The Einstein-Podolsky-Rosen paradox and the screw model of elementary particles

Antal Rockenbauer

Abstract: The space and time are defined as fictitious coordinates in the state of non-interacting elementary objects. The hidden parameters suggested originally by Einstein, Podolsky and Rosen (EPR) as a deterministic extension for quantum mechanics are postulated in this work as local indefinite quantities, which definition excludes the principle of counterfactual definiteness and the Bell’s inequality. In the screw model the phase of self-rotation is considered as a local indefinite parameter, which assumption allows deterministic interpretation for the elementary processes described mathematically by the inherently probabilistic formalism of quantum mechanics. The uncertainty relations of quantum mechanics are related to the non-observable indefinite phase of the self-rotation of photons. The anomalous terms in the perturbation procedure of quantum electrodynamics are interpreted by the fictitious time and space. A few cases of thought experiments are discussed in terms of the outlined concept providing resolution for the EPR paradox.

Keywords: EPR paradox; hidden parameter; counterfactual definiteness; fictitious space and time

PACS Nos.:  03.65.Ud;  03.65.Ta

1. Introduction

In the previous paper [1] we suggested a screw model for the elementary particles in order to rationalize the role of Feynman’s arrows [2] in quantum electrodynamics (QED). The most important conclusion was the assumption of the strong gravitation, which could explain the origin of mass, charge and spin of the elementary particles produced by the self-rotation of space points with the speed of light.

In the present paper we focus on the question whether the screw model can give an answer for the quantum mechanical paradox put forward by Einstein, Podolsky and Rosen (EPR) [3]. The quantum mechanics can tell the probability of microscopic events when great number of photons has interactions with matter, but this theory cannot predict the outcome of experiments when only individual photons or particles are involved in the process. EPR investigated the consequence of this characteristic feature of quantum mechanics by a few thought experiments and concluded that quantum mechanics was a non-complete theory and suggested the existence of hidden variables (parameters), which can causally control the outcome of experiments including individual photons or particles.

In the subsequent years this question became a controversial issue and great efforts were invested to see if hidden parameters could exist at all. The best studied example is the case of two particles created in a single event and the question was raised whether these particles could have correlated polarization at distant places (see references in [4]). The experiments gave positive answer: such a correlation indeed exists between the simultaneously created “twin” particles.  E.g. Aspect [5] found opposite polarization for two photons emitted in the same process if the photons were detected in opposite direction at equal distance from the source. The central issue of debate was whether the correlation can be explained by hidden variables as suggested by EPR [3] or by

the non-local nature of interaction between the spatially separated twin particles [4] The latter explanation defines a particular quantum state for the two particles, what are called as entangled particles or photons The problem is that both explanations violate certain basic laws of physics.

The assumption of hidden variables was ruled out most convincingly by Bell [6], who devised a set of experiments where the overall probability in the spin polarization experiments yielded an inequality rule, which was found incompatible with experimental findings. In this analysis Bell defined the hidden variable as a parameter controlling the polarization of photons at any time and took into account the rules of the uncertainty relations in quantum mechanics. Since the Bell’s inequality seemed to exclude the concept of hidden variable to interpret the EPR paradox, quantum mechanics needed a new approach, which lead to the assumption of entangled state of the particles created in a single event. In this state the twin particles should always remain in a correlated state by a non-local interaction. In the Copenhagen interpretation of quantum mechanics [7] the reduction or collapse of wavefunction is assumed when an experiment is carried out. According to this concept, when the wavefunction of the first particle is collapsed so has to do the second, it means that polarization of the first particle immediately changes polarization of the second particle at a separated spatial location. For resolving the evident contradiction, the customary explanation states that this information cannot be transferred between the two distant measuring teams faster than the speed of light. It is, however, easy to see that the concept of non-local interactions is still in contradiction to the principle of relativity, since the entangled photons can produce interactions between the internal and external zones of the space-time cones. Suppose a supernova explosion billion years ago if entangled particles really exist, these pairs of particles should be also emitted. One particle of this pair can reach one galaxy, while the other can encounter another galaxy. If as a consequence of encountering, the polarization of the first particle is changed, then, according to the definition of entangled particles, at the same time the polarization should be changed for the other photon in the other galaxy. It means that an event in one galaxy has an immediate impact in the other galaxy.

