Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment will explain the alternative states of the particle discerned in self interference, while the maintenance of equilibrium in the face of such fluctuations becomes the source of the Born probabilities. In this scheme, the probability wave is a mathematical artifact, epistemic rather than ontic, and akin in this respect to the simplifying constructions of geometrical optics.
Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment will explain the alternative states of the particle discerned in self interference, while the maintenance of equilibrium in the face of such fluctuations becomes the source of the Born probabilities. In this scheme, the probability wave is a mathematical artifact, epistemic rather than ontic, and akin in this respect to the simplifying constructions of geometrical optics.
Classically, probability is considered in terms of the number of possible outcomes. For example, a die toss has six possible outcomes and a coin toss, two. Probability calculations make use of probabilities and hence of the total number of possible outcomes. Thus, they are not deterministic calculations which follow “what happens” as in Newtonian mechanics. We suggest that if free particle quantum mechanics is probabilistic, it must also involve the notion of possible outcomes in an experiment and not represent a deterministic approach. We suggest, however, that something interesting applies to quantum mechanics because we have suggested that free particle quantum mechanics arises from the Lorentz invariant A = -Et+px. We note that there exist x,t trajectory points which follow x=vt. We also note, however, that one may introduce the idea of intervals dx, dt (because Newton’s dx→0, dt→0 is an idealization) and that A is unchanged for x,t and x+hbar/p , t+hbar/E. In other words, we suggest that there are intervals with probability about each x,t trajectory point. A trajectory point is associated with deterministic physics, but probability about this point is not. In other words, one has a kind of hybrid probability scheme. Thus, exp(ipx) and exp(-iEt) really represent fluctuation probabilities about a trajectory point x and t. These ranges of possible x and t fluctuations about a trajectory point x,t allow for further probability to occur in certain interactions. We consider two examples. The first is 2-slit interference which involves a deterministic particle moving along a straight line towards a 2-slit mechanism perpendicular to its path. At the 2-slit apparatus, one considers a probabilistic calculation as the uncertainty in x, i.e. dx=hbar/p allows for possible interaction with both slits. This involves considering all possible outcomes (i.e. motion through one slit or the other which is a classical situation), but exp(i p dot r1) and exp(i p dot r2) “sit on top” of these trajectories at the 2-slit apparatus and one has interference of the probabilities linked with each classical possible outcome. Thus, there are two sets of probabilities which are intertwined, the probability range hbar/p for each path and the two possible paths which have equal probability. One must consider the possible outcomes for both sets together. We suggest that a similar analysis applies to the case of 1-D reflection-refraction for x=0 at an n1-n2 index of refraction junction. Thus, we suggest that a deterministic free particle with x=vt may encounter probabilistic interaction situations, such as a two-slit apparatus or an n1-n2 index of refraction junction. These are probabilistic only because there is a probability fluctuation scheme in x associated with each deterministic x point. It is this probability which allows for a second probability to arise due to interaction with the slits or at the 1-D n1-n2 junction. In such a case, one must consider all possible outcomes which means that one does not only consider the exp(ipx) type probabilities, but also those linked with the physical interaction, i.e. two possible paths, one from each slit, or an incident, reflected and refracted photon at x=0 (n1-n2 junction). It is a combination of all possible paths which must be used in calculations. We thus suggest that even though there is a sense of determinism, i..e free particles move as x=vt and these exist in the 2-slit case and the 1-D reflection-refraction case, in a probabilistic calculation one must consider all probabilistic outcomes consistent with these. Thus, quantum mechanical calculations are true probabilistic calculations in the sense that they involve all possible outcomes in an analysis.
This chapter introduces quantum mechanics through the experimental discoveries that revealed the limits of classical physics. Beginning with the historical debate over whether light is a wave or a particle, it examines Young’s double-slit experiment and its modern single-particle versions, which demonstrate that quantum objects can exist in superpositions of mutually exclusive states. The chapter explains how interference arises when alternative possibilities are not measured and how interaction with the environment suppresses these effects through decoherence, giving rise to classical behavior at macroscopic scales. A sequence of thought experiments involving interferometers and Stern–Gerlach devices highlights the counterintuitive structure of quantum measurement and the incompatibility of certain physical properties, as captured by the uncertainty principle. The chapter emphasizes that quantum mechanics does not describe particles taking multiple paths simultaneously in a classical sense but rather requires a new framework for probability based on amplitudes and interference. Finally, the discussion connects these foundational ideas to emerging technologies such as quantum computing, showing how superposition and entanglement can be harnessed to perform computations that have no classical analogue.
