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Young’s one-dimension-double-slit experiment represents the basic mystery of quantum world and was extended to which-way-1D-double-slit experiment. To explore the mystery, 2D-cross-double-slit apparatuses have been proposed, which consists of more than one double-slits intersecting to each other. In this article, we report which-way-2D-cross-double-slit experiments by detecting which slit of a double-slit of 2D-cross-double-slit apparatus a photon would pass through. The experimental results show that photons passing through the detected double-slit behave as particle, while photons passing through other undetected double-slit(s) distribute as wave in the same experiment with the same apparatus. Namely the particle nature and wave distribution coexist, which violates Bohr’s complementarity principle. We suggest that photon’s “particle nature” is intrinsic, while the term “wave nature” represents a wave-like distribution, which is a consequence of movement of photon as particle. It is a challenge to interpret mathematically those observations consistently.

Quantum theory stipulates that if two particles are identical in all physical aspects, the allowed states of the system are either symmetric or antisymmetric with respect to permutations of the particle labels. Experimentally, the symmetry of the states can be inferred indirectly from the fact that neglecting the correct exchange symmetry in the theoretical analysis leads to dramatic discrepancies with the observations. The only way to directly unveil the symmetry of the states for, say, two identical particles is through the interference of the original state and the physically permuted one, and measure the phase associated with the permutation process, the so-called particle exchange phase. Following this idea, we have measured the exchange phase of indistinguishable photons, providing direct evidence of the bosonic character of photons., Comment: 16 pages, 7 figures

The behavior of a photon is strange. It possesses both wave nature and particle nature. Some experiments show both behaviors of photons can exist simultaneously, while some other experiment state that both properties do not co-exists simultaneously. According to electromagnetic theory, the rest mass of photon in free space is zero and also photon has non-zero rest mass, as well as wavelength-dependent. The very recent experiment revealed its non-zero value as 10 - 54 kg ( 5.610 × 10 - 25 MeV c - 2 ) . Even experimental results concluded that within matter (dispersive) the photon shows its imaginary rest mass. We have no exact answer as to why photon incarnates itself with versatile mass. Here we try to theoretically investigate about the rest mass of a photon. When it touches the surface of matter, it makes illusion and mathematically the rest mass is a complex number. Rest mass of photon depends upon scalar curvature of the surface of matter and wavelength of the photon. Photon itself reveals illusion posing with mass because of its dual nature. We have investigated the wave-particle duality of light, coexistence of wave and particle nature through morphing due to pliable character of light wave. Our theoretical work about the photon’s illusive mass will have to be experimentally verified and it might open plausible new applications in the secure communication of information.

The recent criticism of Vaidman's propsal for the analysis of the past of a particle in the nested interferometer is refuted. It is shown that the definition of the past of the particle adopted by Englert et al. [Phys. Rev. A 96, 022126 (2017)] is applicable only to a tiny fraction of photons in the interferometer which indeed exhibit different behaviour. Their proof that all pre- and postselected particles behave this way, i.e. follow a continuous trajectory, does not hold, because it relies on the assumption that it is intended to prove., Comment: Comment on quant-ph 1704.03722

We present a paradox involving a particle and a mirror. They exchange a nonlocal quantity, modular angular momentum Lz mod 2ћ, but there seems to be no local interaction between them that allows such an exchange. We demonstrate that the particle and mirror do interact locally via a weak local current 〈Lz mod 2ћ〉w. In this sense, we transform the “interaction-free measurement” of Elitzur and Vaidman, in which two local quantities (the positions of a photon and a bomb in the two arms of a Mach-Zehnder interferometer) interact nonlocally, into a thought experiment in which two nonlocal quantities (the weak modular angular momentum of the particle and of the mirror) interact locally.

An analysis of the existing theoretical ideas as to the relationship between the spectrum of collective density excitations and the spectrum of single-particle excitations in liquids with a Bose-Einstein condensate. Using available experimental results, we examine the problem of the relationship between the collective phonon-roton excitations in different liquids, and the Bose-Einstein condensate.

