In last week’s post on entropy, I blithely referred to black holes as spontaneously increasing in entropy. This may seem counterintuitive (as much as anybody can have “intuition” about black holes). If we view the increase in entropy as a system moving from order to disorder, how would a singularity become more disordered? How could the contents of a black hole spread out in a more disordered manner if they are supposed to take up an infinitely small amount of space? If we use the other definition of entropy, the dispersal of energy, then that would imply that a black hole leaks energy into the surrounding void of space. But nothing is supposed to escape the black hole’s event horizon—not even light. The second law of thermodynamics demands that entropy increases, but for a long time even scientists could not determine how that would happen in a black hole. The problem was cracked in the 1970s by Stephen Hawking, who proposed that black holes have a set temperature proportional to their surface area that disperses into the surrounding void in the form of Hawking radiation. Hawking radiation explains how black holes increase in entropy over time, but it also presents a whole new set of questions that physicists continue to grapple with today. Hawking radiation also sets the scene for how the universe may die in the far, far future. It seems not even black holes are safe from the ravages of time.
The common, simplified description of Hawking radiation explains the phenomenon in terms of “virtual particles.” These are small particles of matter and anti-matter that spontaneously pop into existence and immediately annihilate each other. But at the edge of a black hole, one of these virtual particles may appear inside the event horizon. The particle, like light, cannot escape the singularity’s gravitational pull. As the particle is swallowed by the black hole, its opposing twin radiates away from the black hole with nothing to annihilate it. Positive energy from this jilted virtual particle appears to leak out of the black hole as radiation. Simultaneously, the particle that fell into the black hole imparts negative energy, reducing the surface area of the event horizon. Small black holes leak their energy faster than big black holes, meaning that small black holes appear much “hotter.” But, over time, black holes evaporate completely into nothing but random energy.
The “virtual particles” description of Hawking radiation is a convenient way to frame Stephen Hawking’s extremely complex calculations. But you may be wondering why these virtual particles would be popping in and out of existence in the first place. In Hawking’s original calculations, these “virtual particles” arise from fluctuations in the quantum field. Quantum field theory is far too complex for me to explain in this blog post, but the PBS Space Time video above does a great job of explaining how it works in terms of Hawking radiation, and it links to some of their other videos about quantum mechanics.
In simplified terms, quantum field theory defines every particle of matter or energy as a set of discrete oscillations in the quantum field. Like a guitar string oscillates back and forth when plucked, the quantum field of even empty space oscillates as you move forward and backward in time. “Virtual particles” are really just “random” fluctuations in the quantum field that arise from uncertainty. These fluctuations occur in identical pairs, with one moving forward in time (a particle) and one moving backward in time (an anti-particle) so that they cancel each other out when they combine (you can imagine this as the same phenomenon active noise-canceling headphones use to “destroy” ambient sound).
But in areas where spacetime is extremely curved, like near a black hole, the quantum field fluctuations are disrupted. The result of this disruption is that the vacuum around the black hole contains fluctuations moving forward in time that look like particle radiation. The black hole has absorbed the corresponding “negative” fluctuation, meaning it loses energy and mass. (This may be confusing but, if you think about it, a quantum fluctuation moving backward in time would mean that there was more energy in the past than there is in the present).
A black hole moving through space can gain mass, which translates to event horizon surface area, by consuming any planets, stars, and gas that falls into it. But eventually, through Hawking radiation, black holes do become smaller and less massive until they evaporate away. However, black holes are still some of the most stable entities in the universe. Black hole evaporation happens on massive time scales that are dependent on the size of the initial black hole. For a supermassive black hole, it would take a googol, 10100, years for the black hole to completely evaporate. For comparison, the universe has only been around for roughly 1010 years, an infinitesimal length of time compared to the life of a black hole.
The universe is currently in what scientists call the Stellar Era, a period of time in which most of the universe’s energy comes from the thermonuclear fusion inside stars. New stars are still being born from gas clouds, but within 1014 more years (roughly 10,000 times the current age of the universe), all of the gas will be used up and even the most stable stars will have run out of fuel. Next, we will enter the Degenerate Era, a period of slowly cooling, dead stars. Stars that are not massive enough to form black holes will collapse and cool into degenerate husks. Protons decay over a time scale of 1032 years. Therefore, scientists estimate that all matter (the planets and remnant stars) will disintegrate into free leptons (the smallest, most elementary particles like electrons, positrons, muons, etc.) within 1037 years. Once all the matter has decayed, the only structures remaining in the universe will be black holes. We enter the Black Hole Era.
Because of the stability of black holes, the Black Hole Era will last longer than any other age of the universe. The lifespan of all matter in the universe, roughly 1037 years, makes up less than 0.0000000000000000000000000000000000000000000000000000000000001% (10-61%) of the lifespan of a black hole. Life, matter, and energy are characteristics of the universe in its infancy. The overwhelming majority of the universe’s life is empty, dark, and cold. Once all the black holes have evaporated, we enter the Dark Era, a period of cooling photons tending towards uniformity and maximum entropy. When the universe reaches a uniform minimum temperature, time becomes meaningless.
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