Sun 2 Mar 2008
Sum Over Histories
Posted by Greg Molyneux under Philosophy, Science
Richard Feynman’s multiple histories (sum over histories) was a monumental advancement in quantum mechanics. In essence, Feynman demonstrated that subatomic particles traverse infinite paths through spacetime, implicating infinite histories for any one particle. Stephen Hawking explains:
With each trajectory Feynman associated two numbers, one for the size - the amplitude - of a wave and one for its phase - whether it is a crest or a through. The probability of a particle going from A to B is found by adding the up the waves associated with every possible path that passes through A and B.
Without looking further at the mathematics, this notion makes perfect sense when you couple it with the uncertainty principle, which tells us that we cannot know the exact position of a particle at any one time. The more precise we are with the particle’s velocity the less certain we are about its position, and vice versa. Feynman’s sum over histories makes this phenomenon first postulated by Heisenberg fundamentally easier to grasp.
In 1965, Feynman was awarded the Nobel Prize for Physics, and ever since scientists have been trying to marry the sum over histories with general relativity. Their goal is to develop the Grand Unified Theory (GUT) that will finally allow us to understand the early universe where our classical laws breakdown.
The part of Feynman’s theory I would like to focus on applies to large bodies (such as ourselves). At the macroscopic level his rule for assigning numbers (explained above) ensures that all paths with the exception of one cancel out when they are summed. This may not seem like much, however it is really quite remarkable considering the one remaining path linked to large objects precisely coincides with the law of motion given to us by Newton.
What really gets my head spinning is when I think of what all this means in terms of destiny. Here we are the end result of infinite paths that have thusly canceled out leading us here, to this blog (sad I know). This notion becomes even more profound when you consider the second law of thermodynamics. Somehow, our chosen path has led us here despite a closed existence of increasing chaos. Could this give credence to the saying God only gives us that which we can handle? Do these laws demonstrate the natural selection of our universe, allowing it to flourish and understand itself? It is with an unfathomable complexity that single cell organisms were able to manifest from star stuff, let alone the chain of events that were required to produce beings that can sit here and question the origin of all things.
We are a way for the universe to know itself.
I really think Carl Sagan did say it best.
Image Used in this Post
Richard Feynman image courtesy of Flickr user Wolf Gang published under the CC license.
5 Responses to “ Sum Over Histories ”
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September 8th, 2008 at 8:40 pm[...] some fourteen billion years ago, wondering what kind of particles they just might see. History too, you see, is governed by the very laws of physics and always has a way of repeating itself. [...]









March 2nd, 2008 at 11:42 am
Speaking of Feynman and history, that book, “Surely You’re Joking, Mr. Feynman”, is one of my favorites. I highly recommend picking it up (Greg, I own it, so you can borrow it if you’d like).
March 2nd, 2008 at 11:44 am
Excellent, I really want to learn more about this guy. Apparently he had a passion for picking locks to safes while working for the Manhattan Project at Los Alamos.
March 2nd, 2008 at 3:40 pm
Wow, a good part of that went right over my head. Enjoy it, for you’ll seldom get such an admission out of the Man Overboard.
March 2nd, 2008 at 8:14 pm
The first I heard of Feynman’s theory was in the book “The Tao of Physics” which is required reading for anyone who is consistently baffled (or babeled?) by the mystery of duality.