Is the universe a cellular automaton?
Apr. 30th, 2011 12:51 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mmcirvinContinuing my series of posts about cellular automata...
The idea that the whole universe is a cellular automaton—some sort of grid of finitely spaced cells, with a finite number of states, interacting locally with regular time ticks—is a really popular one among geeks of a certain stripe, especially if their specialty involves computers. I've always been skeptical.
My main reasons to be skeptical are (1) relativity and (2) quantum mechanics, neither of which seems to really fit well with CAs. There are probably ways around these objections but I doubt they are terribly elegant.
CAs seem initially attractive, I think, because they are sort of like a discretized version of classical field theories in physics, in which everything's described by a bunch of continuous quantities at every point in space, and the rules for iterating the numbers forward in time are deterministic and local. In a CA, everything's described by discrete quantities at every point on the grid, and the rules for ticking them forward in time are deterministic and local.
If you believe that everything has to be describable with finite integer quantities (which seems to be a popular attitude among computer and software types), it's a natural way to go. There's also a vague idea that quantum mechanics involves going from continuous to discrete quantities, so this might be in some sense the quantum version of a classical field theory. (It's not, though.)
First, relativity: Our world seems to have a lot of rather remarkable continuous symmetries built into it on a pretty low level. One is rotational symmetry; the rules of fundamental physics don't seem to change if a system is rotated by even a small angle. A CA, of course, breaks that down to a finite symmetry of rotations of whatever grid it uses. Now, there are ways around this; there's a CA simulation of an ideal gas in which rotational symmetry reappears as an emergent property on large scales, even though it's not there on the microscopic scale.
But then there's the extension of that to kinematic relativity, more precisely Lorentz invariance (but Galilean invariance would be just as hard to deal with, maybe worse). In CAs, there's typically a sharp distinction between "still lifes" (things that just sit there), "oscillators" (things that cycle through a repeated sequence of states), and "spaceships" (things that move along at some speed, usually a fixed speed).
In our world, every still life or oscillator (on the quantum level they're all really oscillators) is also a spaceship, and every spaceship, with the important exception of the ones that go at the speed of light, is also a still life or oscillator. Spaceships with one velocity can be easily turned into spaceships with a different velocity. There's no preferred rest frame. In a CA, there always is one: the rest frame of the grid. This has a lot of profound effects. Generally speaking, it's hard to come up with a complicated pattern that can move around at an arbitrary velocity. Often just to make the velocity variable, you have to invoke things like programmable universal constructors that can build the future instance at another location.
It's entirely possible, I suppose, that kinematic relativity could be another emergent property of a deeper system that has a grid frame. Certainly, many theorists assume that space-time itself as we know it is some sort of emergent property of a deeper physics. But to me, this particular dissimilarity makes CAs seem less natural as models for the underlying physics. There's no reason to suppose a CA is better for the purpose than anything else (spin networks, strings, loops, what have you).
Second, quantum mechanics. In some ways, quantum mechanics does involve going from continuous to discrete quantities, and there's an idea that CAs are a move in that direction. But actually quantizing a field theory tends to take it further away from being a CA. States of a system end up involving probability amplitudes, which are continuous and interfere with each other.
Quantum systems can also exist in superpositions of correlated states, which can be correlated over long distances. If a particle has two spin states, call them plus and minus, I can have a pair of them be in the state (1/sqrt(2)) (|+>|+> + |->|->), even if they're six miles apart. There's no obvious CA analog of this.
The discretized version of a quantum field theory is lattice field theory, which is a big subject in computational physics. But running a lattice field theory is not running a CA; you don't just tick it forward deterministically, you basically have to do a path integral sum-over-histories of all the possible ways all the values of the field could have changed with time. (It takes a while, even with simplifying approximations. This is the kind of thing people like to do with supercomputers made of a room filled with microprocessors.)
Of course, the mapping between the CA and our world could be not-obvious. Many CAs are computation-universal, and I suppose it's possible our world is a giant lattice-QFT integral being done on a computer that happens to be implemented on a CA. But there's no reason to suppose that's a natural or elegant way to get the world we've got.