In a delayed-choice experiment the decision to measure the particle or wave nature comes after the photon enters the interferometer. An atomic version of the experiment provides the same outcome despite the mass and internal structure of the atoms.

Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisingly rich character. Here, we study many-particle interference using three photons. We show that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behavior in a scattering process, but that a collective phase, the triad phase, plays a role. We are able to explore the full parameter space of three-photon interference by generating heralded single photons and interfering them in a fiber tritter. Using multiple degrees of freedom-temporal delays and polarization-we isolate three-photon interference from two-photon interference. Our experiment disproves the view that pairwise two-photon distinguishability uniquely determines the degree of nonclassical many-particle interference.

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] does not test the past of the photon as characterised by local weak traces. Instead of answering the questions: (i) Were the photons in A? (ii) Were the photons in B? (iii) Were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) Were the photons in A? (ii) Were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. A simple variation of the modified experiment does provide good evidence for the past of the photon in agreement with the results Danan et al. obtained., 3 pages, accepted for publication in Chinese Physics Letters

The nonlocal relativistic theory of transport processes is applied to the investigation of massless particles including photons. The problem of a “single photon” is considered with the aim to describe the boundary between the particle and field descriptions of photon gas. Analytical solutions of nonlocal nonstationary 2D equations are obtained for the physical system near the state of thermodynamic equilibrium.

Quantum mechanics, one of the keystones of modern physics, exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. These and corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarisation of a single protected photon. This is the first realisation of quantum protective measurements., Comment: Nature Physics, in press (this version corresponds to the one initially submitted to Nature Physics)

We propose a scheme for preparing multi-photon entangled state which is useful for sub-shot-noise sensitivity with beam splitter, where the entangled degree is measured by the reciprocal of the mean quantum Fisher information per particle (RMQFIP). The multi-photon entangled state can be prepared by adjusting the transmissivity of the beam splitter and the better multi-photon entangled state can be prepared by increasing the total number of photons.

We investigate the connection between the particle nature of light and its nonclassical character. When we can associate a precise number of photons, in some sense, to a particular state of light, the state possesses a full particle nature. We show that whenever a complete particle nature emerges in the state of light, the corresponding nonclassical measure becomes unity, and the state becomes maximally nonclassical.

Allowing photons to bear mass, the electric and magnetic flelds of a steadily moving charge are no longer perpendicular to each other, as anticipated from Biot-Savart law. The electric and magnetic flelds of such a particle depend on the gauge potentials, ' and ~ A. The orthogonality relations of the particle flelds and the direction of motion depend on the mass of the photon. The non-relativistic correction to the particle flelds was found to be related to the Lorenz gauge condition. It is shown that the existence of magnetic monopoles inside matter is inevitable when magnetic fleld is applied in a conductor. Their existence is a manifestation of the massive nature of the photon inside matter. Neither electric nor magnetic current is separately conserved for photons, but their sum is. Massive photons are found to produce electric and magnetic flelds. A force proportional to the square of the current is found to act along the wire, F = 1 "0I 2 , where "0 is vacuum permeability.

In a recent paper [Phys. Rev. A 94, 032115 (2016)], Griffiths questioned---based on an interesting consistent-histories (CH) argument---the counterfactuality, for one of the bit choices, of the protocol of Salih et al. for communicating without sending physical particles [Phys. Rev. Lett. 110, 170502 (2013)]. Here, we first show that for the Mach-Zehnder version used to explain our protocol, contrary to Griffiths's claim, no family of consistent histories exists where any history has the photon traveling through the communication channel, thus rendering the question of whether the photon was in the communication channel meaningless from a CH viewpoint. We then show that for the actual Michelson-type protocol, there is a consistent-histories family for each cycle that includes histories where the photon travels through the communication channel. We show that the probability of finding the photon in the communication channel at any time is zero---proving complete counterfactuality.

Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [ Phys.\ Rev.\ A 87 (2013) 052104 ], and agree with a conclusion reached by Li et al.\ [ Phys.\ Rev.\ A 88 (2013) 046102 ]. However, the analysis casts serious doubt on the claim of Salih et al.\ (whose authorship includes Li et al.) [ Phys.\ Rev.\ Lett.\ 110 (2013) 170502 ] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons., Comment: 18 pages, 1 figure. Minor revisions have been made to produce a manuscript accepted for publication in Phys. Rev. A

Establishment of an LC equation and of a local fields equation describing permanently localized photons from the analysis of kinetic energy circulation within the energy structure of the double-particle photon that Louis de Broglie hypothesized in the early 1930's. Among other interesting features, these equations provide a mechanical explanation to the localized photon properties of self-propelling at the speed of light and of self-guiding in straight line when no external interaction tends to deflect its trajectory. This paper summarizes the seminal considerations that led to the development of the 3-spaces model.

The measured data on transverse momentum spectra for production of direct photons in hadron–hadron, hadron–nucleus, and nucleus–nucleus interactions at high energies are compiled. Besides, data on some other aspects related to these pT-spectra are also assorted in the present work. The pT-spectra for production of direct photons at pT > 1 GeV/c are, then, fitted here by using two parameterizations, which essentially approach the power-law dependence at high transverse momenta. The power indices range between 16 to 7 depending on the interacting particles and the centre-of-mass energy of the system. The power index decreases gradually with increasing energy, with a variation of the rate of fall for various energy ranges. The formulae applied here phenomenologically bring out the main features of the data characteristics in a modestly satisfactory manner. This provokes us to raise some serious questions about the existing “theoretical” approaches, all, or most of which, lack in the first-principle derivations of the actual working expressions used to finally describe the nature of the measured data on direct photons, or for that matter, on any other secondary particle.PACS Nos.: 25.75.–q, 12.38.Mh, 13.85.Ni

Some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons, in first-quantization quantum electrodynamics., Comment: 19 pages, including two Figures. [The source-file is in Word]

A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances, but it is never detected in two (or more) places. This strange phenomenon is explained in quantum theory by what Einstein repudiated as "spooky action at a distance": the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. We demonstrate this single-particle spooky action, for the first time with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing if the choice of measurement in one lab really causes a change in the local quantum state in the other lab. To this end, we use homodyne measurements with six different measurement settings and quantitatively verify Einstein's spooky action by violating an Einstein-Podolsky-Rosen-steering inequality by $0.042 \pm 0.006$. Our experiment also verifies the entanglement of the split single photon even when one side is untrusted., Comment: 8 pages, 5 figures

Quantum Optics The radiation pressure from a focused laser beam used to cool and trap particles is the basis for advanced optical tweezing methods that have found a diverse range of applications in biology, chemistry, and physics. When a trapped particle is subjected to a force, it shifts its position in the trap, thereby providing the possibility of sensing that force. By confining a 50-nm-diameter silica bead in an ultrahigh vacuum, Jain et al. isolated the particle from environment-induced jiggling and effectively restricted the particle's motion to that due to quantum optical forces. They then showed that they can measure the recoil rate of photons from the particle, providing the possibility of exploiting the effect for highly sensitive force measurements. Phys. Rev. Lett. 116 , 243601 (2016).

A two-particle interferometer is theoretically analyzed, to show how decoherence induced by interactions with the environment affects time correlations, a process we call time-correlation de-coherence. Specifically, on the basis of simple mathematical analysis we show how the interaction between a bipartite entangled system and a photon bath representing the environment can efface the oscillations in the coincidence-detection rate of the interferometer. We discuss the dependence of this kind of decoherence on the photon energy and density., 10 pages, 2 figures, Will appear in Braz. J. Phys, volume 44

We demonstrate the nonlocal wavefunction collapse for a single particle, the idea of which dates back to Einstein’s first argument on his concerns about quantum theory, by performing EPR-steering using heralded single photons.

Atom interferometers are powerful tools for the study of fundamental issues in quantum mechanics. This paper describes the use of our atom interferometer [1] for an experimental realization of Feynman's gedanken experiment in which the observation of photons scattered off of particles emerging from a double slit is used to obtain which path information. This determination, in principal, of the particle's path, destroys any interference effects downstream. The interference can be regained by observing only those particles which scatter a photon into a small range of final directions.

