ProWave Interpretation of Quantum Mechanics

Mon, 26 Jun 2006 13:15:50 -0700

Dan R. Provenzano, PhD student at Caltech in Applied Physics

Abstract: It is widely accepted in Quantum Mechanics that measurements reveal the particle nature of elementary quanta, but there are many interpretations on how these ``particles'' move from the emitter to the point of measurement. This paper introduces in the ProWave (for ``PropagatingWave'') Interpretation of Quantum Mechanics, The basic idea is that elementary quanta always exist in the form of a wave, and always travel in the form of a wave, described by Schrödinger evolution, but are alwaysmeasured each at a single location. This concept replaces all interpretations based on quanta traversing a particle path with the notion of a propagating wave coupled with a new concept of ``Quantum Energy Localization.'' It is argued in this paper that the ProWave Interpretation explains all known experimental results in a ``realistic'' way that would have pleased Einstein, Schrödinger, deBroglie and all those who are currently looking for a sensible way to understand the implications of Quantum Theory. As examples, the 2-slit experiment, and EPR experiment, and a quantum eraser are interpreted in the ProWave picture.

Introduction

Classroom education on Quantum Mechanics (QM) concerns the various quantum phenomena and how to deal with them mathematically. In the laboratory, we use QM as a tool to predict measurement statistics. The experiments are repeatable, and the results are not in dispute. But when it comes to the interpretation of the theory of QM, there is much discomfort in the community. Sure, quantum phenomena are so removed from our daily experiences, and in many aspects are so counter intuitive, that it might seem only natural that our interpretation of the theory and corresponding view of reality must reflect that. Furthermore, the Complimentarity Principle simply states that the elementary quanta are neither particles nor waves, but some entity that transcends both of their natures and only displays one of these attributes at a time. This principle is merely a statement of our conceptual difficulties with QM, but doesn't really attempt a solution.

A semiclassical interpretation was put forth by Schrödinger who suggested that the wavefunction for matter waves is analogous to the field variables in electromagnetic waves. This interpretation was rejected long ago due to its intrinsic ``nonlocality problems.'' However, the Bell Inequality [2] and its numerous experimental verifications have since dictated the need for a nonlocal interpretation of quantum theory. Thus, we can start with Schrödinger's original idea, and build on it to provide an understanding as to what happens during a measurement or ``collapse of the wavefunction.''

The ideas for the ProWave Interpretation resulted from desperately trying to make some sense out of the various experiments and connecting them with accepted quantum theory. We now think it is possible to (at least) conceive of how these bizarre quantum effects could come about in a sensible way.

The Experiments

To date, quantum theory has been overwhelmingly confirmed by physical experiments. The need for such a theory in the first place began as the experimental results of the early 1900's could not be explained by contemporary theories. For compactness, I will describe only the quantum interference effects of photons, but note that electrons and neutrons have been observed to display quantum interference as well. Below is a review of three interesting experiments, our understanding of which is controversial. These provide a good survey of the weirdness of QM. In Sections 5 and 7, the ProWave Interpretation is applied to these experiments.

A) The infamous two-slit experiment involves passing light through two slits and allowing the radiation from both slits to diffract and overlap on a distant screen. The interference fringes that are observed are attributed to the wavelike and coherent nature of the photons as they emerge from the slits. If the flux of photons is low enough such that one photon is present in the system at once, then each photon (event) produces only one localized detection at the screen. By integration of many such events, an interference pattern emerges, as predicted by the probability distribution of the wavefunction. Note that if the screen were placed sufficiently close to the slits so as to prevent overlap of diffracted waves from the slits, then each event induces local detection corresponding to the photon having been present at one of the two slits. In this case, the system probability is determined by an incoherent mixture of quantum states, where the quantum states refer to slit passage. The philosophical question raised by this whole experiment is: Does the photon pass through only one slit, or both, or can we even ask this question?

B) The Einstein, Podolsky, Rosen (EPR) Paradox [1] has been the subject of many discussions on quantum interpretations. In 1985, Alain Aspect et. al. measured the polarizations of two correlated photons at various rotation positions of his detectors [3, 4, 5]. Their coincidence count violated Bell's Inequality and experimentally verified that the nonlocal nature of quantum theory is real. The main question here is: How can two particles apparently ``instantaneously'' communicate with each other while being physically separated by an arbitrary distance?

