Quantum mechanical wave function predicts probabilities of finding a ‘particle’ at different points in space, but at the time of detection a particle is detected only at one place. The question is: how this place gets decided, and can be predicted. To seek answer to this, we assume here that a ‘particle’ has some “diameter”, in stead of being a ‘point-particle’ of mathematical zero dimension; and depending upon the relative velocity between this particle and observer, its “diameter” experiences ‘Relativistic length-contraction’. Then we Fourier-transform this ‘length-contraction’ in ‘space-domain’ into ‘spectral-expansion’ ∆ω in ‘frequency-domain’, and find that momentum of a particle can be expressed as: m v = h ∆ω / 2 π c, and de Broglie’s wavelength, λB = 2 π c /∆ω ; as was derived in [ref.1 and 2. In the ref-2 it was shown that: in fact it is the ‘expansion of spectrum’ in the frequency-domain, which is the physical-cause for the Relativistic length-contraction.] Then we notice that the frequency-domain translation of the particle’s length in space-domain has a continuous spectrum; i.e. it contains a set of frequencies ranging from ωmax to ωmin . Therefore, as we found in ref. [3], this wide set of waves coherently add only at discrete points in space, and mutually nullify their amplitudes at rest of the places. And the place at which all the spectral-components of the wide band of waves will add constructively, will depend on the relative phase of all the spectral components. It is proposed here, that we need to know the relative phase angles of every spectral-component contained in the wide set of waves contained in the expanded wide band, for predicting the exact place of detection of the ‘particle’.
Quantum mechanical wave function predicts probabilities of finding a ‘particle’ at different points in space, but at the time of detection a particle is detected only at one place. The question is: how this place gets decided, and can be predicted. To seek answer to this, we assume here that a ‘particle’ has some “diameter”, in stead of being a ‘point-particle’ of mathematical zero dimension; and depending upon the relative velocity between this particle and observer, its “diameter” experiences ‘Relativistic length-contraction’. Then we Fourier-transform this ‘length-contraction’ in ‘space-domain’ into ‘spectral-expansion’ ∆ω in ‘frequency-domain’, and find that momentum of a particle can be expressed as: m v = h ∆ω / 2 π c, and de Broglie’s wavelength, λB = 2 π c /∆ω ; as was derived in [ref.1 and 2. In the ref-2 it was shown that: in fact it is the ‘expansion of spectrum’ in the frequency-domain, which is the physical-cause for the Relativistic length-contraction.] Then we notice that the frequency-domain translation of the particle’s length in space-domain has a continuous spectrum; i.e. it contains a set of frequencies ranging from ωmax to ωmin . Therefore, as we found in ref. [3], this wide set of waves coherently add only at discrete points in space, and mutually nullify their amplitudes at rest of the places. And the place at which all the spectral-components of the wide band of waves will add constructively, will depend on the relative phase of all the spectral components. It is proposed here, that we need to know the relative phase angles of every spectral-component contained in the wide set of waves contained in the expanded wide band, for predicting the exact place of detection of the ‘particle’.
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 alternatively interpreted here, different from the current, ‘probabilistic interpretation’. 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 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. In the particle-interference-experiments, they are the wide band of ‘pre-quantum-waves which interfere physically. This physical interference of the pre-quantum-waves determines the position and time of emergence of the ‘impulse in space’ detectable as the ‘particle’. In the real-world-situation, the ‘pre-quantum-waves of a wide bandwidth arrive from all the directions, so the amplitude and phase of every constituent wave keep changing; so the place of constructive superimposition of all the spectral-components, keep varying unpredictably; and only the ‘probability’ of detection in a given volume is possible in practice. Thus, form the theoretical view-point, there are only the pre-quantum-waves; and ‘particle’ is a specific situation of constructive-superimposition of all the spectral-components of pre-quantum-waves; so there is no wave-particle-duality. The ‘probabilistic-interpretation’ is only a ‘practical-limitation’, detector being able to detect only the ‘particle’, and not the spectrum of constituent waves.
