MathJax

MathJax

Thursday, September 26, 2013

A Jewel at the Heart of Quantum Physics - Some Thoughts

Browsing through my daily dose of slashdot I found a link I just had to follow, A Jewel at the Heart of Quantum Physics. This article described a mathematical structure that enabled one to solve calculations of particle interactions that had formerly been completely beyond calculation, in some cases on a sheet of paper. In order to arrive at this simplification the theory requires abandoning two core ideas:
Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.
In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.
After reading the article, a number of questions occur to me which I do not have the mathematical chops to even begin to answer.
  1. Is this the only structure possible, or are there  a large, or even infinite number of similar structures, each of which could form the basis of a potential universe?
  2. Is this structure hidden in the quantum wave equation when you look at it  in the right way? It seems it really should be.
  3. I am imagining something like a standing wave pattern that might have formed by addition with each phase transition of the Big Bang. Does this work at all?
  4. Is this structure stable and eternal essentially, or is it temporary?

Friday, September 20, 2013

Money - value

Money is a strange thing, completely abstract and mathematical in certain regard, yet held to be the most tangible of all things. Lately, people have been making the rounds on NPR, etc., expressing the thought that our ability to rapidly and accurately assess value is increasing, and will increase greatly in the future. This will make it possible to end "second chances," and rapidly sort the productive from the unproductive. Value and money are actually rather trickier concepts than this, and their relationship rather more complex. Financial panics would not occur if our ability to assess value were truly as advanced as such claims would have us believe, since a financial panic is a market perception that monetary valuation and emotional and tangible valuation are seriously out of alignment. Money is a very strange instrument. Consider the case of Long Term Capital. Here, a hedge fund constructed a mathematically formula which enabled them to sell the risk out of their portfolio, while keeping the profit, thus apparently being able to invest with no risk at all. No real asset that one could use money to purchase behaves in such a manner. A farm, or factory, or piece of equipment all have risk of loss or damage attached inescapably to any investment. I would argue that a market panic is an essential process which forces market valuations back into conformity with emotional and tangible valuations.