As a way of introducing quantum mechanics (QM), many sources begin with what are known as the double-slit experiments. I had initially wondered whether the double-slit experiments were a straightforward (or necessary) vehicle for discussing QM. Now, however, after reading (and re-reading) descriptions of the experiments in several non-technical books and articles, I have a better idea of their usefulness. Specifically, the double-slit experiments convey at least two central concepts of QM, its probabilistic nature and the idea of a small particle seemingly being able to be at two places at the same time.
In fact, in John Gribbin's book The Search for Superstrings, Symmetry, and the Theory of Everything, it is indeed a double-slit experiment that he cites as "contain[ing] the essence of quantum physics and lay[ing] bare its central mystery" (p. 27).
Those of you who took physics or other science courses in high school may remember the idea of light existing as both a wave and a particle. I’ll first describe the double-slit experiment from the perspective of light as a wave.
Whether from being in the ocean at the beach or among a crowd at a sporting event doing “the wave,” we know that a wave is a curvy, undulating structure with some segments that are high (a rising wave or a section of fans rising out of their seats) and other segments that are low. One type of wave might look like the following:
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In his book The Fabric of the Cosmos, Brian Greene describes an experiment where a laser pointer shines light at a sheet of a certain kind of film with two vertical lines scratched away (the double slits). On a detector screen behind the double-slit screen, what will show up is a series of vertical light and dark stripes, varying in their thickness and intensity. Summarizes Greene:
Light is an electromagnetic wave; when it passes through the two slits, it splits into two waves that head toward the screen. …the two light waves interfere with each other. When they hit various points on the screen, sometimes both waves are at their peaks, making the screen bright; sometimes both waves are at their troughs, also making it bright; but sometimes one wave is at its peak and the other is at its trough and they cancel, making that point on the screen dark (p. 85).
The following website by Dave Jarvis, though focused primarily on quantum entanglement (a topic I'll take up at some future point), begins with an excellent introduction to waves, including discussion of how waves combine with each other.
So far, everything probably seems reasonable. What if, instead of shining waves of light through double slits, we sent particle entities of various sizes through the slits?
As described in a June 2005 Discover magazine profile of Sir Roger Penrose (here's another profile of him), as well as in Greene’s book (pp. 86-87) and other sources, if we shot bullets (everyday life-sized particles) through two slits, we’d end up with a pile (or distribution) of bullets behind each of the slits. If the bullets stuck in a board behind the slits, they might look something like this:
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(If the bullets were shot at varying angles through each slit, they might not end up in two perfectly straight lines, but you get the idea. A University of Colorado webpage illustrates such a shooting exercise with an animation.)
Experiments have been conducted where electrons (and other extremely tiny particles) have been fired at a double-slit apparatus, and this is where things start getting bizarre! As summarized in the aforementioned Discover article in a sidebar box about the double-slit experiments:
When electrons or atoms run through the double-slit experiment, they create interference patterns. In other words, the particles act like waves, not like bullets. Weirder, the same pattern appears even if the particles pass through the experiment one at a time. Since there is no other “wave” to interfere with, the only way this can happen is if each particle passes through both slits, interfering with itself along the way! …This behavior sounds crazy, but it has been confirmed by countless experiments.
Another book by Gribbin, the small (72 pages) paperback Quantum Physics: A Beginner’s Guide to the Subatomic World, also has a nice display on experiments that send single particles through double slits. This book notes that, in addition to those with electrons, “Exactly equivalent experiments have also been done with photons (particles of light)” (pp. 28-29).
Let’s recap for a minute. A light wave going through double slits will split into two waves, which then either reinforce or cancel each other in certain places to produce a multi-stripe band of alternating lightness and darkness (known as an interference pattern). Electrons (or other small particles), when fired one at a time, will eventually build up an interference pattern, too. This suggests that each individual electron must pass through both slits (i.e., be in two places at once). As the Discover profile of Penrose states:
…the ability of particles to exist in two places at once is not a mere theoretical abstraction. It is a very real aspect of how the subatomic world works, and it has been experimentally confirmed many times over. One of the clearest demonstrations comes from a classic physics setup called the double-slit experiment (p. 31).
Not only must a particle have been in two places at once in terms of passing through both slits. It presumably must have some type of wavelike property to do the interfering with itself. Here, things continue to get bizarre. Greene provides a nice summary of this area:
If an individual electron is also a wave, what is it that is waving? …In 1927, Max Born put forward a different suggestion… The wave, he claimed, is not a smeared-out electron, nor is it anything ever previously encountered in science. The wave, Born proposed, is a probability wave… Places where the probability wave is large are locations where the electron is most likely to be found. Places where the probability wave is small are locations where the electron is unlikely to be found… No one has ever directly seen a probability wave, and conventional quantum mechanical reasoning says that no one ever will… (excerpts from pp. 88-89).
Gribbin, in The Search..., cites the physicist Paul Davies as making an analogy between probability waves in physics and crime waves. As Gribbin quotes Davies:
Crime waves are not waves of undulating stuff but probability waves... crime waves, like fashions or unemployment, may move about -- they have dynamics -- but an individual crime still occurs, of course, at a place. It is the abstract probability which moves (Gribbin, p. 47, quoting Davies).
Here's also a web document that illustrates probability waves.
After noting that, “…there is still no universally agreed-upon way to envision what quantum mechanical probability waves actually are,” Greene offers the following as a possible explanation of the single-particle, double-slit experiments:
…the explanation quantum mechanics gives for individual electrons, one by one, over time, building up the pattern of light and dark bands… is now clear. Each individual electron is described by its probability wave. When an electron is fired, its probability wave flows through both slits. And just as with light waves and water waves, the probability waves emanating from the two slits interfere with each other (pp. 91-92).
To me, a probability wave seems like a mathematical curve that might be used in a statistics lecture, not something that would actually travel through double slits. Gribbin, in his summary of the single-particle, double-slit experiments in Quantum Physics, tries to comfort readers about these unusual phenomena: “You don’t have to understand this – nobody understands it. You just have to accept that this is the way the quantum world works” (p. 28).
Some physicists suggest that even human beings are subject to probabilistic waves, in terms of someone's location. Michio Kaku is quoted as follows in a BBC documentary on Einstein (transcript):
The quantum theory makes even bizarre events possible. For example walking across the street we expect to wind up on the other side, however there is a finite calculable probability that you will dissolve and wind up on mars, dissolve and wind up on the earth again. Of course we will have to wait longer than the lifetime of the universe but in principle it could happen.
A few months ago, I was participating in a research meeting with some Texas Tech graduate students and fellow faculty members. One of the other faculty members, who was in charge of organizing the meeting, had sent out conflicting e-mails leading up to the meeting, in terms of where the meeting would be held (either in Room 102 or 224). Once everybody finally showed up to the room where the meeting actually was taking place (102), I quipped that, "Under quantum mechanics, it's possible that the meeting is taking place in both 102 and 224."
