Let’s recall. There was: • Robbie, in the TV series (guess the answer) • HAL 9000, in …………… • Mr. Data, in ………….. • Marvin the Paranoid Android, in ………………. Some here will think of many more. Can machines be taught to really think? Perhaps more importantly, are we merely very complex computers? Or is “mind” more than a collection of neurons?
Quanta and Consciousness An overview of two significant and surprising developments in 20th-century science, one in physics and the other in mathematics. Both of these have implications regarding the nature of perception and consciousness. First, some background . . .
The development of quantum ideas • James Clerk Maxwell
Erwin Schrodinger “If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory”
These are the conditions under which Einstein wrote he would agree to continue to live with Mileva in Berlin: • A. You will see to it that: 1. My clothes and laundry are kept in good order; 2. I will be served three meals regularly in my room; 3. My bedroom and study are kept tidy, and especially that my desk is left for my use only. B. You will relinquish all personal relations with me insofar as they are not completely necessary for social reasons. Particularly, you will forgo my: 1. Staying at home with you; 2. Going out and traveling with you. C. You will obey the following points in your relations with me: 1. You will not expect any tenderness from me, nor will you offer any suggestions to me; 2. You will stop talking to me about something if I request it; 3. You will leave my bedroom or study without any back talk if I request it. D. You will undertake not to belittle me in front of our children, either through words or behavior. • Mileva Maric left Berlin with the children shortly after this.
Einstein generally worked alone. In addressing a government agency after WW2, concerning what could be done with out-of-work scientists, he said in all seriousness that jobs such as “lighthouse keeper” would be ideal for many scientists. • Bohr was a gregarious Dane who founded and built up an institute in Copenhagen. There are still physicists from all over the world who can say “I worked with Bohr” or at least their doctoral advisors did.
The “Copenhagen interpretation” • Quantum theory is probabilistic in nature. One can calculate exactly what an outcome will be --- one can only calculate the probability of obtaining one outcome or another. • These probabilities are contained in the “wavefunction” of the system. Before we do the observation, the wavefunction may contain many possible, overlapping outcomes. During the measurement, one of these outcomes is “selected.” • Example: the position of an electron in an atom: the original “Bohr model” vs the “electron cloud.”
Another example: decay of a nucleus. In a uranium atom, one can picture an alpha particle (two protons/two neutrons) bouncing back an forth against a potential barrier. Every time it hits, there is a probability that it will escape --- to tunnel through the barrier. In a certain time, we cannot predict whether the particle will escape or not, but we can predict the probability that it will escape in that time. (This would be like rolling a ball up a hill. Instead of stopping an rolling back down, there is a probability that it would disappear and reappear on the other side of the hill.) • (More on this later)
A central part of quantum theory is the Heisenberg Uncertainty Principle, which puts certain limits on our possible knowledge of the state of a quantum system. In a nutshell, it states that we cannot know two “conjugate variables” to arbitrary precision at the same time. For example, we cannot know the position and the velocity of a particle at the same time; there must be an uncertainty in our measurement. To wit, • (Delta)x times (Delta)v >= Planck’s constant
Einstein’s take on all this • (From a letter to Max Born, 1926): “Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.”
The “EPR” paradox • To illustrate deficiencies in the quantum theory, Einstein came up with many “gedanken experiments.” Bohr always came up with resolutions to Einstein’s proposed contradictions, but Einstein doggedly kept at it. In 1934, in one of his rarely co-authored papers, Einstein issued one last challenge. This was the famous Einstein, Podolsky, and Rosen (EPR) paper. It caused quite a stir.
Excerpt from a letter by Wolfgang Pauli to Heisenberg: “Einstein has once again expressed himself publicly on quantum mechanics. . . .(together with Podolsky and Rosen --- no good company, by the way). As is well known, every time that happens it is a catastrophe.”
The original EPR paper dealt with the linear momentum (mass times velocity) of two particles which interact but are then separated. A fundamental tenet of the paper is that after the particles separate, there is a “local reality” associated with each. The idea that one particle could affect the other, say, when on opposite sides of the solar system seems preposterous. In this way, EPR seemed to “get around” the limitations of Heisenberg uncertainty. • This time, Bohr did not have an iron-clad comeback. He eventually said that “the trend of their argumentation. . . does not seem to me to meet the actual situation with which we are faced in atomic physics.” As lame as this was, most physicists seemed to buy his arguments, gave a sigh of relief, and went back to “real” work.
Bohr talked of his arguments with Einstein until the day of his death in 1962. He had countered every attack on the theory as if it had been a personal one. The issue then lay more or less dormant for many years.
Entanglement • In 1952, David Bohm changed the setting of the EPR paper in a way that made the issues more clear and concise. He reduced the problem to two particles and only one variable for each: the spin or polarization. He also championed the notion of “hidden variables” which provide a complete picture of quantum reality. • John Bell was a researcher at CERN (a high-energy facility in Geneva), and in his “spare time” worked on the deeper issues of quantum theory. In the mid sixties, he published two ground-breaking papers. Bell’s Theorem, as it was called, provided a means for real experiments to test alternatives to quantum ideas.
