3 The Critique

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.

1 The stan­dard axioms

“It is safe to say that nobody under­stands quantum mechanics.” — Richard Feynman

2 Time sym­metric quantum mechanics

“There is no descrip­tion of what hap­pens to the system between the ini­tial obser­va­tion and the next mea­sure­ment.” — Werner Heisenberg

3 Inter­pre­ta­tional strategy

“We do not know where we are stupid until we stick our necks out.” — Richard Feynman

4 The two-​​​​slit exper­i­ment revisited

“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

5 The impor­tance of detectors

“To restrict quantum mechanics to be exclu­sively about pid­dling lab­o­ra­tory oper­a­tions is to betray the great enter­prise.” — John Bell

6 Spa­tial aspects of the quantum world

“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

7 The macroworld

“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

8 Par­ti­cles

“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

9 Man­i­fes­ta­tion

“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

10 The Aharonov–Bohm effect

“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

11 The clas­sical limit

“People are all in favor of new ideas, pro­vided they are exactly like the old ones.” — Charles Kettering

12 An infi­nite force

“Quantum mechanics is magic.” — Daniel Greenberger

13 Why the laws of physics are just so

“If the laws of physics be for us, who can be against us?” — Frank J. Tipler

14 Fine tuning

“What really inter­ests me is whether God had any choice in the cre­ation of the world.” — Albert Einstein

15 Quanta and Vedanta

“Reality leaves a lot to the imag­i­na­tion.” — John Lennon

16 Invariant speed and local conservation

“The greatest obstacle to dis­covery is not igno­rance — it is the illu­sion of knowl­edge.” — Daniel Boorstin

17 A tale of two worlds

“It is impos­sible for anyone to begin to learn that which he thinks he already knows.” — Epictetus