WE ARE ALL GEOCENTRIST NOW:

[I]'m not as sure as I once was about the future of quantum mechanics. It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. The dispute arises chiefly regarding the nature of measurement in quantum mechanics. This issue can be illustrated by considering a simple example, measurement of the spin of an electron. (A particle's spin in any direction is a measure of the amount of rotation of matter around a line pointing in that direction.)

All theories agree, and experiment confirms, that when one measures the amount of spin of an electron in any arbitrarily chosen direction there are only two possible results. One possible result will be equal to a positive number, a universal constant of nature. (This is the constant that Max Planck originally introduced in his 1900 theory of heat radiation, denoted h, divided by 4π.) The other possible result is its opposite, the negative of the first. These positive or negative values of the spin correspond to an electron that is spinning either clockwise or counter-clockwise in the chosen direction.

But it is only when a measurement is made that these are the sole two possibilities. An electron spin that has not been measured is like a musical chord, formed from a superposition of two notes that correspond to positive or negative spins, each note with its own amplitude. Just as a chord creates a sound distinct from each of its constituent notes, the state of an electron spin that has not yet been measured is a superposition of the two possible states of definite spin, the superposition differing qualitatively from either state. In this musical analogy, the act of measuring the spin somehow shifts all the intensity of the chord to one of the notes, which we then hear on its own.

This can be put in terms of the wave function. If we disregard everything about an electron but its spin, there is not much that is wavelike about its wave function. It is just a pair of numbers, one number for each sign of the spin in some chosen direction, analogous to the amplitudes of each of the two notes in a chord. The wave function of an electron whose spin has not been measured generally has nonzero values for spins of both signs.

There is a rule of quantum mechanics, known as the Born rule, that tells us how to use the wave function to calculate the probabilities of getting various possible results in experiments. For example, the Born rule tells us that the probabilities of finding either a positive or a negative result when the spin in some chosen direction is measured are proportional to the squares of the numbers in the wave function for those two states of the spin.

The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities. We can live with that. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton's equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics?

One common answer is that, in a measurement, the spin (or whatever else is measured) is put in an interaction with a macroscopic environment that jitters in an unpredictable way. For example, the environment might be the shower of photons in a beam of light that is used to observe the system, as unpredictable in practice as a shower of raindrops. Such an environment causes the superposition of different states in the wave function to break down, leading to an unpredictable result of the measurement. (This is called decoherence.) It is as if a noisy background somehow unpredictably left only one of the notes of a chord audible. But this begs the question. If the deterministic Schrödinger equation governs the changes through time not only of the spin but also of the measuring apparatus and the physicist using it, then the results of measurement should not in principle be unpredictable. So we still have to ask, how do probabilities get into quantum mechanics?

One response to this puzzle was given in the 1920s by Niels Bohr, in what came to be called the Copenhagen interpretation of quantum mechanics. According to Bohr, in a measurement the state of a system such as a spin collapses to one result or another in a way that cannot itself be described by quantum mechanics, and is truly unpredictable. This answer is now widely felt to be unacceptable. There seems no way to locate the boundary between the realms in which, according to Bohr, quantum mechanics does or does not apply. As it happens, I was a graduate student at Bohr's institute in Copenhagen, but he was very great and I was very young, and I never had a chance to ask him about this.

Today there are two widely followed approaches to quantum mechanics, the "realist" and "instrumentalist" approaches, which view the origin of probability in measurement in two very different ways. For reasons I will explain, neither approach seems to me quite satisfactory.

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