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.
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.
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
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.
It is well known, that in some experiments, light exhibits ‘wave’ property; like interference and diffraction; whereas in other experiments, like photoelectric effect, it shows ‘particle’ nature. So, the physicists currently think in terms of ‘wave-particle-duality’ of light, their mutual exclusiveness, and complementarily. Here, in this paper, this ‘wave-particle-duality’ is explained; that at the frequencies of light, very narrow-band filtering, and generation of purely monochromatic light, of one Hz bandwidth, are not technically possible; so there is always some bandwidth and ‘line-width’, due to which the waves form wave-packets, localized in space, as ‘particles’. Then this familiarity with waves is applied to understand the observations of ‘cosmological red shift’.
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.
In a recent paper, titled “Explanation for the observed wave-particle-duality of Light” (Tank, H.K. http://vixra.org/abs/1402.0153, 2014) it was explained that: “Since at very high frequencies, narrowband filtering and generation of purely monochromatic light of one Hertz bandwidth is not yet technically possible, there has been quite a wide bandwidth of waves involved, in the double slit experiments and photoelectric experiments performed so far. And since this wide ‘band’ of waves coherently add only at discrete points in space and time, we get ‘particles’ at the detectors.” Now, to further confirm the validity of this explanation, a new kind of experiment is proposed here, in which protons and electrons are accelerated at appropriate velocities vp ve , such that their de Broglie wavelengths are equal; i.e. ( h / mp vp )= ( h / me ve ) and let them pass through closely spaced slits so that they can interfere with each other. Similarly, in another experiment, their wave-functions: A exp i ( kp X - ωp t ) = A exp i ( ke X - ωe t ) , and let them pass through closely spaced slits, and see how the two matter-waves interfere.
For centuries Young’s double-slit interference continues to be a hot discussion subject about whether light is waves or particles. This work unravels the self-interference parados, and sheds light on such a concept that assumes a photon can split, self-interfere, and recombine. This work elucidates how coherent photons from a laser source could produce a double-slit interference pattern without the hypothesis of unphysical splitting and recombination of a single photon. Unlike the conventional single wave-function description for the whole ensemble of particles, we develop a pilot-wave trajectory approach to track every photon’s wave-packet propagation and calculate the evolution of the interference intensity in time. We demonstrate how wave packets and phase coherence affect the interference pattern. To resolve the century-old self-interference paradox, we show that such an hypothesis is unnecessary, and the illusion is due to the long coherence length of laser photons and overlaps of delocalized light wave packets.