Posts Tagged ‘pseudo random numbers’

Reflections on Waves

May 16, 2012 Leave a comment

In my recent post series, Making Waves (starting here), I outlined a very simple system for duplicating the kinds of effects seen in the Double Slit experiment, which Richard Feynman famously described as “the only real mystery in quantum mechanics”. The approach I used was completely discrete, and one for which pseudo-random numbers will happily suffice instead of the ‘pure randomness’ that’s often stated as a prerequisite for any QM model.

In the wake of these posts, I decided that it was only appropriate to talk a little about the limitations of the approach I outlined, and also to address some of the questions or yes-buts that I imagine some readers may have.

First, the limitations.

Relativity: It’s not that hard to come up with different interpretations of QM, so long as you don’t have to worry about reconciling it with relativity. Any Causal Set enthusiasts looking over my work might well point out that my spatial model isn’t Lorentz invariant, and therefore hard to take seriously. As it stands, this observation is absolutely right. And we can go further. In Scott Aaronson’s review of New Kind of Science, which I have mentioned in previous posts, he points out that a network-based approach to QM simply won’t work with a discrete model of spacetime, if we respect the Minkowski metric in that model. Fortunately, as I’ve outlined in previous posts, we simply don’t have to use that metric. Using causal sets to describe spacetime is a nice approach with lots of potential, but by no means a necessity. So while the model I’ve mentioned here is limited, future posts will show at least one way it can be extended.

Bell inequality violation: The particle I use here doesn’t have any properties as sophisticated as spin. It’s pretty clear, then, that as it stands, we wouldn’t be able to extrapolate it to that most marvelous demonstration of quantum effects at work: Bell’s experiment. However, the reason for that is a little different from the one that makes most models fall at this hurdle. Usually, the problem lies in getting around the limits imposed by locality. With a network-based approach, non-locality doesn’t present a problem. However, making particles with persistent orientation is harder. While I’ve been able to produce such particles, they currently still have limitations and currently don’t follow all paths.

Scale: The algorithm I described in the last post isn’t among the world’s most efficient, and it’s hard to imagine it replacing lattice QCD any time soon as the simulation engine of choice. So while the implications for QM may be interesting, it’s hard to scale the approach up enough to show what it’s really capable of. This means that the results I get are going to be noisy and incompletely convincing unless someone happens to have a whole bunch of supercomputer time that they’re giving away. This is something I’m prepared to live with.

And now, some yes-buts.

Randomness: People are fond of saying that QM is random, and therefore that exploring an algorithmic approach such as the one I’ve shown doesn’t make sense at some fundamental level. However, this statement is just wrong. You can know that a variable is unpredictable, but you can never know that it’s random, unless you have an infinite amount of computing power with which to prove it. So long as you have finite computing power, the variable you’re considering may simply be the output of a computing machine that has one bit more reasoning power than yours does. Thus you can say that it’s effectively random from your perspective, but no more. And when considering a universal algorithm, it’s completely acceptable to propose algorithms that use the entire state of the universe at any one iteration step to calculate the next. Thus, unless you’re outside the universe, you’d have no way to predict the behavior of even a single atom.

What a theoretical model can do is assert that quantum events are random, even when no proof can ever be supplied, which is what we currently do. I confess that I’m not a big fan of faith-based approaches, when it comes to randomness or anything else.

Efficiency: In Seth Lloyd’s eminently readable pop-science book, Programming the Universe he suggests that the universe is a quantum computer computing itself. Why not an ordinary computer, given that the set of problems that can be solved by both types of machine is exactly the same? Because quantum computers are massively more efficient. To his mind, it doesn’t make sense to consider nature as an ordinary computation because achieving what nature does takes ordinary computational models huge swathes of time.

However, when considering algorithms that potentially run the universe, and through which all reference frames are determined, I would propose that efficiency is irrelevant. In order for us to care about efficiency of the algorithm, we’re also tacitly proposing that someone is making a design choice about the universe, which seems like a ridiculous assertion to me. The reason to pursue a computational model of the nature is because it presents a more concrete, more reductionist, and more scientific view of how the universe operates. Not less. We don’t need someone to have designed the universe to justify digital physics any more than a continuum theory requires that someone be running the universe on a large array of valves and rheostats.

Usefulness: The reaction to the digital physics approach to QM that I have the most respect for is the experimentalist shrug. It’s completely fair to say at this point that the kind of algorithm I’ve outlined is far less useful as a scientific tool than what is currently being used. It’s also fair to say that experimental evidence for discrete spacetime is scant and elusive. And while these things are true, I see no reason for most physicists to alter their approach in any way.

However, I have two caveats. First, those theorists considering Theories Of Everything have no excuse to not consider discrete models. The set of physical systems that can be described by them is very much larger than the set that is conveniently differentiable. To assume that the universe lies in the differentiable set is rather like the man who looks for his car keys in the study rather than the street, because the light is better indoors. Such attitudes are particularly indefensible when, rather than considering systems of minimal complexity, we instead are expected to suspend disbelief about parallel universes, hidden dimensions, and tiny vibrating strings with no width.

The second caveat is that I suspect the game is about to change. The coming era of quantum computation will test our understanding of QM more thoroughly than anything that has come before, and I will be heartily surprised if there are not surprises that come with it. While digital physics represents a philosophical distraction now, I very much doubt that the same will be true in a hundred years.