Beyond Maxwell-Lorentz Electrodynamics

(George Galeczki)

I. Maxwell's Equations

Freeman Dyson published twelve years ago [1] "Feynman's proof of the Maxwell equations". He recalls that in 1948 Feynman showed him this "proof assuming only Newton's law of motion and the commutation relation between position and velocity for a single particle." Although formally obtaining the two "vacuum equations" (i.e. those without source terms), the claimed "proof" of the full Maxwell equations is wrong mathematically, physically and conceptually. On top of all this, it expresses the - nowadays common - arrogance of mathematical physicists giving priority to formalism against empirical facts.

As a matter of fact, Maxwell's equations (ME) represent the mathematical expression of the experimentally discovered laws of Gauss, Ampère and Faraday and are widely used in physics and engineering. Several remarks and comments are in order, each of them being subsequently discussed in more detail:

1/ The basic formulation of ME - as derived from experiments - is in integral form

pertaining to a finite, closed area or volume.

2/ The ME are formulated for continuous fields and are called, therefore, field equations.

3/ ME hold for closed circuits only.

4/ The sources of the fields are continuous charges and continuous current densities.

The discrete, quantized charges introduced in Maxwell's theory are foreign elements.

5/ ME are tautological in the sense that they merely represent relationships between fields

and their sources. One has to provide the initial charge distribution in order to be able to

calculate the field distribution, or vice versa.

6/ ME is unable to describe the interaction between two discrete charges.

7/ ME is unable to supply the equation of motion of one charge in the field produced by all

others.

8/ ME are not suited for the description of open circuits like antennas.

9/ ME are unable to prescribe the exact conditions under which a system will radiate, or not.

The notorious example is Bohr's planetary model of the hydrogen atom.

10/ ME are unable to provide a stable model for the elementary charge.

11/ ME are generally covariant and do not single out the Lorentz transformation (LT) of the

"special" theory of relativity (STR).

12/ ME are formulated in terms of independent, Eulerian coordinates x, y, z, t and partial

derivatives / x , / y , / z , / t .

ME in their original, integral form and in modern notation are:

E.ds = -( B/ t).da                                B.da = 0                                     (1)

D.da r dV                                         H.ds = (j + D/ t).da          (2)

Contained in the above is the equation of continuity:

j.da = -r dV                                                                                                     (3)

where r and j denote charge and current density, respectively.

In all cases the regions of integration are assumed to be stationary and mechanically rigid.

ME in differential form , as derived from (1), (2) and (3) by means of Stokes' and Gauss' theorem, are:

Ñ ´ H = j + D/ t Ñ ´ E = - B/ t                                                                             (4)

Ñ . D = r Ñ . B = 0                                                                                                          (5)

and the corresponding equation of continuity:

Ñ . j = - r / t                                                                                                                  (6)

ME in differential form express the relationship that must exist between the four field vectors E, D, H and B at any point within a continuous medium (?). In this form, because they involve space derivatives, they cannot be expected to yield information at points of discontinuity in the medium. However, the integral form can always be used to determine what happpens at the boundary surface between different media. It follows then, that the tangential components of E and H (except perfect conductors) and the normal components of B and D (if no surface charges are present) have to be continuous at the interface.

II. Maxwell's Equations and "Special" Relativity

As already said, besides generalizing Ampère's circuital law by introducing the "displacement current", Maxwell's achievment was to express the experimental laws of Coulomb, Gauss, Ampère, Faraday in mathematical terms. The modern, vector form of ME was introduced by Gibbs. Einstein's "special" relativity of 1905 has built heavily upon electromagnetism and, assuming the validity of ME in all inertial frames of reference (IFR's) introduced the incomprehensible "postulate of light velocity invariance". This constancy is not that refering to the light source - a wellknown fact in classical wave theory - but to the independence of the velocity of light from the uniform velocity of the observer/detector relative to the source.

Since in the special case of vacuum-as-continuous-medium the ME displayed covariance (not invariance!) under the so called Lorentz transformations (LT), ME and STR became indissolubly tied together, one implying so to say the other. This strategy proved itself very useful, since every criticism of STR was authomatically seen as criticism of ME, thus contributing to the survival of the contradiction ridden STR.

