Quantum Mechanics and Consciousness
Einstein was thought to be a bit eccentric for his quantum (photon) idea, although it's what he eventually got the 1921 Nobel Prize for (and not relativity). Everything physicists had done for 100 years indicated that light is an electromagnetic wave, not a particle. As a prime example of this skepticism, Robert Millikan, an American, carried out a series of highly precise experiments on the photoelectric effect, in which he was able to verify Einstein's 1905 prediction that the increase in stopping voltage as the light's frequency increased was not just any kind of increase but was a straight-line increase on a graph. Millikan was awarded the 1923 Nobel Prize in part for this achievement. Yet when he accepted the prize in Stockholm, Millikan couldn't bring himself to accept that Einstein's idea was correct: He stated in his public lecture that even though his experiments had verified Einstein's straight-line equation, the quantum concept that had led Einstein to that equation was still "far from established."
But things started looking up for the quantum hypothesis in 1923, when another American named Arthur Compton shined X-rays at various materials such as iron and graphite; electrons in these materials scattered the X-rays and increased the X-rays' wavelength in the process. This made no sense if X-rays behave like light waves: When you look at something in the mirror, does reflection (scattering) increase the light's wavelength so that blue things now look red and red things become invisible infrared? Of course not. But Compton's data made perfect sense if light is particles, quanta: the X-ray quanta reached the material, "banged into" electrons like a cue ball on a break, sent the electrons flying, and lost energy in the process. Since lower energy quanta correspond to lower frequency light waves, and lower frequency light waves correspond to longer wavelength light waves, it works.
So strange was the quantum idea, however, that some physicists (most notably Niels Bohr) still weren't convinced. However two follow-up experiments in 1924 clinched it, with both experiments designed to look for the recoiling electrons. One, carried out by Compton, showed that the electrons always traveled in the expected direction. The other, carried out by Bothe and Geiger, showed that the electrons were always sent flying at exactly the same time that the X-rays scattered, proving that the two events were directly related.
A lot of folks who read about the history of science wonder why a brilliant guy like Einstein spent the last three decades of his life fighting unsuccessfully against quantum physics. But if you think about the story so far, it's not such a mystery. His 1905 work on special relativity and the existence of atoms was fantastic. He stubbornly worked on gravity for eight incredibly difficult years, despite being warned by Max Planck not to take on such an impossible problem, and in the end he came up with the magnificent general theory of relativity. And for almost 20 years he stood virtually alone in saying that light should be thought of as having particle properties, and finally in 1924 everyone else had to admit that they had been wrong and he had been right. In short, he had a pretty good track record by 1925. Why shouldn't his instincts turn out to be correct yet again?
In seeking to understand light's dual identity -- wave and particle -- he encouraged the concept of "matter waves" or "de Broglie waves." We've established that light is weird, but in 1924 a French doctoral student by the name of Louis de Broglie suggested that Nature might be weird but symmetric. That is, if things that were traditionally thought of as waves were also particles, wouldn't it be aesthetically pleasing if things that were traditionally thought of as particles were also waves? In other words, might electrons, atoms, and bowling balls have wave properties?
For reasons I won't go into, de Broglie proposed the following relationship between the particle model and the wave model:
Particles with large masses and large speeds correspond to short wavelength waves.
In other words, λ = h / (mv). This relationship explains why we never see bowling balls acting like waves and diffracting around bowling pins: Their wavelengths are so ridiculously tiny that any slit or obstacle will be huge by comparison. Diffraction of any wave is negligible when the wavelength is much smaller than the size of the opening or obstacle.
(Remember, the wavelength of a bowling ball -- a wave property -- has nothing whatsoever to do with the ball's diameter -- a particle property. In order to picture the ball's wavelength, you first have to think of it as something that's oscillating and spread throughout the entire bowling alley rather than resting in your hands. If you find that difficult to visualize, join the club.)
Electrons, on the other hand, are almost the least massive particles known (other than zero-mass particles like photons), so their "de Broglie wavelengths" are small but not impossibly small. By 1927 electrons had been bounced off of crystals -- whose regular arrangement of atoms make them sort of like complicated 3-D diffraction gratings -- and had produced diffraction patterns on a phosphorescent screen. (Remember, traditional televisions and computer screens glow due to electrons striking a phosphor coating.) It was clear that de Broglie was right.
(I note in passing that this technique is used today in studying crystals, molecules, viruses, and so on. In lab, a widely spaced double-slit interference pattern told you that the slits were close together. Similarly, the diffraction pattern produced by X-rays, electrons, or neutrons scattered by a crystal tells you something about the arrangement of atoms within the crystal. We also rely on de Broglie's ideas every time we operate an electron microscope, a widely used device that uses "electron waves" rather than light waves to study small objects.)
