Warped Passages - Lisa Randall [67]
The answer is the one I gave earlier. You can see the wave pattern only when you record many electrons. Each individual electron is a particle. It hits the screen in a single location. However, the cumulative effect of many electrons being shot at the screen is a classical wave pattern, reflecting the fact that the two electron paths interfere. You can see this in Figure 45.
The wavefunction gives the probability that an electron will hit the screen in any particular location. The electron might go anywhere, but you would expect to find it only at some particular place with a definite probability given by the value of the wavefunction at that point. Many electrons together produce the wave that you could derive from the assumption that the electron passes through both slits.
In the 1970s, Akira Tonamura in Japan and Piergiorgio Merli, Giulio Pozzi, and Gianfranco Missiroli in Italy actually saw this explicitly in real experiments. They shot electrons through one at a time and saw the wave pattern develop as more and more electrons hit the screen.
Figure 46. Some important length scales and energy scales in particle physics. Larger energies correspond (via special relativity and the uncertainty principle) to smaller distances—a more energetic wave is sensitive to interactions that occur over shorter distance scales. The gravitational interaction is inversely proportional to the Planck scale energy. The large Planck scale energy means that gravitational interactions are weak. The weak scale energy is the energy which sets the scale (via E = mc2) for the weak gauge boson masses. The weak scale length is the distance over which the weak gauge bosons communicate the weak force.
You might wonder why it took until the twentieth century for anyone to notice something as dramatic as wave-particle duality. For example, why didn’t people realize any earlier that light looks like a wave but is actually composed of discrete nuggets—namely, photons?
The answer is that none of us (with the possible exception of superheroes) sees individual photons,* so quantum mechanical effects cannot be easily detected. Ordinary light doesn’t look as if it’s made up of quanta. We see bunches of photons that constitute visible light. The large number of photons together act as a classical wave.
You need a very weak source of photons, or a very carefully prepared system, to observe the quantized nature of light. When there are too many photons, you can’t distinguish the effect of any single one. Adding one more photon to classical light, which contains many photons, just doesn’t make a big enough difference. If your lightbulb, which behaves classically, emitted one additional photon, you would never notice. You can observe detailed quantum phenomena only in carefully prepared systems.
If you don’t believe that this one last photon is usually insignificant, think about how you feel when you go to the voting booth. Is it really worth the time and trouble to vote when you know that your vote can’t possibly make a difference in the outcome, since millions of other people are voting? With the notable exception of Florida, the state of uncertainty, one vote generally gets lost in the crowd. Even though an election gets decided by the cumulative effect of individual votes, a single vote rarely, if ever, changes the result. (And, to take the comparison a step further, you might also observe that only in quantum systems—and in Florida, which acts like a quantum state—do repeated measurements produce different results.)
Heisenberg’s Uncertainty
The wave nature of matter has many counterintuitive implications. We’ll now turn from electoral uncertainty to Heisenberg’s uncertainty principle, a favorite of physicists and after-dinner speakers.
The German physicist Werner Heisenberg was one of the major pioneers of quantum mechanics. In his autobiography, he told how his revolutionary