The Theory of Virtual Particles as an Alternative to Special Relativity

Transcription

1 International Jornal of Physics, 017, Vol. 5, No. 4, Available online at Science and Edcation Pblishing DOI: /ijp The Theory of Virtal Particles as an Alternative to Special Relativity Lidmila B. Boldyreva * The State University of Management, Rssia *Corresponding athor: boldyrev-m@yandex.r Abstract Special relativity (SR) made it possible to explain a nmber of ysical enomena, which shows that its postlates: the principle of constancy of the speed of light and the principle of relativity (the latter sggests the invariance of ysical laws with respect to Lorentz transformations reflecting the dependence of mass and size of moving bodies on their speed) are based on the properties of a ysical process. It is shown in this paper that sch a process is the creation in the ysical vacm of a virtal particles pair by the qantm entity that is a singlarity in electric and/or magnetic fields and sch properties are properties of this virtal particles pair, in particlar, the dependence of its mass and size on the speed of the entity creating the pair. Based on the properties of virtal particles we may assme that theory of virtal particles may be an alternative to SR, it may describe the ysical enomena withot sing the for-dimensional kinematic formalism, remaining in the framework of the model of three-dimensional space and independent time. A sbstantiation of this assmption is that the eqations describing the ysical enomena derived in SR can be derived as well by taking into accont the creation of virtal particles pairs by qantm entities while sing the Galilean addition of velocities. Keywords: special relativity, virtal particle, Doppler effect for light, spin-orbit interaction, relationship between mass and energy, qantm mechanics Cite This Article: Lidmila B. Boldyreva, The Theory of Virtal Particles as an Alternative to Special Relativity. International Jornal of Physics, vol. 5, no. 4 (017): doi: /ijp Introdction Special relativity (SR) made it possible to explain a nmber of ysical enomena, some of them as it was formerly spposed might be described only by the formalism of SR (for example, the spin-orbit interaction of electron in an atom, the enomena relating to optics of moving bodies, in particlar, the transverse Doppler effect for light) [1]. The fact that SR may describe ysical enomena correctly shows that SR postlates: the principle of constancy of the speed of light and the principle of relativity (the latter sggests the invariance of ysical laws with respect to Lorentz transformations reflecting the dependence of mass and size of moving bodies on their speed) are based on the properties of a ysical process. It is shown in this paper that sch a process is the creation in the ysical vacm of virtal particles pair by the qantm entity, which is a singlarity in electric and/or magnetic fields, and sch properties are properties of this virtal particles pair. Lorentz transformations reflecting the dependence of mass and size of a moving entity on its speed express essentially the dependence of mass and size of virtal particles pair created by the moving qantm entity on its speed. It is shown also that the second SR postlate (the principle of constancy of the speed of light in all inertial systems) is associated with the interaction of the virtal particles pair that constittes a oton with virtal particles pairs created by qantm entities that constitte the inertial reference system. It is shown in this paper that the theory of virtal particles may be an alternative to SR, it may describe the ysical enomena withot sing the for-dimensional kinematic formalism, remaining in the framework of the model of three-dimensional space and independent time. A sbstantiation of this assmption is that the eqations describing the ysical enomena derived in SR can be derived as well by taking into accont the creation of virtal particles pairs by qantm entities while sing the Galilean addition of velocities. Based on sch properties of virtal particles pair as the existence of spin, electric dipole moment, mass [,3], it is possible: 1) to obtain the relationship U = mc between energy U and mass m, ) to obtain the eqation for spinorbit interaction of atomic electron (determining the fine strctre of energy levels of atoms), 3) to dedce the eqation for the longitdinal and transverse Doppler effects for light (which coincides accrate to β inclsive with the eqation describing the Doppler effect in SR [4]), 4) to describe the origin of spin magnetic moment of elementary spin-1/ fermions [5], 5) to develop a model of magnetic field created by moving charges [6]. Note. It is well-known that derivation of the relationship U = mc was performed by Einstein both with and withot the mathematical formalism of SR while

