Quantum states are probability algorithms. Think of them as machines with inputs and outputs: you enter the actual outcome(s) and time(s) of one or several measurements, as well as the possible outcomes and the time of a subsequent measurement — and out pop the probabilities of these outcomes.
Although the time dependence of a quantum state is thus clearly a dependence on the times of measurements, it is generally interpreted — even in textbooks that strive to remain metaphysically uncommitted — as a dependence on “time itself,” and thus as the time dependence of something that exists at every moment of time and evolves from earlier to later times. Hence the mother of all quantum-theoretical pseudo-questions: why does a quantum state have (or appear to have) two modes of evolution — a continuous and predictable one that applies between measurements, and a discontinuous and unpredictable that kicks in whenever a measurement is made?
The problem posed by the central role played by measurements in all standard axiomatizations of quantum mechanics is known as the “measurement problem.” Although the actual number of a quantum state’s modes of evolution is zero, most attempts at solving the measurement problem aim to reduce the number of modes from two to one. As an anonymous referee once put it to me, “to solve this problem means to design an interpretation in which measurement processes are not different in principle from ordinary physical interactions.” The way I see it, to solve the measurement problem means, on the contrary, to design an interpretation in which the central role played by measurements is understood, rather than swept under the rug.
“It is safe to say that nobody understands quantum mechanics.” — Richard Feynman
“There is no description of what happens to the system between the initial observation and the next measurement.” — Werner Heisenberg
“We do not know where we are stupid until we stick our necks out.” — Richard Feynman
“We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about ‘and’.” — Arthur Eddington
“To restrict quantum mechanics to be exclusively about piddling laboratory operations is to betray the great enterprise.” — John Bell
“The most satisfying way to end a philosophical dispute is to find a false presupposition that underlies all the puzzles it involves.” — B.C. Van Fraassen
“There is a straight ladder from the atom to the grain of sand, and the only real mystery in physics is the missing rung. Below it, particle physics; above it, classical physics; but in between, metaphysics.” — Tom Stoppard
“In the fall of 1940, Feynman received a telephone call from John Wheeler [Feynman’s thesis advisor] at the Graduate College in Princeton, in which he [Wheeler] said that he knew why all electrons have the same charge and the same mass. ‘Why?’ asked Feynman, and Wheeler replied, ‘Because they are all one and the same electron.'” — Jagdish Mehra
“And it should be the law: If you use the word ‘paradigm’ without knowing what the dictionary says it means, you go to jail. No exceptions.” — David Jones
“Somewhere in our doctrine there lurks a conception not justified by any experience, which will have to be eliminated in order to clear the way.” — Max Born
“People are all in favor of new ideas, provided they are exactly like the old ones.” — Charles Kettering
“Quantum mechanics is magic.” — Daniel Greenberger
“If the laws of physics be for us, who can be against us?” — Frank J. Tipler
“What really interests me is whether God had any choice in the creation of the world.” — Albert Einstein
“Reality leaves a lot to the imagination.” — John Lennon
“The greatest obstacle to discovery is not ignorance — it is the illusion of knowledge.” — Daniel Boorstin
“It is impossible for anyone to begin to learn that which he thinks he already knows.” — Epictetus