The article that follows 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 (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. In this essay I will think about how quantum state reduction might be related to the passage of "now".

In the classical systems we considered previously, the state of the system could be expressed as the position and momentum of the moving parts of the system. There was a hidden assumption in this description. That was that position and momentum had specific values at specific times. The uncertainty principle renders that assumption false. I suspect this is going to be troublesome if we try to follow a similar path as we took in considering the classical systems.

There appears to be a quantum analog of my separation of classical state changes into passive and active. A quantum system behaves one way when no one is looking and another way when any measurement is made of the system state. An equation, worked out by Erwin Schrödinger, describes the evolution of a quantum system in the absence of interference. The solutions to Schrödinger equation are called wave functions. If you plug some state variable values into a wave function and take the square of the absolute value of that, you get the probability that the system has that set of values for those state variables.

If you actually make a measurement, the result will probably not be the one with the highest probability as found above. The act of measurement cannot be accomplished without disturbing the system on which the measurement is made. That is due to the extreme smallness of the objects we deal with in quantum mechanics. It is possible to predict the average value, called an expectation value, measured in a number of repetitions of an experiment but that value might never actually be realized.

I find this all somehow disreputable. I like carefully crafted questions to have definite answers. The mathematical treatment of quantum mechanics was not built up by rigorous proof from the firm foundation of established mathematics. Even the experts can't agree on what quantum reality looks like, or if indeed there is a quantum reality. 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. It seems that Nature is not impressed with my disapproval.

One of the mysteries in quantum mechanics is the role of the observer. Until someone actually looks at a quantum system by means of some kind of experiment, the wave function represents the quantum system's evolution. Contained in the wave function are all the possible ways in which the system might evolve. Many experts hold that until an observation is made, the system includes a mix of all of those possibilities. Schrödinger himself had a problem with this view. He devised an absurd example to make his point. - which brings us to Schrödinger's cat.

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 mixed quantum mechanical state 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", not some future time when the chamber may be opened. The notion that it is the passage of "now" rather than the act of observation that brings about the quantum state reduction is different than the usual quantum mechanical interpretation of events.

Clearly I have not made the case for my inclination to blame "now" for quantum state reduction. I do not know enough to lay out any set of logical steps connecting the choice of which of the possibilities is realized by the passage of "now". As far as I know, no one who might make such an argument has tried to do so. There is at least one well respected thinker of deep thoughts who shares 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. I wonder if it is not simply the passage of time that effects the quantum state reduction.