The said bi-univocal correspondence between ME and STR is manifested, however, only if one has in mind the differential form of ME. The reason is that STR is a local, point-event theory, with local simultaneity and position and velocity dependent time! Due to this feature of STR, only local conservation laws of energy and momentum are compatible with STR. While valid in the hydrodynamic approximation - a continuum theory - the local, differential conservation laws fail in the case of discrete, extended systems. The global time required in this case, independent of position and velocity, is anathema to STR. Farady's law of induction assumes tacitely such a global time and distant simultaneity, thus allowing the definition of inductance and self-inductance for macroscopic, closed circuits. Since the stationary circuits appearing in the integral form of ME are incompatible with STR, it is quite understandable why the STR "philosophy" gave almost exclusive prominence to ME in differential form and eliminated the integral form from physics textbooks and monographies. As a matter of fact, this form - more rich in physical information - is actively in use in engineering books on electromagnetism [2].

III. General covariance of Maxwell's equations

It was repeatedly and forcefully pointed out by Post [3] that Maxwell's equations are general covariant. Post quotes that Kottler, Cartan and van Dantzig (KCD), quite independently of one another concluded on the natural invariance of ME, independent of any metric or linear connection. Post strongly emphasized the clean functional separation obtainable between the constitutive equations { D(E), B(H), J(E) } and the field equations. In this approach the constitutive equations instead of ME carry all the metric information, while the field equations (4) and (5) are covariant under all possible space and time coordinate transformations: Galilean, Lorentzian, conform and so on. The use of (E, D, B, H) rather than two field vectors eliminates the cgs free-space field identification. The latter tied the cgs situation irrevocably to an inertial reference frame. A free-space inertial situation is defined by an explicit constitutive relation:

D = e 0E             ,                 B = µ0H                                                                                    (7)

Which can be proven to be invariant under the Lorentz group, as well as under scale changes of the conformal group. Here is the place to mention the qualitative difference between invariance and covariance: a physical law is said to be invariant under a coordinate transformation when the vectors/tensors entering the law remain unchanged, while in the case of covariance the components of the vectors/tensors are transformed, or in Thomas Phipps' words "scrambled", according to the same rules as the coordinates,. Only after performing this scrambling the equations in question remain form invariant.

The superiority of the KCD approach is that the field equations retain their form when a transition is made from an inertial to a non-inertial frame, in particular a rotating frame. (N.B. Jan Evert Post was the chief theoretician of the ring laser gyro project, which produced the most sensible detector of rotation, i.e. of the degree of non-inertiality). Moreover, the form invariance of ME is independent of whether the fields exist in free space or in matter. The information about the reference frame and the state of motion of the matter therein is conveyed exclusively by the nature of the constitutive equations. The general form of these equations is tensorial and the applications to specific problems was intensively investigated by Post.

IV. The force of Lorentz and Maxwell's equations

It is clear from what has been said till now that the Maxwell field equations (4) and (5) expresses a law of nature and will retain their validity so long their limitation to closed circuits is assured. The tautological nature of ME follows from the absence of "detector charges" in the rhs, since only the source charges and their distribution is considered. It means that the ME are intrinsically unable to provide either a force law between discrete charges, or an equation of motion for individual charge within a system of charges. Here I can mention another fundamental difficulty connected with the discrete vs. continuum dichotomy, reflected in the use of two different kinds of coordinates: the already mentioned four independent, Eulerian x, y, z, t and the three time dependent Lagrangean coordinates x(t), y(t), z(t). The former are suited for field theories, while the later for particle dynamics. Fields are functions of x, y, z, t, meaning that they have different values at the points of a 4D continuum. They don't "propagate" in the 4D continuum. The solutions x(t), y(t), z(t) of the dynamical equations of motion, on the other hand, are 3D vectors and the coordinates "move - so to say - with the particle". This already shows that STR is at least formally compatible with pure field theories, but incompatible with (discrete) particle dynamics [4]. Anyway, quite independently of STR, in order to brake the tautology, ME have to be completed by a force law and an equation of motion for discrete charges, the very program of Lorentz who introduced the quantized electrical charges into Maxwell's field theory. The ME supplemented by the Lorentz force-law (LF) is called Maxwell-Lorentz electrodynamics (MLE). Lorentz himself remained unsatisfied with his force-law:

FL = q (E + v ´ B)                                                                                                     (8)

In his own words [5]: "It is got by generalizing the results of electromagnetic experiments. The first term represents the force acting on an electron in an electrostatic field [F1=qE] . On the other hand, the part of the force expressed by the second term may be derived from the law according to which an element of a wire carrying a currect is acted on by a magnetic field [dF2 = (qv x B , assuming Jds = qv ] . After having been led in one particular case to the existence of the force [F1 = qE] and in another to that of the force [F2 = qv x B ] , we now combine the two in the way shown in the equation, going beyond the direct result of experiments by the assumption that in general the two forces exist at the same time."

(a) The two 'particular cases' here 'combined' are, however, quite incompatible. In one case we have a charge at rest, in the other the charges are moving.

(b) Experiments with 'a wire carrying current' have to do with neutral currents, yet the derivation contradicts this neutrality. The discovery of the Hall effect, formally described as a "modified Ohm's law":

j = s E + k(E ´ B)                                                                                                     (9)

where s is the conductivity and k a constant, seemingly supports (8), but everybody familiar with the experimental set-up used in the Hall effect studies will agree that E and B above belong to different systems: a dc - or ac - source for E and a completely separated permanent or electro-magnet for B. Maxwell's theory requires, however that E and B belong to the same system of charges and currents. As shown elsewhere [6], the Lorentz force should have been written as:

FL = q (E(1) + v ´ B(2))                                                                                             (10)

i.e. a phenomenological external force, rather than fundamental force acting on a charge belonging to the same system, as implied by ME. The upper indexes (1) and (2) indicate that the electric, respective magnetic field belong to different systems, therefore ME and LF do not form a coherent Maxwell-Lorentz theory as claimed in present day textbooks and monographies! The reason for this persisting mess is the seeming compliance with SRT's LT. This belief is, however, totally wrong, since: (a) The LT apply only to E and B belonging to the same system and (b) The velocity v in most applications is a non-uniform velocity between magnets an current carrying wires, while the velocity entering the LT is the uniform relative velocity between two inertial frames of reference. This confusion goes back to Einstein's failure to distinguish between his theory involving schesic velocities referred to abstract "reference frames" and relative velocities between moving masses, as implied by Mach's program. For this reason STR is not a true relativity theory! Using a somewhat different terminology - 'principle of relativity vs. 'principle of relative motion' - this point was discussed in a paper by Bartocci and Capria [7], too. This explains also why the aged Ernst Mach unmistakable declined the rôle of spiritual father of the "special" (very special, indeed!) theory of the young Einstein.

V. Magnetic field, vector potential and induction

In the spirit of the ME in their integral form, B(2) in (10) has always to be produced by a closed current loop:

B(2)(r) = I' (ds' ´ R)/R3                                                                                         (11)

where R = r - r' and the integral is performed around the closed current loop. Attempts to generalize the Biot-Savart law for time-variable magnetic fields have been made by Jefimenco [8] in the form:

B = (µ0/4p ){[j]/r² + (1/rc) [j]/ t} ´ (r/r) dV'                                                 (12)

where [..] denotes the retardation symbol indicating that the quantities between the square brackets are to be evaluated for t' = t - r/c , where t is the moment for which B is calculated. It is interesting to note that that Eq. (12) does not contain displacement currents, thus indicating that although time-dependent magnetic fields and displacement currents are coupled together, displacement currents are not sources of magnetic fields in the conventional sense.

Definition (11) of the magnetic field B - rightly called magnetic flux density in older books - is incompatible with the "Lorentz transformed E field" definition of B in "special" relativistic electromagnetism:

B = V ´ E                                                                                                                     (13)

valid for uniform velocity V only! This incompatibility brings us to the most important issue of (electromagnetic) induction and the status of Faraday's "flux rule". According to textbook (and also monography) knowledge, electromagnetic induction were always due to a time variable magnetic flux crossing a closed conducting loop. Although Faraday discovered both this so called transformer induction as well as the motional induction, only the first is embedded in the integral form of ME formulated for stationary integration regions. This deficiency of the integral ME is, of course, transferred to the differential form of the Maxwellian law of induction:

Ñ ´ E = - B/ t                                                                                                         (4)