John Bell and his wife Mary, also a physicist. • David Bohm
Bell’s Theorem • John Bell knew that Einstein and colleagues were partly correct: the “EPR paradox” was no paradox at all. What was wrong was their insistence on “local reality” --- that the total, “mixed” wave function could not extend across large regions of space. • Thus, Bell viewed two alternatives: (1) Quantum theory is right, or (2) local realistic models are right. But both cannot be right. • Bell produced a mathematical theorem containing certain inequalities. He suggested that if his inequalities could be violated by experimental tests, it would provide evidence in favor of orthodox (Copenhagen) quantum theory.
Tests of Bell’s Theorem • With apologies I am leaving out the work of Shimony, Clauser, Horne, Aravind, Zeilinger, and others. • The most convincing tests of Bell’s inequalities has been done by Alain Aspect (in France).
We conclude that “hidden variables” or other forms of local reality are NOT correct. “Spooky action at a distance” (to use Einstein’s description) correctly describes quantum systems. • By the way, the notion of entanglement is absolutely fundamental to the development of quantum computing, a hot topic these days. Now, back to some “old” stuff……
The role of the “Observer” • Schrodinger’s cat.
The probabilities that are computed in quantum mechanics are probabilities of outcomes of measurements. • The observer is outside the system. He intervenes in the system by making a measurement. The observer’s intervention takes one out of the realm of the hypothetical and into the realm of the actual. • One might think we could give a complete mathematical description of not only the experimental devices but of the observer herself, at least in principle. But this cannot be done!
If we could describe by the mathematics of quantum theory everything that happened in a measurement, even up to the point where a definite outcome was obtained by an observer, then the math would have to tell us what the outcome was. But this cannot happen, for in quantum theory the math will yield only probabilities. • In short, the mathematical descriptions of the physical world given to us by quantum theory presuppose the existence of observers who lie outside those mathematical descriptions. And the theory works. What about the line between the “system” and the “observer”?
Godel’s theorem • Kurt Godel was an Austrian logician and a good friend of Einstein. • (In the movie “IQ”, Walter Matthau played Einstein and Lou Jacobi played Godel. Meg Ryan played Einstein’s niece.)
The theorem - 1931 • Godel proved that in any consistent formal mathematical system (in which one can at least do arithmetic and simple logic), there are arithmetical statements which can neither be proved nor disproved using the rules of that system but which are nevertheless true statements. • These are called “formally undecidable propositions” of that system. • Moreover, Godel showed how to find, in any particular consistent formal system, how to actually find one of its formally undecidable-but-true propositions.
If F is any consistent formal system that contains logic and arithmetic, Godel showed how to find a statement in arithmetic, which we may call G(F), that is neither provable nor disprovable using the rules of F. He further showed that G(F) is nevertheless a TRUE arithmetical statement. • This can be applied to computer programs. For a computer program P that is known to be consistent, one can find a statement in arithmetic, G(P), that cannot be proven nor disproven by that program. And one can show that G(P) is a true statement.
The Lucas-Penrose argument. • In 1961, John R. Lucas, a philosopher at Oxford U., set forth an argument based on Godel’s Theorem, to the effect that the human mind cannot be a computer program. • Roger Penrose, the widely-known mathematician and physicist, revived Lucas’ argument in the late 80’s. His book The Emperor’s New Mind was published in 1989. In answer to the large amount of criticism it provoked, Penrose published a second book, Shadows of the Mind. While no one has succeeded in refuting the Lucas-Penrose argument, it has not changed many minds.
The argument • Suppose someone shows me a computer program, P, that has the ability to do simple arithmetic and logic. I know this program to be consistent, and I know all the rules by which it operates. Then as Godel proved, I can find a statement in arithmetic (call it G(P)) that the program P cannot prove (or disprove.) But following Godel’s reasoning, I can show G(P) to be a true statement of arithmetic. • So far, no big deal. The programmer could modify the program so that it can also prove G(P). But I know all the new rules, too, so I can find a new statement which is true but which cannot be proven or disproven by the new program. Again the programmer could improve the program, and we can keep playing this game, with me always “outwitting” the new programs. However….
Suppose I myself AM a computer program: call me H (for human). When I prove things, it is just by some computer program running in my brain. And now suppose I am shown that program, learning in complete detail how H works. Then assuming I know H to be a consistent program, I can construct a statement in arithmetic, call it G(H), that cannot be proven or disproven by H, but which I, using Godel’s reasoning, can show to be true. • Contradiction: it is impossible for H to be unable to prove a result that I am able to prove, because H is me! • (Thanks to Stephen Barr for this concise description of the Lucas-Penrose argument.)
Our assumptions were: • (a) I am a computer program. • (b) I know that the program is consistent. • (c) I can learn the structure of the program in complete detail. • (d) I have the ability to go through Godel’s “steps.” • A materialist has “escape routes” by denying (b), (c), or (d) instead of (a).
In conclusion • Herrmann Weyl, one of the great mathematicians and physicists of the twentieth century, wrote in 1931: • “We may say that there exists a world, causally closed and determined by precise laws, but . . . the new insight which modern [quantum] physics affords opens several ways of reconciling personal freedom with natural law. It would be premature, however, to propose a definite and complete solution of this problem. One of the great differences between the scientist and the impatient philosopher is that the scientist bides his time. We must await the further development of science, perhaps for centuries, perhaps for thousands of years, before we can design a true and detailed picture of the interwoven texture of Matter, Life, and Soul. But the old classical determinism of Hobbes and Laplace need not oppress us longer.”
Postscript • The answer is NOT “42”. (With apologies to Douglas Adams, who wrote The Hitchhikers Guide to the Galaxy.)