By the late 1950s it was technologically possible to manufacture tiny double-slit patterns, send electron beams through the slits, magnify the resulting pattern, and verify that electrons behave just like waves. The weird part is that they also behave like particles: they have mass; they have charge; and they make a little "blip" on a phosphorescent screen when they strike it. That last bit is the really hard part to imagine, because a wave is a spread-out pattern -- and a spread-out thing can't make a flash of light at just one tiny place on a screen. If you try to imagine a water wave that makes the seaweed rise and fall at just one tiny spot along the coast, you'll start to see the problem.
Don't forget: All particles have wave properties. It's just easiest to observe this with electrons.
Werner Heisenberg's uncertainty principle states that we cannot simultaneously know, to arbitrary precision, both where something is and how fast it is moving. If we precisely measure an object's location, we have no idea what a subsequent measurement of velocity (speed + direction) will give us. A highly precise velocity measurement, on the other hand, causes the object's probability cloud to "spread out," so that we have no idea where the object will show up if we now measure its position.
This is in accord with our ideas on wave/particle duality, since all "particles" (electrons, molecules, armchairs) have wave properties, and waves don't have definite locations. The term "uncertainty" is misleading, since it implies that objects have definite positions and velocities, but that we just can't know what they are. Sending electrons one at a time through a double slit demolishes that idea. If electrons had well-defined but unknown trajectories, we still could be sure that each one would go through either one slit or the other, but not both; yet when we actually do the experiment, the electrons slowly build up an interference pattern, showing that in some sense each one goes through both slits. Thus objects really don't have definite positions and velocities, a situation sometimes referred to as "quantum indeterminacy" rather than "quantum uncertainty."
It's important to note that the "uncertain" quantities aren't actually position and velocity, but position and momentum, where momentum equals mass times velocity. This is important because ordinary objects (like bowling balls) have very large masses and thus very large momenta. Hence the tiny quantum imprecision in their momentum is of no practical consequence. Electrons, on the other hand, have tiny masses and thus tiny momenta -- so quantum indeterminacy is a major factor in their behavior.
Quantum indeterminacy shows us why Bohr's 1913 "planetary" model of the atom can't be right: electrons can't have a definite (circular) trajectory if they can't have a definite position and velocity at any one time. Bohr knew this and was in the forefront of pushing the new quantum ideas in 1926, even objecting to Heisenberg's interpretation as not radical enough. Heisenberg thought that each electron has a definite position and momentum but that we can't know both of these things to infinite precision, since the act of measuring, say, the position will randomly change the momentum so that we can no longer say much about it. Bohr insisted that, no, the electron doesn't have a position or a momentum until we measure it.
Heisenberg came up with an (at the time) odd way of computing quantum outcomes -- say, an electron in an atom's third energy level jumping downward to the second level -- using matrices to do the math in a way that paid no attention at all to what actually happened to bring about a given outcome. There was no cause and effect, no process unfolding in space and time, just a starting condition and an outcome with no satisfying link between the two.
Erwin Schrödinger didn't have much use for this approach, so he came up with something more to the liking of most physicists: he described the behavior of electrons (and other particles) by means of a mathematical wave function, Ψ, computed by means of a mathematical expression today known as the Schrödinger equation. Both the equation and the resulting wave functions involve complex numbers -- that is, numbers that include the square root of -1. The good part was that Schrödinger hoped to have found an equation that would restore cause and effect, that would show how an electron-wave's behavior would depend on its environment, just as (for example) there are wave equations that show how a water wave's motion depends on the depth of the water it passes through. One problem, though, was that measurable physical quantities never involve the square root of -1. Even worse, Schrödinger eventually was able to show that his equation and Heisenberg's matrices, despite looking nothing at all like each other, were in fact mathematically equivalent ways of doing things: They would always yield the same numerical answers to any question. He hadn't done away with "this damned quantum jumping" after all. What kind of wave did this wave function describe?
In 1927 Max Born answered that question: The wave function describes probabilities. Suffice it to say that this function represents a "waving" of a complex sort, and that we can manipulate this function (by means of a sort of complex squaring operation) to obtain the probability of any quantum outcome we might choose to consider. In fact, we often refer to a pictorial representation of the squared wave function as a "probability cloud." (Chemists generally call it an "orbital.")
If you want to know the probability that a neutron will be found in some location, or that an electron is moving at some speed, or that a sodium atom will emit a yellow photon, or that a carbon-14 nucleus will undergo radioactive decay, just use Schrödinger's equation to compute the wave function for that object and then square it.
The uncertainty principle can be stated in terms of the wave function. For example, if an electron has a well known position, the wave function will give you little idea of what the velocity is: a wide range of velocities will have roughly equal probabilities. If you now precisely measure the velocity, the wave function changes at that instant. The new wave function tells you that the electron's velocity is almost certain to be whatever you just measured it to be. But it no longer gives you much of an idea of where the electron is: the probability cloud has spread out. You can only "ask" about one aspect of the electron at a time, you can't know everything at once -- a concept Bohr referred to as "complementarity."