2 14 International Jornal of Physics analyzing the pressre of light on matter [7]. As shown in this work, the Einstein s derivation is based essentially on the properties of virtal particles pair that constittes the oton Some Properties of a Virtal Particles Pair In this paper the term qantm entity is sed. It refers to the entity whose behavior is described by a wavefnction. If the entity has an electric charge and/or dipole magnetic moment and/or dipole electric moment, it is said to be a singlarity in electric and/or magnetic fields. According to contemporary concepts of qantm mechanics, the qantm entity that is a singlarity in electric and/or magnetic fields prodces in the ysical vacm a pair of oppositely charged virtal particles having spin [,3]. The nmber of ysical enomena explained by the properties of virtal particles pairs created by qantm entities is continosly being increased. Among sch enomena are the van der Waals force between two atoms, Casimir effect (attraction between a pair of electrically netral metal plates), Lamb shift of atomic levels, the spontaneos emission of a oton dring the decay of excited atom or excited ncles, the so called near-field of radio antennas [8,9]. The virtal particles pair has the following properties [,3]. 1) The virtal particles pair is created in the region whose size is of the same order of magnitde as the wavelength of qantm entity that created this pair. The wavelength of any qantm entity relates to its momentm q p q as [10]: q = / pq, (1) where is Planck s constant. ) The virtal particles pair has spin, S v, sch as S v =. () The spin of those particles has the same properties as spin of real particles, i.e. has no definite direction and by the magnitde of spin the magnitde of its projection onto a preferential direction is meant: that can be interpreted as a precession of the spin abot the preferential direction. The precession freqency ω v of virtal particles pair is eqal to the freqency of wavefnction of qantm entity creating this pair [11]. For example, for virtal particles pair that constitte the oton of freqency ω it holds that ω = ω. (3) v 3) The virtal particles pair has mass m v that manifests itself, for example, in that the pair of virtal particles that constittes a oton may be converted in the decay of the latter into a pair of real particles of nonzero mass [10]. 4) As follows from experiments, virtal particles conserve energy and momentm [1]. 5) In the virtal particles pair the virtal particles have opposite electric charges q v. The electric properties of virtal particles are the same as those of real particles. From this it follows: first, an electric field E v exists between the virtal particles inside the virtal particles pair; secondly, the virtal particles pair is an electric dipole, the electric dipole moment d v of the pair is directed oppositely to electric field E v [13]: As it is shown in [6]: E v. (4) S v. (5) 1.. The Mass-energy Relationship The oton in the pre state (not interacting with other objects) has circlar polarization. That is, the oton electric component E performs circlar motion in the plane perpendiclar to its velocity c: E c, (6) with freqency of circlation eqal to oton freqency ω. As the oton is a qantm entity that is a singlarity in electric and magnetic fields, it is itself a virtal particles pair. Conseqently, electric field E is electric field E v existing between virtal particles inside the virtal particles pair that constittes the oton: = v E E. (7) Ths the precession of E, according to (4), (5) and (7), means the precession motion of both spin S v and electric dipole moment d v of virtal particles pair that constittes the oton; the freqency of precession ω v is determined by eqality (3). In trn, the precession motion of electric dipole moment d v means a circlar motion of mass m v of the pair (that is, of mass of electric dipole) with freqency ω v. Conseqently, the energy W m associated with mass m v contains two terms. The first term is the kinetic energy mc v / of translational motion of the center of mass, in which all the mass m v is assmed to be contained. (An inertial frame of reference where the sorce of oton is at rest is considered. According to experimental data the speed of light relative to the sorce is eqal to c.) The second term is defined [14] as: Jvω v /, where J v is the anglar momentm connected with the circlar motion of mass m v. Ths the energy W m is determined as Wv mc v Jω v v / = +. (8) Eqation (8) is written for the virtal particles pair that constittes a oton, and taking into accont the property 4 of virtal particles (Section 1) the following may be accepted: Wm = U ( U is the oton energy). Taking into accont eqality (3) and assming that for the virtal particles pair that constittes a oton J v =, eqation (8) may be written as

