Synchronicity by Paul Halpern

Author:Paul Halpern [Paul Halpern, PHD]
Language: eng
Format: epub
Publisher: Basic Books
Published: 2020-08-18T00:00:00+00:00

Matter Waves

About half a year after Heisenberg advanced his idea of using matrices to model the probabilities of various types of discrete quantum jumps, the Austrian physicist Erwin Schrödinger independently developed an alternative called “wave mechanics” that was meant to offer a more tangible explanation of the workings of the atom. Drawing from an idea proposed by the French physicist Louis de Broglie, Schrödinger postulated that electrons are “matter waves” that obey a dynamical equation of motion—similar in spirit to Maxwell’s description of light as electromagnetic waves. These quantum wave solutions, conceived as distributions of the mass and charge of an electron throughout a region of space, would become known as “wave functions.” Wave functions evolve in a predictable, deterministic way according to Schrödinger’s equation.

Soon thereafter, however, Born demonstrated that Schrödinger’s wave functions well matched the quantum states described by Heisenberg if one equates them with probability waves, rather than matter waves. Instead of delineating an actual spread of matter, Born posited that they mapped out the chances that an electron would be located in a particular region of space. Following the notion that probability is proportional to amplitude squared, one must square the value of the wave function to get the probability distribution.

To find the exact location or speed of the electron, one must take a measurement of either one or the other. Similar to matrix mechanics, each type of measurement would be associated with a unique operator—which in this case would be a combination of mathematical operators that act on the wave function. Depending on that choice, the electron’s wave function would instantly “collapse” into one of a particular spectrum of solutions of Schrödinger’s equation connected with either position or momentum values, respectively—but never both at the same time.

Wave function collapse is akin to a bakery that prepares fresh loaves of bread from a homemade dough. Throughout the baking process, the ingredients and methods are so standard, no choices are made. Therefore, assuming no mistakes, it is perfectly deterministic. After the bread is ready, customers are given the choice of short slices or long slices. A slicing machine can be set up in one of two perpendicular ways: across the thin side of the bread or along its length. If the customer chooses “short,” the slicer divides the entire loaf widthwise and randomly ejects one of the short slices. Similarly, it can pare out long slices, but never both short and long at the same time.

By analogy, the “slicer” of quantum measurement carves out a spectrum of Schrödinger’s equation solutions, called eigenfunctions, based on the type of measurement being performed (position, velocity, and so forth). These are the equivalent to the eigenstates in the matrix mechanics approach. Each eigenfunction is associated with a certain eigenvalue, or measurement result. As soon as an experimenter takes a certain measurement, the wave function collapses randomly into a particular eigenfunction connected with a specific outcome. For a position measurement, for instance, it would collapse into position eigenfunction, associated with a certain position value.

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