There seems to be a philosophy emerging that one can never understand how matter can be both waves and particles and should not even try. This paper counters that trend by examining a speculative model that could, at least in principle, explain this duality of nature. The key assumption is that fundamental particles create their own ‘ethers’ by polarizing the space around these particle in a manner similar to long-range van der Waals dispersion forces. The ‘ether’ created by a particle is at rest relative to that particle. Photons and other particles move through these ‘ethers’ as waves in such a way that the speed of light is constant relative to each particle. Electron waves are created when one electron moves through the polarized space domains of another particle by transmitting its kinetic energy to these domains. Using this model, I show that an electron develops waves which follow Broglie's relationship between wave length and electron energy. The results are rather surprising and show, that at least in principle, one can develop reasonable scientific models which at least partially explain the dual-nature of matter.

Within a standing-wave approach, we determine the quantized velocity of a single photon in a one-dimensional cavity by considering the photon as an ultrarelativistic particle of non-zero rest-mass. As a matter of fact, this ultrarelativistic nature is regarded as well as the mathematical expression involving the photon modes in the cavity, and de Broglie relationship for the wave-particle dualism.

The radiation caused by particles of one bunch in the collective electromagnetic field of the short oncoming bunch is studied. Quantum effects are calculated for the spectrum of radiated photons. Using this spectrum, the dependence of the relative energy loss δ on a quantum parameter K is discussed. It is shown that the behaviour of δ changes considerably with the increase of that parameter. In the classical regime (K ≪ 1) the energy loss is proportional to the incoming particle energy, while in the extreme quantum regime (K ≫ 1) the energy loss becomes a constant. The coherent e+e− pair production for γe colliders as cross-channel to CBS is considered.

Light can exert radiation pressure on any object it encounters and that resulting optical force can be used to manipulate particles. It is commonly assumed that light should move a particle forward and indeed an incident plane wave with a photon momentum ħk can only push any particle, independent of its properties, in the direction of k. Here we demonstrate, using full-wave simulations, that an anomalous lateral force can be induced in a direction perpendicular to that of the incident photon momentum if a chiral particle is placed above a substrate that does not break any left–right symmetry. Analytical theory shows that the lateral force emerges from the coupling between structural chirality (the handedness of the chiral particle) and the light reflected from the substrate surface. Such coupling induces a sideway force that pushes chiral particles with opposite handedness in opposite directions., Light carries momentum and therefore can be used to push small particles forward. Here, Wang and Chan demonstrate that under the right conditions a light beam can also exert sideway forces on chiral particles.

The meanings of Mass, Momentum, Force and Energy of a substance are clearly defined. Their relationships to each others are discussed. The reasons that a Photon has energy E = hν and momentum P = h/λ are explained. Light travels in vacuum at a constant speed C = 3 x 108 m/sec while converting from Wu’s Particle through the separation and ejection processes from its parent substance is discussed in details based on Yangton and Yington theory. In Black Body radiation, a Photon emitted at high temperature having smaller size, higher frequency and higher energy is also explained.

We show that the Casimir-Polder potential of a particle in an energy eigenstate at nonretarded distance from a well-conducting body of arbitrary shape is independent of the environment temperature. This is true even when the thermal photon numbers at the relevant atomic transition energies are large. A compact expression is obtained for the temperature-independent potential, which can greatly simplify calculations in nontrivial geometries for experimentally relevant systems such as Rydberg atoms and polar molecules. We give criteria for the validity of our temperature-independent result. They are illustrated by numerical studies of a particle near a gold sphere or inside a gold cylindrical cavity., 5 pages, 2 figures

