Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe

by Brian Greene

The Thinker can think without the need to purge heat so long as the Thinker never erases a memory. But assuming the Thinker is of finite extent, it will have a finite memory capacity that will sooner or later fill to its limit. Once it does, all the Thinker can do internally is reshuffle the fixed information it has in memory, endlessly ruminating on old thoughts—not a version of immortality many of us would choose.

If, as the data currently suggest, the accelerated expansion continues unabated, then as we encountered on floor 12, distant galaxies will disappear as if they have fallen over a cliff at the edge of space. That is, we are surrounded by a distant spherical horizon marking the boundary of what, even in principle, we can see. Everything more distant than the boundary recedes from us at greater than light speed, and so any light emitted from such distances will never reach us. Physicists call the distant boundary our cosmological horizon.

The temperature arising from the cosmological horizon behaves differently. It’s constant. It’s tiny—based on the measured rate of accelerated expansion, it’s about 10−30 kelvin—but it’s enduring. And in the long run, endurance matters.

This implies that the hibernation strategy is destined to fail. As the Thinker continues to decrease its temperature (which, remember, is what allows it to continue thinking indefinitely on a finite energy budget), sooner or later it will reach the tiny value of 10−30 kelvin. At that point, game over. The universe won’t accept its waste. One more thought (or, more precisely, one more erasure) and the Thinker fries.

Indeed, if the accelerated expansion does not slow, there will come a time when thought takes its final bow. Our understanding is too coarse to make a precise prediction, but putting rough numbers into the equations suggests this could happen within the next 1050 years. A big unknown, as we noted at the outset, is whether intelligent life will be able to intercede in the cosmic unfolding, perhaps affecting the evolution of stars and galaxies, mining unanticipated sources of high-quality energy, or even controlling the rate of spatial expansion. Because of the complexity of intelligence, it is impossible to weigh in with anything more than wild conjecture, which is why I’ve chosen to avoid such influences entirely. So, putting intelligent intervention to the side and diligently hewing to the second law of thermodynamics, we conclude that by the time we climb to the fiftieth floor, the universe may very well have hosted its final thought.

To me, the future that science now envisions highlights how our moment of thought, our instant of light, is at once rare, wondrous, and precious.

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THE TWILIGHT OF TIME

Quanta, Probability, an...

And if there truly is no end date for time, then any and all outcomes not strictly forbidden by the quantum laws—familiar to bizarre, likely to implausible—can rest assured that sooner or later they will be given their moment to shine.

The Disintegration of Black Holes

The math shows that the radius of the event horizon is proportional to the mass of the black hole: less mass entails a smaller horizon, more mass a larger horizon.

Bekenstein elevated the pattern to a proposal: the total entropy of a black hole is given by the total area of its event horizon (measured in Planck units).

The view, coarsely put, was that black holes cannot carry disorder because there is nothing within them to be disordered.

Hawking’s analysis not only confirmed Bekenstein’s, but also revealed complementary surprises: black holes have a temperature and black holes glow. They radiate. Black holes are black in name only. Or, said more precisely, black holes are black only if you ignore quantum physics.

Although the black hole emits Hawking radiation, on balance it will take in more energy than it releases, slowly increasing its heft. Because even the smallest black holes so far discovered by astronomical observations are much more massive than the moon, they are all in the process of plumping up. However, as the universe continues to expand, the microwave background radiation will continue to dilute and its temperature will continue to cool. In the far future when the background temperature of space drops below that of any given black hole, the energy seesaw will pivot, the black hole will emit more than it receives, and it will start shrinking as a result.

In the fullness of time, black holes will waste away too.

1068 years after the bang, such black holes will have radiated away.

The Disintegration of Extreme Black Holes

An End of Time

The Disintegration of Emptiness

Higgs proposed, when you push on a particle it feels massive because it is plowing through the resistance exerted by the Higgs field. The more hefty a particle the more it resists your push, which according to Higgs means the particle experiences a stronger resistance from his space-permeating field.

Higgs was suggesting that if space were truly empty in the conventional and intuitive sense, particles would have no mass at all. He thus concluded that space must not be empty, and the peculiar substance it harbors must be just right for imbuing particles with their evident mass.

When two particles, say two protons, slam together at high speed, the collision should jiggle the surrounding Higgs field. On occasion, this would theoretically knock free a tiny droplet of the field, which would show up as a new type of elementary particle—a Higgs particle—what Nobel laureate Frank Wilczek calls a “chip off the old vacuum.”

The relevance of the Higgs field for our journey on the cosmic timeline comes from a related but distinct consideration—at some point in the future the value of the Higgs field may change. And much as the drag experienced by a Wiffle ball would change if the density of air it encountered was different, the masses of the fundamental particles would change if the value of the Higgs field they encountered was different. For all but the most minuscule of shifts, such a change would almost certainly destroy reality as we know it.

If you change the masses of the fundamental particles you change how they behave, and so you change more or less everything.

The relevant physics for a Higgs jump is called quantum tunneling,

Sometimes the electron disappears from the trap and rematerializes outside it.

I’ve described quantum tunneling in terms of a particle penetrating a barrier, changing its location from here to there, but it can also involve a field penetrating a barrier, changing its value from this to that. Such a process, involving the Higgs field, may determine the long-term fate of the universe.

Why 246? No one knows.

But why has the Higgs value been stable for billions of years? The answer, we believe, is that the Higgs value, like the marble in the flute or the electron in the trap, is hemmed in on all sides by formidable barriers: if the Higgs field was to try migrating from 246 to a larger or smaller number, the barrier would forcefully drive it back to its original value, much like the marble would be driven back to the bottom of the flute should someone momentarily shake the glass. And were it not for quantum considerations, the Higgs value would permanently remain at 246. But as Sidney Coleman discovered in the mid-1970s, quantum tunneling changes the story.

