This web page is on a topic that I have wondered about. I would appreciate any feedback that you might be able to provide. Especially errors in concept or calculation. Please send an email to jdj@mcanv.com if you would care to comment.

In part 1 of this topic I proposed the mechanism for how a single state of a classical/relativistic (non-quantum-mechanical) dynamical system is selected from all the possible future states, to become the state that is to be found in that system's past. We know that this classical/relativistic view of things is only an approximation that is good enough to give useful answers to the question, "How does nature work?" in all our everyday experience.

In the systems we considered previously, the state of the system at any instant could be expressed as the position and momentum of the moving parts of the system at that instant. There is a hidden assumption in this description. It was assumed that position and momentum could be expressed by simple numbers which had specific values at specific times. In the first quarter of the twentieth century it was discovered that this is not true. In order to calculate results that agree with experiments on very small systems we must treat position and momentum as operators rather than numbers. Operators have the property that the order in which they appear may matter, so for a position, x, and a momentum, p, the expression xp differs from the expression px. In fact xp-px = 1.055X10^-34m²kg/s times the square root of minus 1. This difference is so close to zero that we never directly experience the weird effects of quantum mechanics on systems large enough to be observed directly.

A popular interpretation of quantum mechanics holds that an isolated quantum system behaves one way when no one is looking and another way when any observation is made of the system state. An equation, worked out by Erwin Schrödinger, describes the evolution of a quantum system in the absence of observation. The solutions to Schrödinger equation are called wave functions. If you operate on the wave function with some mathematical trickery you can get a numerical answer to the following question: "If I make a measurement at a future time of a particular property of a large number of identically prepared systems, what would be the average of those measurements?".

If one actually makes a measurement at that future time, the result will almost certainly not be the one found above. The wave function contains all of the possible future states of the system. Nature decides which of the possible future states is actually measured, reducing the possibly large number of possible future states to the single observed state. In effect the measurement collapses the wave function to a single state.

I find this all somehow disreputable. I like carefully crafted questions to have definite answers. And, I find it an odd notion that nature depends on human consciousness (the act of observation) in wave function reduction. Even the experts can't agree on what quantum reality looks like, or if indeed there is a quantum reality. The mathematical treatment of quantum mechanics was not built up by rigorous proof from the firm foundation of established mathematics. People like Erwin Schrödinger, and more recently Richard Feynman, just sort of jumped from their understanding of physics to calculational techniques that produce results in such excellent agreement with the way nature actually works as to be almost miraculous. Quantum-mechanical calculations have led to almost all of modern electronics: TVs, computers, cell phones, music players, etc. It seems that Nature is not impressed with my disapproval.

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

I am with Schrödinger on this one. It is true that when a quantum system is observed, it will be found in a definite state but I am inclined to think that it was the passage of "now", not the observation that reduced the combination of quantum mechanical states described in its wave function (psi-function) to a single reality. The radioactive sample in the Schrödinger cat example will emit radiation, or not, in an hour independent of whether the chamber is opened, and whenever the trap is sprung on the poor cat it will be "now" for the cat, not some future time when the chamber may be opened.

There are well respected thinkers of deep thoughts who share my suspicion that there is an objective reality that explains quantum state reduction, independent of any observer. In his 2004 book "The Road to Reality", Roger Penrose writes in chapter 29:

The final possibility ... is that present-day quantum mechanics is merely an approximation to something better, and that — in this improved theory — both of U and R take place objectively as real processes; moreover, it is part of the perspective ... that future experiments should be able to distinguish such a theory from conventional quantum mechanics.

The "U and R" in the Penrose quote refer to the wave function evolution and the quantum reduction process respectively. It turns out that professor Penrose suspects that gravity plays a more significant role in quantum mechanics than is currently attributed to it. A theory of quantum gravity has yet to be developed.

Theoretical Physicist Wojciech H. Zurek makes a case in his paper Decoherence and the Transition from Quantum to Classical, that in reality there are no observable, isolated, quantum systems. In effect the environment interacts with the system under consideration so as to very frequently (nearly continuously) reduce the wave function to a mixed state consisting of an ensemble of possible classical states. It remains to be explained how this ensemble is reduced to the single state that we observe as reality.

I wonder if it is not simply the passage of time that effects the final quantum state reduction. The temporal domain of Schrodinger's equation with its superposition of all possible quantum states is the future. The past is contains only definite classical states. All that lies between the uncertain quantum future and the unchangeable classical past is "now".