(By the way, the jargon for this sudden change in Ψ is "state reduction" or "collapse of the wave function." In class, we've sometimes simply said that the electron "decides" what to do at this instant, or that Nature "rolls the dice.")
The most infamous wave function of all is that of "Schrödinger's cat," so you should understand this thought experiment. According to the Copenhagen interpretation, until someone or something "measures" the cat by observing its state, the wave function is the sum of two mathematical terms, one of which describes a live cat and one of which describes a dead cat. (The technical term for this sum -- that is, for multiple possible outcomes existing simultaneously -- is a "quantum superposition.") Now, if only we understood what such a sum actually means, we'd be set. Schrodinger's point, of course, is that we don't really know what it means for electrons, or for neutrons, or for radioactive carbon-14 nuclei, and so on. This, he felt, shows us that this quantum stuff may produce useful answers, but if it implies that a cat could be both alive and dead simultaneously then it must be wrong. Einstein and de Broglie agreed with him, but few other physicists did (or do).
At what point do the radioactive nuclei in the box "decide" whether or not they have decayed, so that the cat can "decide" whether or not it has died? Is it true that the act of swinging a macroscopic hammer causes the nucleus to have definitely decayed, so that the cat is entirely described by a "dead" wave function? Is it instead true that the cat really is both dead and alive until human consciousness -- some person opening the box and looking at the cat -- stimulates a decision? Or is the cat conscious enough to ponder the fact that it is still alive, and thus collapse its own wave function so that it describes a living cat? Stranger still, do the two halves of the wave function correspond to two "parallel universes," one with a dead feline and one with a live one? All of these suggestions (and many more exist!) have their complications or drawbacks, and you should be somewhat familiar with these.
Einstein came up with his own thought experiment to demonstrate the absurdity (in his mind) of quantum mechanics. After 1930 he gave up trying to show that quantum mechanics is incorrect -- that its predictions could be contradicted by lab measurements. Yet Einstein still felt that quantum mechanics is incomplete, that there's more to reality than what wave functions can tell us, contrary to the claim of Bohr et al. Put another way, Einstein was convinced that there's a real world out there, that a complete theory wouldn't just give us the probabilities of various outcomes (as quantum mechanics does) but would also tell us where particles are and how they're moving even when we're not measuring them.
He published his new thought experiment in 1935 together with Boris Podolsky and Nathan Rosen, so it's become known as the EPR experiment. It has to do with two "entangled" particles -- let's call them A and B -- that are in a superposition of quantum states, meaning that their properties (according to Bohr and company) aren't defined until we measure them, at which point Nature "flips a coin" (collapses the wave function) to choose an outcome. But the added ingredient is that this particular wave function guarantees that the states of A and B are perfectly correlated with each other, so that measuring A immediately tells us what we'll get when we measure B. One example is a pair of electrons that are guaranteed to have opposite spin directions, except that neither one is either spin-up or spin-down until you actually measure the spin for one of them. The wave function of these two electrons taken together represents a superposition of the two possibilities: (A up and B down) + (A down and B up). The example we considered in class is a pair of photons -- created when a calcium atom makes a rapid pair of downward quantum jumps -- that are guaranteed to have the same polarization. For this situation the wave function is the superposition (A vertical and B vertical) + (A horizontal and B horizontal), but until we measure the polarization of one of the two photons, neither one is either vertically or horizontally polarized, and hence we don't know whether we'll measure that both are vertically polarized or instead that both are horizontally polarized.
Let's go with the two-photon example. If we send A and B in opposite directions and Alice eventually measures A, finding (for example) that A is vertically polarized, then we know that Bob must measure photon B to be vertically polarized as well, no matter how soon he measures it after the measurement on A. So a measurement of photon A must instantaneously influence photon B -- B must "know" how the random coin toss came out for A and must be sure to behave in the same way when measured -- even if B and A are many light-years apart by this time, in each other's absolute elsewhere. Einstein derisively called this instantaneous communication between the distant photons "spooky action at a distance." He insisted that reality couldn't be this strange, that B's polarization must have been definitely vertical from the time the two photons parted company, that B's polarization couldn't have been instantly influenced by a faraway measurement made on A. Einstein, in other words, felt sure that Nature obeys the principle of "locality" (also known as "separability"): it's possible for two objects A and B to be separated by such a great distance that a measurement made on the one can't possibly influence a measurement made on the other. Einstein's common sense view was that both locality and realism (the idea that a real world exists independent of our measurements) are valid concepts; this combined notion is called "local realism." Bohr, naturally, disagreed, because quantum mechanics denies the validity of both locality and realism.
