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| The End of Certainty by Ilya Prigogine |
One of Prigogine's notions is that, inasmuch as atoms are made up of particles and these particles are in motion, they are dynamical systems. As such, the motion of electrons and other particles in an atom possesses an "arrow of time." So there ought to be a way to mathematically model the quantum behavior of subatomic particles such that time appears in the equations as an irreversible variable.
In standard quantum theory, time is a reversible variable. The equations normally used apply equally well to forward-directional time as to reverse-directional time.
In fact, the forward and reverse directions of the flow of time are not apparent in the standard quantum equations. Accordingly, at least as far as quantum phenomena are concerned, many theorists attribute the arrow of time that we experience, to the effects on a quantum system of its being observed, as scientists study it from the outside.
When scientists try to measure the position of an electron, they can pinpoint that position only if they abandon hope of also knowing the electron's momentum: its velocity in a particular direction, times its mass. Hence measuring the electron's position is incompatible with measuring its velocity, and observing its velocity makes it impossible to know its position precisely.
Think of trying to photograph the end of a horse race. If a flash photo is taken right at the finish line, it freezes the horses' motion. The stop-motion photo thereby pinpoints which horse's nose crossed the line first — i.e., the relative positions of the horses at the finish of the race. On the other hand, if a non-flash, time-exposure photo is taken, using a long exposure time, the lead horse's nose will be but a blurred streak in the picture. The form and length of the streak will be a function of how fast the horse was moving — its speed, which relates to its velocity.
Therefore, how you set up the camera determines whether it captures position or momentum. Either alternative can be measured with certainty only if the other alternative is sacrificed.
The stop-action alternative which pinpoints the horses' relative positions has no time dimension whatever. The blurry-streak alternative which records the horses' speed does not, meanwhile, tell you in which direction the horses really moving. Common sense tells us, it is quite true, that horses run "forward," i.e., with their noses out in front of the rest of them. But strictly speaking, the camera does not know this. The blurry streak formed by the moving equine noses would look just the same if the horses were being transported backward!
So either act of photographic commemoration, stop-action or blurry-streak, lacks an arrow of time. We, of course, supply one when we look at and interpret the blurry-streak photo.
Similarly, the standard equations of quantum theory lack an arrow of time. Yet various interpretations of the theory exist in which time irreversibility is imposed by virtue of acts of external observation. I discussed one such interpretation, which exalts the importance in quantum phenomena of outside observers' choices as to what to observe and how, in my earlier post Genesis by Observership.
In a well-known thought experiment in quantum physics, that of Schrödinger's Cat, a live cat is imagined to be put in a closed box with a mechanism that may (or may not) indirectly cause the cat's death by at some moment releasing (or not releasing) a radioactive particle as a trigger to the breaking open of a vial of poison gas. In our imagination, we let the experiment run unobserved for a period of time. Then, after a while, we open the box and see whether the cat is alive or dead.
It is only at the moment we do so, Schrödinger showed mathematically, that the outcome becomes etched in stone ... even though the release of the fateful particle and the resulting death of the cat happened (if at all) earlier in time! Inconceivable as it seems, apparently no other understanding is consistent with the laws of standard quantum mechanics. Our observation of the event alone is what makes that (earlier) event certain.
Thus, in this interpretation of the mathematics of quantum theory there can be no arrow of time, except under conditions of external observation.
Prigogine objects to that approach. He seeks (and finds) an alternative mathematical formulation of quantum theory which builds in the arrow of time from the get-go. In return, it trades in the (limited) certainty which the standard equations can yield and replaces those equations with probabilistic formulas that are unable to pinpoint which event, out of a multitude of possibilities, is actually so.
The standard equations can yield certainty in the limited way a photo of a horse race's finish can: one variable can be pinpointed with certainty by sacrificing another. But those standard equations lack an arrow of time. That leads to, among other paradoxes, the one concerning Schrödinger's imaginary cat in which a seemingly later "photo" — a visual observation, that is — determines a seemingly earlier event.
Prigogine's equations remove that proneness to paradox in quantum theory at the expense of making certainty fundamentally impossible at the level of subatomic phenomena. But his equations do successfully account for the arrow of time.
More than that, they generalize to other types of systems involving physical "stuff" in dynamical motion. Such systems include thermodynamic systems, with their vaunted entropy, and dissipative systems which self-organize and evolve in seemingly the opposite direction. They also include systems whose futures are in thrall to "deterministic chaos."
Dissipative systems are quite important to us. After all, all living things are dissipative systems. So, too, are various kinds of non-living physical and chemical systems, at least under certain circumstances.
Prigogine's equations involving "probability distribution functions" are basically the same for all these kinds of dynamical systems.
My thought about all this is that those other, non-quantum kinds of dynamical systems might, like quantum systems, have alternative mathematical models in which acts of external observation would successfully change probabilities into certainties — just as they do in the study of quantum phenomena, at least according to some interpretations of the relevant theory.
For brevity, I'll refer to such hypothetical alternative mathematical models as AMMs. If an AMM exists for, say, a dissipative system, certain things would likely result. One of them is that the choice of which new stable state a dissipative system enters at a dynamical "bifurcation point" is not a coin flip but reflects an act of external observation. The event which results from the bifurcation in turn can depend on an act of choice made by the outside observer (see Genesis by Observership for more on the astounding consequences of observational choices).
If an AMM exists for a living, evolving, dissipative system, it just might be that the bifurcation events of its evolutionary pathways are determined by choices made by God, who sees all worldly events from outside the context of irreversible time. Hence, such an AMM would be expected to represent time as reversible, just as do the equations of standard quantum theory. Accordingly, such an AMM would violate one of Prigogine's foundational assumptions: his preference for a mathematical model in which time is irreversible.
Moreover, if such an AMM exists for a living/evolving/dissipative system, that AMM would very likely allow the chance-based alternatives intrinsic to a mathematical model such as Prigogine's to be supplanted by descriptions of events which are knowable (at least in limited fashion) as certainties.
At the same time, such an AMM would not be wholly deterministic. There would be types of systems experiencing types of situations in which the future is not set. There would be an element of surprise in these systems' future evolutionary paths that could not even in concept be eliminated by our gaining more thorough knowledge of their present states.
Such an alternative mathematical model would not invalidate Prigogine's, any more than Riemannian geometry invalidates Euclidean. Prigogine's model succeeds in accounting in a very general way for the arrow of time as it affects many different types of systems which are usually treated as separate. If you are interested in a purely physical-world approach, it looks to me (as admittedly a layman) that Prigogine's mathematics are spot on target when it comes to explaining time's irreversible flow.
The alternative approach I am suggesting seems to require that there be an observer outside the world system whose observational choices we experience as the workings of chance.
Prigogine's original description of bifurcation points in dissipative systems is a case in point. It involves chance fluctuations, which "choose" which path the systems will take out of states of instability. His probabilistic, statistical mathematical model replaces this description by one in which chance (another name for probability) is involved at a fundamental level, at all times, not just at discrete points of instability.
The Prigogine model accepts both chance (or probability) and the arrow of time as brute facts or bottom-level realities in our world. The AMM I seek sees them both as artifacts of the choices made by God in his "observation" of our otherwise freely evolving world.
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