Introduction In this chapter we show how the quantized detector network (QDN) formalism describes the double-slit (DS) experiment. This is arguably the simplest experiment that demonstrates quantum affects such as wave–particle duality and quantum interference. It continues to be the focus of much debate and experiment (Mardari, 2005), because theoretical modeling of what is going on reflects current understanding of quantum physics and hence physical reality.We will apply QDN to two variants: the original DS experiment and the monitored DS experiment, where an attempt is made to determine the imagined path of the particle. The DS experiment is widely acknowledged by physicists to be of importance to the understanding of quantum mechanics (QM). So much so that in 2002, the single electron version, first performed by Merli, Missiroli, and Pozzi (Merli et al., 1976), was voted by readers of Physics World to be “the most beautiful experiment in physics” (Rosa, 2012). The DS experiment can be discussed in terms of three stages, shown in Figure 10.1. By the end of the preparation stage, Σ 0 , a monochromatic beam of light or particles has been prepared by a source P , such as a laser. The beam emerges from point O and then passes through an information void V 1 to the first stage, Σ 1 , which consists of a wall or barrier W . This wall has two openings denoted A and B that allow parts of the beam to pass through into another information void V 2 and onto the second and final stage Σ 2 , which consists of a detecting screen S . The screen S is in general some material that can absorb and record particle impacts. In reality, any screen will consist of a finite number of signal detectors, such as photosensitive molecules, but the typical QM modeling is done as if there were a continuum of sites on the screen, such as C , that could register particles.
Introduction In this chapter we show how the quantized detector network (QDN) formalism describes the double-slit (DS) experiment. This is arguably the simplest experiment that demonstrates quantum affects such as wave–particle duality and quantum interference. It continues to be the focus of much debate and experiment (Mardari, 2005), because theoretical modeling of what is going on reflects current understanding of quantum physics and hence physical reality.We will apply QDN to two variants: the original DS experiment and the monitored DS experiment, where an attempt is made to determine the imagined path of the particle. The DS experiment is widely acknowledged by physicists to be of importance to the understanding of quantum mechanics (QM). So much so that in 2002, the single electron version, first performed by Merli, Missiroli, and Pozzi (Merli et al., 1976), was voted by readers of Physics World to be “the most beautiful experiment in physics” (Rosa, 2012). The DS experiment can be discussed in terms of three stages, shown in Figure 10.1. By the end of the preparation stage, Σ 0 , a monochromatic beam of light or particles has been prepared by a source P , such as a laser. The beam emerges from point O and then passes through an information void V 1 to the first stage, Σ 1 , which consists of a wall or barrier W . This wall has two openings denoted A and B that allow parts of the beam to pass through into another information void V 2 and onto the second and final stage Σ 2 , which consists of a detecting screen S . The screen S is in general some material that can absorb and record particle impacts. In reality, any screen will consist of a finite number of signal detectors, such as photosensitive molecules, but the typical QM modeling is done as if there were a continuum of sites on the screen, such as C , that could register particles.
Quantum theory is a mathematical formalism that allows physicists to predict the probability of observing different outcomes in experiments on sub-atomic systems. It has been tested more rigorously than any theory in science, and has never been wrong. However, strictly speaking it does not “explain” the behavior of sub-atomic systems, since it does not propose a mechanism to account for it. It tells us that they will behave in certain ways, but not why . Thus, quantum mechanics is not a theory in the sense familiar to social scientists, namely a body of laws that explains some part of reality. The explanatory question is the subject of the interpretive debates that surround the theory, not of the theory per se. That said, the literature routinely refers to quantum mechanics as a theory, and I shall use the terms interchangeably below. A common way to introduce quantum theory is through some of the key experiments that have confirmed its predictions. In this chapter I describe three of the most well-known: the Two-Slit Experiment, the Bell Experiments, and the Delayed-Choice Experiment. While painting the same overall picture, each reveals distinct features of the quantum realm. While their interpretation is contested, here I will do my best to present just the theory's findings, saving interpretive questions for later. The Two-Slit Experiment This experiment actually had its origins long before the quantum revolution. One of the most controversial questions in classical physics was whether light was made of particles or waves. In keeping with his atomistic worldview, Newton favored the particle or “corpuscular” theory of light, which was the majority view among physicists through the eighteenth century. However, in 1801 Thomas Young performed an experiment that seemed to prove conclusively that the wave theory was correct. In his experiment, Young set up a light source behind an opaque screen with one small opening or slit, through which the light passed in a concentrated beam.
