NON-POTENTIAL OBJECTS
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Non-potential object dependents from its source and independents from
destination body, and this object moves in
space without difference a some kind of potential. Two examples: light
and radio-wave, and may be other rays and particles.
To clarify our point of view and to intensify discussion, main result
of attached work can be expressed in following form:
1.We did not find unity of the electromagnetic theory behind the
Maxwell’s electromagnetic hypothesis of light
and relativistic theory, because conceptions of static charges and
kinetic charges by the Maxwell’s definition and by experiments
so different that they cannot be included in the same equation. If we
have function of static charges, for example E(q),
and function of kinetic charges ( or current ), for instances H(j),
than we cannot use them in the same equation too.
2.We did not have reasons to accept the Maxwell’s electromagnetic
hypothesis of light, because we do not have
physical basement this hypothesis – we still do not observe charges
and/or currents into light. We cannot even call any
equation for “empty space” as Gauss’s law, or Faraday’s law or
Ampere’s law or Maxwell’s equations –
this equation for empty space should be established by experiment.
We do not have mathematical basement – light has non-potential
property and we cannot use the Maxwell’s theory based
on the potential theory.
3.We did not find necessity to use the Einstein’s postulate of
invariance of finite speed of light in inertial system of references
to explain result of the Michelson-Morly’s experiment, and this
result can be explained by very well-known conceptions:
the Newton’s corpuscles of light and the Galileo’s transformations
of speed.
4.We have found that four-velocity of light on relativistic theory is
equal infinity and that contradicts to observations of
finite speed of light and to the Einstein’s postulate. We have
postulate for object that does not be described by theory –
“postulate without theory”, we have theory that does not describe
object of its postulate and we should exclude this postulate –
we have “theory without postulate”, and so we lose “unity”
again, unity of the Einstein’s postulate and relativistic theory.
Let's note that field is declared as physical reality but it is pure
mathematical object by definition as a set equations
for empty space. In this case field is similar to menu: menu describes
diner, but does not have energy of diner,
and so field describes something, but field is not real physical
object. We should separate objects physical reality and
objects mathematical abstraction.
NON-POTENTIAL PROPERTY OF LIGHT BY MAXWELL
Copyright © 2005 by Viktor Moroz
(Notepad version, to take Word-version with good formulas, please send
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Abstract
From physical point of view consider the Maxwell’s electromagnetic
hypothesis of light
and modern equations this hypothesis, analyze conception of electrical
displacement in Maxwell’s
meaning and from modern point of view, compare static and kinetic
electricity, consider properties
of potential objects and the potential theory, discuss velocity of
light into relativistic mechanics.
From analysis was obtained opposite to Maxwell results. We cannot
combine static and
kinetic charges into the same equation even they consists the same
nature of particles and have
the same dimensions. The potential theory has properties which limited
its expansion: can describe
interaction at least two participants, cannot describe interaction one
participant with itself, and from
physical point of view cannot describe source-free space. We do not
have enough reasons to accept
the Maxwell’s electromagnetic hypothesis of light. We shown also that
modern electromagnetic
theory of light is pure mathematical theory in classic and relativistic
cases. We should follow Maxwell
and rediscover light and radio - waves as non-potential objects.
1. Introduction.
2. Maxwell’s Electromagnetic Hypothesis Of Light.
3. Modern Form Maxwell’s Equations.
4. Displacement Of Electricity.
5. Comparison Of Static And Kinetic Electricity.
6. Properties Of Potential Objects And The Potential Theory.
7. Velocity Of Light In Relativistic Mechanics.
8. Contradiction Of Einstein’s Postulates.
9. Conclusions.
1.Introduction.
In [2. pp. 490, 491] Maxwell write:
Quotation 1. “There is, on the contrary, the greatest possible
difference between the transmission of potential,
according to Neumann, and the propagation of light. A luminous body
sends forth light in all direction,
the intensity of which depends of the body which is enlightened by it.
An electrical particle, on the other hand, sends forth a potential,
the value of which, ee’/r, depends not
only on e, the emitting particle, but on e’, the receiving particle,
and on the distance r between the particles at
the instant of emission.”
