The role of the beads in a quantum abacus is usually performed by fundamental particles, which means that even a tiny amount of heat will have this ruinous effect. Quantum computer designers here on Earth have been forced to advance the state of the art of extreme refrigeration. The machines have to be run at ultracold temperatures.
There are other ways to deal with the issue, however. One potential way to reduce the heat problem is with a topological design. Topology is a field of mathematics that describes how things connect. For instance, if you put a bead on a circular wire, the rules of the game change because pushing up on a bead that is already up will force it around to become down. The meaning of an “up push” becomes dependent on the previous push. When you change the way things connect, you change the kinds of information that can be contained in those things. An example from human cultural history is that the ancient Incas used elaborate knots called khipu as a record-keeping scheme and a form of written language.
If you use topology to hold information, you don’t have to worry about heat quite as much as you do when you are moving bits around within a fixed topology. Instead of just moving a bead, for example, you could also bend and change the connections of the wire so that the bead moves in different ways. In addition to loops, you might explore various knots, branching structures, and so on. Enough heat could still melt the wire and ruin your topology, but if the heat is only enough to jiggle the beads, then the topology won’t be harmed and you can preserve a lot of information.
Physicists like Nobel laureate Frank Wilczek are trying to figure out how to make a practical topological quantum computer on Earth. The general idea is to move around artificial, flat, fundamental particles called anyons (which we first encountered in Jim Gates’s work) within tiny confines so as to tie knots with the paths that they trace as they move. This is a remarkable idea because the knots are only knots if you think of time as one of the dimensions within which the strands are held tight.
So far, so good: none of these ideas about quantum computers is anything other than mainstream, not radical. But Lanier and I went a step further to propose that alien computers are not only topological quantum machines, but that they are gravitational. The particles they tie knots with are gravitons. And this takes quantum computers into the realm of dark energy.
As we have discussed, dark energy is treated as synonymous with the idea of the cosmological constant these days. That wasn’t always the case. When Einstein formulated the theory of general relativity in 1915, the math predicted that the universe should be expanding. That seemed wrong, so Einstein added the cosmological constant so the universe would be static. Then in 1925 Edwin Hubble gathered data that showed that the universe actually was expanding, so Einstein got rid of the constant. Then, in 1998, our friend Berkeley astronomer Saul Perlmutter gathered even better data and showed that not only is the universe expanding, but the rate of expansion is accelerating. And so physicists brought the cosmological constant back, but with a new value. And that’s what we call dark energy, and in case you forgot, it’s weird: it behaves like a repulsive fluid with negative pressure that fills all the space around us, pulling everything apart. Given a choice, it doesn’t sound like the sort of fluid you’d want to swim in, but we are swimming in it.
As we have seen, at present there is no solution to the dark energy problem. Prominent physicists like Ed Witten have called it the greatest embarrassment of theoretical physics. It has forced physicists back to the drawing board—all the way back to the foundations of quantum mechanics and general relativity. And for me and Jaron Lanier, that meant quantum computers.
Before we get to the alien computers, however, I want to consider one last difference between Einstein’s general relativity and quantum field theory that has kept physicists from reconciling them. That is the passage of time. In general relativity there is no master clock, but in quantum field theory time is expressed using a master clock that sort of lives off to the side in a metaphysical realm. There are certain phenomena, like black holes and the vacuum, which can be approached by either theory. In the case of the vacuum, we can clearly see some ways in which quantum field theory is unsatisfying. For instance, remember that general relativity is all about curved space-time. In fact, the cosmological constant is just an adjustment of the curvature. It turns out that a detailed mathematical analysis reveals that quantum fields in the curved spaces of general relativity don’t have unique quantum states. An example of this strange state of affairs is called the Unruh effect, named after Bill Unruh, a physicist who described it, which predicts that the vacuum will appear hotter to an accelerating observer. If the effect is eventually observed, then most of what we write here will be rendered wrong, but for the purposes of our argument we’re assuming the prediction is wrong and that the nonrelativistic inner self of quantum field theory is at the root of the mistake.
Recall one of the usual images invoked to describe general relativity: if you try to use a passing train naively as a pitch pipe, you’ll inevitably sing out of tune. This is because the train’s whistle seems to go up and down in pitch as it flies by. What’s really going on is that sound waves wash over you in different concentrations depending on where they were emitted as the train travels relative to you. When they get bunched up, because the train is approaching, they seem to be higher in pitch. That creates an illusion of a changing tone when the train goes by.
In the same way, quantum field theory asks a traveler in an accelerating spaceship to consider an absolute clock, but that clock’s time cannot be taken at face value, just like the sound of the moving train whistle can’t be used as a steady reference. Screwing up the measurement of time screws up everything else. The vacuum should seem hot, according to quantum field theory, for the same reason the whistle seems to get higher. Relativity doesn’t make this mistake, but quantum mechanics, the grandfather of quantum field theory, has passed on this “bad gene.” Within the context of quantum field theory, we don’t have a truly relativistic platform with which to describe the vacuum.