C) In one type of quantum eraser experiment, polarization-correlated photon pairs are emitted in opposite directions [11]. (Refer to Figure 3 later in Section 6.) They are allowed to recombine and interfere at a 50% beam splitter, with detectors at each output port. The apparatus is set up and phase controlled such that both photons of each pair are detected by the same detector, as predicted by QM. Now, a half-wave plate is inserted in one of the paths so as to rotate the polarization by 90° with respect to the other path. This removes the guarantee of interference at the beam splitter, and it becomes possible to get one ``click'' at each detector from a pair of correlated photons. Building on this further, inserting linear polarizers at 45° (with respect to each photon path) directly in front of each detector returns the original interference results. It is amazing that we no longer see the effect of the half-wave plate. We have essentially erased its effect. The deepest question raised by this experiment seems to be: Can we affect the nature of the photons in the past by manipulating the present?

Current Interpretations

The myriad of interpretations of quantum theory are all attempts to explain the meaning of reality consistent with what we know about how the the quantum world behaves. All popular interpretations are consistent with quantum theory and experimental results, and acceptance of any given interpretation implies acceptance of certain consequences regarding objective reality. We will mention a few of the more popular ones, but others can be found in the references.

The Copenhagen Interpretation denies any deep physical reality. Since elementary quanta cannot have simultaneous values for non-communiting observables, reality itself cannot be defined until a measurement is made.
The Many Worlds Interpretation accepts the existence of an infinite number of universes (complete with physical energy like our own). Several new ones are created every time a quantum system is forced into one of its eigenstates after previously existing in a coherent superposition of any basis states.
The Many Histories Interpretation establishes that trajectories taken by elementary quanta are obtained by ``summing over the possible histories.'' For example, in the quantum erasure experiment, the linear polarizers have changed the set of possible histories of the photons' behaviors, thus affecting the possible outcomes of the experiment.
The Transactional Interpretation supports that the emission and absorption of energy quanta is an indivisible, fundamental event. The nature of these events, such as when and where, are determined a priori outside of time and before the transaction takes place. Note that under this interpretation, a photon absorbed by your skin from a star 1 million light years away was a predetermined event, 1 million years ago.
The Neorealist Interpretation maintains that the world is made up of ordinary objects as we are used to, but permits that some of these object move faster than the speed of light. Consequences of this interpretation include the possibility of reverse causality.
The No Collapse Interpretation maintains that the wavefunction describing a quantum system never collapses. We only observe and ``think'' that it has collapsed, while all the other non-measured states of the wavefunction are forever inaccessible. After the measurement, the continuing wavefunction no longer describes the probability of what can be measured. As an aside comment: the mathematics used in this interpretation begins with wavefunctions with several vector spaces involved, such as a measuring apparatus. Classical correlations emerge when one only studies the states of the apparatus. A major problem is that the mathematics needs to assume ``collapse'' theory to even begin writing down an initial wavefunction. Otherwise, each quanta has an incredibly complex past wavefunction whose components in each space are likely to posses orthogonalities, destroying quantum interference. In short, this interpretation contains initial conditions which seem inconsistent with its conclusions.

All of these interpretations require belief in realities beyond the scope of scientific experiment. This is the price paid for claiming that the formal theory of QM describes all physical processes. The ProWave Interpretation pushes quantum weirdness back into the realm of physics, and therefore does not force us to postulate and philosophize about inaccessible realities.

The ProWave Interpretation

ProWave makes no assumption of localization of the photons before measurement. In fact, it rejects the common notion of wave-particle duality. Recent teaching by laser physicist W.E. Lamb Jr. supports this line of thinking [13]. Maintaining any sort of particle nature of elementary quanta is what has led us into trouble, philosophically. Let's start with a list of the assumptions made in the ProWave Interpretation:

Elementary quanta of matter and energy exist as their wavelike behavior suggests (wave packets), always.
Their time evolution is described by the Schrödinger equation (or better yet, by the Heisenberg equation of motion for the density operator).
Energy transfer, in quantum amounts, takes place locally. Thus, when a photon is absorbed and measured, its energy is transferred at only one point in space (Basically, this is only a defining property of ``quantum'').