The idea that the whole universe is a cellular automaton—some sort of grid of finitely spaced cells, with a finite number of states, interacting locally with regular time ticks—is a really popular one among geeks of a certain stripe, especially if their specialty involves computers. I've always been skeptical.
My main reasons to be skeptical are (1) relativity and (2) quantum mechanics, neither of which seems to really fit well with CAs. There are probably ways around these objections but I doubt they are terribly elegant.
CAs seem initially attractive, I think, because they are sort of like a discretized version of classical field theories in physics, in which everything's described by a bunch of continuous quantities at every point in space, and the rules for iterating the numbers forward in time are deterministic and local. In a CA, everything's described by discrete quantities at every point on the grid, and the rules for ticking them forward in time are deterministic and local.
If you believe that everything has to be describable with finite integer quantities (which seems to be a popular attitude among computer and software types), it's a natural way to go. There's also a vague idea that quantum mechanics involves going from continuous to discrete quantities, so this might be in some sense the quantum version of a classical field theory. (It's not, though.)
First, relativity: Our world seems to have a lot of rather remarkable continuous symmetries built into it on a pretty low level. One is rotational symmetry; the rules of fundamental physics don't seem to change if a system is rotated by even a small angle. A CA, of course, breaks that down to a finite symmetry of rotations of whatever grid it uses. Now, there are ways around this; there's a CA simulation of an ideal gas in which rotational symmetry reappears as an emergent property on large scales, even though it's not there on the microscopic scale.
But then there's the extension of that to kinematic relativity, more precisely Lorentz invariance (but Galilean invariance would be just as hard to deal with, maybe worse). In CAs, there's typically a sharp distinction between "still lifes" (things that just sit there), "oscillators" (things that cycle through a repeated sequence of states), and "spaceships" (things that move along at some speed, usually a fixed speed).
In our world, every still life or oscillator (on the quantum level they're all really oscillators) is also a spaceship, and every spaceship, with the important exception of the ones that go at the speed of light, is also a still life or oscillator. Spaceships with one velocity can be easily turned into spaceships with a different velocity. There's no preferred rest frame. In a CA, there always is one: the rest frame of the grid. This has a lot of profound effects. Generally speaking, it's hard to come up with a complicated pattern that can move around at an arbitrary velocity. Often just to make the velocity variable, you have to invoke things like programmable universal constructors that can build the future instance at another location.
It's entirely possible, I suppose, that kinematic relativity could be another emergent property of a deeper system that has a grid frame. Certainly, many theorists assume that space-time itself as we know it is some sort of emergent property of a deeper physics. But to me, this particular dissimilarity makes CAs seem less natural as models for the underlying physics. There's no reason to suppose a CA is better for the purpose than anything else (spin networks, strings, loops, what have you).
Second, quantum mechanics. In some ways, quantum mechanics does involve going from continuous to discrete quantities, and there's an idea that CAs are a move in that direction. But actually quantizing a field theory tends to take it further away from being a CA. States of a system end up involving probability amplitudes, which are continuous and interfere with each other.
Quantum systems can also exist in superpositions of correlated states, which can be correlated over long distances. If a particle has two spin states, call them plus and minus, I can have a pair of them be in the state (1/sqrt(2)) (|+>|+> + |->|->), even if they're six miles apart. There's no obvious CA analog of this.
The discretized version of a quantum field theory is lattice field theory, which is a big subject in computational physics. But running a lattice field theory is not running a CA; you don't just tick it forward deterministically, you basically have to do a path integral sum-over-histories of all the possible ways all the values of the field could have changed with time. (It takes a while, even with simplifying approximations. This is the kind of thing people like to do with supercomputers made of a room filled with microprocessors.)
Of course, the mapping between the CA and our world could be not-obvious. Many CAs are computation-universal, and I suppose it's possible our world is a giant lattice-QFT integral being done on a computer that happens to be implemented on a CA. But there's no reason to suppose that's a natural or elegant way to get the world we've got.