your disbelief that the Big Rip is a valid theory, being that you believe w = -1. When, then, do you think the universe will end?


Our own Annalee Newitz has long speculated about the end of the world. I, myself, have even dabbled, although my thinking tends to be on the scale of billions of years, rather than hundreds or thousands. But these thoughts tend to be human-centric, and we may or not be the final word on consciousness in our universe. So how long does life itself have, human or otherwise?


As recently as a few decades ago, there seemed to be the very real possibility that the universe would end by collapsing in on itself, at which point all supercivilizations would likely be destroyed. If so, we've only got a few tens of billions of years left. The big question was whether there was enough matter in to "close" the universe, and ultimately end and reverse the expansion.

There isn't.


As near as we can tell, our universe will go on expanding forever. That may seem like good news, but it turns out that even with an infinite number of hours remaining, we can't get an infinite amount done.

To understand why, I need to say a few things about the universe really is made of.


Where we are and where we're going

The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter, Adam Riess and Brian Schmidt for the discovery that the expansion of the universe is accelerating. Cosmologists attribute this acceleration to an as-yet not entirely understood field known as "Dark Energy."


And while we don't know much about it, we have a pretty good idea of one or two particulars. We know, for instance, that it seems to currently account for about 68% of the energy budget of the universe.

We also know something about the pressure of Dark Energy – a detail that might seem kind of irrelevant on first blush, thought it's actually kind of a big deal. One of the great predictions of General Relativity – Einstein's Theory of Gravity – is that all forms of energy, including pressure, momentum density, and the like, contribute to the gravitational field of the universe. For substances that permeate the entire universe, like Dark Energy, the density matters quite a lot.

The pressure of a substance like dark energy is described using a number called w (also known, if you like words, as "the equation of state."). For a pure Cosmological Constant (essentially, the simplest form of Dark Energy, and mathematically identical to the form of Einstein's "greatest blunder") w=-1, which causes the accelerating universe. In the previous article that Tony alluded to, I noted that if w is less than -1 (even by a little bit), the universe will not only continue to accelerate, but even the acceleration will accelerate to the point where all atoms will be ripped apart.


I've said (and maintain) that when the dust settles we'll most likely find w=-1; an opinion shared by most cosmologists. But, it's at least worth mentioning that the Pan-STARRS survey puts the estimate at around -1.186, albeit with systematic errorbars that don't rule out -1. In other words, take the result with a grain of salt.

For today's doomsday scenario, I'm going to simply assume that we live in an ordinary Cosmological Constant universe with no other shenanigans going on like a cyclic universe. If we believe we know anything about gravity, then the universe has no end. It will last literally forever.

But that doesn't mean that there's an infinite amount of future history.


The timeline of Future History

I'll get to the challenges of a supercivilization in due course, but let me begin with some of the problems with sticking around here (and in our puny meat bodies) for too long, by walking you through some of the more obvious milestones in our eschatology.

t+1 billion years - The earth is burnt to a crisp. As I've noted in previous columns, the sun is getting hotter and hotter. In the 4 1/2 billion years since it started out, the sun has increased in luminosity by about 40%. The timescales involved are much longer than man-made climate change, so humans dominate on the century timescale. But on the timescales of billions of years, the sun wins. Eventually, we're going to need to get robot bodies or get out of town.


t+4 billion years - The Milky Way collides with the Andromeda galaxy (or vice-versa, depending on how you look at it). This doesn't necessarily spell disaster, but it is one of the first in a long line of coalescent events, which will culminate in us living in a lonely island universe that will play out over the next hundred billion years or so.

t+5 1/2 billion years - The sun will become a red giant, utterly enveloping the husk of what we once called our planet.

t+2 trillion years - The accelerating universe isolates us utterly. One of the side effects of living in a Dark Energy dominated universe is that structures – galaxies, clusters and superclusters of galaxies – that aren't bound to us by gravity are getting further and further from us at an accelerating rate. Extended far enough into the future, those galaxies are entirely disconnected from us. We couldn't get there even if we had all of the light-speed propulsion in the universe, and even the light emitted from their earliest moment will have lost so much energy in transit that anything outside of our local supercluster will be completely invisible to us. The maximum communication and travel distance, not surprisingly, is known as the "event horizon" and in case you missed it, this is almost exactly the same as what happens when you fall into a black hole.


