September 11, 2020
Introduction to some Interpretations of Quantum Mechanics
There are various interpretations of Quantum Mechanics (QM) because it is not something that is intuitive. The rules seem to be in conflict with common sense. We know how to make calculations on the behavior of physical systems using QM, but we have been unable to agree on what is happening “really”. First, to introduce this subject, we need to describe a little of how quantum mechanics works. In quantum mechanics, all objects have wave-like properties (ie. de Broglie waves). For instance, in Young’s double-slit experiment, electrons can be used in the place of light waves. Each electron’s wave-function goes through both slits, and hence has two separate split-beams that contribute to the intensity pattern on a screen. According to standard wave theory, these two contributions give rise to an intensity pattern of bright bands due to constructive interference, interlaced with dark bands due to destructive interference, on a downstream screen. This ability to interfere and diffract is related to coherence (classical or quantum) of the waves produced at both slits. See Appendix A below for an explanation of coherence. The association of an electron with a wave is unique to quantum theory.
The Copenhagen Interpretation of Quantum Mechanics
One of the first interpretations to be developed is the Copenhagen Interpretation. The Copenhagen interpretation is an expression of the meaning of quantum mechanics that was largely devised from 1925 to 1927 by Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, and remains one of the most commonly taught. The following is brief explanation of it, but you can read about it in more detail here. (https://en.wikipedia.org/wiki/Copenhagen_interpretation).
What we call particles in the Copenhagen interpretation are described as “wave functions” with the Schrodinger equation. This interpretation says that when we are not looking at a particle, it is a wave, but when we look at it (ie. measure it), the wave function collapses and it becomes a particle. The location of a measurement cannot be predicted absolutely but only with a certain probability that the Schrodinger equation calculates. That is why the wave described by the equation is called a probability wave in this interpretation.
Over the years, there have been many objections to aspects of the Copenhagen interpretation, including: discontinuous jumps when there is an observation, the probabilistic element introduced upon observation, the subjectiveness of requiring an observer, the difficulty of defining a measuring device, and the necessity of invoking classical physics to describe the “laboratory” in which the results are measured.
The de Broglie–Bohm theory
The de Broglie–Bohm theory, also known as the pilot wave theory, Bohmian mechanics, Bohm’s interpretation, and the causal interpretation, is an interpretation of quantum mechanics. In addition to a wavefunction on the space of all possible configurations, it also postulates an actual configuration that exists even when unobserved. The evolution over time of the configuration (that is, the positions of all particles or the configuration of all fields) is defined by a guiding equation that is the nonlocal part of the wave function. The evolution of the wave function over time is given by the Schrödinger equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992). A more complete description of this theory is given in Wikipedia (https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory).
The “Many Worlds” Interpretation of Quantum Mechanics
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wavefunction collapse. This implies that all possible outcomes of quantum measurements are physically realized in some “world” or universe. In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic. Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957. Bryce DeWitt popularized the formulation and named it many-worlds in the 1960s and 1970s.
In many-worlds, the subjective appearance of wave function collapse is explained by the mechanism of quantum decoherence. Decoherence approaches to interpreting quantum theory have been widely explored and developed since the 1970s, and have become quite popular. MWI is now considered a mainstream interpretation along with the other decoherence interpretations, collapse theories, (including the Copenhagen interpretation), and hidden variable theories such as Bohmian mechanics.
The many-worlds interpretation states that there are very many universes, perhaps infinitely many. It is one of many multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realized. This implies that there are many more Universes than there are particles in our Universe. This is intended to resolve some paradoxes of quantum theory, such as the EPR paradox (spooky action at a distance) and Schrödinger’s cat, since every possible outcome of a quantum event exists in its own universe. Read about the many worlds interpretation here. (https://en.wikipedia.org/wiki/Many-worlds_interpretation).
There are at least 19 other interpretations of quantum mechanics. This article is not a review of all of them. Just some of the most important theories are given just to give you an idea the developments that have been made. You can read about them in Wikipedia here (https://en.wikipedia.org/wiki/Category:Interpretations_of_quantum_mechanics).
The Karpinsky Interpretation
The Karpinsky Interpretation of Quantum Mechanics is a work in progress. But this is a summary of how it works (so far). This interpretation says that the space in the universe is filled with waves, and nothing but waves. Space is created by the fields that it contains, which are electromagnetic, Higgs, Strong force, and Weak force waves. The formulations of Quantum Mechanics, and General Relativity are taken as a given. What they mean Philosophically might be different, but the behaviors of the particles and waves the equations describe are taken to be correct (unless otherwise stated later). Empty space is filled with these four types of waves. They form a background in which more energetic particle waves interact. This background is sometimes called the quantum foam. It is not zero energy, but if there are no particles, the energy is, on average, less than enough energy to form a particle. The quantum foam is very noisy in a manner similar to electronic noise in a circuit. It is an ocean of waves that is not directly observable. These waves travel in space-time in all directions and with all possible wavelengths. Thus, they are always interfering with each other in (as far as we know) a random manner. So, I will model this as random noise in all space at all times.