This letter proposes an explanation for the century-old puzzle of the wave-particle-duality of light, which thousands of physicists, including Einstein, Plank, Feynman …, have been trying to resolve. Since a ‘particle ’ is localized in space, it is mathematically characterized here as an impulse-function in space. Then it is argued that if this ‘particle’ has anything to do with waves then we can know it by taking Fourier-transform of the impulse-function in space. When Fourier-transformed into wave-number-domain; we find that a ‘particle ’ should contain a wide ‘set ’ of waves, and not just a single frequency. Then we show that in the experiments performed so far [1] the red lasers had significantly wide line-width, means the sources have been producing a wide set of waves, and not just a pure single frequency. Similarly, in the single-particle interference-experiments incandescent filament-lamps were used with green filters inserted to isolate single photons; but it is obvious that at the frequencies of light very narrow-band-filters are not yet technically feasible, so the green filters used allowed significantly wide band of waves. So in the experiments performed so far we got ‘particles ’ localized in space. And in the double-slit-interference-experiments this wide band of waves passed from both the slits, interfered like waves, and whenever and wherever they got coherently added, a ‘particle ’ called ‘photon ’ got detected. Atoms emit short-duration pulses of radiation, so their Fourier transform contains a wide band of frequencies. And at the time of detection, an atom needs only a small piece of continuous ‘wave’, of a suitable duration, amplitude and frequency, for ejection of an electron. So it is concluded here that: emission and detection of light is in the form of ‘photons’; whereas its propagation in space is in the form of a wide band of ‘waves’. 2
Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM) assume different answers to this question. It is shown in this article that the assumption that the wave-function is a real wave entails a contradiction with the predictions of the QM, when the special relativity is invoked. Therefore, this text concentrates on interpretations that conjecture that the reality that moves in our apparatuses is particles, and they move under the constraints of the wave-function. The de Broglie-Bohm interpretation, which matches this picture, assumes that the particle travels along a continuous trajectory. However, the idea of continuous trajectories was proved to lead to a contradiction with the quantum predictions. Therefore this interpretation is not considered here. S. Gao conjectured that the particle is in a permanent random and discontinuous motion (RDM). As it jumps all the time from place to place, the total set of occupied positions at a certain time is given by the absolute square of the wave-function. As motivation for his idea, Gao argued that if a charged particle were simultaneously in two or more locations at the same time, the copies of the particle would repel one another, destroying the wave-function. It is proved here that the quantum formalism renders this motivation wrong. Although refuting this motivation, the RDM interpretation is examined here. A couple of problems of this interpretation are examined and it is proved that they don’t lead to any observable contradictions with the QM predictions, except one problem which seems to have no solution. In all, it appears that none of the wide-spread interpretations of the QM is free of contradictions.
This letter attempts to propose explanations for the century-old puzzle which thousands of physicists, including Einstein, Plank, Feynman …have been trying to resolve. A ‘particle’ is first mathematically characterized here as an impulse-function in space; and then Fourier-transformed into wave-number-domain; showing that a ‘particle’ contains a ‘set’ of waves, and not just a single frequency. Then a small ‘set’ of waves is taken and its sum is plotted showing that at most of the places the wave-amplitudes mutually nullify each-other and constructively add only at discrete points in space and time; agreeing with our mathematical characterization. Then we show that in the experiments performed so far the red lasers had at least a few thousand Hz wide line-width; means the sources have been producing a wide set of waves, and not just a pure single frequency. Similarly, in the single-particle interference-experiments incandescent filament-lamps were used with green filters inserted to isolate single photons; but it is obvious that at the frequencies of light very narrow-band-filters are not yet technically feasible, so the green filters used allowed significantly wide band of waves. This wide band of waves passed from both the slits, interfered like waves, and whenever and wherever they got coherently added, a ‘particle’ called ‘photon’ got detected.
Is wave function collapse a prediction of the Schrödinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include local entanglement of two systems, including a macroscopic one. This property of local entanglement, which results directly from the Schrödinger equation but is unrelated with observables, is measured by local probabilities, fundamentally distinct from quantum probabilities and evolving nonlinearly. When applied to a macroscopic system and the fluctuations in its environment, local entanglement can also inject a formerly ignored species of incoherence into the quantum state of this system,. When applied to a quantum measurement, the conjunction of these two effects suggests a self-consistent mechanism of collapse, which would directly derive from the Schrödinger equation. (This work develops and improves significantly a previously circulated version with the same title [23])