CONTRO "the ....... arrogance of mathematical
physicists giving priority to formalism against empirical facts.....".
E' uscito nel secondo volume del sesto numero di "Episteme" nel 2002
http://www.dipmat.unipg.it/~bartocci/ep6/ep6-II.htm)
un interessantissimo
articolo di G.Galeczki che si collega in modo essenziale con la PNN teorica e
sperimentale e che peggiora
ulteriormente il significato fondante che ha la Maxwell - Lorentz teoria per tutti
i MATEFICENTI (MATEmatici FIsici sediCENTI) : E.Fabri, G.Comoretto,
G.Pierpaoli, E.Smargiassi ,....etc ....... della gothalist http://www.asps.it/gotha.htm .
Come dice George Galeczki essi sono
"the... arrogance of mathematical physicists giving
priority to formalism against empirical facts.....".
Pertanto invito tutti i non
benpensanti , invito tutti gli eretici a stanare questa gente dai loro rifugi
cattedratici e di internet, dalle loro funzioni di interdizione a base di
"rispetti di forma" (ovvero del potere loro) , ovvero di " minuetti
riverenziali verso loro che ovviamente ne sanno di piu' ", invito a
inchiodare questi censori del libero approccio
empirico alla conoscenza alle loro responsabilita' .
Roma 21 Ottobre 2002
E.Laureti
####################
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, Ampre 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:
H = j + D/ t E = - B/ t
(4)
. D = r . B =
0
(5)
and
the corresponding equation of continuity:
. 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 Ampre's circuital law by introducing the "displacement
current", Maxwell's achievment was to express the experimental laws of
Coulomb, Gauss, Ampre, 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 = 0H (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 rle 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 = (0/4p ){[j]/r + (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:
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)( 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. )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. )A + (A. )v (18)
Although
the vector identity:
(v.
)A + (A.
)v + A (
v) - (v.A) = -v ( A) = -v B
(19)
for
v.A = const. and 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. )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.
)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 F = 0 (F denotes here the scalar potential),
A/ t = 0 and B = 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:
E =
0
;
D = r
(21)
and
B = j
;
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, Ampre, 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 Ampre's law between metallic current elements:
dFA
= (I.I'R/R3)[-2ds.ds' + 3(R.ds)(R.ds')/R]
(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 +
V/c - 3(V.R)/2cR + R.dV/dt.c]
(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 Ampre'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 Ampre'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. Ampre 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
Ampre 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,
Ampre'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!
VII. Some comments on rapidly varying fields and radiation
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 Linard-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
v/c)(R - vR/c)/(R - R.v)3 + qR {(R - vR/c) a}/(R - R.v/c)3c
(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
Linard-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 Linard-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 Linard 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.
-
Ampre and Weber's force law accounts for all electrodynamic phenomena in which
radiation
can be neglected.
-
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
Ampre",
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., "Thorie du Champ" (ditions 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.