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.

According 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.

Calculational scheme for electromagnetism

Figure 3.12.1 Cal­cu­la­tional scheme of clas­sical elec­tro­mag­netic theory

Calculational scheme for the quantum theory

Figure 3.12.2 Cal­cu­la­tional scheme of the quantum theory

Using 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.