The correct expression for the induced electromotive force (emf), in terms of the vector potential A, follows from the integral form:

emf = E.ds - (d/dt)B.da = -(d/dt)(Ñ ´ A).da = -(d/dt)A.ds                 (14)

which provides the formula:

Eind = -dA/dt                                                                                                                 (15)

for the induced electric field Eind. Keeping the integration region stationary, one gets the 'transformer field':

Eind = - A/ t                                                                                                                 (16)

The difference between Eq. (15) containing the total time derivative d/dt and Eq. (16) containing the partial time derivative / t is huge and has fatal consequences for "special" relativity! This is obvious, since in ME the four partial derivatives / x , / y , / z , / t are on equal footing (see, for example, Eq.(6)) and obey the LT. The presence of the total time derivative, by giving to the time derivative a distinct status, destroys the Lorentz covariance of ME!

Here is the place to mention the incompleteness of the traditional formula for the total derivative of a vector field:

dA/dt = A/ t + (v.Ñ )A                                                                                             (17)

and the time rate of change "seen" by a point moving with velocity v in a vector field A [9]:

dA/dt = A/ t + (v.Ñ )A + (A.Ñ )v                                                                             (18)

Although the vector identity:

(v.Ñ )A + (A.Ñ )v + A ´ (Ñ ´ v) - Ñ (v.A) = -v ´ (Ñ ´ A) = -v ´ B                             (19)

for v.A = const. and Ñ ´ v = 0 leads to the 150 years old formula of Neumann:

Eind = - A/ t + v ´ B                                                                                                        (20)

equation (18) covers all known situation of electromagnetic induction, including those where Eq. (19) fails. Eq. (20) is still in exclusive use, although it has never been rigorously justified. Neumann - just like later Lorentz with his force law (8) - just juxtaposed Faraday's and Maxwell's transformer field and the empirical field found in the unipolar induction experiments of Faraday and in the (then) recently discovered Hall effect, called motional induction field. Wesley derived for the first time (!) the most general law of induction which includes (20) as a particular case. The surprising result is that the law based upon (18) is able to describe phenomena governed by the term (v.Ñ )A like the Aharonov-Bohm (AB) effect and the Marinov motor [10]. The demystification of the "strange quantum-mechanical (AB) effect" [10] and its explanation in the framework of electrodynamics has been a real tour de force. The term (A.Ñ )v is presently insufficiently investigated, but preliminary results seem to support its explaining the interaction between two toroidal magnets (closed magnetic field configurations) [11], which, according to Maxwell's electromagnetism should not interact. The local form of the correct law of induction, involving the total derivative (18), puts an end to the perennial disputes between the supporters of fields and potentials, respectively. It has to be clear that the description by means of A is more general than the usual by means of B, since it provides an induced electric field even if Ñ F = 0 (F denotes here the scalar potential), A/ t = 0 and B = Ñ ´ A = 0 .

One is tempted to say that Maxwellian electrodynamics overcame all difficulties and retained its original form since, after all, the use of the truncated form (17) for the total derivative was not Maxwell's fault. The painful fact for STR-supporters is, however, that Eqs. (4) and (5) do not cover all experimental situation and - acutely painful - that they do not remain Lorentz covariant if one replaces the partial time derivative with the total one!!

VI. Beyond the Lorentz force law

The force law of Lorentz (8) applies only in situations where the fields E and B are static, or quasistatic, when radiation could safely be neglected. In such situations, however, Eqs. (4) and (5) decouple in two pairs of electrostatic and magnetostatic equations, respectively:

Ñ ´ E = 0                     ;                       Ñ D = r                                                           (21)

and

Ñ ´ B = j                     ;                         Ñ B = 0                                                           (22)

This explains the upper indexes appearing in Eq. (10), indicating that the sources of E(1) and B(2) are different. Moreover, as already pointed out, the field B has to be produced by a closed current loop. It follows then, that the force of Lorentz can by no means be applied to a system of two charges, so that charge (1) moves in the field B(2) and vice-versa:

d(m1v1)/dt = q1(E(2) + v1 ´ B(2))         ;         d(m2v2)/dt = q2(E(1) + v2 ´ B(1))            (23)

No wonder that this two-body problem would violate the linear momentum conservation law, since the sum of internal forces would be different from zero! The replacement of particle linear momentum p by (p - q.A) - as suggested by the "operator formalism" of quantum mechanics - doesn't save the conservation law.

