Via Slashdot, I came by this article describing an apparently major breakthrough in quantum physics at Harvard, Princeton, and Cal Tech, allowing particle calculations that are normally incredibly long and complex to be boiled down to a relatively simple geometric object. What would have been hundreds of pages long is now mind-numbingly simple (from the perspective of a theoretical physicist), and may ultimately be extended to form the basis of a unified physics that elegantly encompasses all known phenomena. The oddest implication of the work is that space and time may both be illusions, and that the universe may actually be an unchanging geometric object. The article is long and involved, but understandable and fully worth reading.

One of the more irritating features of quantum physics has been its mathematical "wordiness" - the need to engage in math that's thousands upon thousands of terms long, and often need supercomputers just to figure out relatively simple particle interactions on a fundamental level. What the new research indicates is that this is doing things the incredibly hard and stupid way, and completely unnecessary. Instead, they've found that a higher-dimensional geometric object they're calling an "amplituhedron" (yeah, descriptiveness trumped aesthetics there) can be articulated whose simple volume calculations that can be done on napkins do the same work as 500 pages of ordinary quantum algebra. Here's a representation of an amplituhedron:

The current work only covers the quantum realm, and does not bridge the generations-old conundrum of gravity, but the researchers involved seem to think it will. If so, it would not only be scientifically Earth-shattering, but also philosophically: It would in essence bring us back to a way of seeing reality with a greater resemblance to the ancient Pythagoreans than to Einstein or Newton - a universe that is basically a crystal existing in however many dimensions, and time and perceived change would merely be illusory properties of its facets.

But leaving aside the headier stuff, the fact that the current work reduces a novel-length of insanely tedious math that tries even the patience and resources of computers down to something like this...

...should radically increase the pace of further progress in physics. Imagine if mathematicians and researchers lacked the concept of multiplication and instead just did everything as additions and subtractions. Instead of 7 x 14, you can only write out and articulate it as 14 + 14 + 14 + 14 + 14 + 14 + 14. For exponential terms that could get pretty hairy pretty fast. You're not likely to discover a lot if you have to work like that. But if you can express it compactly, suddenly it's much more manageable. In other words, the most mathematically laborious and complex field of theoretical physics has just increased its own efficiency by a factor of a gajillion.

I never got far enough in math or physics to claim I understand the concept specifically, but the notion of a timeless universe expressible in manageable terms through geometric shapes seems intuitive. It's the basis of calculus, just to use one example, and is also deeply attractive to the scientific yearning for elegance. The algebra-rrhea of quantum calculations has always irked that aesthetic sensibility, and now it looks like they have something far more beautiful to work with. Something that may ultimately extend to a related geometric object encompassing gravity. In other words, we may be able to some day see the mathematical shape of reality. Or at least a projection of that higher-dimensional shape on to a two-dimensional surface or 3D object, as in the "amplituhedron" describing quantum particle interactions.

Every once in a while there will be semi-speculative scientific papers that claim one possible avenue or another toward a unified theory, but the fact that this work has immediate and drastic practical implications for quantum physics - not to mention the level of uncharacteristic enthusiasm on the part of the experts discussing it - suggests this is something unusual and worth watching.

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