It is proved that for a double slit diffraction experiment,superposition principle of probability amplitudes means the probability amplitude of the event that an electron passes through a certain slit and falls on somewhere of the screen has nothing to do with the condition whether or not the other slit is open,from which it is concluded that the probability itself does not obey superposition principle.Consequently,the total probability formula as a relation among the measurable probabilities is invalid herein.As a result,it is unnecessary to give up the classical idea that an electron moves along an orbit,and thereby it is unnecessary to distinguish between classical physics and quantum physics.
It is proved that for a double slit diffraction experiment,superposition principle of probability amplitudes means the probability amplitude of the event that an electron passes through a certain slit and falls on somewhere of the screen has nothing to do with the condition whether or not the other slit is open,from which it is concluded that the probability itself does not obey superposition principle.Consequently,the total probability formula as a relation among the measurable probabilities is invalid herein.As a result,it is unnecessary to give up the classical idea that an electron moves along an orbit,and thereby it is unnecessary to distinguish between classical physics and quantum physics.
It is proved that in a double slit diffraction experiment, superposition principle of probability amplitude means (the probability amplitude of the event) that an electron passes through a certain slit and arrives somewhere on the screen under the condition that two slits open simultaneously, is equal to the sum of two probability amplitudes of the same event under the condition that two slits open in turn. From this thesis it is concluded that the probabilities do not obey superposition principle, which is just the reason that classical probability theory is inapplicable for the very experiment. Kolmogorov's probability theory is based on two foundations: frequency definition of probabilities and Boolean algebra of event operations. In micro processes, the former holds true while the latter, especially its multiplicative permutation law is violated. So long as we do not deal with event operations, joint probabilities holds good in micro processes. But, the event operation formulae provided are applied and the wrong conclusions present probably. The famous Bell's inequality is a wrong conclusion. (Nature and Science. 2005;3(2):82-91).
It is proved that: What the two-slit experiments have refuted is the preconceived idea that of the event that a micro particle passing through one slit arrives somewhere on the screen is irrelative to the condition that whether or not the other slit is open. Consideringaddition theorem of probabilities, the above idea can be expressed as follows:
(a)Assum that a beam passes through a partition with two slit and arrives a screen. The of the event that an indivedual particle falls on somewhere of the screen under the condition that two slit open simultaneously, is equal to the sum of two of the same event under that two slit open in turn.
Defining the experimental condition such as two slit open simultaneously or in turn as passage the proposition (a)is manifested as probabilities is independent of passage conditions.
On the other hand, in terms of the above, superposition principle of in quantum mechanics ought to be indicated as probability amplitudes is independent of passage conditions. Correspondingly, (a)is named hereof as superposition presumption of probability.
For lack of the conception of passage conditions, (a)is confused with theorem of probabilities. As a result, classical physics tacitly approve (a), and thereby it fails to comprehend the two-slit experiments. In reverse, to explain two-slit experiments, quantum mechanics spurns addition theorem of so that it meets with various difficults about explanation.
Any alternative of quantum mechanics must be able to explain two-slit experiments, therefore it must contain passage conditions or amplitudes. But hidden variable theory Bell used dissatisfies such a prerequisite. It comes thus into conflict with experiment facts inevitably. As a result, Lochak's argument that Bell's inequality is irrelative to locality is rediscovered.
The mainstream quantum mechanics uses “probability wave superposition and single-electron self-interference” to explain electron single-slit and double-slit diffraction. This theory deviates from the essential nature of real particle interactions and has fundamental logical flaws. The electron is a negatively charged real particle with a definite physical size and high-frequency transverse oscillation; a single real particle has no physical basis for self-interference. Abandoning the abstract probability wave hypothesis, this paper establishes a complete real-interaction model including electrostatic repulsion deflection, surface electron exchange, collision scattering, microscopic refraction, and barrier diffraction, based on the three-dimensional random transverse oscillation and charge repulsion of electrons. The model uniformly explains the real formation mechanism of electron single-slit diffraction and double-slit interference fringes. This paper proves that in single-electron sequential emission, each electron passes through only one slit; all bright and dark fringes are the statistical result of multiple microscopic interactions between electrons and slit walls or the central barrier. The disappearance of fringes under observation is caused by external disturbance to the inherent oscillation and wall-interaction equilibrium, not by wave function collapse. This paper further clarifies that whether an electron can pass through a slit is determined by its transverse oscillation amplitude, not by wavelength. Amplitude directly corresponds to slit width and is the core controlling variable of diffraction. Meanwhile, if no slit is placed, electrons flying directly to the screen produce no diffraction or interference fringes, proving that electrons themselves have no self-interference ability. Fringes are generated by slit structures, not by intrinsic wave interference of electrons. This study corrects the century-long misunderstanding of electron diffraction and establishes a new microscopic diffraction mechanism consistent with classical real-particle physics.
Abstract In the explanations of the double slit experiment it is usually assumed that the superposition of the diffracted waves by two separate slits (one open and another closed) is the same as superimposing the diffracted waves when both slits are open at the same time. This naïve use of the superposition principle is generally not valid in either classical electromagnetism or quantum mechanics. As we will see, the diffraction diagram of one of the slits is altered when the other is open and when the slits are closer, the interaction between them is greater. In this work we will analyse the interaction between different types of sources (antennas, loudspeakers and, of course, slits) and we will show how this interaction explains the apparent anomalies in energy conservation and also the recent results of Young’s interference that show that the total diffracted intensity is reduced or increased depending on the distance between the slits. We also make a brief comment on the contributions of our work to the supposed looped trajectories of energy in interference phenomena.
Probability and interference According to Feynman, single-particle interference is ‘the only mystery’ of quantum theory (Feynman, Leighton and Sands 1965, ch. 1, p. 1). Feynman considered an experiment in which particles are fired, one at a time, towards a screen with two holes labelled 1 and 2. With both holes open, the distribution P 12 of particles at the backstop displays an oscillatory pattern of bright and dark fringes. If P 1 is the distribution with only hole 1 open, and P 2 is the distribution with only hole 2 open, then experimentally it is found that P 12 ≠ P 1 + P 2 . According to the argument given by Feynman (as well as by many other authors), this result is inexplicable by ‘classical’ reasoning. By his presentation of the two-slit experiment (as well as by his development of the path-integral formulation of quantum theory), Feynman popularised the idea that the usual probability calculus breaks down in the presence of quantum interference, where it is probability amplitudes (and not probabilities themselves) that are to be added. As pointed out by Koopman (1955), and by Ballentine (1986), this argument is mistaken: the probability distributions at the backstop – P 12 , P 1 and P 2 – are conditional probabilities with three distinct conditions (both slits open, one or other slit closed), and probability calculus does not imply any relationship between these. Feynman's argument notwithstanding, standard probability calculus is perfectly consistent with the two-slit experiment.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.