In this paper we make an effort to show that the assumption of underlying deterministic and causal laws for the elementary processes can be reconciled with the probabilistic character of quantum mechanics. The arguments are partially based on our previously introduced screw model and partially on the concept of fictitious space and time related to the state when the studied particles or photons do not interact with the surroundings. We connect the “strange” behavior of the virtual photons in the theory of QED [3] to the fictitious character of space and time. We demonstrate that the above concepts can alleviate interpretational problems of the EPR paradox by giving a less stringent definition for the hidden parameter compared to the assumptions of Bell [6]. In order to emphasize this definition, we introduce the term “indefinite parameter”, which can prescribe the outcome of individual elementary processes even though the value of this parameter remains indefinite. The indefiniteness involves an inherent statistics yielding to the probabilistic laws of quantum mechanics. This indefinite character also obliterates the counterfactual definiteness, which principle was considered by Blaylock [4] as decisive for interpreting the EPR paradox.

2. Theory

2.1. Quantum mechanical probabilities and the intrinsic phase of screw motion

In the screw model, we can assign an intrinsic phase for the temporary state of self-rotation:

φ = 2πυ (t –t₀) + φ₀                                                                                                (1)

Here φ₀ depends on the prehistory of photons or electrons applied in the experiment. The phase of screw motion plays an analogous role as the direction of arrows in the QED concept of Feynman [2], and furthermore, it can be related to the phase of the imaginary argument of wavefunction for the quantum mechanical objects. We can extend Feynman’s concept devised primarily for photons by assuming arrows also for the self-motion of fermions. When the outcome of any individual physical events is considered, e.g. the probability of reflection or transmission when the light reaches the surface of glass, the probability of event can be characterized by the scalar product of arrows representing the phases of incident photon and the interacting electron in the glass. The other factor influencing the elementary process is the frequency, since all transitions take place as a resonance when the frequency of incoming photon is equal to the frequency difference between the respective states of electrons. Actually quantum mechanics considers only the frequency fit without taking into account the role of phase agreement. The probabilistic description of elementary processes is a consequence of missing information for the intrinsic phases, since we can not control the prehistory of particles, neither for photons nor for electrons involved in the interaction. We postulate also indefinite phase for the orbital motion of electrons. The unknown phase makes impossible guarantying identical experimental conditions and, for this reason, only a statistical prediction can be given for the outcome of measurements where the impact of possible phases is averaged. This situation does not influence the result of experiments if great amount of photons and particles are involved in the processes, but makes impossible predicting the outcome of the individual elementary events. The theory of quantum mechanics is in accordance with this situation, since the computation of expectation values and transition probabilities include averaging processes, which eliminate the unknown phase of wavefunction in the final formulas.

2.2. Uncertainty principle in the screw model

The uncertainty of any physical observables can be connected to the properties of photons carrying information on the transition between two states of the elementary system. If, e.g., the photon bears large energy hn, we can obtain precise information for the position, but poor for the momentum. If subsequently a second photon is applied with small energy, we can improve the precision for momentum measurement, but this system is no more in the same state as before, since the investigated object has been already disturbed by the first photon. Thus the uncertainty rules are related to the fact that we cannot carry out two experiments under identical conditions for any elementary process. In the measurement of position, the phase uncertainty limits the resolution, since it does not allow measuring the position of any objects by a better precision than the spatial separation between two turns in the screw motion of photons. Furthermore in the course of screw motion, the direction of momentum also depends on the unknown phase causing an uncontrolled change of the object’s momentum, which limits the precision of measurement in the amount of . (Here we disregard numerical factors in the order of unity.) Consequently, the product of these uncertainties cannot be less than the Planck constant h. The same holds for the product of time and energy uncertainties, since the phase uncertainty limits the precision of time determination by the period of one turn in the screw motion  and the energy of object can be altered by the quantum of photon. The product of the two uncertainties is again the Planck constant.

