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Sum over histories

  1. Oct 22, 2011 #1
    I'm working on an article about sum-over-histories. Could folks more knowledgeable than I review this and point out any errors? Thank you.

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    The 1920's were an exciting time, with unexplained experimental results all over the place. Eventually someone would get the math to pretty much work, but then another unexplained effect would show up. The other problem was that they had working math but no one could really get an intuitive grasp on it. To predict what might happen in some new situation the best they could do was to go through a lot of complicated calculations.

    As the decades passed the math got better and better but it still didn't seem natural. This persisted until about 1950 when Richard Feynman came along. His good friend and fellow Cornell professor Freeman Dyson writes:

    [ Quotations skipped ]

    Dyson finally got used to what Feynman was doing so that he could do it to and figure out what the rules were. Dyson was able to show that the results from sum-over-histories were the same as from the more respected and elegant theories. I'm told that today Feynman's concepts are used for intuition, while the more elegant stuff is used to do the calculations. By the way, Dick didn't beat Einstein at his own game: he couldn't get gravity to fit in there, and to this day no one else has been able to do it either.
    So.... what are those simple rules? Start with a a particle, say an electron. It is incapable of just sitting there doing nothing: it is simultaneously following every path that it possibly could. Eventually something comes and whacks into the electron, and by some mysterious process one of those paths is selected and the electron has one history.

    The subtlety is that those other unselected, potential histories influence the selection of the one actual history. This happens in a special way. The electron seems to have a little clock in it with one hand, and as the electron moves around that hand moves. Let's say the electron in History A moves to a certain spot and the same electron in History B moves to the same spot, but in such a way that the clock hands in the two histories are pointed in opposite directions. Then the two histories cancel each other out and neither history will appear. Let's say the electron in History A moves to a certain spot and the same electron in History B moves to the same spot, but in such a way that the clock hands in the two histories are pointed in same direction when the electrons meet. Then the two histories reinforce each other out and the histories are more likely to appear. There can be all the in between probabilities too. So the many histories interact in such a way that some histories are more likely to become The Chosen History.

    Note that the many histories do not interact in any other way. In each history the electron is solo and is not affected by the electron in the other histories at all. The only way they affect one another is through the probability of which history gets chosen. The histories are all independent, but they sum in this way to affect the probability of what actually happens when something whacks into the electron. Weird, huh? No wonder scientists are starting to believe in other dimensions.

    Now you might ask, how much of a whack does it take to cause this one history to be chosen? The answer is that it is uncertain too. There is no definite boundary and it happens gradually. Some of the electrons go to the single history and some remain ambiguous. Recently there have been experiments testing this. They used buckyballs, hollow balls of carbon shaped like a soccer ball. In order to get the buckyballs to completely stop showing this sum-over-histories effect they had to heat the balls to 1700 degrees centigrade, which was hot enough to make the balls glow. I would have thought it would have been much less. So the effect is more robust than I'd thought.

    Summing it all up, any particle can have multiple histories. The sum over histories tells us which histories are more and less likely to be chosen when the Big Whack comes. When it comes, there is only one history. There is a strange retroactiveness about this, almost like the present is changing the past, but it doesn't really change it, it selects or defines it. Strange, you think. But it works.

    Now let's take this a step further. Let's take a chunk of empty space and say that it is a particle. We are mathematicians, so we can define whatever we like as long as it is consistent, so let's try it and see whether it is consistent. It turns out that empty space does exactly the same thing. It is following every possible path. Particles of all sorts are constantly appearing and disappearing. The have a sort of shadow existence that is so brief that in some ways they might as well not be there. So how do we know this is happening? Their subtle influence can be detected in that calculations won't come out quite right unless they are taken into account. For example we were taught that the charge of the electron decreases over a distance by a certain simple rule, but if you measure it very carefully you will find that it actually decreases a little faster than that. The shadow particles mask some of the charge. These days it is believed that most of the "forces" that physicists talk about are due to shadow particles like this. Not only that, while their mass is very small, there is a great deal of empty space and it all adds up, so it has now been measured that most of the mass [energy and matter] of our Universe may be in these shadow particles. Shadows rule! (Maybe, but that's what the smart money is betting on.)

    Another way you can tell they are there is that if you concentrate enough energy in a small enough space then the particles will materialize and become quite real. This is why this is done with collisions: collisions are very sudden. If you try to build up the energy gradually you can't do it, because some lower-energy particle you don't want will materialize and explode, carrying away the energy. It has to be done very suddenly. So that's why they build those huge colliders. They've materialized many the particles that they theorized.

    Now remember how even Albert Einstein and Richard Feynman couldn't unify this particle stuff with gravity and still no one can. So today's scientists have a more modest goal, unifying with inertia. That's the difference between matter and energy: energy always moves at the speed of light relative to matter, because matter has inertia and energy doesn't. So they worked out all the math, figured out what the inertia particle had to be like, built the huge machine and... no particle. So far they haven't been able to get it to materialize. Oh well. If it doesn't show up soon it's back to the drawing board.
     
  2. jcsd
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