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Spacetime contains all places and all times, so there’s no the time any more than there’s the place.
When Einstein wrote that “The distinction between past, present, and future is only a stubbornly persistent illusion,” he was referring to the fact that these concepts have no objective meaning in spacetime.
Since spacetime is static and unchanging, no parts of it can change their reality status, and all parts must be equally real.1
Figure 11.2: The distinction between past, present and future exists only in the frog perspective (right), not in the bird perspective of the mathematical structure (left)—in the latter, you can’t ask, “What time is it?”; merely, “When am I?”
In summary, time is not an illusion, but the flow of time is. So is change. In spacetime, the future exists ...
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One of the most fundamental concepts in modern physics is that of a field, which is just this: something represented by numbers at each point in spacetime.
For example, there’s a temperature field corresponding to the air around you: there’s a well-defined temperature at each point, totally independent of any human-invented voxels, and you can measure the temperature number by holding a thermometer there—or your finger, if you don’t need great accuracy. There’s also a pressure field: at each point, there’s a pressure number which you can measure with a barometer—or with your ear, which will hurt if the number is too extreme and which can detect sound if the pressure is fluctuating over time.
These electric and magnetic fields can be elegantly unified into what’s known as the electromagnetic field, represented by six numbers at each point in spacetime. As we discussed in Chapter 7, light is simply a wave rippling through the electromagnetic field, so if our physical world is a mathematical structure, then all the light in our Universe (which feels quite physical) corresponds to six numbers at each point in spacetime (which feels quite mathematical). These numbers obey the mathematical relations that we know as Maxwell’s equations, shown in Figure 10.4. There’s a caveat here: what
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Just as the strength of the electromagnetic field corresponds to the number of photons at each time and place, there are other fields corresponding to all the other elementary particles known.
In quantum field theory, the wavefunction specifies the degree to which each possible configuration of each of these fields is real.
As we discussed in Chapter 7, we physicists still haven’t found a mathematical structure that can describe all aspects of reality, including gravity, but so far, there’s no indication that string theory or any of the other most actively pursued candidates for such a description are any less mathematical than quantum field theory.
Whereas most of my physics colleagues would say that our external physical reality is (at least approximately) described by mathematics, I’m arguing that it is mathematics (more specifically, a mathematical structure). In other words, I’m making a much stronger claim.
if two structures are equivalent, then there’s no meaningful sense in which they’re not one and the same,
This means that if some mathematical equations completely describe both our external physical reality and a mathematical structure, then our external physical reality and the mathematical structure are one and the same, and then the Mathematical Universe Hypothesis is true: our external physical reality is a mathematical structure.
since the mathematical description is supposedly perfect, accounting for everything that can be observed, those additional bells and whistles that would make our Universe nonmathematical would by definition have no observable effects whatsoever, rendering them 100% unscientific.
Figure 11.4: Complexity is a hallmark of life. The motion of an object corresponds to a pattern in spacetime. An inanimate clump of ten particles accelerating toward the left constitutes a simple pattern (left), while the particles that make up a living organism constitute a complex pattern (middle), corresponding to the complex motions that accomplish information processing and other vital processes. When a living organism dies, it eventually disintegrates and its particles separate from each other (right). These crude illustrations show merely ten particles; your own spacetime pattern
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I think that consciousness is the way information feels when being processed in certain complex ways.
The key difference lies not in the neurons that carry this information, but in the patterns whereby they’re connected. Although your perception of yourself and your perception of the strawberry are extremely different, it’s therefore plausible that they’re both fundamentally the same kind of thing: complex patterns in spacetime. In other words, I’m arguing that your perceptions of having a self, that subjective vantage point that you call “I,” are qualia just as your subjective perceptions of “red” or “green” are. In short, redness and self-awareness are both qualia.
One of the key purposes of science, and indeed one of the key purposes of having a brain, is predicting our future. But if time doesn’t flow, then what do we even mean by predicting our future? Figure 11.6 illustrates how we can reformulate this as a sensible question even without the notions of change or the flow of time.