3. Results and discussion

3.1. Local indefinite parameters and fictitious coordinates of space and time

3.1.1. The strange behavior of photons in the theory of QED

In the screw model of photon, one can raise the question how a cylindrical motion can represent spherical propagation for the light. For answering this question we can start from the concept of the spatial “direction” in the case of the elementary processes. In the macroscopic world this concept is developed in our mental perception in order to organize information transferred by great amount of photons arriving from different points in the space, accordingly, the direction can not be considered as an a priory category, it depends on how we compare the different information collected in the course of observation. When the propagation of a single photon is mathematically described in a state lacking any interaction with its surrounding, we cannot compare the orientation of propagation with any external information, thus in the non-interacting state of photons the category of direction becomes meaningless, or in other words, the direction represents a fictitious coordinate. The situation is analogous when the polarization of photons or other particles is measured. The measuring device constitutes a macroscopic instrument including great number of atoms and molecules. The flood of photons arriving from the constituents of apparatus defines the direction, which serves as a base for the measurement of polarization. For this reason this measurement utilizes the information obtained not only from the individual photon under investigation but also from a large amount of photons emitted by the macroscopic instrument. A further question can be raised about the definiteness of polarization in the state preceding the interaction between the investigated photon and the measuring device. Obviously in the non-interacting stage, the photon state is not affected by any properties of the experimental device, that is, no information is available for the spatial direction defined by the instrument, which fact is expressed in the quantum mechanical formalisms by the principle of superimposition and identical probability amplitudes are postulated at all directions. For this reason we can consider the direction as a fictitious coordinate and speak about spherically propagating photons when the self-motion is presented by a helical screw. The appearance of superimposition in the mathematical formalism is the basic turning point that separates quantum mechanics from classical physics and assigns a wave character for the particles. This distinction can give a clear explanation to the dilemma of Schrödinger’s cat [8]. While for the quantum system, we can speak about a non-interacting state with fictitious space and time, the cat in the sealed box is always in an interacting state where the space and time are real. The interaction with the surroundings of cat is very different if the animal is dead or alive, thus we can not describe the state of the cat by neglecting the impact of surrounding and we can not apply the superposition principle, which is valid only for the fictitious space and time.

The distances and time become also fictitious for non-interacting photons, which is in accordance with the theory of special relativity [9] rendering zero length for the traveling path due to the Lorentz contraction and zero time due to the time dilution in the self system of photon. The time dependence is also missing for electrons orbiting in stationary state. Originally Bohr [10] introduced the concept of stationary orbits in atoms when he defined an orbital motion for electrons without electromagnetic radiation. In quantum mechanics these orbits are described by the time-independent eigenfunctions of the Hamiltonian. The time-independent orbital motion is again a consequence of the fictitious time.

The fictitious nature of space and time also rationalizes the appearance of unusual perturbation terms in the theory of QED [3] when the anomalous magnetic moment is calculated. The computations include also perturbation terms visualized by the Feynman diagrams when the impact of virtual electron-positron creation is taken into account even before the pair formation. Since in the QED formalism the virtual photons are described by fictitious coordinates, the usual constraints of real space and time are released, which are exemplified when the local motions can be faster than the speed of light and the flow of time can be reversed. The fictitious character of space is also manifested in the propagation of photons in which all points in the itinerary are considered as creating centers for new spherical waves, which are represented by sequences of the local arrows in the interpretation of Feynman. These arrows form a complex network for a single photon, while the actual interaction is determined by a resulting arrow composed as a sum of all possible individual arrows for which the orientation is governed by the “internal clock” of photon. The individual arrows represent the potential steps in the elementary process, while the final arrow indicates which possibility is realized in the experiment. As we pointed out in our previous paper [1], these arrows can be represented by the temporary phase in the screw motion, and the final phase of the resulting screw can determine which one is actually realized among the possible outcomes of an elementary event.

3.1.2. Bell’s inequality and counterfactual definiteness

In the screw model we postulate an intrinsic phase for the emitted photons, and we investigate if this phase can ensure determinism in the elementary processes. The internal “clock” of the photon is connected to the real time only at the two observable processes, namely at the creation and at the absorption, thus these events determine the real time elapsed in the course of photon propagation, which time prescribes the overall change of phase. As concerning to the spatial orientation for the propagation of photon, before the detection the intrinsic phase is not yet connected to the direction prescribed by our measuring device, consequently, we cannot assign a definite polarization to the intrinsic phase of the non-interacting photon. The polarization remains indefinite even if it has already been measured right after the emission, since the interaction will change the original phase and we cannot have any definite relation between the final polarization and the original phase of photon. This fact makes a decisive difference between the intrinsic phase in the screw model and the hidden variables assumed by Bell [7], namely the former parameter can not be considered as a classical variable, while the latter one is defined under the principle of classical physics. To accentuate this difference we introduce the term local indefinite variable or parameter for classifying the intrinsic phase of screw motion and speak about fictitious direction for the propagation of photon. In the derivation of Bell’s inequality, the basic point is the assumption of counterfactual definiteness [4], stating the outcome of any (even counterfactual) events is completely defined. This definition postulates the hidden parameters according to the concept of classical physics and for this reason the Bell’s inequality leads to the conclusion, that we can not extend quantum mechanics by any classically defined hidden variables. More concretely, while Bell’s concept of hidden variables assigns definite polarization for the photons at any time, in the case of indefinite variables, the polarization is defined only when the measurement has already been completed. It is the reason why the existence of local indefinite variables does not contradict to the laws of quantum mechanics, and the principle of determinism is in line with a probabilistic theory for elementary processes.

