14 DAY TRIAL // In his lectures on quantum mechanics, Richard Feynman has said that the whole mystery of quantum mechanics is incorporated into one single experiment ? the experiment showing that individual electrons exhibit a probabilistic interference pattern. The same experiment was also voted by the readers of the Physics World magazine as the most beautiful experiment in physics.
The classic experiment involves an "electron gun" that releases electrons toward a wall with two tiny holes in it very close apart. The electrons pass through one hole or another and than hit a screen in various points. When a sufficient number of electrons have passed, an interference pattern forms on the screen ? the pattern that one usually sees when waves pass through such a wall with two holes.
This phenomenon is known as wave-particle duality. There are various experiments that show that all quantum particles are emitted, absorbed and travel as particles, but nonetheless the probabilistic outcome of their non-deterministic motion is described by the mathematics of waves. It is as if their probability distribution (their probability of being in one place or another) is a wave that accompanies them.
Yves Couder and Emmanuel Fort from the University of Paris have now managed to observe a similar phenomenon with a macroscopic object ? a silicon oil drop. The droplet was about 1mm in size, 10 million times larger than an atom. It is also one million times larger than the second largest object whose wave-particle duality was observed in 2003 (a 2-nm molecule called a buckyball).
The droplet was released on a liquid surface. As it bounced on this surface, it produced a wave and then started to "surf" on this wave. "The breakthrough came when we found that a bouncing drop could 'surf' on its own wave and form what we called a 'walker'," Couder said. "A walker is an object having some properties due to the drop, together with others due to the wave. The walker's wave is similar to the surface wave of a raindrop falling on a puddle, but here it is emitted periodically by the bouncing drop."
What makes this experiment particularly interesting is that the motion of this "walker" is non-deterministic ? the droplet can "surf" in different directions at random. Moreover, the probabilistic law that describes this motion is the same as that in quantum mechanics.
Couder and Fort proved this by gluing three thick strips to the bottom of a cell placed in the tank. This reduced the depth of the liquid above the strips creating the equivalent of a wall with two holes like the one in the classic experiment.
They found that each "walker" appeared to deviate at random when it passed through one hole. One could not predict what would happen to a particular "walker", but after taking into consideration many "walkers", the ensemble as a whole revealed an interference pattern ? just like it happens in the experiment with the electrons' interference!
"There is a mysterious aspect to the single particle interference experiments in quantum mechanics," Couder said. "When you have two slits, a single particle passes through one or the other (as checked experimentally by Grangier and Aspect). But interference patterns can also be observed as if each single particle had passed through both slits. In quantum mechanics, both measurements cannot be performed simultaneously. If one measures through which slit the particle passes, no interference is observed. But if one observes the interference, then everything is as if the particle had passed through both slits. These results are entirely predicted in the formalism of theoretical quantum mechanics, even though it is difficult to get an intuition for them.
"In our macroscopic experiment, even though we can observe the whole trajectory, we recover two features of the quantum mechanics experiments. For one, the individual deviation of a given walker becomes uncertain because of the spatial limits imposed on its wave. Also, interference patterns are recovered in the statistics of successive individual events."
The discoverer of the wave-particle duality, Louis de Broglie, had always thought that the waves associated with the quantum particles are more than just probability waves. He thought they were as real as the particles themselves and that the waves were guiding the particles' motion. (De Broglie's hypothetical waves are called "pilot waves".) However, neither he nor other physicists ever managed to create a good theory for these waves ? their attempts either offered predictions that failed or didn't offer any additional predictions to set them apart from orthodox quantum mechanics. (The main reason of their failure was that they tried to make the whole situation deterministic and to attribute the probabilities to our lack of knowledge; but the situation is intrinsically non-deterministic.)
Although the experiment performed by Couder and Fort doesn't necessarily support de Brogie's view, it offers a strange remainder of it. In their experiment, there really is a material medium that oscillates together with the particle, unlike the situation of quantum particles where we know of no such medium (there are only the particles themselves).
What's really interesting here is that the probabilistic law that describes the outcome of this macroscopic experiment is given by the wave formalism. Why is this so noteworthy? It is because this wave approach to probabilities is not in accordance with the classical probability theory.
In the usual theory of probability when you have two possible alternatives, A or B, the probability that either A or B happens (but not both) is the sum of the probability that A happens and the probability that B happens. For instance, the probability that a die falls on either side 1 or side 4 is p(1) + p(4) = 1/6 + 1/6 = 1/3. (The individual probabilities that the die falls on a particular side is 1/6. The probability that the die will fall on either of two given sides is 2/6 = 1/3.) But in the interference experiment this law does not hold.
If you close one hole, you would get a hill-like distribution on the screen behind the hole. If you close the other hole, you would get another hill-like distribution on the screen behind that hole. But if you open both holes, and thus you allow the particles to go through either hole A or hole B, you don't obtain a probability distribution that is the sum of the previous two distributions ? i.e. a camel-like distribution with a hump behind each hole. You obtain the interference pattern which has one hump in the middle and many alternating humps on the sides.
In the same way as the general theory of relativity had shown that Euclidean geometry is not something to be taken for granted as if geometry simply could not be otherwise (the geometry is a physical problem), quantum mechanics had shown that the laws of probability are not to be taken for granted either ? even if they are a physical problem. This is significant because the laws of classical probability theory describe how we conduct inductive reasoning - how we infer certain conclusions from incomplete information (how we attribute various plausibilities to various alternatives). Logic, the theory that describes deductive reasoning, is itself a particular case of probability theory - the limit case when we have all the needed information.
Until now, virtually everybody assumed that everything macroscopic respects the classical theory of probability. Apparently this is not so. There are examples, such as this oil droplet experiment, when the non-deterministic motion of a macroscopic object is ruled by a quantum mechanical statistical law.