This property of light – independence from properties of destination
body – we call the non-potential
property of light, and we can note that radio – waves have this
property – independence from properties
of receiver. The Neumann’s potential is potential energy one charge
near another and we can find this potential
in Maxwell theory too, and dependence forces or potential energy from
two participants we find in any potential
theory, particularly in the Maxwell’s electro-magnetic hypothesis of
light we see equation of the total current,
but current depends from two participants – two points with different
potential.
Below we consider the Maxwell’s electro-magnetic hypothesis of
light, the modern form of Maxwell’s
equations, analyze conception of electrical displacement in Maxwell’s
meaning and in modern expression,
compare static and kinetic electricity, consider properties of
potential objects and the potential theory, discuss
velocity of light in relativistic mechanics.
2. Maxwell’s Electromagnetic Hypothesis of Light.
To remind the Maxwell’s electromagnetic hypothesis of light,
consider general equations of
electromagnetic field [2 pp.258, 259]:
Magnetic induction: B = V.∇A; (1)
Electromotive force: E = V.G B - Á - ∇Ψ; (2)
Mechanical force: F = V Q B + e E - m∇Ω; (3)
Magnetization: B = H + 4π J; (4)
Electric currents: 4π Q = V. ∇ H; (5)
Ohm’s Law: K = C E; (6)
Electric displacement: D = 1/4 π K E; (7)
Total current: Q = K + D΄; (8)
Magnetization: B = μ H; (9)
Electric volume-density: e = S.∇ D; (10)
Magnetic volume-density: m = S.∇ I; (11)
Magnetic force: H = - ∇ Ω; (12)
Where:
V - indicates that the vector part of result of this operation is to
be taken.
S - scalar part.
∇ = id/dx + jd/dy + kd/dz; (13)
A – A(F,G,H) the electromagnetic momentum at a point.
G – G(x’, y’, z’) the velocity of a point.
Ψ – the electric potential.
E – E(P,Q,R) the electromotive intensity.
Ω – the magnetic potential (where it exists).
J – J(A, B, C the intensity of magnetization.
Q – Q(u, v, w)the total electric current.
K – K(p, q, r) the current of conduction.
D – D(f, g, h) the electric displacement.
C - is the conductivity for electric currents.
K - is the dielectric inductive capacity.
μ - is the magnetic inductive capacity.
From the equations of the Ohm’s Law: (6), the Electric displacement
(7), and the Total current (8) Maxwell
get next equation [2, p.434]:
μ (4πC + K d/dt )( dJ/dt – ∇^2 Ψ ) = 0; (14)
Where:
J = dF/dx + dG/dy + dH/dz; (15)
For a non-conductor medium C = 0 the equations become:
K μd^2F/dt^2 + ∇^2F = 0; (16)
We have the same wave equations and for components G and H [2,p.434].
The velocity of propagation of
electromagnetic disturbances in a non-conducting medium is [2, p.434]:
V = 1/root(K μ); (17)
and it equals speed of light.
Quotation 2. “… If it should be found that the velocity of
propagation of electromagnetic disturbances is
the same as the velocity of light, and this not only in air, but in
other transparent media, we shall have strong reasons
for believing that light is an electromagnetic phenomenon”[2, p.431
].
Let’s note that from equivalency of speed of light and the
electromagnetic disturbances directly does not
follow the electromagnetic hypothesis of light because we have two
choices: speed equal but nature these phenomenon
is different, or light has nature of electromagnetic disturbances.
We can note also that the speed of a electrical current in a metallic
conductor, as a speed of a electromagnetic disturbance,
not as a speed of electrons, equal the speed of light, but it is not
light, because the metallic conductor is opaque.
In a transparent medium, like a glass of a spectrum prism, rays of a
different color have a different speed, but we cannot say
that they have different nature. Therefore, similar or difference of
speed is not enough to make decision about nature of
a physical phenomena.
An electrolyte is a good conductor and, regarding to Maxwell wave
equation, must be opaque if light is the
electromagnetic wave, but electrolyte is transparent.
Quotation 3.“There is thus no true conduction through the
electrolyte, no loss of electric energy, and
consequently no absorption of light.”[2, p.446].
