©Fernando Caracena 2013
Is The Wave Function a Real Entity?
A recent article in Scientific American [2013 June, vol. 308, No. 6] entitled, "Quantum Weirdness? It's All In Your Mind, " got me started thinking about quantum weirdness and other such philosophical issues. This Scientific American article describes a new theory of quantum mechanics that suggests that the wave function is part of each scientist's belief system, which is supposed to explain away some of the weirdness associated with the behavior of the wave function: the wave function is not real, it represents a set of odds based on Bayesian probability analysis, which is valid only for the individual's own experience, thus that person's belief system.
Ever since Schrödinger came up with his wave equation describing the quantum mechanical motion of subatomic particles and other small-scale composites,physicists realized that the wave function had some properties that made it difficult to take it as something real. Specifically, during the process of measurement, the wave function collapses from a superposition of various quantum states, into the one having eigenvalues that correspond to the system's measurements that characterize its measured state. Other properties of quantum states of matter, such as the bonding of atoms to form molecules, was taken as evidence that the wave function should be taken seriously and not be considered a convenient calculational fiction.
I have explored idea that the electron's wave function may really be a composite of its own motion and a distortion of all the electronic states (or normal modes) of the space through which it moves. It is a merry chase that has led me through the physics of inflation in Big Bang cosmology, to warp-speed of Star Trek, and the subtle force of zero-point energy in the Casimir effect.
Bonding of atoms in molecules suggests that the wave function is a real object
The reality of the wave function (ψ) for orbital electrons in atoms is suggested by the nature of the chemical bond that forms molecules from atoms, which Linus Pauling studied. The electron basically occupies shaped distributions within the atom in a way as if its properties are smeared out over that space and locally weighted by the density of the distribution implied by the wave function (ψ*ψ). The electron as opposed to a photon is a type of particle [having half integer units of spin] that satisfies Fermi-Dirac statistics and conforms to the Pauli Exclusion Principle: no two electrons can occupy the exact state of motion at the same time. The photon [or any particle with an integer unit of spin] satisfies Bose-Einstein statistics, meaning that any number of such particles can occupy the same energy state. Lasers, for example, are made possible because photons satisfy Bose-Einstein statistics.
All Fermions of the same kind [such as electrons] and Bosons [such as photons] are basically identical particles. Unlike the difference between ordinary material objects of our experience, there is no distinction between any two electrons other than the quantum numbers that distinguish their states of motion. Fermi-Dirac statistics enforce the Pauli Exclusion Principle by specifying that Fermion wave functions are antisymmetric in the exchange of labels between any two otherwise identical particles. Bose-Einstein statistics are enforced by the principle that the wave function for otherwise identical bosons is symmetric in the exchange of any pair of particle labels.
The electron having one half unit of intrinsic angular momentum [½ħ], or spin, and a whole unit of electronic charge [-e] produces, by its spin, a magnet aligned in the direction of its spin axis, which is called a magnetic moment. This means that an electron can be oriented either parallel or anti-parallel to an external magnetic field. By flipping from one orientation to the other, the electron exchanges one unit of angular momentum with whatever particle is created in the process, a photon for example, which can carry away a whole unit of angular momentum [ħ]. Because of the spin degree of freedom of the electron, every electron state in the atom has two degrees of freedom in addition to all the other orbital constraints. That means that electron states fill atomic quantum states in pairs that have their spins oppositely oriented—they are entangled.
The chemical bond happens when two atoms come near each other and the outer orbital electrons flip their spins to become oppositely aligned. This results in their being able to occupy the same spatial orbit. Because the orbit is symmetrical to the exchange of particles, their common spatial orbit can bunch up between the two positive ion cores. The resulting particle sandwich, a proton [+e] to the left and another to the right [+e] of a negatively charged cloud of two electrons in the middle [-2e] is held together by electrostatic forces. In this case, a symmetry principle in the type of particle overrides the electrostatic force, and the electrostatic force responds to produce the bonding. What is this principle that enforces symmetry without adding or subtracting energy from a physical system? Is it the hand of God?
The big question is, if the wave functions of atoms are belief systems of scientists, how can they account for the real force of atomic bonding?
Some philosophers looking at quantum behavior have come to the opposite opinion about the reality of the wave function, see for example a past blog, Web notes on quantum mechanics 9 May 2013, which covered an article about Jill North's view about Quantum reality.
Wave-particle duality is demonstrated by the Double Slit Experiment.
One of my favorite lectures by Feynman is his analysis of how the Double Experiment demonstrates the wave-particle duality. I wrote something about this paradox in a previous blog, "Wavicles–quantum quanderies." Recently, Feynman's thought experiment has been carried out to show that the wave function is a property of each single electron as Feynman and others proposed. If the wave function for an electron traversing a double slit is not a real object, how can one account for the objectively observed interference pattern as a belief-based Baysian prediction?
Empty space is not nothing
Atoms and subatomic particles were found by following a line of reasoning called reductionism, which is defined in Wikipedia by the following statement: "Reductionism is a philosophical position which holds that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents.[1] This can be said of objects, phenomena, explanation, theories, and meanings.[2]" When atoms were discovered, physicist were following the ancient Greek atomists paradigm that everything in the world consists of atoms in the void. The problems with our ideas about the wave function may result from the philosophy of reductionism itself. Elementary particles are pictured as being very small, almost points, or at least, strings of zero thickness moving in a multidimensional space. Yet the wave function is an extended object that can fill portions of that space. However, suppose that a particle is not a simple component, but is a complex object that represents a disturbance of that space. Suppose that space is not emptiness but is actually an object that is not subject to reductionism, but rather can be understood only through a complex mathematical analysis because it is actually filled with activity.
