Thursday, October 1, 2009

A New Kind of Hobby

Having been out of mainstream physics for a [surprisingly] significant amount of time now, it has been a while since lofty ideas about the inflation of space-time and the unification of quantum field theory (QFT) and gravitation (in the form of general relativity, GR) have been anywhere near the front of my mind. So, while my friend Paul came into town to visit I felt like it was sort of a crash course in remembering and catching up on the current state of affairs.

While it still makes me feel weird to imagine abstract but almost inescapable conclusions about the fate of the universe, I realize that being outside the field may have rejuvenated or given me new perspective on topics that were very important to me once. One of the properties of physics or any of the hard sciences that I have always appreciated is the required practice of always questioning long lines of traditional results. In science we never attempt to prove anything, we only seek to disprove hypotheses. When one of those hypotheses stands the test of time, we begrudgingly call it a theory. It is safe to say that nearly all scientists' lines of work have them engaged in trying to tear down the theories that came before them or even the ones that they created themselves.

One startling issue with QFT and GR is that they are masters of their domains, the microscopic scale and the cosmic scale respectively. Both theories have been independently verified in thousands of tens of thousands of ways. Assumptions that both of these theories rely on or extend have also been tested, the very existence of operating particle accelerators tests every day (sometimes 24 hours a day) the workability of special relativity. But not a single test has conclusively invalidated any crucial component of either theory, which for a scientist is the worst possible scenario because we still have two independent theories that seem to be mathematically incompatible at least to our current set of tools.

Much of physics these past two decades centered around this problem, and a lot of great and new discoveries have come from studying it, but each discovery is still compatible. If both theories are the large-scale and small-scale approximations of some greater theory, then we should expect that failures would happen at the boundaries of those two pictures. The problem again here is that the mathematics used in phrasing these problems results in quickly intractable problems, mind not the additional complications of obtaining data relevant to these regions. That leads me to wonder about the strategies people are taking right now, essentially relying on the same methods we have used to create these recent discoveries in our attempts reconcile their differences. The well-known methods of guessing/deducing partial differential equations or exploiting the presence or lack of some symmetry in natural phenomena have brought us great success, but as many people have postulated these same methods will most likely not work because every well-trained physicist knows them, and the cross-section of IQ and dedication in that field is quite large. I think if those methods were going to work they would have worked by now.

I am definitely not the only one who has thought this way, and there is definitely a small, noisy, and generally safely ignored section of people thinking along the same lines that if we are to move forward we need to attempt to break the most cherished and rock-solid assumptions that our theories take on in order to find new physics. For me, the best way to figure out how something works is to see it when it's completely inoperable. I live for the boundary cases (weak pun). One especially cherished quality that is interesting to examine is the continuity of space-time, which is the mathematical basis for all of our more advanced mathematics we use to tackle physical problems. Human perspective on the world, centered around eyesight, tends to cause us to imagine space as a continuous span of points or locations, separated by spatial distance and volume which acts the background for matter to exist. All of our higher dimensional playthings have generally that same structure.

Mathematicians have always been interested in reducing such ideas to their barest elements, and any senior mathematics undergraduate student can explain to you the structure of the real numbers using Dedekind cuts and the difference between countable and uncountable cardinality. I do not find it startling at all that Cantor, who is responsible for much of our understanding of cardinality in infinite sets (the difference between continuum and discrete models) was driven insane by his study. There are many mind boggling concepts surrounding uncountable sets, and while that alone is not startling -- we have supposedly finite minds after all -- there is legitimate mathematical concern about the structure of such sets. They can be defined self referentially, but there is no axiomatic system which can uniquely specify such a set without specifying another set of unequal cardinality. That is, the very proposition of attempting to produce a set of axioms intended to pick out a certain infinite set will have multiple interpretations as to its cardinality. The properties of real numbers can be equivalently constructed using a set of lower cardinality. Couple this with problems surrounding the axiom of choice and the notion of incompleteness and I think we have some strong suggestions that such structures may be overly complicated for use in physics. This is not physical reasoning, but more an eliciting of a path which has not been investigated much. The road less traveled by and all that. If we can recover empirical validity without using these assumptions then there was never a need for them in the first place, and I have hope that would lead to a contradiction with either accepted theory at some point. That is a boundary, and that is fun!

That leads me to my decision to join others in this hobby of "investigating" in a broad sense alternatives to our typical view of space-time, and I think there is no better time to do it really. Computing power is incredible now, and the intersection of computational models such as cellular automata and causal networks with physical ideas has been introduced by the aforementioned small group. This makes for a relatively accessible line of research while I am outside the ivory tower, and combines with my interest in using machines for fundamental research.

So, I hope to now use this space as a collection of investigations I have done on my own along with my methodology and questions and overviews of other results too, both for my own reference and others if I make anything worthwhile.

My first contribution is an article that is about two years old now written by Stephen Wolfram, the author of a "A New Kind of Science" and one of the pioneers in this new little niche. He spells out simply what the mission is and some good explanations of potential snags when you try to think in the mold of older results.:

My Hobby: Hunting for Our Universe by Stephen Wolfram

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