Back to the possibility of gravitonic topological alien computers! Recall the earlier image of the many copies of a quantum abacus, distributed across many realities, all working in parallel. When we move to topological abacuses, where the wires can be tied into loops, trees, knots, and so on, what is going on in all those parallel universes? There is an interesting divergence. On one hand, there can be a bead that is jiggling between the up and down positions on a wire. But although topological quantum computers would rely on changing the shapes of the wires, the shapes themselves are definite. They cannot jiggle themselves into loops that are simultaneously open and closed, in what you might call “sort of loops.” A wire is either a loop or it isn’t.
The interesting thing to notice is what happens if you superimpose all the versions of a quantum abacus from the various realities it’s in. The superposition changes depending on the role that topology plays in your computer. The complexity of a nontopological (nonknotted) superposition is linear, which means simply that it’s exactly as complicated as you’d expect from summing up the complexity of its parts. If, however, you superimpose knotted, topologically interesting abacuses, the result will not be linear, because not all the intermediate states are possible. If you superimpose a loop and a nonloop, you don’t get a distribution of possibilities including a “sort of loop.”
Now recall that we just mentioned something else that isn’t linear: relativity. Space-time is curved, not linear. This is what we observed when criticizing the prediction of the Unruh effect. The quantum state of gravity, which can be thought of as the superposition of the quantum abacuses that either are or describe (depending on your philosophical preference) the state of space-time and/or gravity in the universe, is not linear. Could that be because gravity’s abacuses are knotted?
So here’s a scenario of what might have happened in the history of our universe. These days we take matter for granted as a dominant component of reality, but whe
n the universe was younger, it was too hot for matter to be commonplace. Eventually the universe cooled down and matter became an important phenomenon. With matter came chemistry, and with chemistry came life and evolution, leading to smart aliens who experienced their own Moore’s laws, which drove them to develop gravitonic quantum computers.
As it happens, the amount of dark energy in the universe reduced rapidly just as matter became important. In terms of our thought experiment, that was not a coincidence. It was because the aliens used dark energy as a resource to run their ultimate computers in much the same way we devour oil to run our cars and jets.
Before we continue, there is an even more daunting issue that sneaks up on anyone who tries to explain away the cosmological constant problem: Why now? I had tried to tackle this when I was at Stanford. The surprising thing is that today the cosmological constant/dark energy is not zero but proportional to the dense matter; it seems to be tracking the amount of matter. The approach Lanier and I took in our thought experiment was to turn the question of “Why now?” into a new form: Why here? Recently a consistent cosmology with no dark energy has been proposed by a large number of respected cosmologists, like Joe Silk and Subir Sarkar, who argue that if we live in a region void of the excess dark matter then we can do away with dark energy. Likewise, our aliens come from a region void of dark energy because this void represents a biosphere of computational activity. According to a detailed multidata analysis of the latest measurement of the cosmic microwave background, the Sloan Digital Sky Survey and type Ia supernovae observations, such a region exists. Working with my colleagues at Penn State and CERN, we were able to show that all that data is consistent with a region void of dark energy spanning some two hundred megaparsec. This is a huge region; for comparison, ten kiloparsec is about the radius of a typical spiral galaxy like our own Milky Way, and a parsec itself is already pretty big, at more than three light-years. So we at least have a spot where these aliens could live with their computers. Everywhere outside the aliens’ existence, where there are no computers, the dark energy would exist.
How would this work? In our idea, aliens use the vacuum state as a “reservoir” of qbits. As they do computation, they tie more and more complicated knots in the gravitational, or space-time, quantum state of the universe, which we can think of as all those knotted, superimposed abacuses. This has the effect of “using up” the curvature due to the vacuum energy.
Thus, instead of seeing the enormous value we would predict naively from thinking about a vacuum state that hadn’t been tampered with, we instead see the tiny cosmological constant that Saul Perlmutter measured. If this is correct, then that would mean that the aliens have almost, but not quite, maxed out the computational potential of the universe!
Our thought experiment didn’t quite lead us to an idea of how alien gravitonic computers could work, but we do have some hints. Vacuum energy universally interacts with the gravitational field. There are some important direct channels through which this interaction between gravity and the vacuum energy takes place. It was shown long ago by Einstein and Élie Cartan that fermionic matter (like electrons) will universally mediate vacuum energy with gravity. But there are many types of fermions, of course, and theorists have shown that chargeless fermions (similar to neutrinos) will have the most resonance with the vacuum energy. To highlight the computational mechanism, consider an analogy with superfluid helium. Helium atoms behave like inert fermions, and at very low temperatures a quantum interaction between the helium atoms make them condense into a superfluid with astonishing emergent properties; one is that the superfluid has a negative pressure, just like we considered before for vacuum energy. A quantum field theory calculation successfully predicts this about helium, and Nobel Prizes were earned for the experimental verification of this superfluid state. It turns out that coincidentally gravity mediates exactly the same type of quantum interaction between chargeless fermions!