3 International Jornal of Physics 143 U = mv c / + ω /. (9) Using the expression for the oton freqency in eqation (9) we have for m v: ω = U / (10) mv U / c. = (11) The right side of expression (11) determines the relativistic mass m of oton [15], and conseqently the eqation (11) is eqivalent to the following eqation: m U / c. = (1) Using eqations (11) and (1) in eqation (9) we obtain the expression for the oton energy in an inertial frame of reference where the sorce of oton is at rest. U = m c / + ω /. (13) De to creation of virtal particles pair by the qantm entity, the total mass M of qantm entity of nonzero rest mass eqals the sm of two smmands: the rest mass m 0 of the qantm entity and mass m v of virtal particles pair created by the entity. M = m0 + m v. (14) If for determining the mass m v of virtal particles pair created by a qantm entity of nonzero rest mass to se an eqation analogos to that sed for determining the mass of virtal particles pair that constittes a oton (eqation (11)), then we have: where mv Uq / c, = (15) U q is the energy of the qantm entity that created the virtal particles pair of mass m v. If Uq m 0 / = ( is the qantm entity speed), then sing eqation (15) in eqation (14) we have: M m0 m 0 /( c ) expression for M at with Lorentz transformation [1]: c = +. This << accrate to ( ) m 0 M = = m o, 1 / c c c where ( / ) / c coincides o c are smmands of a lower order of magnitde than / c. Note. It is known that Einstein also derived the relationship between energy and mass withot sing the mathematical formalism of SR while analyzing the pressre of light on matter [7]. His derivation is based on the fact that the momentm which is imposed on matter by a short flash of light is eqal to its energy divided by c. This means that in Einstein s derivation the oton momentm p eqals p = U / c. According to eqation (11), p = mc v, that is, p is defined by the properties of the virtal particles pair that constittes the oton. Ths one may state that in this case Einstein while deriving the relationship between energy and mass sed the properties of virtal particles pair that constittes the oton The Doppler Effect for Light (Longitdinal and Transverse) In this Section it will be shown that sing the eqation (13) for the energy associated with the oton mass, it is possible to describe both the longitdinal and the transverse Doppler effect on the basis of the Galilean addition of velocities, see also [4]. Consider an inertial frame of reference fixed relative to the detector, where the sorce of light is moving at velocity v. The sorce of light is assmed to be at rest with respect to the Earth, and according to experimental data the speed of light relative to the sorce is eqal to c. It is also experimentally established [10] that the absorption of light occrs in qanta of energy ωd, where ω d is the freqency of the light being detected. If the mass of the detector as well as the mass of the sorce are great, both the motion of the sorce de to recoil in the emission of oton and the motion of the detector de to the pressre of light can be neglected. Then in the interaction of the oton and the detector all the energy U of the oton in the inertial frame fixed relative to the detector is eqal to the detected energy ωd, that is, U = ωd. For determining the freqency ω d, eqations (10), (1) and (13) are sed. Taking into accont that the first smmand in eqation (13) defines the kinetic energy of relativistic mass of oton and that the detector moves relative to the sorce at velocity v, the eqation for determining the freqency ω has the form: ω ( c+ v) ω d = +, c ω (16) where ω is the oton freqency in the frame of the sorce of otons. Introdcing the vector w directed from the sorce to the detector, w = c+ v, eqation (16) can be expressed as: ( ) 1 ωd ω w = +. c (17) Qantity w/ c can be derived from the following eqation: c = ( w v ) = w + v wv cos θ ( θ is the angle between vectors w and v). Dividing both sides of this eqation by c and denoting β = v/ c we obtain / βcos θ / (1 β ) 0 ( w c) ( w c) =. Hence / = cos ± 1 sin w c β θ β θ = β β sin θ ± 1 β sin θ. d