The complexity of something is usually defined as the smallest number of bits required to fully describe it (a bit is a zero or a one). For example, a diamond describable as 1024 carbon atoms arranged in a perfectly regular lattice pattern has very low complexity compared to a hard drive with a terabyte of random numbers, since the latter can’t be described with less than a terabyte (about 8 × 1012 bits) of information. Yet that hard drive is much less complex than your brain, where more than a hundred quadrillion (1017) bits of information are needed just to describe the state of its synapses
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information is a measure of how much meaning complexity has. If you fill your hard drive with random numbers, then it contains no information about the outside world, but if you fill it with history books or with movie clips of your family, then it does. Your brain contains a vast amount of information about the outside world, both in the form of memories of distant times and places and in the form of its continually updated model of what’s happening around you right now.
The core idea is that for an information processing system to be conscious, it needs to be integrated into a unified whole that can’t be decomposed into nearly independent parts.2 This means that all parts need to compute jointly with lots of information about each other—otherwise there would be more than one independent consciousness, such as in a room full of people or, perhaps, in the two brain halves of a patient whose connecting corpus callosum has been cut. If there are fairly independent parts that are too simple, then these won’t be conscious at all, like the independent pixels of a
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Generations of physicists and chemists have studied what happens when you group together vast numbers of atoms, finding that their collective behavior depends on the pattern in which they’re arranged: the key difference between a solid, a liquid and a gas lies not in the types of atoms, but in their arrangement. My guess is that we’ll one day understand consciousness as yet another phase of matter. I’d expect there to be many types of consciousness just as there are many types of liquids, but in both cases, they share certain characteristic traits that we can aim to understand.
Why do we perceive the world as stable and ourselves as local and unique? Here’s my guess: because it’s useful. It appears that we humans have evolved self-awareness in the first place because certain aspects of our world are somewhat predictable, so that being good at modeling the world, predicting the future and making smart decisions increases our reproductive success. Self-awareness would then be a side effect of this advanced information processing.
Although what’s useful and thus perceived varies among species, certain basic considerations appear to be shared among all life-forms. For instance, it’s only useful to perceive aspects of the world that exhibit enough stability and regularity that information about them can help predict the future. If you’re looking out over a stormy ocean, perceiving the exact motions of trillions of water molecules would be rather useless because they tend to collide with each other and change directions within less than a trillionth of a second. On the other hand, perceiving that a humongous wave is headed
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Even if there exists an identical copy of you a googolplex meters away, or in a decohered part of the quantum Hilbert space, no information can be transferred between the two of you, so both of you might as well keep things simple and act as if the other copy doesn’t exist.
To me, science is all about understanding reality and our place in it. From a pragmatic perspective, it’s about building a model of reality that lets us predict our future as successfully as possible, so that we can choose to do what we predict will have the best outcome—my guess is that it’s to help accomplish this task that we’ve been fortunate enough to evolve consciousness.
Thinkers throughout the ages have tried to formalize this scientific process, and I think most contemporary scientists agree that it boils down to this: 1. Make predictions from assumptions. 2. Compare observations with predictions, update assumptions. 3. Repeat. We scientists often call a collection of assumptions a theory.
During World War II, the Allied forces successfully estimated the number of German tanks from their serial numbers. If the first captured tank had the serial number 50, then this ruled out the hypothesis that there were more than a thousand tanks with 95% confidence, since the probability of capturing one of the first fifty ones built was less than 5%. The key assumption is that the first tank captured can be thought of as a random one from the reference class of all tanks.
I view the measure problem as the greatest crisis in physics today.
What’s the measure problem telling us? Here’s what I think: that there’s a fundamentally flawed assumption at the very foundation of modern physics. The failures of classical mechanics required switching to quantum mechanics, and I think that today’s best theories similarly need a major shakeup. Nobody knows for sure where the root of the problem lies, but I have my suspicions. Here’s my prime suspect: ∞. In fact, I have two suspects: “infinitely big” and “infinitely small.” By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there
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If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places. In practice, we physicists have never managed to measure anything to more than about sixteen decimal places.
So why are today’s physicists and mathematicians so enamored with infinity that it’s almost never questioned? Basically, because infinity is an extremely convenient approximation, and we haven’t discovered good alternatives. For example, consider the air in front of you. Keeping track of the positions and speeds of octillions of atoms would be hopelessly complicated. But if you ignore the fact that air is made of atoms and instead approximate it as a continuum, a smooth substance that has a density, pressure and velocity at each point, you find that this idealized air obeys a beautifully
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Figure 12.2: The parallel universes described in this book form a four-level hierarchy, where each multiverse is a single member among many at the level above it.
