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Is The Possible Ontologically Real?

I adduce four lines of evidence for a radical claim: Perhaps the "possible" is ontologically real and the world consists of two realms, "Possibles" and "Actuals."

Empedocles, in ancient Greece, claimed that what was real in the universe was what was Actual. Aristotle flirted with "potentia." Alfred North Whitehead in Process and Reality proposed that Possibles gave rise to Actuals which in turn gave rise to Possibles: P -> A -> P -> A. Few take Whitehead's proposal seriously. Yet maybe he is right.

1. In a previous post, Res potentia and Res Extensa linked, hence united, by quantum measurement, it was argued that Richard Feynman's accepted formulation of quantum mechanics as a "sum over all possible histories" committed Feynman to say in the famous double slit experiment yielding the famous interference bands, that any single photon simultaneously possibly did and possibly did not go through the left slit.

But C.S. Pierce noted that Actuals and Probables obey Aristotle's law of the Excluded Middle: A or Not A, where "A and not A" is a contradiction. But said Pierce, Possibles evade the Law of the Excluded Middle. So too does Feynman's claim about the photon possibly going through the left slit and simultaneously possibly not going through the left slit.

It seems that a realm of real possibles, Res potentia, for unmeasured quantum behavior, and Res extensa, the Actual, following many quantum measurements, is a consistent interpretation of quantum mechanics. More possibilities seem not to be spatially localizable. But in Quantum Mechanics we confront the mystery of non-locality, high correlations in two quantum measurements that arise at distances too fast for light to travel between the events, hence not classically causal. Res potentia may offer a realm for the non-locality of quantum mechanics.

2. Even classical physics seems to appeal to a real Possible. In statistical mechanics, Boltzmann wished to construct a theory for many gas particles, say N large, in a liter box. Each particle has a position, measured on the X, Y, and Z axis, so specified by 3 numbers. and a momentum, mass times velocity, measured at an instant on the X,Y, and Z axis so 3 more numbers. So 6 numbers specify one particle and 6N numbers specify the simultaneous positions and momenta of all N particles in a prestated phase space confined to the liter box.

Now, in principle, one could use Newton's equations of motion in differential form, integrate them given initial and boundary conditions to yield the deduced, hence entailed trajectory (which is purely Actual,that is the trajectory is precisely the Actual positions and momenta of all N particles at each successive instant) of a point representing all N particles simultaneously in the 6N phase space. (In reality, the phase space is 6N - 1 to allow for conservation of energy.) Boltzmann's next move was to divide the 6N-1 phase space into many tiny 6N-1 volumes, called microstates of volume V.

He then imagined the entailed Newtonian trajectory weaving through these microstates. But he knew one cannot know the current state of the 6N-1 phase space, nor integrate the N Newtonian equations of motion. So he invented a critical "ergodic hypothesis" of molecular chaos. The ergodic hypothesis says that in the "thermodynamic limit" of infinite time, the frequency with which the trajectory will be in each microstate is exactly equal to its simple volume, V. So the ergodic hypothesis asymptotically, at infinite time, which is never reached, replaces the Newtonian trajectory with an ergodic probability claim, entirely uncoupled from Newton's equations and their integration. (I thank my colleagues Giuseppe Longo and Gabor Vattay for stressing to me, that the "thermodynamic limit," while infinite in time is also infinite as the number of particles N and volume V increase, but N/V remains constant.) But this implies that Boltzmann needs to say, even in the thermodynamic limit where the total volume V is not occupied by the N particles, hence also the real physical case of finite N and V, that in the infinite time limit, which is never reached, the trajectory "would traverse" all possible points in each microstate of volume V.

Then Boltzmann seems to need an ontologically real Possible, all the Possible points of each microstate of volume V, to make his claim. There is another issue. If the shape of the volume containing the gas were different, the Newtonian trajectory in the 6N-1 phase would be different and thus the Possible for the gas would be different. So the Actuality of the vessel shapes the Possible. And the reshaped Possible reshapes the Actual trajectory in the system of particles in the 6N-1 phase space.

Finally, if we humans are free willed, as I think may be possible as discussed in "Answering Descartes: Beyond Turing," then we humans have the Possibility to reshape the vessel and thereby reshape what is Possible for the gas and its Newtonian trajectory.

3. In Shannon's information theory, a given symbol string, say in bits, e.g. (1111) is chosen and sent down the information channel. Now for the first, left most bit, or 1, in the (1111) to carry information, it is essential that it could possibly have been 0. But that means that if we think information itself is real, then Possible must be real.

4. Finally, ordinary business life. The young founder of Federal Express confronts, we imagine, a venture capitalist.

"Here's my plan: beat the U.S. Post Office with airplanes carrying mail. Save money because we need no windows... ."

"Great, no windows," says the VC.

"Well, here are the risks we see, the potential market, and we think for $40,000,000 we can be in the black in 5 years."

"Do you really think your idea is possible?" says the VC.

"Of course, I've thought it through."

"How likely is your plan?" says the VC.

"I'd give it 85 percent," says the Fed Ex founder. (Note this 85 percent becomes the famous "prior" in Bayesian statistics used all the time.)

"OK" says the VC, I'll take 45 percent of your company and we'll work out the details in the next month." (No VC makes such snap judgements, he too considers the likelihood, risks, potential return, time to break even and so on.)

Now note that both the founder and VC treat the Fed Ex plan as a "real Possibility." This possibility surely seems real. If not, what is it?

I conclude that we may want, with Aristotle and Whitehead to consider the Possible along with the Actual as both real.