Assumption (2) deals with propagation, which is a nonlocal, wavelike phenomenon, and Assumption (3) deals with the creation and destruction of quanta, which is a local phenomenon. These assumptions eliminate the ambiguity of what the electrons and photons do while we don't measure them. They are quantum waves: Electrons orbiting atoms are standing waves of matter-energy, photons are wavepackets of electromagnetic energy, etc. Also, we accept that a photon passes through both slits if both are probable and it was not already absorbed by the wall. The same goes for electrons. In this way, we can reinstate physical reality which is dismantled in any wave-particle duality interpretation. The physical reality is simply that described by the wavefunctions and density matrices of a system, no matter how quantum entangled the states may be. It may be difficult to imagine the states in classical terms, but they are states nonetheless in which these very simple elementary quanta can exist. And they propagate according to the laws described by the mathematics of quantum mechanics.

As the quanta propagate and interact with the macroworld, two separate types of interactions occur. The first is defined as a partial interaction: This interaction reorganizes or redirects the wavefunction designated by a unitary transformation matrix. Examples of such are beamsplitters and magnetic fields. The other type of interaction is defined as a complete interaction: This is designated by the destruction (and creation) of a quantum of energy, for example a bound electron absorbing a photon.

Before applying ProWave to the experiments described earlier, here it's quickly shown that ProWave can add insight into how a cloud chamber can measure the particle-like nature of matter waves. As, say, an electron traverses its ``path'' in the cloud material, it is constantly being forced into localized positions by partial interactions with the material. Thus, the matter wave is being reorganized constantly and not really allowed to diffract much before collapsing repeatedly. The result is a clearly drawn path that was previously believed that only a particle could make.

The ultimate challenge for ProWave is to explain how a spread-out wave can collapse and deliver its energy locally upon absorption. It is helpful to envision wave evolution analogous to blowing up a balloon. Upon measurement, that balloon pops. The collapse (also pertains to reconfiguring the wave's energy) is probabilistic, like not knowing where a balloon will pop first. But once a measurement has been taken (or perhaps the quantum is destroyed) the wave collapses everywhere nonlocally and passes its energy to the absorber as one quanta. Likewise, when a balloon pops, the entire surface of the balloon is quickly affected by the loss of tension in the rubber, however time elapses before the surface collapses. This collapse (for the quantum) need not be instantaneous, but must be faster-than-light to insure that nonlocality still applies. The phenomena of energy absorption and reconfiguration (quantum state changes) are inherently quantum uncertain events and cannot be pinned to ``instantaneous''- only for practical purposes do we assume so. This is not a problem physically because the nature of this collapse is very poorly understood. In fact, I am suggesting the possibility of a more general theory that reduces to QM when the time of the collapse is considered small, in the same way that QM reduces to classical mechanics under certain conditions. This is typically the way physics advances; I don't see this potential for the other, far less intuitive, interpretations.

Explanation of the Experiments

ProWave offers new insights into the experiments involving quantum phenomena, and how nature can produce the results that it does. It is worthwhile to describe how the experimental results mentioned above can make sense given the ProWave view of reality. A deeper, more mathematical description of the experiments is found in the Appendix with ProWave providing a consistent, realistic explanation.

Figure 1: A typical 2 slit experiment showing probability distributions at different distances from the slits.

In the two slit experiment (Fig. 1), a photon enters the two slits as a single, expanding wave. At the wall, its instantaneous probability of impacting on the surface of the wall is quite high. In the event that it makes it through the slits, the wave at the walls disappears and all the energy is collected and passes through the slits. This is governed by the quantum mechanical probability of absorption of the wall. As the wave now interferes with itself upon passing through the slits and propagating some distance to allow overlap, the energy of the quantum is spread out according to its probability distribution function ( ). Absorption of the photon, now, is a local process governed again by probability. Once the probability distribution collapses, the ``balloon pops'' everywhere and the quanta of energy localizes at the point of transfer. This localization need not occur instantaneously, and it makes sense to conceive of it occurring on the timescale of energy absorption. As of today, this notion does not violate any laws of physics because there currently is no description of how a photon's probability distribution collapses upon absorption.