As we discussed in detail in the previous chapter, the MUH says that a mathematical structure is our external physical reality, rather than being merely a description thereof. This equivalence between physical and mathematical existence means that if a mathematical structure contains a self-aware substructure, it will perceive itself as existing in a physically real universe, just as you and I do (albeit generically a universe with different properties from ours). Stephen Hawking famously asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” In
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The German mathematician Emmy Noether proved in 1915 that each continuous symmetry of our mathematical structure leads to a so-called conservation law of physics, whereby some quantity is guaranteed to stay constant—and thereby has the sort of permanence that might make self-aware observers take note of it and give it a “baggage” name. All the conserved quantities that we discussed in Chapter 7 correspond to such symmetries: for example, energy corresponds to time-translation symmetry (that our laws of physics stay the same for all time), momentum corresponds to space-translation symmetry
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So are we simulated? According to the MUH, our physical reality is a mathematical structure, and as such, it exists regardless of whether someone here or elsewhere in the Level IV multiverse writes a computer program to simulate/describe it.
My guess is that this would be a tiny effect at best, so if asked, “Are we simulated?,” I’d bet my money on “No!”
the proposal closest to the Level IV multiverse is the theory of modal realism by the late philosopher David Lewis, which posits that “all possible worlds are as real as the actual world.”
One common criticism of modal realism asserts that because it posits that all imaginable universes exist, it makes no testable predictions at all.
The Level IV multiverse does not imply that all imaginable universes exist. We humans can imagine many things that are mathematically undefined and hence don’t correspond to mathematical structures. Mathematicians publish papers with existence proofs that demonstrate the mathematical consistency of various mathematical-structure descriptions precisely because to do this is difficult and not possible in all cases.
We have argued that the External Reality Hypothesis (ERH), which says that there is an external physical reality completely independent of us humans, implies the Mathematical Universe Hypothesis (MUH), which says that our external physical reality is a mathematical structure, which in turn implies the existence of the Level IV multiverse.
One of the key testable predictions of the Mathematical Universe Hypothesis is that physics research will uncover further mathematical regularities in nature.
I know of no other compelling explanation for this trend than that the physical world really is completely mathematical.
Looking toward the future, there are two possibilities. If I’m wrong and the MUH is false, then physics will eventually hit an insurmountable roadblock beyond which no further progress is possible: there would be no further mathematical regularities left to discover even though we still lacked a complete description of our physical reality. For example, a convincing demonstration that there’s such a thing as fundamental randomness in the laws of nature (as opposed to deterministic observer cloning that merely feels random subjectively) would therefore refute the MUH. If I’m right, on the other
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Parallel universes are not a theory—they’re predictions of certain theories.
what’s scientifically testable are our mathematical theories, not necessarily their implications, and that this is quite okay. As we discussed in Chapter 6, because Einstein’s theory of general relativity has successfully predicted many things that we can observe, we also take seriously its predictions for things we can’t observe—for example, what happens inside black holes. Likewise, if we’re impressed by the successful predictions of inflation or quantum mechanics so far, then we also need to take seriously their other predictions, including the Level I and Level III multiverses.
It’s quite common for mathematical equations to have multiple solutions, and as long as the fundamental equations describing our reality do, then eternal inflation generically creates huge regions of space that physically realize each of these solutions, as we saw in Chapter 6. For example, the equations governing water molecules, which have nothing to do with string theory, permit the three solutions corresponding to steam, liquid water and ice, and if space itself can similarly exist in different phases, inflation will tend to realize them all.
Some of the fine-tuning appears extreme enough to be quite embarrassing—for example, we saw that we need to tune the dark energy to about 123 decimal places to make habitable galaxies. To me, an unexplained coincidence can be a telltale sign of a gap in our scientific understanding. Dismissing it by saying, “We just got lucky—now stop looking for an explanation!” is not only unsatisfactory, but also tantamount to ignoring a potentially crucial clue.
It’s proven remarkably hard to write down a theory that produces exactly the universe we see and nothing more.