4 144 International Jornal of Physics Taking into accont that w/ c > 0 we obtain only one soltion: w/ c = βcosθ + 1 β sin θ sing which in Eq. (17), we obtain: β d = 1+ cos ( cos + 1 sin ). ω ω β θ β θ β θ To an accracy of β 3 the expression for ω d may be written as: ω d = ω β 1+ βcosθ + β cos θ 3 3 β β 3 3 cosθ + cos θ + o β ( ), (18) 3 where o( β ) are smmands of a lower order of magnitde than β 3. Eqation (18) coincides accrate to β inclsive (at ϑ = π / accrate to β 3 inclsive) with the eqation describing Doppler's effect in SR [1]: 1 β ωd = ω 1 βcosθ = ω β 1 + βcosθ + β cos θ. 3 β cosθ + β cos θ + o( β ) Let s consider the special cases. If cosθ = 0, the formla describing the transverse Doppler effect follows ω = ω 1 β /. If cosθ = 1 or from Eq. (18): d ( ) cosϑ = 1, the formla describing the longitdinal Doppler effect follows from Eq. (18): 1 ω ω β β / ω = ω 1 β + β / d = ( + + ) or d ( ) respectively. Note. In the case discssed above, the sorce of light is at rest relative to the Earth. However, Eq. (18) will not change if the sorce does move with respect to the Earth and the oton s speed is made eqal to the fndamental constant c with respect to the Earth, with the energy being transformed according to Eq. (16) The Spin-orbit Interaction A pair of oppositely charged virtal particles is an electric dipole, whose electric dipole moment d v we shall determine according to property 1 of virtal particles pair (see Section 1) as follows [13]: where qv q, = (19) q v is the charge of a virtal particle, q is the wavelength of qantm entity creating the pair. In the electric field E a moment M will act on the electric dipole: M = E. (0) We will show, sing the electron in a hydrogen atom as an example, that it is the moment М that determines the spin-orbit interaction of qantm entity moving in electric field. Let s assme that the specific charge of the virtal particle created by electron is proportional to the specific electron charge (note that the experiments condcted by W. Kafmann on deflection of beta-rays emitted by radim make one believe that the mass of electron is prely of electromagnetic natre [16]) that is, to e/ m e (e and m e are respectively the electric charge and mass of electron). Ths qv / mv = e/ me. Using the latter eqality, eqations (1) and (15), and the expression for Bohr s magneton µ B = e ( me c) in eqation (19), we obtain for d v : µ B Uq =. c p q (1) The energy of electron in a hydrogen atom is eqal to its kinetic energy (withot taking into accont its rest energy), i.e. Uq = m q / and pq = m q. Using the expressions for U q and p q in the eqation (1) we obtain: µ B =. c () If for the virtal particles pair created by electron moving at velocity (<<c) it holds that d v, (3) then from eqations (0), () and (3) it follows: µ M B = ( E ) and the right side of expression for M is c the same as that for maximm vale of the spin-orbit interaction energy of the electron in a hydrogen atom: µ ( U B s o ) = max ( E ). In this case E is the electric c field strength prodced by the atomic ncles at the location of the electron. The eqation for U s o was derived by L. Thomas with de accont of general reqirements of relativistic invariance (introdcing the infinitesimal rotation of electron) [17]. As follows from eqations (4), (6) and (7), d v c, that is, the deflection angle θ v between precessing electric dipole moment d v of the virtal particles pair that constittes the oton and the oton velocity c eqals π /. According to (3), at <<c the deflection angle θ v between the precessing electric dipole moment d v of the virtal particles pair created by electron and electron velocity may be taken to be eqal to zero. Conseqently, while the speed of qantm entity changes from 0 to c, the angle θ v between precessing electric dipole moment of the virtal particles pair created by this entity and its velocity changes in the range from 0 to π / (Figre 1(a)). That is, the vale of sin ( θ v ) changes from 0 to 1 and we may introdce the expression:

5 International Jornal of Physics 145 ( ) sin θ v = / c. (4) According to eqation (5), angle θ v determines also the deflection angle between precessing spin S v of virtal particles pair and velocity of qantm entity that created this pair. Ths projection ( S v ) of spin S v on velocity while taking into accont the eqation () is determined by expression: ( ) = ( π + θ ) Sv cos v. (5) Using eqation (4) in eqation (5) and taking that θ v varies in the range from 0 to π /, we obtain: ( ) = ( θ ) = Sv cos v 1 v / c. (6) Figre 1. The characteristics of the virtal particles pair created by a charged qantm entity: variant (a) the qantm entity has a negative charge, variant (b) the qantm entity has a positive charge. S is spin, v S is the projection of spin on the direction of velocity, θ v is the ( ) v angle between and d v, d v is the electric dipole moment Note. If the qantm entity has an electric charge, then electric field E q of this entity acts on the electric dipole moment of the virtal particles pair created by the entity, that is moment Mq = E q exists. Then the action of moment M q reslts in that the angle θ v between d v and varies in the range from π to π + π /, while the speed of positively charged qantm entity changes from 0 to c (Figre 1(b)). In this case, sing eqation (4) we obtain S : for ( ) v ( ) = Sv 1 v / c. (7) Ths according to eqations (6) and (7), the vale of spin of virtal particles pair created by both positively charged and negatively charged qantm entity decreases in the direction of its motion (at velocity ) by 1 / c times, which is eqal to the Lorentz transformation [1] The Eqalization of Speed of Light in Inertial Systems The second SR postlate (the principle of constancy of the speed of light) states: in all inertial systems the speed of light has the same vale when measred with length measres and clocks of the same kind. In this Section it will be shown that this postlate may be de to the interaction of virtal particles pair created by a oton with virtal particles pairs created by qantm entities that constitte the inertial system (and determine, in fact, its inertial properties). One of the first works containing the ysical interpretation of the eqalization of the speed of light in inertial systems to a definite vale is the work by Fox [18]. The stdies by Fox were directed at spporting the Ritz emission theory, according to which the fndamental constant c is the speed of light with respect to the sorce in the vacm and the Galilean addition of velocities holds [19]. Fox sed the extinction theorem of Ewald and Oseen [0]. The theorem states that if an incident electromagnetic wave traveling at a speed c appropriate to vacm enters a dispersive medim, its fields are cancelled by part of the fields of the indced dipoles (macroscopically, by the polarization) and replaced by another wave propagating with a ase velocity characteristic of the medim. The incident wave is extingished by interference and replaced by another wave. The motion of the sorce and the speed of light relative to it are irrelevant in this theorem. There are, however, some experiments that are not explained by the extinction theorem, for example the experiment performed at CERN, Geneva, in 1964 [1]. In this experiment otons were prodced by the sorce moving at speed of c relative to the measrement devices. Photons speed was measred by time of flight over paths p to 80 meters; within experimental error it was fond that the speed of the otons was eqal to c relative to the same measrement devices. The extinction theorem, in which the interaction of a oton and a medim takes place by means of the magnetic and electric components of oton, does not explain the reslts of the experiment. The eqalization of the speed of light fond in experiments indicates the existence of some other interaction in addition to that. Taking into accont the creation of virtal particles pairs by qantm entities, the extinction theorem mst be extended by considering the interaction of virtal particles pair created by the oton and the virtal particles pairs created by qantm entities that constitte the medim. As follows from Section 3, in the eqalization of the speed of light the oton energy is transformed according to eqation (16).. Conclsion I. Special relativity is based on the properties of virtal particles pairs created by qantm entities in the ysical vacm. 1) For the oton the relationship U = mc is a relationship between energy U of the virtal particles pair, which constittes the oton, and the pair s mass m (c is the grop speed of light). ) The total mass M of a moving qantm entity is the sm of two masses: the rest mass m 0 of this entity and the mass of the virtal particle pair created by the moving qantm entity. If the energy of qantm entity eqals its kinetic energy and speed of the entity meets the condition << c, then expression for M accrate to ( / c ) coincides with Lorentz transformation: m 0 M = = m o, 1 / c c c