In the Coulomb gauge formulation of quantum electrodynamics, elementary particles interact via two mechanisms: (1) An instantaneous Coulomb interaction and (2) a retarded interaction mediated by transverse photons. In the present chapter we shall study the electromagnetic interaction between just two particles (e.g., electrons) or composed particles (atoms, molecules, quantum dots, mesoscopic particles, etc.). In all cases, it is assumed that the probability density distributions of the two particles do not overlap in space. When composed particles come so close to each other that the tails of the density distributions begin to overlap electrons can move from one particle to the other by quantum mechanical tunneling, and if the distance is made sufficiently small one cannot in a meaningful manner treat the global system as a two-particle object

We extend the study of Kapitza-Dirac diffraction to the case of two-particle systems. Due to the exchange effects the shape and visibility of the two-particle detection patterns show important differences for identical and distinguishable particles. We also identify a novel quantum statistics effect present in momentum space for some values of the initial particle momenta, which is associated with different numbers of photon absorptions compatible with the final momenta., Minor changes with the published version

Half-integer photon-resonances in a periodically shaken double well are investigated on the level of the N-particle quantum dynamics. Contrary to non-linear mean-field equations, the linear N-particle Schrodinger equation does not contain any non-linearity which could be the origin of such resonances. Nevertheless, analytic calculations on the N-particle level explain why such resonances can be observed even for particle numbers as low as N = 2. These calculations also demonstrate why fractional photon resonances are not restricted to half-integer values., 7 pages, 5 figures

We study a new kind of tunneling of particles through a barrier particular to quantum field theory. Here, the particles traverse the barrier by splitting into a virtual pair of particles of a different species which interacts only very weakly with the barrier and can therefore pass through it. Behind the barrier, the pair recombines into a particle of the original species. As an example, we discuss the case where photons split into a pair of minicharged particles. This process could be observed in experiments of the light-shining-through-a-wall type and may be used to search for minicharged particles in laboratory experiments., Comment: 20 pages, 9 figures

We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to `keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive particles as to photons and as such this scheme could be used to show the nonlocality of atoms., Comment: 10 pages, 5 figures

A two-photon interferometric experiment is proposed. The idler and signal photons of two non-overlapping frequencies, ω i and ω s , which can be created in the process of parametric down conversion are mixed together and directed to two interferometers. The photodetectors behind the interferometers respond to both frequencies. The correlated detections of photons exhibit dependence on the length of the optical paths within the interferometers and the beat frequency ω i -ω s . Violation of Bell's inequalities is predicted.

One of the great achievements in the history of physics was the use of a wave picture to explain the marvellous phenomenon of interference. When electron beams were made to interfere in the 1920s, this interpretation meant that wave properties could also be attributed to particles. Combined with experimental evidence of the "corpuscular" properties of light (i.e. the existence of photons), the wave-like properties of electrons gave rise to the concept of wave – particle dualism.

We describe a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe. After outlining the principle, we discuss specific realizations both with electrons in mesoscopic Aharonov-Bohm rings and with photons in standard Young's double-slit or coherent-backscattering interferometers., 5 pages, 3 figures, epl2, uses pstricks.sty

Theory on the creation of exactly n photon added pure quantum state is presented and its nonclassical property is studied.

Light may behave both as a particle and as a wave. Newton conjectured the particle aspects and observed wave aspects (“Newton's rings”). Young showed wave interference in his double-slit experiments, and Einstein formulated light as particles (photons) to explain the photoelectric effect. This dual description leads to two different speeds for light: the wave speed, which for a plane wave in vacuum is the now fixed constant, c ; and the particle or “group” speed at which energy or information propagates, which can be less than c —even zero, in some cases. On page 857 of this issue, Giovannini et al. ( 1 ) convincingly show that individual photons can have a speed less than c . In order to show this, the individual photons were prepared with transverse structure, so they cannot be represented as truly plane waves.

