12 An infinite force

Dieks finished by saying that “paradoxes and bewilderment only occur if one wonders about how the calculated and predicted experimental outcomes can be realized by natural processes.”

The question of how the predicted outcomes can be realized by natural processes assumes that they are realized by natural processes. Let’s take a look at how physicists used to bamboozle themselves into believing that such was the case.

input-output classicalAccording to classical electrodynamics, the calculation of electromagnetic effects can be carried out in two steps: (i) given the distribution and motion of charges, one calculates six functions of time and position using Maxwell’s equations, and (ii) given these six functions (the components of the so-called electromagnetic field) as well as the position of a “test charge,” one calculates the effect that the former charges have on the latter charge using the Lorentz force law. To make themselves believe that this calculational scheme was realized by natural processes, all that physicists had to do was to reify a calculational tool — to transmogrify the six components of E and B into a physical medium by which charges act on charges.

input-output quantumUsing the corresponding scheme of the quantum theory, one calculates a probability. This too can be done in two steps: (i) given the time and the actual outcome of an (in general) earlier measurement, one obtains a density operator, a state vector, or a wave function, and (ii) given this as well as the time and a possible outcome of an (in general) later measurement, one obtains the probability of that outcome. To make themselves believe that this calculational scheme is realized by natural processes, physicists would have to reify another calculational tool — to transmogrify the state vector or the wave function into a physical medium by which actual measurement outcomes determine the probabilities of possible measurement outcomes. What causes the paradoxes is the attempt at this sleight-of-hand, and what causes the bewilderment is that it invariably leads to paradoxes.

One attempt of this sort — the so-called many-worlds interpretation — leads to Schrödinger’s notorious cat paradox:[1] the cat ends up being both dead and alive, the experimenter ends up both finding a dead cat and finding a living cat, her colleague ends up both being told that she found a dead cat and being told that she found a living cat, and so on ad absurdum. As van Kampen remarked,[2] “I find it hard to under­stand that some­one who arrives at such a con­clu­sion does not seek the error in his argu­ment.”

Apart from the fact that the reification of a mathematical symbol, expression, or equation has never been more than a sleight-of-hand, there are a number of reasons why it no longer works. One is that the time on which a quan­tum state func­tion­ally depends is the time of a mea­sure­ment; the probability algorithms of quantum mechanics are not (nor do they represent) instan­ta­neous states of affairs that evolve from ear­lier to later times. Another is that state vectors and wave functions are neither gauge invariant nor invariant under Lorentz transformations; they thus lack the invariance necessary for being thought of as anything more than calculational tools.

The principal reason, however, is that real­ity is struc­tured from the top down, by a self-differentiation (of an Ultimate Reality, UR) that does not bot­tom out. (Let’s keep in mind that this conclusion is drawn not from untestable meta­phys­i­cal assump­tions about what hap­pens between mea­sure­ments but from testable statistical predictions of measurement outcomes.) The many-worlds interpretation in particular is thereby ruled out of court, for by attributing a continuously evolving state vector to the universe it implies that the spatiotemporal differentiation of the universe is complete.

By this self-differentiation, UR manifests the world, or manifests itself as the world, without losing its intrinsic unity: one and indivisible, it is both every particle in existence and coextensive with the world in its spatiotemporal totality. The force by which UR manifests itself therefore does not act solely in or across time and/or space. It brings forth the spatiotemporal whole from an indivisible “standpoint” that thereby comes to be coextensive with the spatiotemporal whole. Primarily it acts from this standpoint, and secondarily it acts from a standpoint that is one with every existing fundamental particle.

It stands to reason that the force inherent in UR is infinite, and quantum mechanics gives every indication that this is indeed the case. For quantum mechanics implies that almost everything is possible, in the sense that almost every possible measurement outcome has a probability greater than zero. This is exactly what one expects from an infinite force that works under self-imposed constraints. We therefore have no reason to be surprised by the impossibility of understanding how the predicted experimental outcomes can be realized by natural processes. It would be self-contradictory to invoke natural processes to explain the working of an infinite force. What needs explaining is why this force works under self-imposed constraints, and why under the particular constraints that are known to us as the laws of physics.

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1. [↑] Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics). Naturwissenschaften 23, 807–12; English translation in Wheeler, J.A., and Zurek, W.H. (1983), Quan­tum The­ory and Mea­sure­ment, Prince­ton Uni­ver­sity Press, pp. 152–67.

2. [↑] van Kam­pen, N.G. (1988). Ten the­o­rems about quantum-mechanical mea­sure­ments. Phys­ica A 153, 97–113.