3.1.3. The reduction of wavefunction

 A clear distinction of fictitious and real time is also important for interpreting the “reduction” of wavefunction [9]. It is customary to speak about the reduction or collapse of the wavefunction when a measurement is carried out. Before the physical object interacts with the measuring device, the quantum mechanical system can be characterized by superimposition of states rendering probability distribution for the studied physical quantity, but as a consequence of measurement the measured quantity should have a well defined value, which corresponds to one of the eigenstates. According to our concept, the reduction of wavefunction just reflects the idea that before the interaction, which is necessary for gaining information for the physical quantities, we can use only fictitious coordinates and have only limited knowledge about the elementary system, and this limitation is acknowledged in quantum mechanics by introduction of the probability amplitudes. When the measurement is carried out, the obtained information is manifested by a definite wavefunction without any statistical character. In other words, the state of the microscopic system is not collapsed; this reduction is simply a mathematical operation when the fictitious coordinates are replaced by the real coordinates as the result of a real interaction.

3.2. Indefinite variables in atoms and molecules

In order to develop a consequent deterministic picture for all elementary processes, we have to postulate indefinite variables not only for the self-motion of particles, but also for the orbital trajectories of electrons in atoms and molecules. According to quantum mechanics the wavefunction can tell the spatial distribution of orbits, but no information can be given for the temporary position of electrons in the stationary states. The deterministic model is not equivalent to a completely defined classical motion for the electrons, since it requires at least two indefinite parameters in the course of orbital motion, namely the phase and the orientation. The phases of the orbital- and self-motion can be connected, but this relation is also indefinite.

For elementary objects the local symmetry reflects information deficit when certain orientations can not be distinguished. For this reason in quantum mechanics the symmetry plays a decisive role and the wavefunction is classified according to the irreducible representations of symmetry group [11]. The symmetry defines non-distinguishable quantum mechanical states where the dimension is given by the irreducible representations. In order to obtain deterministic theory, we assume indefinite variables that could resolve this ambiguity. Elements of the symmetry group are defined by the transformations not modifying the overall Hamiltonian of system, in atoms it is the rotational-inversion group, in crystals the finite point groups, respectively. The dimension of space formed by the indefinite variables depends on the actual symmetry: the higher is the symmetry the larger can be this dimension. In molecules and crystals the electrons have interaction with a set of nuclei, which gives information about the directions, and due to this additional information the number and degree of indefinite variables become smaller, which is reflected in the smaller dimension of irreducible representations of point groups compared to that of the spherical group.

As an example let us look the motion of electrons in atoms. Here the wavefunction is classified by the l orbital quantum number assigned to the 2l+1 dimensional irreducible representations of rotation-inversion group. The integer l value gives also the angular momentum in ħ units.  The seeming contradiction can be again explained by the fictitious direction leading to identical probability amplitudes at all orientations. Thus we attribute the isotropic distribution of s electrons to the fictitious direction of linear trajectories and not to any kind of secondary motion, which would rotate the orientation of linear trajectories. It means that in quantum mechanics the concept of isotropy is equivalent to the missing information about orientation. As we have already mentioned, the same concept can also explain how the cylindrical screw motion of photons can result to spherical waves.