The inability of Lorentz force to describe the simplest system of two interacting charges is presented in textbooks and monographies as due to the fact that "at least one charge path has to be closed", which is obviously false! In a dense plasma, for example, even in external magnetic fields, where charges are permanently colliding with each other, there may well be no closed paths at all. The fact that the external magnetic field is produced by the closed circuits of the electromagnets is irrelevant for the plasma system!

There exists a rich experimental evidence for the failure of Maxwell-Lorentz electrodynamics at low velocities (v/c << 1), which is lethal to MLE, since the laws of Gauss, Ampère, Faraday were all formulated according to the experimental results obtained for low velocities. Moreover, the interactions between electric currents and magnets were all investigated by using metallic conductors. The microscopic nature of currents in metallic conductors remained undecided, till Weber introduced atomism, i.e. quantized electric charges in physics. He assumed that electric currents consists of a stream of electrons and made first the identification:

Ids = qv                                                                                                                     (24)

With this, Weber succeeded to derive Ampère's law between metallic current elements:

FA = (I.I'R/R3)[-2ds.ds' + 3(R.ds)(R.ds')/R²]                                                         (25)

(I, I' denote currents and R = r - r') from his interaction law between discrete, moving electrons in a metallic conductor:

FW = (qq'R/R3)[1 + V²/c² - 3(V.R)²/2c²R² + R.dV/dt.c²]                                             (26)

vhere V = v - v' and dV/dt denote the relative velocity and the relative acceleration between the moving charges. This truly relativistic (Machian) and instantaneous force law explains all known experiments at low velocities with metallic currents, including Ampère's moving bridge one and the 'electromagnetic rail gun' used in frame of the SDI program [12] which both imply longitudinal forces between parallel metallic current elements. It is notorious that the Lorentz force - acting perpendicular on current elements - is unable to account for these experiments. In spite of this, the belief in uniqueness of the Grassmann-Biot-Savart-Lorentz (GBSL) force law is so strong, that Ampère's law (25) - called by Maxwell "the cardinal formula of electrodynamics" - is not even mentioned in the vast literature on electrodynamics. Once again, this belief is motivated by the seeming compliance of the Lorentz force (8) with the LT, i.e. with STR. Wesley put his finger on the sorepoint of the interminable controversy about Lorentz vs. Ampère force. The supporters of the LF cramp to the equivalence of the two forces when two closed current loops are involved. This is totally irrelevant as it is only a question of the analysis of the mechanical forces between the two objects, the metallic bridge and the remainder of the circuit as a mechanical object. However, Grassmann's derivation of his law (equivalent with that of Lorentz) is only valid for mechanically rigid electrical circuits. This means that the GBSL law cannot be applied to the electrical circuit involved in the non-rigid Ampère bridge!

Weber's law correctly describes the motion of electric charges in vacuum - for example in the electron microscope - since in this case E and B are external and B is produced by closed current loops. The useful phenomenon of "self-focussing", or "pinch effect" wellknown to electron microscopist, is also explainable within the traditional frame of Maxwellian electrodynamics, as attraction between parallel currents.

Remarkably, Ampère's and Weber's laws comply with Newton's third law (actio = reaction), since the forces act instantaneously along the line joining the current elements, or the moving charges. This condition for law velocities is one of the requirements for a system being non-radiating even for charges moving with high (v >> c) velocities. As a matter of fact, both the hydrogen atom and the 'rotating ring electron model' are conservative, i.e. non-radiating, provided the forces are of Weber type!

1/ The characteristic feature of Maxwell's equations is the presence of the terms D/ t and B/ t which couple the electric and magnetic fields and lead to the existence of electromagnetic waves, or radiation. The field equations completed with the Lorentz force law (the MEL equations) are therefore incoherent, since the fields in the LF expression are static, or quasistatic, which means that radiation is neglected. No wonder that the attempts of Dirac and others to add "radiation terms" to the equation of motion of the electron leads to strange "runaway solutions" and other unsolved difficulties.