Each type of wave has its own amplitude and characteristics. They don’t need to be the same unless they are the same type of wave. I will start analyzing the matter waves of the Higgs field, because this is what ordinary matter is made of.
All the energy that creates matter came from the Big Bang. That energy never goes away due to the conservation of energy. It can, however, be transformed into matter, and many other types of particles following the laws of Physics. If we follow an electron in space, it is a coherent matter wave. But it is embedded in the quantum foam. It will look something like this.
This is one cycle of an electron wave. In actuality, it is three dimensional, but is shown here in two dimensions. It has two coherent peaks because the probability amplitude of the wave function is squared so there is no negative probability. This is modeled as Gaussian noise from the background added to the coherent electron wave. When this wave approaches another particle, the highest noise peaks will interact with the particle first, and an interaction will occur. An interaction with another particle is more likely at the noisy peaks. This noise causes the uncertainty in the location of the interaction. This is what some interpretations of QM call wave function collapse. It does not make sense to call it that. All it is, is an interaction of one particle with another that is well described by QM. The mystery that they are trying to solve is: Why is the location random, but with a probability distribution that matches the wave function described by the Schrodinger equation? The noisy background of the quantum foam explains that.
For an interaction of an electron and an atom, both particles have the noise added to their coherent wave. The atom should look something like a fuzzy ball to the electron. So we have peaks of the matter wave reaching out, at random in all directions from both particles. When these peaks meet, an interaction occurs. Let’s assume that the atom has a vacancy in an electron shell and the electron is drawn into that shell. In my interpretation, from that peak caused by noise, the energy of the electron wave is captured, and even though the electron wave is somewhat delocalized, the whole electron is captured. The electron in free space is a coherent wave, and thus entangled with itself. This kind of entanglement, causes the “spooky action at a distance” that has perplexed everyone including Einstein. All of the energy of the electron wave is now part of the atom’s wave function. This is called a measurement if we are looking at it. If we are not looking at it, it happens anyway. The interacting particles do not care if we are looking at them or not.
The Karpinsky Interpretation does not have questionable postulates such as locality, which has been disproven by Bell’s inequality, and many worlds that are included in many of the other interpretations. This interpretation says that the space in the universe is filled with waves, and nothing but waves. What we call particles are formed in regions of space where the energy is large enough too manifest a particle. When a particle is formed, it has mass, charge, or spin depending on the type of particle. The Schrodinger equation describes this particle and is used to calculate its actions, and has been demonstrated to be correct to an incredible accuracy. It has been proven that matter is made of waves, and QM uses that fact to do the calculations. But, the Karpinsky interpretation does not call the waves “probability waves”. They are “matter waves”. The probability comes from the random noise of the quantum foam.
Here is an example of how this works to produce virtual particles. Let’s start with an electron in free space. It is an electron wave. It has an energy of 0.511 Mev/c² . The energy of space without an electron is less than that. The energy needs to exceed or equal this energy before an electron can exist. The waves below that threshold are not observable. These sub threshold waves have no mass, no charge, and no spin. But once the energy exceeds that threshold, the electron has all of those qualities. It is a kind of phase transition. We describe the electron particle with mass, charge, and spin, but it is still really an electron wave. But the empty space has sub threshold matter waves. These matter waves are flowing in all directions at all possible frequencies and interfering with each other resulting in a very noisy environment. Because these waves are random, occasionally the amplitude of the wave will exceed a threshold of two times 0.511 Mev/c² (the energy of an electron and positron) to produce an electron-positron pair. These pairs have real physical effects that can be measured, so we know this happens often. The space-time density of these virtual particles should provide a measure of the amplitude of the noise in the vacuum. But, I don’t know this density. The pair then annihilate each other and sink back into the sub-threshold waves.
This explanation does not contradict any of the findings of QM. But it does remove the need for radical explanations such as the infinite number of Universes and many other explanations. I am not claiming that there could not be some problems with this explanation, but I am sure that it is testable to find out if it is true. The statistics of experiments should be able to test it. I do not know what the statistics for this are. It could be Gaussian or Bayesian.
The figure above is for Gaussian statistics, but that is not necessarily the correct statistics. Regardless of the statistics, the point is that the uncertainty is not due to the wave function itself, but the noisy matter wave environment. We do not even know the spectrum of this noise because it is not directly observable. Is it white noise or 1/f noise both of which are common in electronics? But Gaussian noise is a good approximation for low frequencies. Using that, we can see if the results of QM calculations match the calculations that result from this change in the model. I am not going to try to do that in this article. This is just the start of exploring what this means.
Wave Function Collapse
Here we examine different theories and compare them to the Karpinsky Interpretation. Objective-collapse theories, also known as models of spontaneous wave function collapse or dynamical reduction models, were formulated as a response to the measurement problem in quantum mechanics, to explain why and how quantum measurements always give definite outcomes, not a superposition of them as it seems to be predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate.