Evidence for space as being a real entity comes from the existence of a force produced between polished metal plates that are held parallel to each other at a very small distance apart, which is called the Casimir force. At a distance of about 100 atomic diameters, the Casimir force amounts to about the pressure of one atmosphere. The explanation for the Casimir force involves the notion that empty space is really filled with an enormous amount of energy in a form called zero point energy. Some physicist think that this energy is the dark energy that is accelerating the observed expansion of the universe.
Elementary particles are quanta of various types of fields that occupy space. Each normal mode of vibration of a particle field is a harmonic oscillator that can be excited in units of energy corresponding one quantum (ħω) and having lowest states of energy of a half quantum (½ħω) that on the average is locked in and cannot be given up. When all matter is removed from a given volume of space, the vacuum that remains is filled with a gas-like cloud of zero-point energy in the form of these half quanta, which are called virtual particles. A very small charged object such as a charged particle induces a redistribution of charge in the field of virtual particles through a process called vacuum polarization, which acts to reduce the electric field at very small distances and redistribute the charge over a larger volume. There is even an analogy to Brownian motion in a gas or liquid, which was taken as evidence for the existence of otherwise invisible gas molecules. The solution for velocity components of relativistic electrons described by the Dirac equation exhibit a jittering motion called Zitterbewegung, which results from the interference of positive and negative energy states of the particle through virtual processes. The picture that we have of an electron is something that does not exist in isolation, but rather it acts as a center in interaction with a cloud of virtual processes in the physical vacuum.
The explanation for the Casimir forces is that two electrically conducting plates standing side by side in a vacuum modify the spectrum of virtual field quanta in such a way that the zero-point energy density between the plates is reduced over what exists outsides the enclosed space of the plates in the outward directions toward the rest of the universe. The plates constrain the electromagnetic field between them to oscillate in a denumerable set of modes which have wavelength components in the direction perpendicular to the plates of integer sub divisions of the separation between the plates, L,
λn=L/n, (1a)
whereas in the space outside the plates the range of wavelengths is almost continuous or at least a denser denumerable set given the much larger volume of the rest of the universe.
Two flat, uncharged, metal plates held suspended a small distance apart attract each other with a force that rapidly increases inversely as their distance of separation because of the distortion that they produce on the physical vacuum, which results in the redistribution of zero-point energy. Warping of space is thought by some scientists as a means of achieving faster than light travel. NASA scientists are seriously considering a warp-drive similar to that of the Star Trek video series to gain faster-than-light travel.
Warp Idea based on Einstein's General Relativity Theory
Miguel Alcubierre published a peer reviewed paper [Class. Quantum Grav. 11 -5, L73-L77 (1994), arXiv:gr-qc/0009013 5 Sep 2000] entitled "The warp drive: hyper-fast travel within general relativity." I do not know how long the link will remain open, but you can find an electronic copy of the paper here.
Space is a unique type of substance then, which can be modified by physical processes, but has no mass nor absolute position. The theory of the Big Bang (based on relativity), for example, features a faster-than-light expansion rate of space which began 10−36 seconds after the creation of the universe, a process called inflation. There is also a horizon in our universe imposed by Hubble expansion, the rate of which is a function of distance. At the distance of this horizon, the universe beyond is expanding away from us faster than light, so that we cannot see it. Alcubierre' s calculations show that just as inflation and Casimir-force distrotions of space are possible, so it is possible to compress space in front of a space ship and expand it behind in such a way that the ship's position slips forward faster than light from on star to the other. Voila, we have achieved warp speed!
The above kind of thinking has been made possible from the vast scales of distances spanned by physical theory and by the uniformity of application that those theories are supposed to have. If you can have inflation of space, you can have compression of it. If inflation of space separates material objects, compression of it unites them.
Back to the Wave Function
Could it be that the wave function of quantum mechanics is associated with a distortion of the zero-point energy of the vacuum?
The question then is "Does the wave function belong to an electron, to space itself, or to both?" A problem exists in assigning the wave function to the electron alone, because all electrons are identical. Because of this, the wave function of an electron in a particular experiment is also part of the wave function of all electrons in the universe. In the double slit experiment, for example, electrons make up the substance of the slits and they participate in the cosmic dance of all electrons, which causes them to defy labeling.
The two slit experiment revisited
In case you have not read about this phenomenon, or need to refresh you memory, go here.
In the double slit experiment, The environment for the electron's motion is set up well before an electron is sent through it. An electron gun is aimed at a metal baffle that has two narrow parallel slits in it. Then this whole apparatus under glass is evacuated, so that electrons can travel through a good laboratory vacuum. Finally, the experiment is repeated many times by sending an electron as identically prepared as possible through the apparatus, one at a time and spaced in time sufficiently so that there is only one electron moving through the apparatus at a time. What remains the same from one electron's travel to the next is the double slit environment, which consists of an arrangement of atoms that have attached orbiting electrons.
Suppose that the arrangement of matter in the double slit distorts the arrangement of the normal mode structure of electron particle states in the surrounding space. This distortion is subtle because it is wave-length dependant and it is also spatial. The results are intricate and vast in number. The overlap of all such undulatory changes probably result in no net change in the appearance of that space, except for particular normal modes of vibration that are selected out by electron particle states. In this case, an electron fired at the double slit has only certain spatial paths of propagation opened to it that have been created by the distortion of the electronic normal mode structure of that space. In this case, the wave function represents a set of allowable and forbidden motions given the electron with specified quantum numbers by the distortion of the entire normal mode structure of the electron states produced by the distribution of matter in the structure of the double slit.
Upon detection on the other side of the double-slit the electron is detected by going into a new state which registers as a flash (an event specified by position and time), the space-time structure of the vacuum having not been altered by the subtle distortion of electronic states.