2/ The 104 years old Liénard-Wichert formula [9] for the retarded potentials corresponding to a point-charge moving with acceleration a along the positive direction of the x-axis has been seriously questioned by Chubykalo and Smirnov-Rueda [13] and independently by Wesley [9]. This indicates that the "special" relativistic Maxwell-Lorentz electromagnetism is an unsatisfactory theory by itself, although the reason is hidden in the mathematics of d'Alembert's wave equation, rather than in the ME themselves.

It is textbook knowledge [13] that the solutions of the wave equation (d'Alembertian) are:

F[r ]/R.dV + F 0 ; A[j]/R.dV + A0                                                      (27)

which are the retarded potentials. F 0 and A0 denote the solutions of the homogeneous wave equation. This is OK. From here one usually derives:

F = q/(R - v.R/c) ; A = qv/(cR - v.R)                                                                             (28)

and the fields:

E = - q(1 v²/c²)(R - vR/c)/(R - R.v)3 + qR ´ {(R - vR/c) ´ a}/(R - R.v/c)3c²               (29)

B = (R ´ E)/R

Chubykalo and Smirnov-Rueda show that formula (29) does not satisfy the d'Alembert equation along the x-axis at any time. This follows from the fact that the wave equation for Exdescribes only transverse modes and - on the other hand - the x-component according to (29) is different from zero. Thus, the Liénard-Wichert potentials, as solutions of the complete set of Maxwell equations, are inadequate for describing the properties of electromagnetic field along the direction of an arbitrarily moving charge. Whitney [14] found another inadequacy of the Liénard-Wichert potentials for describing the properties of relativistic fields. Further, it is easy to verify that the Poynting vector calculated with Eq. (29) equals zero, i.e. no energy transport takes place along the x-axis, while the energy conservation law requires both energy density and divergence of the Poynting vector to be different from zero!

The criticism of Wesley [9] is even more fundamental and relies upon the fact that in the wave equation of a field theory, the four variables x, y, z, t have to be independent (Eulerian) as explained also in [4]. Despite this clear mathematical requirement that r' and t' be independent variables, in the integral representation (28) of the retarded potentials Liénard and Wiechert argued incorrectly that the independent space variable r' is a dependent function of the time variable t'.The change in the 'delta function' - which accounts for the point-like nature of the charge - leads to the correct expressions for the retarded Coulomb potential:

F r = q'/Rr                                                                                                                     (30)

where Rr = R(t)/(1 - v/c) for an observer moving directly away with v < c from the point charge.

3/ The ubiquitous presence of radiation, i.e. of electromagnetic fields detached from their fields requires the existence of a unique, fundamental frame of reference, relative to which the energy transmission velocity is "c". This is a consequence of the fact that the velocity of light doesn't obey either the hypotheses of Ritz ("ballistic propagation", or dependence on the state of motion of the source), or the untenable second postulate of "special" relativity which is discused in [15]. The existence of a fundamental frame of reference which could be experimentally approached by successive approximations, is in line with Maxwell theory, but disagrees with "special relativistic electrodynamics" which states the validity of ME in any inertial frame of reference.

VIII. Conclusions

- Maxwell's equations (ME) retain their validity for closed current loops.

- ME have to be completed with a force-law and a corresponding equation of motion.

- In all applications the force of Lorentz is a phenomenological external force, with different

sources for E and B, the latter being produced by closed circuits.

- MLE fails to explain low-velocity experiments with non-rigid loops.

- Ampère and Weber's force law accounts for all electrodynamic phenomena in which

- MLE in its accepted form is unable to account for all induction phenomena.

- The correct law of induction is given by the total derivative of the vector potential. This is

compatible with ME, but destroys the Lorentz covariance of the theory.

- The vector potential is of primary importance and is uniquely defined for specific systems.

- There is no "gauge invariance".

- Low-velocity Weber electrodynamics is truly relativistic in the sense of Mach.

- The presence of radiation requires an absolute, fundamental frame of reference.