Quotation 4.“Of all electrical phenomena electrolysis appears the
most likely to furnish us with a real insight into
the true nature of electric current, because we find currents of
ordinary matter and currents of electricity forming essential
parts of the same phenomenon.” [1,p.375] Let’s note - “the true
nature of electric current” with “no true conduction”.
We saw that in (8) there two parts: Ohm’s law and derivation from
the electrical displacement. For light first part was
excluded and considered non-conducting media. This follows from
Maxwell’s assumption of a dielectric vacuum [1, p.68]:
Quotation 5.”That the energy of electrification resides in the
dielectric medium, … even what is called a vacuum, …”
and Quotation 6.”…in the dielectric there is a force which we have
called electric elasticity which acts against the electric
displacement, and forces the electricity back when the electromotive
force is removed;…” [1, p.69]
Maxwell should have reasons to refuse the electromagnetic hypothesis
of light because:
- Equivalence of speed of light and the electromagnetic disturbance is
not enough to make decision about nature
of light or electromagnetic disturbance.
- Maxwell’s theory does not resolve contradiction of “ the true
nature of electric current” with “no true conduction”
for electrolyte.
- Light has non-potential properties in meaning dependence from
properties of source body and independence
from properties destination body, when in potential theory we find
dependences of interaction at leas two participants from
properties both of them.
Maxwell’s theory is theory of sources, which have particular
properties, and we will discuss them later together with
properties of the potential theory.
We also saw from (7) that the electrical displacement depends from one
kind of static charge on the contrary to
Neumann’s theory. Before we discuss in detail the electrical
displacement let’s consider modern form of Maxwell’s equations.
3. Modern Form Maxwell’s Equations.
Lets consider the differential modern form of the Maxwell equations
[3]:
curl E = - 1/c ∂H/ ∂t, (18)
div H = 0; (19)
curl H = 1/c ∂E/∂t + j; (20)
div E = q; (21)
>From well-known equation of the Lorentz’s force:
F = qE + q [v H]; (22)
we can note that E and H are not forces because they do not have
dimensions of force, and any derivations or integrals of these
values do not forces or energies. From mathematical point of view the
equations (18 – 21) are dynamical equations because
consist derivatives with respect to time, but from physical point of
view, they do not dynamical equations, because do not
consist any forces or energies.
Now lets consider well-known mathematical proof of existing of the
electromagnetic wave in source-free space [3, p.116]:
Quotation 7.“The electromagnetic field in vacuum is determined by
the Maxwell equations in which we must set q = 0, j = 0.
We write them once more:
curl E = - 1/c ∂H/ ∂t, (23)
div H = 0; (24)
curl H = 1/c ∂E/∂t, (25)
div E = 0; (26)
These equations possess nonzero solutions. This means that an
electromagnetic field can exist even in the absence of any charges.
Electromagnetic fields occurring in vacuum in the absence of charges
are called electromagnetic waves.”
We can see the simplest approach: deleting the explicit written in (18
– 21 ) charge q and current j and mathematical
manipulation with the rest of symbols of the Maxwell equations. If we
did the same for original Maxwell’s equation (8), then we
could lose a wave equation automatically.
There are well-known substitutions for E and H [3, p. 51]:
E = - 1/c ∂A/∂t – grad φ; (27)
H = curl A; (28)
Where:
φ = - q/r; (29)
A = 1/c∫ j/R dV (30)
>From formulas (27 – 30) we can see if q = 0 and j = 0, then A = 0 and
φ = 0, and E = 0, H = 0. From zero values we cannot get
non-zero solution. If we establish functions E(q) or E(q, j), H(j),
φ(q), and A(j), then we remove q and j from these definitions,
we will change dimensions these functions and cannot use the same
abbreviations of functions as more the same equations
which we obtain for charges q and current j. Therefore in (23 -26) we
have at best a pure mathematical model without
a experimental establishment of analogical values E and H and a
experimental proof these equations for source-free space.
We can see also from (8, 20, 25) that the electrical displacement play
main role to get wave equations from Maxwell’s
equations in original and modern form. Let’s consider conception of
electrical displacement.
4. Displacement Of Electricity
We have two meaning of the electrical displacement: first one is
Maxwell’s meaning, second – modern point of view.
