With a single slit, the light (or electrons, or whatever) will simply show a diffraction pattern. If the width of the slit is on close order of half the wavelength of photon, you esssentially get a normal distribution. There’s nothing all that interesting about that; it’s all very classical, if you accept the fact that tiny perturbations aren’t going to allow each photon to make exactly the same path through the slit. However, with two slits that are positioned at the right increment relatively close to each other, instead of just getting the superposition of twi distributions, giving you a twin hump, you’ll get a diffraction pattern similar to two expanding radial waves on the surface of a pond meeting, with alternating heavier and lighter stripes on the target where the wavefronts of the photons are addative, and where they subtract out. This clearly indicates that photons have a wave-like nature.
However, we know from the the photoelectric effect (among others) that light also has a quantum nature, where a particular frequency of photon has a certain energy, and they don’t just add together. (Specifically with regard to the photoelectric effect, it was found that photons of a given frequency caused the surface of a metal foil to emit electrons; a larger quantity of photons of this frequency caused a linear increase in the number of electrons emitted; however, twice the number of photons at half the frequency caused no photons emitted, indicating that the energy in photons came in quanta, or little packets.) This is where we get the alleged “dual nature” of light (and other fundamental particles), though it’s not that they actually flip back and forth between one and another but rather exhibit properties of both in a way that we simply can’t analogize to our macroworld experiece. As a result, we treat the situation mathematically as being sometimes wave-like and sometimes particle-like as fits what we’re trying to do.
Heisenberg himself referred to the characteristic of the now eponymous principle as “indeterminacy” (and discouraged the application of his name as being associated with it in titular fashion), which is probably a better, or at least less confusing description. In general terms, Heisenberg’s genius was in throwing away all assumptions about anything like classical Newtonian behavior on the scale of subatomic particles and assigning them properties that were “quantized”; that is, occur in discrete steps. This got rid of the whole problem with bizarre, three-dimensional atomic orbits which required constant radiation of excess energy in order to be stable; however, it was a seemingly artifical hack that worked for no good reason whatsoever. However, the hack has continued to work, and work very well, to the point of being the essential basis for a vast subfield of natural science that has been very, very successful in predicting a wide range of cool behavior.
The most common expression of the intederminacy principle is that the change in position times the change in momentum has to be greater than or equal to the modified Planck constant (hbar) divided by 2. This gives a lower bound on how accurately you can determine these qualities about a particle, and more interestingly, a limit on how definitely you can indentify the particle (which is otherwise indistinguishable from other particles of the same type) in the future. There are other formulations, all also involving two characteristics in an inequality, that are equivilent to this. Again, this all seems very arbitrary, but it works, which is more than one can say for Reaganomics or British automobiles.
The net result is that, yes, an unrestricted photon not only can, but does travel all possible paths to get to a particular endpoint, and the “speed” of the components of an individual particle varies based on the paths they follow. Even more strangely, it communicates “with itself” along the way; for instance, if you emit a photon into a waveguide (such that it is reflected and can’t leave the waveguide until it gets to the target) and then split it between two waveguides that take widely seperated paths, it’ll communicate “with itself” such that detection of the photon along one path will prevent the creation of an interference pattern on the target. The only accepted way to cope with this is to adopt the notion that there are either some kind of “hidden variables” by which the photon “agrees with itself” about what’s going to happen before it splits up, or that there are “non-local” (i.e. instantaneous) connections between the various bits of photon that are in constant communication despite being physically seperated. Most of the guys working in QM grew to accept this as a matter of course without getting too worked up about the apparent paradox of the whole thing–Neils Bohr famously made the pronouncement “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature,”–but it did and still does make for some great late-night dorm room bull sessions about the Whole General Wiggy Mishmash Of It All, and What It Means In Terms Of The Nature Of Reality, and How We Can Use This To Turn A Profit. (The latter seems to be the most difficult problem of all in quantum physics, and despite the publication of numerous popular science works by the likes of Richard Feynman, Brian Greene, and Lisa Randall, most people working in fields relating to quantum mechanics live in the sort of quiet, near-ruinous despiration that leads to great starving poetry, unfashionable attire, and university tenure.)
Anyway, adopting the principle of indeterminacy, along with Bohr’s model of the atom (or rather, the valence shell theory derived from it) and his notion of complementarity (the idea that the wave and particle natures of quantum entities exist simultaneously but are expressed in complementary proportion to one another depending on which one you’re trying to measure at the time and how much you squink), allows for describing various diffraction and interference phenomena in quantum terms (the field of quantum electrodynamics, or QED), but requires that you accept that, on the quantum level, photons can actually travel a path from Point A to Point B that requires them to move faster than classical electrodynamic theory or Special Relativity allows.
Are we worried about this? Not particularly; the average velocity of the particle is still c (or for massy particles, less than c), and quantum mechanicists are very relaxed about the fact that this is but one of a whole range of phenomena that is totally and completely impossible on everyday scales but which nonetheless works out with mathematical treatments and the validating experiements that are performed on the behavior of fundamental particles and their first level constructs, like nucleons such as the proton and neutron. By the time you get to the point of dealing with collections of particles, whether they be a group of millions of photons, or a collection of atoms jumbled together via ionic or covalent bonds, this is no longer an issue, and the completely ridiculous behavior of the extremes is lost via decoherence in the average, and all the odd bits wash out so you’re left with only behavior that is agreeably in line with Newtonian and Einsteinian mechanics.
In short, going about trying to apply things like “logic” and “reason” and “Newtonian mechanics” to quantum entities is a fool’s errand that will only give you migranes and make you consult your occulist more frequently than would be otherwise necessary. Go out and enjoy the sunlight without thinking about the fact that its composed of individual particles that have filled the entire universe with probability waveforms existing in an entirely abstract and unmanifest state all the way to the point at which they contacted your retina and collapsed just so it looks like they came straight from the Sun without a bunch of circuitous touristing. And never mind the fact that everything you believe to be solid and immutable, inclulding the materials that make up your own body, is actually just a collection of interfering waveforms that could spontaneously and discourteously disappear at any moment leaving you–perhaps literally–without a leg to stand on. Don’t worry about any of that at all. We can say almost definitely–with only a very, very slight amount of uncertainty–that it won’t happen, or at least, not in the next ten minutes.
Sweet dreams.
Stranger