A particle $\phi$ coupling to two photons couples also to charged particles, like protons, through a loop. If the particle is a light scalar this induced coupling to protons leads to non-newtonian forces. We show that the experimental constraints on exotic, fifth-type forces lead to stringent constraints on the $\phi\gamma\gamma$ coupling., Comment: With respect to v1, we have extended the paper, also new authors have joined. Submitted to PRL

We argue that the theories of Volokitin and Persson (Comment arXiv:1405:2525), of Dedkov and Kyasov (J. Phys.: Condens. Matter 20 (2008) 354006), and Pieplow and Henkel (New J. Phys. 15 (2013) 023027) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is 'diluted' to get the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned. Submitted to: New J. Phys. 1. Force per particle of Volokitin and Persson In their Comment (1), Volokitin and Persson (VP) summarize an alternative calculation of the electromagnetic force on a neutral particle moving parallel to a planar half-space. Their approach is 'macroscopic' in the sense that the starting point are two half-spaces (1 and 2, say) sliding one against the other with arbitrary velocity (2). The focus of the present discussion is the lateral force (per unit area) given by a component of the electromagnetic stress tensor, evaluated at the surface of body 1. To arrive at the force between a single, moving particle and a surface, the moving body 2 is 'diluted' by taking the limit (notation of VP, cgs units)

The phase shift experienced by a light wave when it passes through a focus (the Gouy phase shift) can be regarded as a geometrical effect arising, via the uncertainty principle, from a modification of the volume of space available for the propagation of the photon. This effect is closely related to the shift in the phase of the wave function of a particle travelling along a tube; however, it does not require the presence of physical boundaries.

As we know, the values of the mass and charge of electrons, protons, neutrons, alpha-particles, etc., are known with tremendous—accuracy approximately one part in a billion. Their velocities can also be changed by application of electric and magnetic fields. Thus, we usually tend to visualize them as tiny particles. However, they also exhibit diffraction and other effects which can only be explained if we assume them to be waves. Similarly, using light beams, there are experiments on interference, diffraction, etc., which can only be explained if we assume a wave model for light. There are also phenomena, like photoelectric effect, which can only be explained if we assume a particle model of light. Thus, answers to questions like what is an electron or what is light are very difficult. Indeed electrons, protons, neutrons, photons, alpha-particles, etc. are neither particles nor waves. The modern quantum theory describes them in a very abstract way which cannot be connected with everyday experience. To quote Feynman [Ref.1 ]: Newton thought that light was made up of particles, but then it was discovered that it behaves like a wave. Later, however (in the beginning of the twentieth century), it was found that light did indeed sometimes behave like a particle. Historically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither. Now we have given up. We say: ‘It is like neither’. There is one lucky break, however—electrons behave just like light. The quantum behaviour of atomic objects (electrons, protons, neutrons, photons, and so on) is the same for all, they are all ‘particle-waves’, or whatever you want to call them.

The implementation of a quantum Wheeler's delayed-choice experiment defies the conventional boundaries set by the complementarity principle and shows photons coherently oscillating between particle and wave behaviours in a single experimental set-up.

Of course, the photon concept (namely, that light consists of discrete, individ-ual entities) did not settle the wave—particle controversy. There was proof neither that a photon had a wave structure nor that it had a particulate structure. However, probably because a photon was localized and discrete, physicists found it easier to think of it as a particle than as a wave. It’s not surprising, then, that as the concept gained acceptance, people began to question the wave theory of light and to reexamine the evidence that had led to its acceptance in the 19th century.

It is shown that the Hartman-Fletcher effect is valid for all the known expressions of the mean tunnelling time, in various nonrelativistic approaches, for the case of finite width barriers without absorption. Then, we show that the same effect is not valid for the tunnelling time mean-square fluctuations. On the basis of the Hartman-Fletcher effect and the known analogy between photon and nonrelativistic-particle tunnelling, one can explain the Superluminal group-velocities observed in various photon tunnelling experiments (without violation of the so-called "Einstein causality")., Comment: standard LaTeX file; accepted for publication in Phys. Lett. A

According to the complementarity principle, a photon behaves either as a particle or as a wave. That is, if it does not behave as a particle it necessarily behaves as a wave, and vice versa. It has also been argued that particle-like and wave-like behaviours are not mutually exclusive, and that a photon can also behave as a particle and as a wave. Here I propose a variant of a previous experiment in which a photon behaves neither as a particle nor as a wave. An alternative nonlocal realistic interpretation is presented, in which the notion of path followed by the photon can be meaningful.