 For the atomic orbits with non-zero angular momentum, there are degenerate energy levels and the electronic states can be represented by any linear combination in the respective basis. This feature is again related to the fictitious orientation. The inversion symmetry plays also important role in the properties of wavefunction, which is symmetric for even and anti-symmetric for odd l quantum numbers. In molecules and crystals the dimension of indefinite variables is reduced, since we have additional spatial information and in this case there are only finite number of elements in the point group. Look now the three anti-symmetric p orbits when l = 1. For spherical symmetry any linear combinations of these orbits are equivalent due to the lacking information for directions. In the case of rhombic symmetry where only the inversion symmetry exists, we have one-dimensional representations defining separately the p_x, p_y and p_z orbits. The exact determination of these orbits is related to the knowledge of principal directions. Since the angular momentum is non-zero, the orbits have zero probability at the center and due to the anti-symmetry, the probability amplitude changes sign while crossing the center, e.g. above the xy plane p_z is positive, below negative. For this orbit the probability amplitude is zero not only at the center but also in the whole xy plane. The question can be raised how an electron can communicate between the two lobes if we have zero probability for finding an electron in the plane of interception? No classical corpuscular model can answer this question, but it is in accordance to the wave characteristics of particles by assuming interference caused by the alternating sign of wavefunction (there are interference maxima both above and below the plane and minimum at the plane of interception). We assign this wave-like behavior to the inversion symmetry, since we cannot distinguish if the electron is above or below the xy plane. The indefinite character of inversion is expressed in the quantum mechanical formalism by the same absolute value of probability amplitudes for the two lobes of the p orbits. We can postulate as a general rule in quantum mechanics: anything that is not distinguishable experimentally is not distinguished, and everything that is indefinite is not defined.

In the framework of screw model, the wave nature of particles is compatible with the assumption of the deterministic elementary processes if we take into account indefinite variables. Quantum mechanics can tell the probability of transitions between two states of electron, e.g. when an s state is excited into a p state, but for a selected atom we cannot tell when the excitation will take place. In this case the causality requires well-defined relation between the indefinite parameters, and this relation has to be satisfied when the electron is excited to a higher level. This concept can be extended for multi-electron configurations. According to quantum mechanics the electrons are non-distinguishable and the wavefunction of the whole configuration changes the sign when two electrons are interchanged. In this case the permutation symmetry produces indefinite state function, since we do not have any information that could differentiate two electrons in the system.

The concept of indefinite parameters can be extended also to the field of nuclear physics. In this case indefinite variables can be assigned to the internal motion of constituents of the hadrons. The Standard Model [12] can give predictions for the probability of nuclear processes, but not able to tell when e.g. a selected neutron will decompose. For a deterministic theory we can assume a resonance between the rotational phases of three quarks, which can promote the beta decay.

3.3. Interference phenomena and the intrinsic phase of particles

While the phase in the wavefunction is eliminated when the expectation values or transition probabilities are calculated, it has crucial role when interference takes place. Interference can be observed not only for photons, but also for electrons and heavier atomic or molecular objects, which indicates the wave aspect of elementary particles. We interpret the wave aspect of elementary objects by the screw motion of photons and fermions combined with the fictitious nature of space and time coordinates in the non-interacting state of particles. In quantum mechanics interference is considered only between identical objects, like photons with the same frequency, or electrons with the same rest mass. In the screw model we generalize this concept speaking about asymmetric interference between individual photons and electrons: their interaction is determined by the relative phase between the respective self-rotations. In this interpretation the photons reaching the surface of a glass plate will be reflected, when due to the small phase difference, the interference pattern has a maximum, while the photon can transmit the glass if due to the lack of phase agreement an interference minimum is produced. The asymmetry of this interference is manifested by the smaller probability at the maximum than at the minimum.

3.4. Examples of EPR paradoxes

3.4.1. Single photon experiments

There are a few variations of EPR experiments when single-photons or particles are observed. In one of the thought experiment a half transmitting mirror and two detectors are applied for observing either the transmitted or the reflected photon. When single-photons are detected, only one of the two detectors can give a signal. In other arrangement, the photons are emitted from a source inside of a sphere, in which detectors are placed at all directions. If the photons are detected one by one, each time only one detector can give signal, but how this special detector is selected by the photon and why the other detectors remain silent? These questions lead Einstein to the conclusion that quantum mechanics is not a complete theory, and a hidden variable must determine which direction is chosen by the individual photons. The above thought experiment is interpreted by the Copenhagen school [7] as a reduction of the wavefunction claiming the original function describes all possible outcomes of the experiment built up as a superimposition of states, but as a consequence of the detection, the wave function is reduced into one of the states. By the screw model [1] we can interpret this phenomenon in terms of the relative phase between a photon and the interacting electron. The relative phase is an indefinite variable, and when this parameter has the proper value for the electrons in one of the detector, the respective device can give the signal. The observer can not predict the expected outcome of experiments due to the unknown prehistory of particles in the experimental device.