Were this to occur, the Higgs field would not change its value across all of space simultaneously. Instead, in some tiny region singled out by the random nature of quantum events, the Higgs would make its move, tunneling through the barrier to a different value. Then, much as a marble that tunnels through a champagne flute will drop to a lower height, the Higgs field’s value would drop to a lower energy. The lure of lower energy would then coax the Higgs field at nearby locations to make the transition too, a domino-like effect that would yield an ever-growing sphere within which the Higgs value would have changed.

Coleman’s analysis revealed that the boundary of the sphere, marking the transition from old Higgs value to new, would spread outward at very nearly the speed of light.

Physicists cannot pinpoint when the Higgs might make such a jump. The timescale depends on particle and force properties that have yet to be determined with adequate precision. Moreover, as a quantum process, it can only be predicted probabilistically. Current data suggest that the Higgs is likely to tunnel to a different value somewhere between 10102 and 10359 years from now—

Because the Higgs field redefines what we mean by emptiness—the emptiest of empty space anywhere in the observable universe contains the Higgs field with value 246—quantum tunneling of the Higgs field’s value reveals an instability of empty space itself.

Boltzmann Brains

All of this is based on a curious fact: everything you know reflects thoughts, memories, and sensations that currently reside in your brain.

From a staunchly physicalist perspective, all of that is in your head right now because of the particular arrangement of the particles that are in your head right now. Which means that if a random spray of particles flitting through the void of a structureless, high-entropy universe should, by chance, spontaneously dip to a lower-entropy configuration that just happens to match that of the particles currently constituting your brain, that collection of particles would have the same memories, thoughts, and sensations that you do. Whether in honor or reproach, I don’t know which, such hypothetical, free-floating, untethered minds formed by the rare but possible spontaneous coming together of particles into a special, highly ordered configuration have become known as Boltzmann brains.

What is the timescale for such resurrection? With a rough calculation (which math enthusiasts can find in the endnotes23) we can estimate that there’s a reasonable chance that a Boltzmann brain will form within 101068 years.

The deep skepticism that emerges from the possibility of spontaneous brain formation forces us to be skeptical of the very reasoning that led us to entertain the possibility in the first place.

Some conclude that Boltzmann brains are much ado about nothing. Sure, this perspective acknowledges, Boltzmann brains can form. But ease your mind. You are definitely not one of them. Here’s how to prove it: Look out on the world and take in all you see. If you are a Boltzmann brain, the odds are overwhelming that a moment later you won’t exist. A brain that can last longer is a brain that’s part of a larger and more ordered support system and thus requires a yet rarer fluctuation to even lower entropy, making its formation that much more unlikely. So if your second glance at the world seems much like your first, your confidence that you are not a Boltzmann brain increases. Indeed, according to this perspective, every next moment of a similar sort makes your argument stronger and your confidence greater.

A more convincing approach is to challenge the underlying scenario itself: Central to the argument for Boltzmann brains is the existence of a distant cosmological horizon continuously radiating particles, the raw materials for building complex structures, including minds. Over the long haul, if the dark energy filling space were to dissipate away, then accelerated expansion would draw to a close and the cosmological horizon would withdraw. Without a distant surrounding surface radiating particles, the temperature of space would close in on zero, and with that the chance of spontaneously forming complex macroscopic structures would close in on zero too. There is as yet no evidence for a weakening (or a strengthening) of dark energy, but future observational missions will study the possibility with greater precision. A conservative assessment is that the jury is still out.

More radical still are approaches in which the universe, or at least the universe as we know it, simply will not exist arbitrarily far into the future.

Is the End Near?

What’s evident, though, is that were the crunch to happen in far less time than 101068 years, the peculiar implications of Boltzmann brains would again be rendered moot.

Tolman found, however, that the second law of thermodynamics thwarts this vision. The continual buildup of entropy from one cycle to the next implies that the universe we currently inhabit could be preceded only by a finite number of cycles, thus requiring a beginning after all.

In their new version of the cyclic approach, Steinhardt and Ijjas argue that they can surmount this problem. They have established that during each cycle a given region of space stretches far more than it contracts, ensuring the entropy it contains is thoroughly diluted. Cycle upon cycle, the total entropy across the entirety of space increases, as per the second law of thermodynamics. But in any finite region, such as the one giving rise to our observable realm, the entropic buildup that stymied Tolman is no longer a concern. Expansion dilutes away all matter and radiation, while the subsequent contraction harnesses the power of gravity to replenish just enough high-quality energy to start the cycle anew.

The duration of each cycle is determined by the value of the dark energy which, based on today’s measurements, sets the duration on the order of hundreds of billions of years. As this is far less than the typical time required for Boltzmann brains to form, cyclic cosmology provides another potential solution for preserving rationality. While there would be ample time during a given cycle to produce brains in the ordinary manner, the cycle would conclude well before there would be time to produce brains in the Boltzmannian manner. With reasonable confidence we could all then declare that our memories were laid down by events that really happened.

In recent years, cyclic cosmology has emerged as a main competitor to the inflationary theory. Although both can explain cosmological observations, including the all-important temperature variations in the microwave background radiation, the inflationary theory continues to dominate cosmological research.

And the inflationary and cyclic theories do make one significantly different observational prediction, which may one day figure prominently in adjudicating between them: The burst of inflationary expansion at the big bang would likely have so vigorously disturbed the fabric of space that the gravitational waves produced might still be detectable. The more gentle expansion of the cyclic model results in gravitational waves too mild to be observed. In the not-too-distant future, observations may thus have the capacity to tip the balance between the two cosmological approaches.