Figure 2: An experiment with EPR correlated particles.

I think the key to understanding any of the EPR correlations (Fig. 2) is to forego the idea that two distinct particles are emitted from some source in opposite directions. Quantum mechanics treats them as indistinguishable and as both being emitted in both directions, so let's treat them that way physically. The sources typically do not prefer a direction upon emission, making the correlated photons themselves spherical waves propagating, overlapping each other (one field). Any effect on one wave has a direct effect on the other wave as well. Thus, say, if a particle is measured at one location (a photon was absorbed locally), then its partner snaps into a state opposite the source and resumes propagation. Analogously, imagine two balloons expanding together with the same radius. If one balloon pops, that causes the other to reconfigure as well. The reconfiguring of the second photon could be conceived of to have occurred instantaneously, but the final act of localization for energy transfer need not be. Again, this is consistent with what is known from QM about spin, polarization, and momentum correlations.

The quantum erasure experiment (Fig. 3) described in Section III is nothing other than a ``directional interference'' effect. No future activities or consciousness effects are needed to explain this experiment. The correlated pair is emitted as two quanta overlapping each other. They interfere at the splitter and the effects are detected. When one path undergoes polarization rotation, we no longer observe the interference of the two paths. This is no surprise because one path has polarization x and one has polarization y, and these are orthogonal. However, both x and y polarizations have a component of polarization in the z direction. These z-components do interfere at the beam splitter and the effect can be observed by putting in a linear polarizer oriented in the z direction directly in front of each detector. Note that the z-polarizer effectively filters out the orthogonal interference which can cancel the z-component interference. In essence, all of these interference effects are present until the complete interaction. The type of interference that is manifested and becomes visible is a function of how the detectors are set up.

Figure 3: The quantum eraser experiment.

Summary

Photons, electrons, and all other elementary building blocks of our physical world represent simplicity in nature and existed long before complex structures like humans existed. Reality is quite real for all forms of matter, although admittedly, it is not always intuitive to rationalize the nature of this simplicity. What is meant by ``simplicity'' here is that just because we need strange quantum mechanical language to describe these systems, quantum mechanics can describe quite accurately their behavior, for example, ``spin up'' and ``spin down'' states. In contrast, in order to accurately describe a structure such as a group of several molecules is a hopelessly more complex calculation. Thus, the quantum world represents simplicity, not complexity.

Whether in the form of leptons or photons, individual quanta of energy are passive creatures and propagate as waves, interfering as expected. These effects are observed only by carefully controlling the ``directions'' (e.g. spin projection, and polarization) in which we choose to observe the waves. The mystery of quantum behavior occurs in the waves' ability to collapse into eigenstate upon absorption or possibly a partial interaction with other matter. There is no wave-particle duality. There are no point particles, only localized energy transfers. The ProWave Interpretation of quantum mechanics is the alternative to the myriad of unpalatable existing interpretations. The building blocks of matter and radiation exist in only one world, and they have only one history.

References

1: A. Einstein, B. Podolsky, and N. Rosen, Phys, 47, 777 (1935).
2: J. S. Bell, Physics (N.Y), 1, 195 (1965).
3: A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 47, 460 (1981).
4: A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982).
5: A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).
6: J. Horgan, Sci. Amer. July, 1992.
7: G. C. Ghirardi, A. Rimini, T. Weber, Lett. Nuovo Cimento, 27, 293 (1980).
8: D. Mermin, Am. J. Phys. 49, 940 (1981).
9: D. Mermin, Phys. Today, Apr. 1985.
10: J. Pykacz, Phys. Lett. A. 171, 141 (1992).
11: P.G. Kwiat, A.M. Steinberg, and R.Y. Chiao, Phys. Rev. A. 45, 7729 (1992).
12: N.J. Cerf and C. Adami, ``Quantum Information Theory of Entanglement,'' Phys. Comp. 96. (1996).
13: W.E. Lamb, Jr., Appl. Phys. B. 60, 77 (1995).