3.4.2. Two-photon experiments

There is another type of EPR experiments when from a source two particles (two photons or an electron-positron pair) are simultaneously emitted and the particles are detected equal distance from the source in opposite direction [5]. If the polarizations are detected in both detectors, the results are correlated; it means that we can have information from a particle at one point when we carry out the measurement at a distant spot. In terms of the concept of Copenhagen school, there is a strict correlation between the two reduced wave functions, which requires that the two particles should be in contact at any distance, that is the interaction has non-local character. The screw model can explain the correlation without assuming non-local interaction. For the simultaneously emitted particles the initial phases of self-rotation are correlated due to the conservation laws, but this correlation does not require the determination of phase, only the difference of phases should be fixed. It means that the assumption of Bell is too stringent when he defines the hidden parameter completely prescribing the starting polarization of simultaneously emitted photons. It is adequate defining the relative polarization of the two photons, which can be emitted with opposite polarization e.g. in the experiment of Aspect [5]. Since the frequency of the two photons agrees and the polarization is measured at equal traveling distance, their relative phase of self-rotation, and consequently the relative polarization still remains the same.

3.4.3. Two-slit experiments

A further type of EPR experiment is represented when the light can transfer in two different slits and interference is observed in a screen for coherent monochrome light. If individual photons are separately detected, the frequency of strikes in the screen agrees with the intensity of interference bands, which means that the individual photon must transfer simultaneously through both slits. It is in accordance with the screw model if we represent the photons by a set of cylindrical screws propagating in each direction by the same probability and the same phase. As we pointed out earlier, the uniform probability distribution is a consequence of the fictitious nature of direction. Actually this model represents a spherically propagating wave where inside a sphere with the radius r = ct each point can be considered as a source of a new spherical wave (here t is the real time elapsed after the emission of photon). The photon reacts predominantly with one of the electrons in the absorbing screen, but it can happen that none of the electrons fulfill the necessary resonance condition. In this case both slits are achieved by the photon where two spherical waves are created, which can produce the interference after the transmission through the slits. Feynman [2] discusses in detail the situation where the photons are detected also on the slits to see which slit that actually transmits the photon. In this case, however, no more interference can be observed on the screen. In the screw model we can explain this behavior by the interaction of the incident photon with the activated electron in the detector. From the two detectors only one can detect the photon, in which the phase of electron is adequately close to the phase of photon. We can not control, however, the prehistory of electrons, thus the interaction will change the original phase of photon at a random way obliterating any interference.

The above examples show how the screw model can resolve the EPR paradox offering an indirect support for the soundness of our previously outlined physical concept.

4. Conclusions

The EPR paradox can be resolved by a model based on the screw motion of particles combined with the concept of fictitious space and time coordinates in the non-interaction state of elementary objects. The key concept is the existence of indefinite parameters, which can offer determinism for the elementary processes without contradicting to the probabilistic laws of quantum mechanics. In the case of indefinite parameters the Bell’s inequality is ruled out, since the principle of counterfactual definiteness is not applicable, and this standpoint makes unnecessary for assuming entangled states and non-local interactions. In this aspect quantum mechanics is considered as a pragmatic theory, which applies an adequate mathematical formalism for describing elementary processes, but this theory avoids interpretation of the metaphysical questions about causality and determinism.

We postulate existence of the indefinite variables for all quantum mechanical processes starting from the self motion up to the propagation and orbital motions of particles or photons. The indefinite character is also related to the limited information of particles about space and time. The indefinite variable controlling the phase of self-rotations as well as the temporary position and momentum of particles can select the time when the elementary events take place, but there is no chance for the observer to determine this parameter due to the unknown prehistory of particles. The reduction of wavefunction in the course of measurement is interpreted by the fictitious nature of space and time in the non-interacting state, which coordinates are replaced by the real space and time when interaction occurs. The fictitious coordinates also rationalize why in the QED formalism the propagation of virtual photons have anomalous properties when e.g. the local speed exceeds the speed of light or the flow of time is reversed.

The above concepts are demonstrated for a few cases of EPR paradox including thought experiments with one- and two-photons; furthermore the problem of single photon diffraction is analyzed in the two-slit experiments.

 Further subjects in the blog, see:  "Paradigmaváltás a fizikában"

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