A commonplace computational practice in quantum mechanics generates the most profound conceptual challenge to the theory. The challenge is called the measurement problem. Here are some quotes summarizing the problem.
“The quantum measurement parodox.. stated succinctly… In quantum mechanics all possibilities… are left open whereas in … experience a definite outcome always (occurs).”
A. J. Leggett in Foundations of Physics. 18, 939 (1988)
“How is the measuring instrument proded into making up its mind which value it has observed?”
Bryce S. Dewitt, Physics Today 23, 30 (1970)
“Some explanation must be provided for the fact that the Hilbert—space vector… collapses onto a certain eigenvector during a measurement process…”
J. Bub, Nuovo Cimento v. 57, Nr.2, 503 (1968)
The probability amplitudes evolve deterministically until a measurement is made: the measurement stops the evolution. What is the essential element that changes the evolution of the system from being in a state
|S> = (superposition sum of many states |n>),
into being in a state, say, |n=3>, one from among the many in the superposition?
Marvin Chester, never published
In quantum mechanics amplitudes for events progress quite deterministically – until a measurement is made. Then the amplitudes for all but the measured event are simply discarded. And the universe begins anew starting with the conditions found in the measurement. So at each measurement the old universe disappears and a new universe begins!
I offer below an animation to portray the idea. Press the particle release button to inject a vertically polarized particle into the magnetic field gradient region. Each press of the release button yields a new particle.
Made visible, here by the red ball-and-pole icons, is something intrinsically invisible and not measurable; the computational element called the particle amplitude. The particle amplitude is split into two by the field gradient through which the particle passes. From this amplitude split arises the particle’s potential to materialize in one or the other detector. But even though it has a 50% chance of appearing in each detector, only one detector registers. That detection tells us that the particle is known, with 100% certainty, to be in the registering detector. So the universe must be reset – from 50/50 amplitude split before detection to certainty for one of the amplitudes at detection.
Thus, on measurement, the particle’s spatial probability distribution is revised and from these new initial conditions a new universe begins its deterministic evolution. In the figure each press of the release button repeats the experiment with a new particle. The counters accumulate the detection events thus revealing the statistics. On repeating the experiment many times one finds particles are registered as often in one detector as the other. This is how the pre-detection 50/50 amplitude split reveals itself experimentally.
The figure shows an idealized laboratory measurement. But measurement events are taking place interminably everywhere. When a photon of sunlight falling on a leaf gets absorbed in photosynthesis, that is a measurement event. The leaf is a photodetector. Every chemical reaction is a measurement event; the reactants disappear and the products appear. Isn’t every inelastic scattering a measurement event?
An important feature of the measurement problem is thus: What constitutes a measurement? Is any elemental process that procedes irreversibly a measurement? These are topics to be explored in further posts.