6 146 International Jornal of Physics where ( / ) o c are smmands of a lower order of magnitde than / c. 3) The vale of spin of virtal particles pair created by qantm entity (both positively charged and negatively charged) decreases in the direction of motion by 1 / c times, which corresponds to Lorentz transformation. 4) The ysical basis of the second SR postlate (the principle of constancy of the speed of light) is the eqalization of the speed of light in an inertial system to the same vale c as a reslt of interaction of the virtal particles pair that constitte the oton with the virtal particles pairs created by qantm entities that constitte the inertial system (and determine, in fact, its inertial properties). II. The theory of virtal particles may be an alternative to SR, it may describe the ysical enomena withot sing the for-dimensional kinematic formalism, remaining in the framework of the model of three-dimensional space and independent time. A sbstantiation of this assmption is that the eqations describing the ysical enomena derived in SR can be derived as well by taking into accont the creation of virtal particles pairs by qantm entities while sing the Galilean addition of velocities. Some examples are the following: 1) The precession motion of spin of virtal particles pair that constittes the oton allows one to dedce the eqation U = mc. ) The properties of virtal particles pair as an electric dipole allows one to dedce the formla for the spin-orbit interaction of an electron in an atom; this formla determines the fine strctre of energy levels of atom. 3) The precession motion of spin of virtal particles pair that constittes the oton makes it possible to dedce the expression for transformation of freqency (and conseqently of energy) of oton when it passes from one inertial system to another inertial system moving relative to the first one at velocity v: ω ( c+ v) ω d = +, c ω (8) where ω is the freqency of oton in the first inertial system, ω d is the freqency of light in the inertial system moving relative to the first one at velocity v. In this case the eqalization of the speed of light in the second inertial system to the same vale c takes place. 4) Using eqation (8) for transformation of freqency of oton when it passes from one inertial system to another inertial system moving relative to the first one at a speed v, the formla describing the longitdinal and transverse Doppler effects for light can be derived. References [1] Born, M, Einstein s Theory of Relativity. Dover Pblications, New York, 196. [] Mandl, F. and Shaw, G, Qantm Field Theory. John Wiley & Sons, Chichester UK, revised edition, 56, 176, 1984/00. [3] Myakishev, G.Ya, Virtal Particles. In book Physics of microworld. Little encyclopedia , Soviet Encyclopedia Pblishing Hose, Moscow, 1988 (In Rssian). [4] Boldyreva, L.B. and Sotina, N.B, Hidden dynamics in relativistic kinematics, Physics Essays, 16 (3), 1-6, 003. [5] Boldyreva, L.B, The Spin Magnetic Moment of Electron as a Photon Property, International Jornal of Physics, 5 (3), 67-3, 017. [6] Boldyreva, L.B, The Model of Magnetic Field Based on the Concepts of Virtal Particles and Qantm Harmonic Oscillators Possessing Zero-Point Energy, International Jornal of Physics, 4 (), 6-31, 016. [7] Einstein, A, Zr electrodynamic bewegter Körper, Annalen der Physik, 3, , [8] Milonni, P.W, The qantm vacm. Academic Press, Inc. Harcort Brace & Company, Pblishers, [9] Baars, J.W.M.; Lcas, R.; Mangm, J.G.; Lopez-Perez J.A, Near- Field Radio Hologray of Large Reflector Antennas, IEEE Antennas and Propagation Magazine, 49 (5), 1-13, 007. [10] Wichmann, E.H, Qantm Physics. Berkeley ysics corse, vol. IV, McGraw-Hill Book company, [11] Boldyreva, L.B, Qantm correlations Spin spercrrents, International Jornal. of Qantm Information, 1 (1), (13 pages), 014. [1] Thomson, M, Modern particle ysics. 1 st edition, Cambridge: Pblisher: Cambridge University Press, 013. [13] Prcell, E.М, Electricity and Magnetism. Berkeley ysics corse, vol., McGraw-Hill Book company, [14] Sedov, L.I, A Corse in Continm Mechanics. Wolters- Noordhoff, Vol. 1-4, [15] Okn, L.B, Mass verss relativistic and real masses, Am. J. Phys., 77, , May 009. [16] Kafmann, W, Die elektromagnetische Masse des Elektrons, Physikalische Zeitschrift, 4 (1b), 54-56, 190. [17] Thomas, L.T, The Kinematics of an Electron with an Axis, Philosoical Magazine, 3 (1), 1-, 197. [18] Fox, J.G, Evidence against emission theories, American Jornal of Physics, 33, 1-17, [19] Ritz, W, Recherches critiqes sr l Électrodynamiqe Générale, Annales de Chimie et de Physiqe, 13, 145, [0] Jackson, J.D, Classical electrodynamics, 3d edition. John Wiley, New York, [1] Alvager, T., Barley, J.M, Test of the second postlate of Special Relativity in the GeV region, Physics Letters, 1, 60, 1964.