2 trillion years is functionally the beginning of the end. Though the universe might well be infinite today, by around 2 trillion years, it's pretty clear that we're going to have to do the remainder of our living with the rather paltry energy sources that can found within a few tens of millions of light-years. This doesn't seem like such a big limitation to us now since we're fairly happy coasting on the energy supply from our solar system, but we may want to stretch our legs some day.

Our local isolation may be the biggest limitation to living eternally in a functional sense. In the late 1970's Freeman Dyson argued that in an old-fashioned open universe – one without a cosmological constant – history could literally go on forever.


t+100 trillion years - Star formation ceases, after which all of the stars, one by one, will burn out and become either black holes (for the most massive stars) or white dwarves and neutron stars (for the rest). After this, without a new source of heat, the temperature will quickly drop, along with the background temperature of the universe which has long since dropped to essentially absolute zero.

We tend to think of the universe as cold already, and it is: around 3 degrees above absolute zero. This is all that remains of the radiation from the Big Bang. But every time the universe doubles in size, that temperature halves. After another 10 billion years, we'll be down to 1.5 Kelvin. After 20, we're down to 0.75K. 100 trillion years in the future and the universal temperature will halve roughly a thousand times. It's not terribly instructive to write out what a miniscule temperature that would be.


But I'll do it anyway...

It's 0.– then 434 zeros – 5 Kelvin.

100 Quintillion (10^20) years - Everything either has become a black hole, or has gotten sucked into a black hole. As astronomical bodies lose energy, their orbits tend to decay and they'll spiral inwards. Even now, massive black holes lurk at the centers of massive galaxies, including ours. But eventually, pretty much everything will get crushed into a singularity.


10^100 years - All of the black holes in the universe will evaporate, leaving us with nothing more than a warm (and quickly cooling) bath of photons. This is the ultimate consequence of the 2nd Law of Thermodynamics: Entropy – disorder, as we usually describe it – will get greater and greater until it maxes out. The universe simply can't be more disordered than a uniform swamp of low-energy photons.


Beyond the End?

There may be other milestones along the way. For instance, presumably at some point all of the protons in the universe will decay, but so far we have no real idea how long that will take – just that experimentally protons seem to last at least 10^36 years. But really, that's just a guess.


But do we need protons? If science fiction has taught us anything, it's that somehow the universe is rife with intelligent creatures made of pure energy. But even they can't last forever.

As I mentioned above, the future history of the universe will technically last infinitely long in terms of years, but that doesn't mean that we (or our pure energy progeny) will be able to get an infinite amount done in that time. Since everything gets colder and colder over time, what happens is that there is less and less energy to power a computer or a brain. This means that thoughts (or processes) would take longer and longer as time went on, eventually to the point where a single final thought would essentially freeze midway through. This, too, is a consequence of the second law of thermodynamics. Even what little energy there is out there can't be used indefinitely without creating heat along the way.

Shortly after it was discovered that the universe was accelerating, Lawrence Krauss and Glenn Starkmann took a stab at the finite resources facing an isolated island universe, including details like how much energy it takes to power a brain and how to power an alarm clock that would wake you up between the eons separating subsequent thoughts. It's a good read, but the upshot is that they put the limits of a supercivilization at only around 10^50 years – much less than the evaporation lifetimes of our black holes – before life runs out of steam.


Fortunately, that's a LOT of zeroes.

Dave Goldberg is a Physics Professor at Drexel University, your friendly neighborhood "Ask a Physicist" columnist, and, most recently, author of The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality. You can also follow him on facebook.


All illustrations by Ron Miller.