The particle- interference-experiments, with the photons and electrons have clearly shown that they are always detected as localized „particles‟; and the density of their detections exhibit a pattern similar to the interference of waves. This experimental-observation is now explained here, making the current, „probabilistic interpretation‟, a past history. The „particle ‟ is first mathematically characterized as an „impulse function ‟ in space; and then Fourier-transformed into the wave-number-domain, as a wide band of constituent-waves as shown in the fig. 1&2. The „particle ‟ is explained as an „event ‟ of constructive-superimposition of a wide band of „pre-quantum-waves‟. This „event ‟ occurs in space at regular distances; and at regular instances in time. We know that even the purest monochromatic laser source has a „line-width ‟ of a few Giga-Hertz, or at least a few kilo-Hertz. So in the particle-interference-experiments, they are these wide bands of waves which pass through both the slits, even in the case of single photon states, and interfere physically. This physical interference of the wide bands of pre-quantum-waves determines the position and time of emergence of the „particle‟. Thus, form the theoretical view-point, there are only the waves, and waves alone; and the „particle ‟ is a specific situation of constructive-superimposition of all the spectral-components of pre-quantum-waves; so there is no wave-particle-duality.
Young's double slit experiments representing the mystery of quantum mechanics have been descripted by wave theories. To study the mystery, the double slit experiments were extended to the cross-double slit experiments. A description should explain all the double slit and cross-double slit experiments consistently. To test the wave description, the two postulates are proposed, which state that before passing through the double slit and before landing on the detector, photons behave as particles, but not as waves. To test the two postulates, the comprehensive double slit/cross-double slit experiments are proposed and performed. By placing shields and/or blockers near the detector/screen, the comprehensive double slit/cross-double slit experiments show that the fringes are created independently and partially, which discloses the particle nature of photons in the double slit/crossdouble slit experiments and violates the wave descriptions. The comprehensive double slit/cross-double slit experiments provide the comprehensive phenomena for developing theoretical model to study the mystery of double slit, complementarity principle, wave-particle duality, and wave theory of light.
3.1 Interference of a Single Photon The kinds of study originally conducted by Thomas Young - in particular, the celebrated "double slit" experiment that we briefly examined in Chapter 1 (see Fig. 1) - provide a capacity to reveal far more than the wave nature of light, important as that is. True enough, the observed characteristic fringe pattern, when monochromatic light passes through two closely spaced slits onto a screen, appears to be simply explicable on the basis of waves from each slit undergoing constructive and destructive interference at different positions on the screen. Yet, astonishingly, these patterns of interference are still exhibited when individual photons of a low-intensity input beam reach the screen one at a time, showing that it cannot in fact be a matter of different photons having to interfere with each other. Indeed, Dirac enunciated the general principle that photons can never directly interact with each other. The double slit and other such experiments indicate that each photon interacts in a delocalized, wave-like manner with both slits at the same time. Successive experiments build interference patterns that conform to an exact mathematical distribution formula, but the position at which an individual photon is detected in any particular instance cannot be predicted; this is a quintessential illustration of quantum uncertainty. Using the path integral approach of quantum theory, the phenomenon is more accurately represented by introducing a summation over all possible routes between the source and the screen on which the pattern appears, signifying an entire "lifetime" for each photon involved in the experiment. This relates to the fact that the actual trajectory is unknown without an observation, and thus we only obtain the probabilities of the photon striking the screen at different positions and times; all trajectories (potentialities) must be considered in a superposition. Each route is considered equally probable, and the variation in phase produces quantum interference. The differences in phase of each trajectory, at varying positions on the screen, generates the fringe pattern. An intriguing variation on this experiment involves "marking" the photons so that the actual route of each photon to the screen is known. Remarkably, in such a case, the fringe patterns do not appear because quantum interference cannot occur. A consequence of the observation of the photon route is an effect that, in other quantum mechanical connections, is known as a collapse of the wavefunction. However, it is possible for the fringe patterns to reappear when information on the route of the photons is lost; this is known as a quantum eraser.
