Constructive and Destructive Interference In Quantum Mechanics

Caveat lector: I begin by reminding you that I am not a physicist.

But I want to draw attention to a well-known feature of the Schrodinger equation that I have never heard discussed and wonder at its possible implications.

Before I do, recall that Quantum Mechanics is very highly confirmed, if deeply puzzling to us all.

The English mathematician and Idealist philosopher Alfred North Whitehead, photograhed circa 1925.

hide captionThe English mathematician and Idealist philosopher Alfred North Whitehead is seen in this photo taken circa 1925.

Hulton Archive/Getty Images

In the Schrodinger linear wave equation, say in the famous two slit experiment, each photon must, says R. Feynman, be thought of as simultaneously taking all possible paths to the photodetector screen beyond the two slits.  We have no idea how this can happen if the quantum world is a world of Actuals, to follow Empedocles who told us 26 centuries ago that what is real in the universe is what is Actual.

Recall that Aristotle wondered if reality came in two “versions”, the Actual” and the “Possible.”  So did Alfred North Whitehead in the 1920s. But for Whitehead, an Actual gave rise to a Possible, which gave rise to an Actual, which gave rise to a next Possible.  Actuals, in Whitehead’s view could act causally on one another.

But can Possibles “act” somehow on one another?  What could that mean, and have we evidence that Possibles can “act,” perhaps acausally, on one another.

In fact, standard quantum mechanics, on the Copenhagen interpretation can be interpreted as saying that Possibles can, indeed, act acausally on one another, as Possibles and not via Actuals.

Watch.

You all know about the Schrodinger wave equation passing through the two slits and giving rise to two “semicircular” spreading waves propagating toward the photodetector screen.  As these waves propagate, where the peaks of two waves arrive at the same point on the photodetector, constructive interference occurs and a bright dot of light is detected on the photodetector screen. The same is true where the valleys of two waves coincide at the photodetector and a bright spot is detected. But where the peak of one wave coincides at the detector with a valley of the other wave propagating from the other slit, the two cancel in destructive interference and no spot is detected on the photodector screen. Thus constructive and destructive interference yields the famous banded light and dark interference pattern in the two slit experiment when both slits are open.

But just how, does this famous and central to quantum mechanics, constructive and destructive interference of the propagating waves of the Schrodinger equation manage to arise?

Think about it.  It seems clear that this inteference, either constructive or destructive, occurs before any spots arise on the screen. This point of view is enhanced by Feynman’s famous recasting of quantum mechanics as the sum of all possible pathways. The photon can simultaneously take on their way to the photodetector screen. Near classical paths interfere constructively along these many pathways and before the waves hit the detector screen, yielding high amplitudes hence, with the moduli squared, high probabilties of a spot via the Born rule squaring the amplitudes of the wave.  Two radically different pathways, wherever they simultaneously are in space, interfere destructively, so yield little probability.

How do these Possible simultaneously propagating “all possible histories,” interfere constrructively or desctructively in this, Feynman’s formulation of Quantum Mechanics, a formulation fully accepted by physicists?

It cannot be the case, that these simultaneously alternative pathways, spatially separated from one another that even a single photon “fired toward the slits once per hour, takes on its way to the photodetector, interact causally with one another as "actuals."  The pathways are not Actuals. They are at best Possibles.

One stance, familiar to all physicists, is that we do not attempt to interpret the formalism and just calculate.

But I believe quantum mechanics can be interpreted in terms of ontologically real “Possibles,” res Extensa and Res Potentia, interacting via the Poised Realm.

But this “ontologically real Possible” interpretation of Quantum Mechanics seems to demand that Possibles can interact simultaneously with one another across spatial distances, with mo mediating actual exchange of causal anything!

But this implies non-local, instantaneous correlations - -constructive and destructive interference —  that are non-causal, very much as in the famous EPR experiments confirmed by Alan Aspect.

In turn, this implies that the “possibility” waves of Schrodinger interact as Possibilities and do so both instantaneously and as “Possibilities”.

Then contrary to Whitehead, Possibles, if Quantum Mechanics deals with Ontologically real possibles, can interact instantaneously acausally across space.

Then recall C.S. Pierece telling us that the Actual and the Probable live in the world of Aristotle’s “Law of the Excluded Middle: A or Not A, there is nothing between them. The Middle is excluded. But as Pierece pointed out over a century ago, the Possible exactly avoids Aristotle’s law of the excluded Middle: A is true, A is Possible, A is false.  A is possible lies smack in the middle of A is true and A is false.

Then recall that confirming the violation of Bell’s inequalities demands either non locality, or alternatively demands giving up the "definiteness of counterfactual statements. So consider: “ A happens then B happens. If  A had not happened, B would not have happened”. This is a definite counterfactual.

Try the same with Possibles, “A happened and B possibly happens and simultaneously B  possibly does not happen, but if A had not happened, B possibly would not have happened and simultaneously B possibly would have happened!’  This is not a definite counterfactual statement!

Thus, we can consider that treating what is waving in the Schrodinger wave as an ontologically REAL Possible, is interpretable as saving locality in physics at the price of accepting that reality is both an ontological Real Possible and an Ontologically Real Actual.

And it requires that Possibles can interact, as in constructive interference a la Feynman’s sum over all possible histories, across space, instaneously, and Acausally via Actuals, by some Non Actual mediated interaction among ontologically real Possibles.

I conclude that it cannot harm us to consider the “possibility” that reality consists of ontologically real Actuals and ontologically real Possibles.

If so, a whole new vision of Reality beckons.

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