The Maxwell’s electrical displacement bases on Maxwell’s assumption
of medium as dielectric, even this medium is
vacuum [1,pp.68, 69]. Modern point of view base on the
“source-free” space because we still did not observe any charges,
current,
or a some new kind of sources in vacuum and light, but name is kept as
“the Maxwell’s displacement”. The Maxwell’s displacement
means displacement of charges of dielectric medium, when we remove
these charges we could remove and the electrical displacement,
and “automatically” lose wave equations from Maxwell’s equations
and lose the electromagnetic hypothesis of light. Modern
approach remove all sources as charges and currents, but we keep
displacement in equations because it is “Maxwell’s displacement”,
and because without displacement current we cannot obtain wave
equation, and cannot accept the electromagnetic hypothesis of light
“automatically”. To avoid this non-coordination two meaning of the
electrical displacement, we could “discover” that pure
mathematical object – the electromagnetic wave by definition (23-26),
is physical reality.
Let’s consider Maxwell’s definition of electrical displacement.
Quotation 8.“The amount of the displacement is measured by the
quantity of electricity which crosses unit of area,
while the displacement increases from zero to its actual amount. This,
therefore, is the measure of the electric polarization.
The analogy between the action of electromotive intensity in producing
electric displacement and of ordinary mechanical
force in producing the displacement of an elastic body is so obvious
that I have ventured to call the ratio of the electromotive
intensity to the corresponding electric displacement the coefficient of
electric elasticity of the medium. This coefficient is different
in different media, and varies inversely as the specific inductive
capacity of each medium.
The variations of electric displacement evidently constitute electric
currents.”[1,p.65].
We have note that the electric displacement has kinetic nature –
“electricity which crosses unit of area”, and “variations of
electric
displacement evidently constitute electric currents”. The electric
current is kinetic phenomenon by Maxwell, and we can say that
the electric displacement is kinetic phenomenon into its static and
volatile state.
Quotation 9.“To fix our ideas of electric displacement, let us
consider an accumulator formed of two conducting plates
A and B, separated by a stratum of a dielectric C. Let W be a
conducting wire joining A and B, and let us suppose that by action
of an electromotive force a quantity Q of positive electricity is
transferred along the wire from B to A. The positive electrification
of A and the negative electrification of B will produce a certain
electromotive force acting from A towards B in the dielectric stratum,
and this will produce an electric displacement from A towards B within
the dielectric. The amount of this displacement, as measured
by the quantity of electricity forced across an imaginary section of
the dielectric dividing it into two strata, will be, according to our t
heory, exactly Q.”[1,p.67].
Here we note that Maxwell take to consideration only one kind
electricity – positive electricity Q, to measure the electric
displacement, but a dielectric consists two kind of charges and both of
them should take participant into the displacement of electricity.
Now, let’s consider the Maxwell’s definition of current:
Quotation 10.“According to Fechner’s and Weber’s theory it is a
combination of a current of positive electricity with an exactly
equal current of negative electricity in the opposite direction through
the same substance. It is necessary to remember this
exceedingly artificial hypothesis regarding the constitution of the
current in order to understand the statement of some of Weber’s
most valuable experimental results.
If, as in Art. 36, we suppose P units of positive electricity
transferred from A to B, and N units of negative electricity
transferred from B to A in unit of time, then, according to Weber’s
theory, P = N, and P or N is to be taken as the numerical measure
of the current.
We, on the contrary, make no assumption as to the relation between P
and N, but attend only to the result of the current,
namely, the transference of P + N units of positive electrification
from A to B, and we shall consider P + N the true measure of the
current.
The current, therefore, which Weber would call 1 we shall call 2.”
[1, p.355].
If we apply this Maxwell’s definition of current to the electrical
displacement, then we should take 2Q electricity instead Q. Next
consider
definition of the displacement of electricity by a resultant electric
intensity:
Quotation 11. “Let e be the charge of the small body, and let the
force acting on it when placed at the point (x, y, z) be Re, and let
the
direction-cosines of the force be l, m, n, then we may call R the
resultant electric intensity at the point (x, y, z).
If X, Y, Z denote the components of R, then
X = Rl, Y = Rm, Z = Rn.