In the Karpinsky Interpretation of QM, wave function collapse does not happen. Instead, the electron’s wave function as a free particle is transformed into a wave function of the electron interacting with an atom and ultimately in the electron shell of the atom. There is no reason to call that a collapse. It is an interaction with another particle that can be well described in QM. In the Karpinsky interpretation, all physical systems are always quantum mechanical. The simple absorption of an electron wave with an atom wave is fully described, and there is no loss of validity with complexity.
In collapse theories, the Schrödinger equation is supplemented with additional nonlinear and stochastic terms (spontaneous collapses) which localize the wave function in space. With the Karpinsky interpretation all these mathematical gymnastics are unnecessary.
Collapse models attempt to provide a unified description of microscopic and macroscopic systems, avoiding the conceptual problems associated to measurements in quantum theory. Because the Karpinsky Interpretation does not have those conceptual problems, this collapse is not needed.
When one of two entangled electrons, for example, is measured to determine the spin of the electron. The other electron’s spin is then known to be opposite the measured electron, because two entangled electrons always have opposite spin. This measurement is said to collapse the wave function. The method of measurement may involve combining the electron with another particle, maybe an atom, or some other measurement method that does not involve combination with an atom. No matter how the measurement is done, the electron still exists. There is no such thing as wave function collapse. The electron is now in a different state, but it still has a wave function. It just has a joint wave function with the nucleus of the atom in the above example. A particle always has a wave function, even if it is in a different state.
In addition, the measurement process involves an interaction between the particle’s wave function and another particle’s wave function. Actually, it is not necessary to ascribe the wave functions with alter-egos of particles, but it is reasonable because they have undergone a phase transition. It is just two wave functions interacting and putting the system in an altered state. Each wave function is a coherent wave with a noisy quantum foam resulting in the quantum uncertainties.
There are a number of experimental approaches suggested by this paper to test some elements of this interpretation. One is to measure of somehow determine to density in space-time of the appearance of virtual electron-positron pairs. That may already be known, but I don’t know it. It must be very rare because most of the literature refers to producing them with high energy photons at or near a nucleus. But if we know the density of production in free space, we can use statistics to calculate the quantum noise of free space.
We also need to investigate how entanglement works. As mentioned above, a radio wave is made of coherent photons. They are entangled because they are coherent, so laboratory experiments should be able to be devised to test the spooky action at a distance that entanglement enables. We may find that it is much simpler than we thought. If we can understand how entanglement works in more detail, we may be able to explain how widely separated entangled particles are linked.
On the theoretical front, we can simulate this picture of the noisy wave function to see if it matches the results of standard QM calculations. The hypothesis is that it will, but that needs to be verified.
Appendix A, Coherence
In physics, two wave sources are perfectly coherent if their frequency and waveform are identical and their phase difference is constant. Coherence is an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets.
Interference is the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves (see Young’s slits experiment). Constructive or destructive interferences are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of lesser amplitude than either one (destructive interference), depending on their relative phase. Two waves are said to be coherent if they have a constant relative phase. The amount of coherence can readily be measured by the interference visibility, which looks at the size of the interference fringes relative to the input waves (as the phase offset is varied); a precise mathematical definition of the degree of coherence is given by means of correlation functions.
Spatial coherence describes the correlation (or predictable relationship) between waves at different points in space, either lateral or longitudinal. Temporal coherence describes the correlation between waves observed at different moments in time. Both are observed in the Michelson–Morley experiment and Young’s interference experiment. Once the fringes are obtained in the Michelson interferometer, when one of the mirrors is moved away gradually, the time for the beam to travel increases and the fringes become dull and finally disappear, showing the loss of temporal coherence. Similarly, if in a double-slit experiment, the space between the two slits is increased, the coherence dies gradually and finally the fringes disappear, showing the loss of spatial coherence. In both cases, the fringe amplitude slowly disappears, as the path difference increases past the coherence length. But when the waves are still coherent, they are entangled, and spooky action at a distance can occur in an interaction. The classical electromagnetic field exhibits macroscopic quantum coherence. The most obvious example is the carrier signal for radio and TV. They satisfy Glauber’s quantum description of coherence. In this case, the wavelength of the radio wave (photon) is typically much longer than the receiving antenna, but in spite of that, whole photons are collected from the air. This is spooky action at a distance as well. But no one seems to be concerned about that. It occurs to me that this should provide an easy way to do experiments on quantum entanglement.
Recently M. B. Plenio and co-workers constructed an operational formulation of quantum coherence as a resource theory. They introduced coherence monotones analogous to the entanglement monotones. Quantum coherence has been shown to be equivalent to quantum entanglement in the sense that coherence can be faithfully described as entanglement, and conversely that each entanglement measure corresponds to a coherence measure.