cat states are explained in a manner consistent with local realism. It is assumed that the particle is some physically real state at all times, albeit that this state may change as the particle adopts one or other channel of an apparatus. Each further quantum state associated with the particle will then be, not a state of the particle itself, but a state of the apparatus - a wave-like reaction in the apparatus of equal but opposite eect to the change in the particle and mimicking the eects of a particle as it propagates through the experiment. In view of the success of standard quantum mechanics (SQM), and the compelling example of self interference, it can hardly be doubted that, at least in some formal sense, the alternative Schrodinger cat states supposed by SQM must exist. However, we argue that these states need not be considered intrinsically probabilistic or otherwise inconsistent with the local realism of classical physics. Assuming that the particle itself is in some physically real state at all times, any further quantum state associated with that particle could simply be an excitation of the apparatus - an oscillatory disturbance that is of equal but opposite eect to the change in the particle and creates the illusion of a further particle state. From Newton's third law, or equivalently conservation, any change in a particle must be accompanied by a change of equal but opposite eect in the agency inducing that change. It is also known that every particle, whether massive or massless, has wave characteristics consistent with its dynamic properties, namely from the Planck-Einstein relation, E = ~!; a frequency !, and from the de Broglie relation, p = ~�; a wave vector �, whereE and p are respectively the energy and momentum of the particle, and ~ is the reduced Planck's constant. Thus what is imparted by particle to scattering agency is never simply some undierentiated amount of four-momentum, but a wave-like disturbance of equal but opposite eect to the change in the particle. All that need be explained then is why the reaction that occurs in the apparatus as a particle is measured should so emulate the eects of a particle as to create the illusion that the particle has somehow divided between available paths. And yet, the simulation
Quantum mechanics is famous for its predictive power, as well as for its paradoxical struggle for ontological validity. How can a theory be so successful without describing reality correctly? A plausible explanation emerges from the distinction between causal descriptions and methodological shortcuts. Quantitative analysis is often designed to exploit underlying symmetries of real processes, in order to simplify calculations by avoiding inconsequential complexities. Due to such a methodological step, the principle of quantum superposition cannot be validated as real, even if probability waves are assumed to exist. This conclusion follows from a qualitative demonstration that linear wave interactions produce irreversible information loss, contrary to the assumptions that have defined relevant debates in classical and quantum physics alike.
A presentation showing how the statements which relate to microphysical objects as they are different from the statements of classical mechanics is made. The determinism of classical and of quantum-mechanical theories is qualified. A (crucial) distinction between causality and determinism is given. Detailed analyses of diffraction as a result of single and double-slit demonstrations point to paradoxes arising from the use of particle or wave models, respectively, for photons and electrons. The compromising wave-packet model is underscored. The meanings for the Psi-function and for |ψ|2 are presented, with an explanation of the limitations that arise from giving an interpretation of |ψ|2 as a probability. The meaning of ψ-waves is analyzed. A case is made for the ψ-function's describing a well-ordered list of betting odds, based on previous statistical experiences, for the different results of specific experiments of a microscopic object of study with macroscopic apparatus. The Schrödinger wave equation is evaluated for meaning and judged as a deterministic expression.
There are many evidences in Quantum Mechanics about the existence of de Broglie waves: the two-slit experiment, self interference when a particle can follow two or more paths that converge, etc.There is not direct evidence of its existence because we use exclusively particle detectors.This paper presents a new evidence of the existence of de Broglie waves grounded in the action reaction principle.The action reaction principle is a fundamental ingredient of Physics: when two systems interact both change of state (i.e., they depart from the free, isolated evolution path in the phase space).A simple experiment using a Mach-Zehnder interferometer is analysed.A representation of the evolution in the phase space for different cases (isolated system and interaction with a detector) is shown.By applying the action reaction principle we show that some subsystem, different from the corpuscular photon, must follow one arm of the interferometer when we can infer that the photon follows the other arm.There cannot be interaction between the photodetector in one arm and the photon following the other arm.This new subsystem would be a distributed de Broglie wave.