In speaking of the resultant electric intensity at a point, we do not
necessarily imply that any force is actually exerted there, but only
that if an electrified body were placed there would be acted by a force
Re, where e is the charge of the body.*
Definition. The resultant electric intensity at any point is the force
which would be exerted on a small body charged with the unit of
positive electricity, if it were placed there without disturbing the
actual distribution of electricity.
This force not only tends to move a body charge with electricity, but
to move the electricity within the body, so that the positive
electricity tends to move in the direction of R and the negative
electricity in the opposite direction. Hence the quantity R is also
called
the Electromotive Intensity at the point ( x, y, z ).
When we wish to express the fact that the resultant intensity is a
vector, we shall denote it by the German letter E. If the body is
a dielectric, then, according to the theory adopted in this treatise,
the electricity is displaced within it, so that the quantity of
electricity
which is forced in direction of E across unit of area fixed
perpendicular to E is
D = 1/4pi K E; (31)
where D is the displacement, E the resultant intensity, and K the
specific inductive capacity of the dielectric.
If the body is a conductor, the state of constraint is continually
giving way, so that a current of conduction is produced and maintained
as long as E acts on the medium.” [1, pp.75, 76].
Now we can adjust formula (31) by the Maxwell’s definition of
current, and we should use here 2K instead K. Let’s note,
if Maxwell’s formula of the velocity of the electromagnetic
disturbance (17) correct, then now we should use 2K in this formula,
and we should obtain speed of the electromagnetic disturbance is less
in 2 = 1.414 times than speed of light, and by Maxwell
we should abandon the electromagnetic hypothesis of light.
Let’s consider equations (7) and (31), where left side of equation
binds with kinetic electricity, and right side of equation binds
with static charges. Maxwell gives us definition of surface charges of
a dielectric:
Quotation 12. “I. Electric Displacement. When induction is
transmitted through a dielectric, there is in the first place a
displacement
of electricity in the direction of the induction. For instance, in a
Layden jar, of which the inner coating is charged positively and
the outer coating negatively, the direction of the displacement of
positive electricity in the substance of the glass is from within
outwards.
Any increase of this displacement is equivalent, during the time of
increase, to a current of positive electricity from within
outwards, and any diminution of the displacement is equivalent to a
current in the opposite direction.
The whole quantity of electricity displaced through any area of a
surface fixed in the dielectric is measured by the quantity
which we have already investigated (Art. 75) as the surface-integral of
induction through that area, multiplied by 14π K , where K is
the specific inductive capacity of the dielectric.
II. Surface charge of the particles of the dielectric. Conceive any
portion of the dielectric, large or small, to be separated
(in imagination) from the rest by a closed surface, then we must
suppose that on every elementary portion of this surface there is a
charge
measured by the total displacement of electricity through that element
of surface reckoned inwards.”[1,p.166]
From the beginning we should consider a dielectric is electrically
neutral, and remind that property dielectric is non-conducting of
electrical charge. The electrical displacement into the dielectric we
can consider as polarization of small, until to molecular level, parts
of dielectric, but each of this part keep electrical neutral, and if
one side of the particle of the dielectric will charge positively then
other side will be charged negatively, and any physically reasonable
– in meaning keep molecules as the smallest particles which keep
properties of particular substance - separation of the dielectric body
could be electrically neutral and polarized. This separation of the
dielectric, even “in imagination”, is analogy to separation of
magnet, which very well describe by Maxwell [1]: any part of dielectric
is
polarized body, but sum of charges equal zero because the conservation
charges law and dielectric does not conduct charges.
In the electrical displacement take participation charges both of kind,
and from kinetic point of view we should consider crossing
these charges during polarization through some of surface in contra
direction to create charged surface of dielectric or
the displacement current. Let’s write in modern abbreviation
equation:
D = f( E ); (32)
Where D is function of kinetic charges in the electrical displacement,
and E is function of static charges. We can write this equation
in meaning that static charges in E can be sources of the displacement
of electricity in D, but physical consideration of kinetic
charges into dielectric above allows us note:
If volume integral ∫ DdV = 0; then ∫EdV = q; (33)
If integral by close surface ∫ DdS = 0; then ∫EdS = q; (34)
If divD = 0; then divE = ρ; (35)
Because (33-35) we cannot combine D and E in the same equation, or we
cannot combine static and kinetic charges.