Therefore the analogy between superfluid helium is quite relevant and important for us because, if a region of space-time is cold enough, the correlations between inert fermionic matter can act as a self-organized medium that tethers the ribbonlike structure of the gravitational-fermionic vacuum energy.1 Very intelligent aliens can achieve quantum computation by exciting the various energy and spin states in this fermion-gravitonic superfluid. How cold does this fluid environment have to be? A back-of-the-envelope calculation reveals that qbit states can be manipulated by turning vacuum energy into thermal radiation so long as the temperature of the superfluid is less than the temperature of the cosmic microwave background, three degrees above absolute zero. However, the region will have to be filled with the neutral fermionic matter that the aliens use to fuel the process. This material can be gotten from supernovae, which emit a huge flux of neutrinos suitable for the purpose. Neutrinos are famously hard to catch, so the aliens will either have to figure out how to trap and contain the neutrinos that pass through their part of the universe, or simply have to inhabit regions rich with supernovae.
It is plausible that the aliens would have control of hot rod gravitational wave detectors, not unlike the laser-interferometer gravitational-wave observatory, or LIGO, that detected gravitational waves first in 2015, that can detect and write information into the topological vacuum state using coherent gravitons, in the same way that our transistors can detect electron currents and switch gates. The gate switching would be powered by the gravitons’ states emitted and absorbed from the vacuum. There have been other proposals to read and write gravity waves. UC Merced physicist Raymond Chiao has proposed a variety of curiously shaped superconducting antennas that might be able to read and write gravity waves.
To push weirdness to the extreme: maybe there could eventually be some way to safely create and manipulate artificial black holes that are analogous to anyons. Maybe moving them around carefully could perform quantum computation. At any rate, ideas about the actual implementation of a topological graviton computer are entirely speculative.
One oddity of gravitonic computers is that while the aliens and the interfaces they use to operate their computers exist locally, just like ordinary objects or like our bodies, the computation itself is not localized. The vacuum state is necessarily nonlocal since the qbits are entangled across our cosmic horizon (the portion of the universe that can be relevant to us as limited by the speed of light), and that region spans three thousand megaparsecs. That’s one big machine room!
It should be, because the computers are stupendous. Paola A. Zizzi of the Università di Padova has calculated that universal information capacity in vacuum energy is approximately 10,120 bits. That’s a lot of bits. How many qbits of computation are required by alien virtual worlds? If we guess how many civilizations there are, we can then estimate the average size of a planetary gravitonic computer. If we conservatively assume just one gravitonic computer per galaxy, we end up with googol-scale capacity—10,100 qbits—for an average alien gravitonic computer. When we try to fantasize what seems to us to be the absolutely ultimate planetary VR computer, assuming that Moore’s law will run into the twenty-second century, we still only come up with a need for a capacity that is perhaps sixty orders of magnitude smaller.
But it’s also true that you can never have enough computation! In fact, there’s a reason alien computers might need to be so huge, and it has to do with heat. Gravitonic computers give off heat just like other computers. Where does that heat go? It is interesting that there are a vast number of highly energetic cosmic ray events and their source remains a mystery. Even so, there isn’t anywhere near as much heat as might be expected from computers of the stupendous size hypothesized here.
You might just take this as a sign that the computers don’t exist, but let’s keep working with the idea that they do. If you want to reduce the heat a computer generates and you have a huge amount of memory, you have an amazing design option, which is called a reversible computer. That means that you change each bit in the whole compu
ter only once, and then move on to another bit. That results in a total record of all computation—and that’s why it’s possible to run the computer in reverse: nothing has been lost. If you move each bead in an extremely capacious abacus only once, you don’t generate the heat you would by moving each bead repeatedly. You can think of it as saving all the information in a tidy way instead of dispersing it. This is also a nice example of Claude Shannon’s famous principle that information and entropy are related.
What will become of our cosmic khipu weavers? They might end up like Maxwell’s demon, a thought experiment important to the development of the second law of thermodynamics that remains important precisely because Maxwell’s demon can never exist. Or maybe the weavers do exist and we’ll meet them. Maybe we’ll eventually weave our own gravitonic khipu.
Of course it’s possible the aliens don’t exist but that graviton weaving will still turn out to be part of the solution to the mystery of dark energy. But that would suggest a natural, self-propelling process that relies on information storage—and that sounds like a definition of something very much like life.
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INTO THE COSMIC MATRIX
All living things are born and change throughout their lifetime. The expanding universe is like this. Because the universe’s space is expanding in time, when we reverse the clock, it returns to an epoch where time itself was born. For many years, I tried to get my mind around the question: What can exist if time ceases to exist?
Fear of a Black Universe Page 16