Feynman's Theory of Alternative Histories

Quantum Systems and Alternate Histories 

Why do Quantum Systems have no Single Past?   

Richard Feynman once wrote, "I think I can safely say that nobody understands quantum mechanics". Now I know this isn't the best opening line to a post that's about to describe an amazing quantum theory concerning the existence of our universe's history. But consider this: Feynman, who was one of the most brilliant theoretical physicists of our time, showed that quantum particles do not have a single history; instead, it has every possible history associated with them, each with its own definite probability!

Of course, it's only natural if you had to read the latter sentence again to completely grasp its meaning. Even Feynman himself was reluctant to accept this weird characteristic of quantum systems. Not only did he mathematically prove that quantum particles have no unique past, but Feynman also theorized something called Sum Over Histories. This in turn resulted in the concept of Alternative Histories, which paved the way to the most mind-boggling modern theories of the universe - the Multiverse Theory. 

But before we delve deep into the notion of multiple paths and alternative histories for quantum particles, let's discuss the famous ground-breaking experiment that marked the onset of modern physics  - the Double-Slit Experiment.

The Double-Slit Experiment

BA Think Pieces - Quora

Although there is a lot of talking about the development of the concept of Alternative Histories in the quantum domain, one of the best interpretations of Feynman's theory of Alternate Histories is described in Hawking's book The Grand Design, which is what this post is based on. The book, co-written with Leonard Mlodinow, describes the peculiarity of paths taken by quantum particles, and this notion is explained vividly through the famous Double-Slit experiment, but with a tiny change. Instead of shining light (or a stream of photons) through the two tiny slits, we fire a beam of electrons through the slits and study the results.

Obviously, just as in the ordinary Double-Slit experiment with a stream of photons, the electrons are fired through the two narrow slits, and there's a screen that records the electrons that pass through both these slits so that it would give rise to a pattern. 

Recall that in the case of an incident light beam through these slits, the resulting pattern on the screen is that of an interference pattern consisting of dark and bright bands with a central maximum. This is not that surprising since we already know that light has wave-like properties associated with it, along with particle nature. The crests and troughs of the wavelets arising out of both slits undergo interference to create an interference pattern on the screen behind them. 

Mpoweruk.com

But the question is would the result be any different in this case? Would we end up with an interference pattern if we choose to fire electrons for photons? The answer is obvious.

The entire domain of quantum mechanics is based on the fact that subatomic particles do possess wave-like properties, and that their position and momentum can only be analyzed in terms of probabilities. This means that the pattern on the screen that we obtain after firing electrons through both slits is no different than the same interference pattern mentioned in the ordinary case (using photons).  This clearly establishes the wave nature of electrons, and with that, the rest of matter particles as well, which is what we call the wave-particle duality in quantum mechanics. 

Still, how do we physically interpret this weird wave nature of such subatomic particles? When we say that electrons possess a wave nature, it doesn't imply that the electrons move as though they are a wave or that they suddenly morph into a wave. When we say that a particle tends to behave as a wave at subatomic levels, it means that its position and velocity cannot be determined at a given time accurately (the Uncertainty Principle). Simply, the particle seems to be spread out everywhere, which implies that the particle is positioned everywhere simultaneously, just like a wave spreads out at a given time. 

Thierry Dugnolle

Although this is the case, some of these positions would have a higher probability of finding the particle than others, which is why we say that quantum mechanical principles bring out the probabilistic nature of the universe. So, we can say that the resulting interference pattern obtained on the screen is made by the electrons that passed through both slits! But again, why the very specific interference pattern? 

This is where Feynman claimed that particles take up all possible paths in the universe simultaneously. If we consider an electron that is being fired, it should, under normal circumstances, go through any one of the slits and reach the screen. However, that is not what actually happens. 

According to Feynman, the particle will pass through both slits simultaneously, and what we obtain on the screen is the interference pattern that arises from the two interfering paths of the same particle! As the particle simultaneously takes all the possible paths in space (in this case, two), the different paths will undergo constructive and destructive interference, thereby giving an interference pattern with dark and bright spots, which gives information about where the electrons fell on the screen eventually.

Feynman's interpretation further implies that none of those electrons in the double-slit experiment has a unique definite history or path it followed, but it has every possible path as its history! Not only that, but Feynman also mathematically showed that the sum of all the probable path waves from one point to another would give the probability of that particle reaching the final point.

Now, coming back to the experiment, what if we close one of the slits and let the electrons only pass through the other slit? The result will be a concentration of spots only on the sides of the screen where electrons were let through to reach. It is to be noted that the pattern we obtain with both slits open is not the sum of the cases where one of the slits is closed and the other is left open. Obviously, this is because the particle has only one probable path it has to follow.

In the book The Grand Design, the authors have gone to great lengths to fully present the concept of alternate histories and Feynman's technique centring the Sum Over Histories. The following chapters in the book also discuss the Feynman Diagrams and their features. But of course, the analysis of the double-slit experiment and its role in revealing the quantum world is undoubtedly one of the most effortless and elegant explanations that are out there! 

Like Feynman said, '...the double-slit experiment contains all the mystery of quantum mechanics...'