Thus, Maxwell shown that the electrical displacement is kinetic
electrical phenomena, and we can see that it keeps
physical object electrically neutral in whole and any part of objects
corresponds to conservation charges law. Next we will discuss
the differences of static and kinetic electricity.
5. Comparison Of Static And Kinetic Electricity.
From experiments with static electricity we can find two kind of
charges: positive q+ and negative q-. The same kind
of charges repel, and different kind – attract each other. At least
in macro level experiment we can separate different kind of charges,
but we working with combine effect these charges and physical body,
which keep together charges the same kind, we cannot separate
“pure” charges the same kind.
Static electricity Qs we can calculate in way:
Qs = ∑q-i + ∑q+j; (36)
Qs ≠ 0; (37)
Forces between bodies with static charges depend from inverse square of
distance:
F = Qs1 · Qs2 / r^2; (38)
Or
F = E · Qs2; (39)
where
E = Qs1 / r^2; (40)
Potential energy one static charge on the distance r from another
equal:
W = Qs1 · Qs2 / r; (41)
Kinetic charges define a electric current:
Is = Qk/T; (42)
Where Is – current through surface S in unit of time, index s -
surface S, index k – kinetic, T – time, Qk – kinetic charge,
which equal:
Qk = ∑ |q-i1| + ∑q+m2 - ∑q+j1 - ∑|q-k2| ≠ 0; (43)
Where indexes 1 and 2 mean contrary directions of motion of charges.
Let’s note that specially for dielectric medium before,
during and after transmission of disturbance we have:
∑ q-1i + ∑q+1m + ∑q+2j + ∑q-2k = 0; (44)
or
Qs = 0; (45)
Particularly we have note that the Faraday’s law is observable for
electrical neutral system Qs = 0: we can take electrical
neutral galvanometer, coil and magnet and watch a current of induction,
and all participants – galvanometer, coil and magnet,
are electrical neutral before, during and after experiment.
And the Ampere’s Law is observable in a electrical neutral system of
wires and sources of current.
As we saw above, Maxwell equations bring together static and kinetic
(current) characteristic of electrical phenomena. Now we
saw important difference between static and kinetic phenomena, namely,
the way of calculation of charges.
We can see from (36) and (43), if for static electricity charges
calculate as sum of charges of the same sign in define volume,
then for current we calculate sum of absolute values of charges –
negative and positive – which pass of a define surface, and
sum of them could equal zero. We can assume “free” electron only as
charges of current, but metallic wire is electrical neutral,
and the Faraday’s law and the Ampere’s law we observe on the
electrical neutral system of circuits, and sum of all charges of all
devices in Faraday’s and Ampere’s experiments equal zero.
Therefore, we shown that it is impossible to combine the static and
the kinetic charges into the same equation because
they calculate in different way and in the same time and the same place
when one of them may be equal zero another not.
The most of kinetic phenomenon we observe for electrically neutral
objects. Hence, we cannot combine E(q) as function of static
charges with H(j) as function of kinetic charges, and we cannot define
the electric displacement - kinetic phenomenon, as function
of static charges.
6. Properties Of Potential Objects And The Potential Theory.
If force between interacted physical objects is proportional inverse
distance or inverse square of distance, then we will call these
objects as potential objects, because we can consider application the
potential theory to describe them. To apply the potential
theory involved function must have second derivative. For the static
electricity was established function (40), and from the
conservation charges law we have:
q = const, (46)
dq/dt = 0; (47)
dE/dt = 0. (48)
>From (46-48) we do not have even first derivative with notice “for
close space”. Let’s consider alternative “open space”.
First of all, in experiments with static electricity we can separate a
kind of charge and still cannot, at least in macro level experiment,
evolve “pure” charge because we have combine result interaction of
charges with physical body as holder these charges together
because the same kind of charge repeal each other. Regarding the
conservation charges law we cannot create or destroy charge,
and in open space we should use second ( third and e.c. ) body to move,
bind or/and separate charges, and action with these
combine objects in open space still outside the potential theory,
because local interaction of charges very strong. Indeed strength
of electrical field near electron on an atomic distance 10-10 m equal:
Ee = e/4π ε0r2 =
= 1.602 ·10^-19C/4/3.1416/8.854·10^-12F ·m^-1/10^-20m^2 =
= 1.4398·10^11 Vm^-1; (49)
Even if we take in consideration distance in thousand times more, we
will have stronger inside field than any outside field which
regarding to potential theory could change density of charge. Unlike
fluid mechanics, where local interaction – attraction of two
volume of fluid, in ~1010 times less than weight this volume or than
outside forces, in case static charges we have inverse relation
between inside and outside forces.
