The Quantum Jump

One of the more vexing features of the quantum theory is the quantum jump or quantum leap. The term refers to a discontinuity in the evolution of an aleatric field or a ghostwave. Such discontinuities occur when a particle or system of particles interacts with another particle or system of particles, thereby causing what physicists call the collapse of the wavefunction.

It began in 1913 with Niels Bohr’s theory of atomic structure. Using what little information was available at the time, Bohr conceived the atom as a tiny, massive nucleus with light electrons revolving about it as the planets of our solar system revolve about the sun. In that model each electron follows an orbit in which it possesses an integer multiple of Dirac’s constant (aitch-bar, equal to Planck’s constant divided by two pi) in angular momentum.

Each electron also possesses a certain quantity of orbital energy and that energy, of course, obeys the conservation law. If an electron jumps from one orbit to one in which it carries less energy, the extra energy will be manifested in a photon in accordance with Max Planck’s 1900 theory of blackbody radiation (showing the emissive aspect of the photon) and Albert Einstein’s 1905 theory of the photoelectric effect (showing the absorptive aspect of the photon). Bohr calculated the wavelengths of the photons that would be emitted by an electron skipping down all of the allowed orbits in a hydrogen atom and thereby deduced a description of the Balmer series, a series of bright lines that appear in the spectrum of hydrogen.

In 1926 quantum jumps became a problem. Erwin Schrödinger had just published his wave-mechanical version of the quantum theory, a version based on the use of smooth, continuous mathematical functions to represent quantum entities and events. The centerpiece of the theory is the state function, which represents a particle’s aleatric field plus ghostwave and enables researchers to calculate probabilities associated with the realization of the particle’s contingent properties. But the probability fields that the state function represents don’t evolve smoothly and continuously; they jump whenever the particle carrying them interacts with something.

Consider a simple particle moving through empty space. Its ghostwave, encoding the particle’s contingent properties, consists of a set of plane waves whose mutual interference envelopes the particle in a wave packet. If the particle collides with another particle, it will rebound in a completely unpredictable direction, its probability field must change instantly to reflect the new direction and quantity of motion, and the state function will contain a discontinuity describing the change. Here we see how the quantum jump brings the requirements of the quantum theory into conflict with the requirements of Relativity: an instantaneous change in a wide-spread entity (the probability field) necessitates that something move much faster than light, which Relativity does not allow.

In a forcefield, such as an electric field, any sudden change in a source particle’s location or motion causes the particle to emit a wave that propagates outward away from the particle’s location at the instant that the change occurred. As that wave crosses any given point it transforms the field from its old form to the new form required by the particle’s changed circumstances. If the field is forcing a second particle to change its motion, there will be a discrepancy between what the old field imposes upon the particle and what the new field would have imposed if the forcefield had changed instantaneously: the wave imposes upon the particle an impact that makes up the discrepancy.

Probability fields don’t work that way. If a particle suffers a collision and a wave of change propagates outward away from the collision point, the particle still has a minuscule but nonetheless nonzero probability of existing beyond that wave and of suffering a second collision the realizes it a second time in accordance with its original ghostwave. But that can’t happen: the conservation laws guarantee that a particle cannot exist at two different places at the same instant.

It’s clear that once the particle properties have been stripped out of the ghostwave by the first collision there can be no second collision. So how are we to understand an empty ghostwave?

We understand it in the same way in which we understand virtual particles – as an element of the quantum vacuum. Just as a vapor of ghost particles fills all of space, so too does an infinite set of empty ghostwaves, probability-carrying waves propagating in all possible directions. And just as a virtual particle can be realized into a real particle by the addition of energy, spin, electric charge, and other particle properties, so too an empty ghostwave can be realized into an actual probability wave by a particle jumping onto it, usually by way of a collision with another particle.

In this model every ghostwave evolves in accordance with Schrödinger’s Equation (or its relativistic analogues). But we only concern ourselves with the ghostwave between the instant when a particle jumps onto it and the instant when the particle jumps off, thereby creating the illusion of a discontinuity. In concept our model resembles a description of a commuter jumping off one bus and jumping onto another: the buses exist and follow their set routes before and after the commuter rides them, but we only want to know where and when the commuter transfers between buses.

I don’t mean for that description to imply that making the ghostwave a permanent part of the quantum vacuum injects any determinism into the quantum theory. The location of the particle on its ghostwave is still perfectly indeterminate until the particle interacts with another particle. But we have eliminated the concept "collapse of the wavefunction" and replaced it with "transfer between wavefunctions". Thus we retain the analogy between quantum waves and forcefields, but eliminate the problems implied in that analogy.

Finally, I’ll lay out one more analogy. In the quantum theory we now have an infinite set of ghostwaves completely filling the quantum vacuum. In Relativity we conceive spacetime as consisting of an infinite set of inertial frames of reference. Given that we can make a one-to-one matching between those two sets, uniquely matching each ghostwave with the inertial frame that moves at precisely the same speed in precisely the same direction, can we assert an identity? If so, then we seem to have at least part of the key to reconciling the quantum theory with General Relativity. But that is a subject for later exploration.

So now we understand the quantum jump as a necessary means of turning a smoothly-evolving, continuous indeterminate state into a discontinuous, deterministic state necessary to connect the quantum-mechanical foundation of Reality to the classical realm of our perceptions. Thus a part of the cosmic sea rises up and becomes the ship that sails upon it.

eabf