Motivation The aim of this book is to introduce, develop, and apply quantized detector networks (QDN), an information-based, observer-centric approach to quantum mechanics (QM). Six reasons motivating our development of QDN are the following. Avoidance of Metaphysical Speculation There is such a variety of unproven (and unprovable) speculation concerning the interpretation of QM that the subject of this book, QDN, may appear at first sight to be yet another in this growing branch of metaphysics. In fact, our motivation is precisely the opposite. QDN was intended from the outset to reduce the level of metaphysics in the application of QM. To achieve this, our strategy is to move the traditional focus of attention away from systems under observation (SUOs) and toward the observers of those SUOs. In QDN, wave functions represent not states of SUOs but states of apparatus. We shall call such states labstates , to distinguish them from states of SUOs (which do have a place in QDN). It is only labstates that observers can ever deal with directly. In this respect, QDN is an attempt at a more laboratory-based description of quantum physics than standard QM, focusing as much on how an experiment is done as on the results of that experiment. For example, instead of talking about the wave function of an electron, QDN talks about the labstate of the signal detectors that allow us to say anything about that electron in the first place. That is all, there is nothing deeper. Whether or not electrons actually “exist” is thereby relegated to an inessential metaphysical issue that we can choose to ignore. It is important to understand what QDN does not say as much as what it does say. QDN does not say that electrons do not “exist”. QDN merely asks for an empirical definition of “existence”. QM Is Much More Than a Calculational Device Many physicists hold the utilitarian view that the success of quantum theory in predicting experimental data is sufficient for their purposes, and that further inquiry is really the business of metaphysics and therefore outside the scope of science proper. We cannot say that this is entirely unreasonable. However, we take the view that QM represents such a radical departure from the principles of classical mechanics (CM) that this pragmatical view cannot be all there is to the subject.
Interferometers IntroductionThe discussion of modules and computerization in previous chapters gives us the means to consider empirically useful quantized detector networks (QDN).In this chapter we shall focus on a particular class of network known as interferometers.Interferometers play a crucial role in quantum mechanics (QM) because they demonstrate the "paradox" of wave-particle duality in a direct way.On the one hand, discrete signals are detected by the observer and those signals are usually interpreted as particles or quanta.On the other hand, the observed frequencies built up over many runs show effects interpreted as due to the interference of waves.In the previous chapter, we used computer algebra (CA) to discuss the Wollaston interferometer (WI), a relatively simple interferometer.We shall use the same approach in the following discussion of the Mach-Zehnder interferometer (MZI), apparatus that allows the observer to investigate optical transmission through various materials. The Mach-Zehnder InterferometerThe basic structure of an MZI is given in Figure 13.1.A source S of light sends a monochromatic, unpolarized beam 1 0 into one input channel of beam splitter B 1 .Output channel 1 1 is deflected by mirror M 1 onto a module labeled φ that contains some medium under investigation, such as a crystal or liquid.The net effect is to create a phase change in that deflected beam by an amount φ, and then that modified beam, 1 2 , is passed into beam splitter B 2 .The second output channel, 2 1 , from B 1 , meanwhile, is deflected by mirror M 2 into beam splitter B 2 .The two deflected beams, 1 2 and 2 2 , that pass into B 2 interfere and are finally monitored by detectors 1 3 and 2 3 .Our analysis of the MZI follows the CA approach used for the WI in the previous chapter.