Today the kind of theory espoused by Einstein is referred to as a "hidden variables" theory: the result of Bob's measurement of photon B's polarization state is determined by some unmeasured property intrinsic to B, not by a distant measurement made by Alice on photon A. Again, this is common sense. If Alice and Bob are identical twins and we measure Alice to have type-O blood, we now can be sure that Bob will also turn out to have type-O blood; but we don't claim that Bob's blood type was undefined until we measured Alice's blood type! No, we recognize that Bob's blood type was type-O ever since Bob was born, due to Bob's genetic makeup; those genes, the unmeasured DNA sequence in Bob's chromosomes, are the "hidden variable" that determined in advance what we would measure for Bob's blood type, whether or not we'd chosen to measure Alice first.
In 1964 John Bell showed, to everyone's surprise, that one could actually test Einstein's idea in the lab, using a setup only somewhat more complicated than the one in the EPR thought experiment. He proved ("Bell's theorem") that if you want to predict correlations between the measured properties of entangled systems such as our two-photon system, hidden variable theories necessarily yield predictions that differ from the predictions of quantum mechanics. That is, if locality holds true in Nature (hidden variables) then the measured correlations must obey certain numerical constraints called "Bell inequalities," whereas if it doesn't hold true (quantum mechanics) then the lab data will violate those inequalities. (Remember, the "correlation" is the percentage of the time that Alice and Bob obtain the same polarization measurement for photons A and B; when the two analyzers are parallel to each other, this correlation is 100%, but when they are rotated relative to each other it changes.) By the early 1980s Alain Aspect and his collaborators had been able to carry out such a lab experiment, even taking care to make rapid changes in the angles of the two measuring devices so that they couldn't communicate with each other and "conspire" to throw the results. Einstein's intuition was wrong, it turns out: The experimental data clearly violated the Bell inequality, instead coming out exactly as quantum mechanics predicted. Locality is not a feature of our universe. Spooky action at a distance is How Things Are.
(We can turn this weirdness to our advantage in quantum computing, quantum encryption, and even quantum teleportation; I recently gave you a few links on these topics, but for the most part the rest of you will need to go to the library or search online if you want to learn more about them.)
All of this, however, came long after Einstein's 1955 death. His final years were devoted to his unsuccessful search for a "unification theory" that would merge electromagnetism with general relativity while doing away with quantum weirdness; he also devoted a lot of time to pacifism and Zionism. Today physicists are following in his footsteps, but realize that first one should unify electromagnetism with the strong and weak nuclear forces (a "grand unified theory") before then attempting to include the vastly weaker force of gravity (a "theory of everything").
Our most recent readings delve further into alternative interpretations of quantum mechanics. Bohr's "Copenhagen" interpretation, long the standard among working physicists, is probably still the standard but is losing ground among those physicists who actively think about these philosophical issues. One possible reason for this change is that it's getting harder and harder to maintain that there's a divide between the submicroscopic world (which behaves according to the weird rules of quantum mechanics) and the macroscopic world of observers and measuring devices (which, according to Bohr, behaves according to common-sense classical rules). For example, a very cold gas composed of certain kinds of particles (called "bosons") can enter a state in which all the atoms behave identically, like a single giant atom: a "Bose-Einstein condensate" that amounts to a quantum system that's a few millimeters across. A few millimeters may be smaller than a breadbox but it's still macroscopic. Another reason that some may be questioning Copenhagen is that if you want to study cosmology -- that is, the history and future of the universe as a whole -- then by definition there's no one "outside" the universe who can observe the universe and collapse its wave function to a well defined state! Thus Copenhagen's need for observers whose measurements turn possibilities into actualities is problematic when the quantum system in question is the entire cosmos.
As mentioned earlier, you should be familiar with the various alternatives discussed in, especially, Chapter 15 of Rosenblum and Kuttner. For example, we discussed the "extreme Copenhagen" interpretation of Aage Bohr (Niels' son) which holds that submicroscopic particles don't exist at all; the GRW hypothesis that wave functions spontaneously collapse once in a very long while; and the transactional interpretation that regards events as a two-way interaction between the past and the future rather than as a one-way influence of the past on the future.
Nevertheless, quantum mechanics leaves open the possibility that consciousness has an influence on physical reality -- a highly controversial conclusion, partly because consciousness is not at all well understood and partly because the idea of the nonphysical mind influencing physical matter (such as the brain) strikes many scientists and philosophers as unseemly mysticism. How does dualism differ from materialism? What is the "hard problem" of consciousness? What would it mean to treat consciousness as an epiphenomenon? Does a species need to have language, or to pass the mirror test, before it can be considered conscious? Would a robot or computer program that could pass a Turing test be conscious -- and, if so, could it collapse an electron's wave function by measuring something about it?