For a layman like me fathoming the concepts embedded in the quantum view of physical reality takes time and effort. What sometimes helps is approaching the same idea from a number of different angles, until one finally breaks through the conceptual fog and “gets it”. Stephen Hawking’s book “The Grand Design” has clarified for me one of the fundamental concepts of quantum mechanics – the path integral formulation by Richard Feynman, also known as “sum-over-histories”.

The best place to start is the famous double-slit experiment which was described by Richard Feynman himself as follows:

We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains theonlymystery. We cannot make the mystery go away by explaining how it works.

I will not go into the minute details of the double-slit experiment – they can be found in numerous online sources. The experiment involves shooting particles at a screen with two parallel slits spaced a distance apart and observing where the particles hit a second, solid screen positioned behind the one with the slits. In essence the results imply that, unless observed prior to hitting the second screen, the individual particles travel through both slits and even interfere with themselves in a wave-like manner. This is a prime example of the wave-particle duality which is one of the cornerstones of quantum mechanics.

I knew that the physical reality underlying this strange behaviour of matter defies comprehension. What I did not realise, prior to reading Stephen Hawking’s book, was that Richard Feynman himself had formulated a mathematical model of the double-slit experiment (and the general way particles travel through space). While the mystery has not gone away thanks to Richard Feynman we at least know “how it works”.

This is where the intellectual challenge starts. The path integral theory asserts that a particle travelling from point A to point B takes **all** possible paths – including the straight line, routes through any slits, around the Moon and back etc. A particle-wave takes all these paths at once and “condenses” at one location in space only when it has been observed/detected. What waves (oscillates) is the probability that a particle will condense at the particular location in space, when detected. This information is carried by a wave property analogous to “phase” known from classical physics. As a particle travels from point A to point B there is interference between the phases (representing probability) of the particle-waves travelling down different routes leading from A to B. Richard Feynman has cracked the maths describing the process and his theory agrees with the physical observations to a tee.

What this means is that, looking backward in time, a particle does not have one, unique history. When a particle hits the detector screen it is pointless to ask which slit it had travelled through. It had travelled through both slits. In fact, any observed/detected particle is a product of the waves travelling down all possible paths. All waves contributed their phase information to the spacial distribution of the probability pattern which governed where the particle has “condensed”. In this sense any particle is a product of all possible histories – a “sum-over-histories”. I will let you ponder on the implications of this mind-boggling physical fact in the privacy of your ward at the local asylum :-).

Just one more insightful comment on the wave-particle duality of electrons. It comes from quantum physicist Amit Goswami who featured in the movie “What the Bleep Do We Know?”. Fronting the camera with a retarded headgear on (a bit similar to Dizzy Gillespie’s caps) he professed:

When we are not looking they are waves of probability. When we are looking they are particles of experience

December 24, 2012 at 01:14

You’re da boss.

December 24, 2012 at 08:36

This whole quantum thing is seriously freaky