References

[1] Dyson F. J. "Feynman's proof of Maxwell equations", Am. J. Phys. 58 (1990) 209-211

[2] Jordan E. C. and Balmain K. G., "Electromagnetic Waves and Radiating Systems"

(Prentice-Hall, Inc., New Jersey, 1968) p. 103

[3] Post E. J. "Formal Structure of Electrodynamics" (North Holland Publ. Co.,Amsterdam,

1962); "Kottler-Cartan-van Dantzig (KCD) and Noninertial Systems", Found. of Physics,

9 (1976) 619-640

[4] Galeczki G., "Minkowski Scalar Invariant Incompatible with any Equation of Motion"

(Proc. 2-nd Intrnational Workshop: "Physics as a Science", Koeln, 1997)

[5] O'Rahilly A., "Electromagnetic Theory: A Critical Examination of Fundamentals",Dover

Publ. Inc., New York, 1965) Vol. 2, p. 561

[6] Galeczki G., "What does the Lorentz force have to do with Maxwell's equations?",

Galilean Electrodynamics, 9 (1998) 95-98; Galeczki G., "What does the Lorentz force

have to do with special relativity?", Galilean Electrodynamics 8 (1997) 1-4

[7] Bartocci U. and Mamone Capria M., "Symmetries and Asymmetries in Classical and Relativistic

Electrodynamics", Found. of Physics 7, (1991) 787-801

[8] Jefimenko O. D., "Comment on "On the equivalence of the laws of Biot-Savart and

Ampère", by T. A. Weber and D. J. Macomb [Am. J. Phys. 57, (1989) 57-59]", Am. J.

Phys. 58, May 1990, 505

[9] Wesley J. P.,"Induction Produces Aharonov-Bohm Effect", Apeiron, 5 (1998) 89-95;

[10] Selected Topics in SCIENTIFIC PHYSICS" (Benjamin Wesley, Blumberg, 2002)

[11] "Force between two identical coaxial toroidal solenoids" (in print)

[12] Graneau P. and Graneau N, "Newton versus Einstein: How Matter Interacts with Matter"

(Carlton Press, Inc., New York, 1993); "Wesley J. P., Selected Topics in Advanced

Fundamental Physics" (Benjamin Wesley, Blumberg, 1991

[13] Chubykalo A. E., "Action at a distance as a full-value solution of Maxwell equations:

The basis and application of the separated-potentials method", Phys. Rev. E, 53, (1996)

5373-5381

[14] Landau L. and Lifchitz E. M., "Théorie du Champ" (Éditions de la Paix, Moscou, 1965)

[15] Whitney C. K. "A quantum of light shed on classical potentials and fields", Apeiron (?)

[16] Galeczki G. and Marquardt P., "Requiem fuer die Spezielle Relativitaet" (Haag und

Herchen, Frankfurt a. M., 1997)

Acknowledgement

I am indebted to Paul Wesley, Thomas Phipps Jr., Jan Post and Patrick Cornille for stimulating exchange of ideas during the years.

- - - - -

George Galeczki received a Licence in Physics from Bucharest University in 1968, M.Sc. (1975) and D.Sc. (1979) degrees from The Technion - Israel Institute of Technology - in Haifa (Israel), for works in the field of ordered magnetism. In 1979 he received the Michael Landau for his research beyond his work toward a degree. After lecturing three semesters at the Technion, he moved to the governmental research center RAFAEL, where he did (mostly classified) work on HgCdTe-infrared detectors. After cumulating two sabbatical years, he left Israel, responding to an invitation from the University of Cologne (Germany). There he did research on heterodyne HgCdTe-infrared detectors for astrophysical applications and continued, in parallel, his critical work on fundamental physics started in 1978 under the influence of Nathan Rosen ("the EPR one") and Marinov's successful experiment to measure the absolute velocity of the Earth. He published about 50 papers on magnetism, narrow-bandgap semiconductor physics, nanoscopy, and about an equal number of papers criticizing "special" and general relativities, Copenhagen quantum mechanics, and Big Bang theory. He is the co-author (with Peter Marquardt) of REQUIEM TO SPECIAL RELATIVITY (in German, published by Haag + Herchen, Frankfurt/Main, 1997) and organizer (with P. Marquardt and J. P. Wesley) of three (1997, 2000, 2002)International Workshops: PHYSICS AS A SCIENCE. He is presently an independent science consultant, science writer, president of the Society for the Advancement of Physics, R.S. and member of the Natural Philosophy Alliance.

Society for the Advancement of Physics, R.S.