17 June 2008

Tegmark's mathematical universe

In his paper The Mathematical Universe, Max Tegmark explores the physics implications of what he calls the External Reality Hypothesis, namely that there exists observer-independent reality. From this he argues for what he calls a Mathematical Universe Hypothesis, namely that the universe is mathematics. This is in the same sense that, say, Newtonian gravitation is just the study of curves in R4 (that is, three space dimensions and one time dimension) with minimum action.

It's interesting, but at thirty pages kind of long; Tegmark has also written a three-page article on the same topics called Shut Up and Calculate!.

I am led to wonder if Tegmark is deliberately referring to the Flying Spaghetti Monster here, in his discussion of Newtonian gravitation. (The "frog" sees only the universe as it exists right now; the "bird" sees the universe "as a whole" and in particular sees all time at once.)
If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton’s laws of motion and gravitation. To the bird, it is described by the geometry of the pasta, obeying the mathematical relations corresponding to minimizing the Newtonian action.
Also of interest is the claim that the Mathematical Universe Hypothesis "banishes... the classical notion of randomness", essentially because all probability can be recast as measure theory. The randomness of quantum mechanics, according to Tegmark, is essentially "epistemological" -- we perceive what looks like randomness because we do not have perfect knowledge. This, of course, is not believed by all physicists; the Copenhagen interpretation of quantum physics does fundamentally include randomness.

And why aren't there other interpretations of quantum mechanics named after cities?


Anonymous said...

That's why I prefer the ensemble interpretation: it's the application of "shut up and calculate" to quantum physics.

misha said...

I had already made a couple of remarks on this article elsewhere. I want to add that even if the universe is a mathematical equation and we know it, it doesn't mean that we can analyze or solve this equation, even numerically, in all the details. The Navier-Stokes equation, that is itself an idealization, is one of the most notorious examples. Even if the unverse had been described exactly by classical mechanics, we would have needed probability theory to deal with thermodynamics, for example. See section 38-6, "Philosophical implications," in Volume 1 of The Feynman Lectures for an insightful discussion. So Tegmark's speculations strike me as more theological than having anything to do with any practical aspects of science.

misha said...
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misha said...

Here is yet another interpretation of quantum mechanics that offers some insight into why the probability is the square of the absolute value of the amplitude. Sorry, it's not named after a city, but the author of this interpretation is a novelist.

Aaron said...

There's an "Ithaca interpretation" of quantum mechanics:


I think it's based heavily on Rovelli's relational interpretation:


Here's another interpretation you might enjoy:


AgainstWords said...

The Many-Worlds Interpretation of QM also wouldn't allow trajectories to be describable by simple strands --- and it is observer independent (in the sense that it considers observers such as ourselves to also be subject to QM, in opposition to the Copenhagen interpretation).

On the other hand, because it posits that all of QM can be reduced to unitary evolution (with apparent collapses being due to bifurcation of conscious experience across different terms of a quantum superposition), it does reduce the evolution of the entire universe to a single curve in a very large phase space.

But yes, as misha remarks, it is all essentially theology.

misha said...
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misha said...

Carver A. Mead expressed some contrarian views on electrodynamics in his article that he later developed into a book containing some sharp criticisms of the dogmas used in quantum theory and an earnest attempt to make "the quantum jumps" understandable, at least in quantum electrodynamics. His interview to the American Spectator contains some interesting observations about sociological aspects of science. Enjoy.