Unlike static electricity, kinetic electricity we can consider as very
well balanced in meaning of static electricity object even
in metallic conductor, because we observe current when outside field is
less than one of millionth volt per meter.
In the potential theory is considered the measure μ [4]:
μ = ρd τ, (50)
where
ρ – the density of a source.
d τ - the volume element of the source.
For dielectric with or without polarization in whole and any part of
dielectric, sum of charges equal zero on molecular and atomic
level: ρ = 0, because number of electrons equal number of protons. In
the electromagnetic theory of light (18 - 21) – at the beginning
we remove charge and current or we could put the density to zero: ρ =
0, and “automatically“ lose the potential theory from kit of
tools to describe light. If we calculate charges in kinetic meaning we
have ρ ≠ 0 even static charge equal zero. Dimensions of the
density of source ρ show us physical application of the potential
theory, in other word, the potential theory empty space does not
have physical sense. Value ρ without dimensions gives us pure
mathematical theory as set of function which satisfy of set
of differential equations. Formal removing or setting dimensions of ρ
does not have sense neither physical nor mathematical
point of view, because this action does not proof existence some
mathematical object as physical reality, and existence in physical
object all properties its math model. We should declare this
“existence” like postulate, but this way leads to building physical
reality from our mathematical imagination, instead to separation of
objects of a mathematical abstraction and objects of
a physical reality.
>From physical point of view forces F and potential energies W of
potential objects depend from three arguments:
F = F(source1, source2, distance12) (51)
W = W(source1, source2, distance12) (52)
Where source1, source2 properties of potential objects like mass,
charge, current and so on, and distance12 is distance between
source1 and source2. If we remove even one argument from these
functions, then we should change dimensions these functions
and should lose forces and energies. If we hide some argument using
unit of value, then we have to remember that dimensions
of unit value can not disappear.
Form of dependences of forces from distance – inverse distance or
inverse of square of distance – is necessary to apply
the potential theory and lead to at least two participants in equations
of force and energy, because the potential theory cannot
describe interaction one sources with itself. To show this point
consider well-known appreciation radius of electron[3,p.97].
R0 ~ e^2/mc^2; (53)
mc^2 ~ e^2/R0 = e · e/R0; (54)
First of all, assumption interaction electron with itself or with its
own electrical field lead to contradiction from physical point of view,
in particularly, force and energy this interaction should be so big
because so small R0, that electron could ignore all outside charge,
even proton in kernel of hydrogen, or other words, could be independent
from another charge that could mean absence of
charge of electron.
Secondly, from equation (54) we see two charges e · e, but electron
has only one e, we still do not observe charges in another objects,
only in electron and proton, field does not have charge, and using two
charges e · e for one electron means violation of conservation
charges law. These two reasons follow to conclusion: the potential
theory can describe at least two participants. Maxwell shows this
for Neumann’s theory, see Quotation 1 [2]. Now, we can note that from
physical point of view the potential theory is theory of sources,
remove these source at best we get pure mathematical theory, for
instance the electromagnetic theory of light, or theory of
the electromagnetic field.
We can suppose that light interact with electron, but light does not
have charge or current, and we should not use the same laws which
we obtain for charges. Let’s follow Maxwell [2. p.491] and write
energy of light in form:
W = W( source_Of_light1 ), (55)
where source_Of_light1 is property of physical illuminated body only,
for example temperature of body.
We see difference between (56) with one argument and (53) with three
arguments, that why we cannot use the potential theory
to describe light, and why property (56) we call non-potential
property. The electromagnetic hypothesis of light does not allow us
look for adequate model interactions of light and electron. Also we can
note that we still do not discover mediator for interactions
of electromagnetic object as physical object which we should separate
from source, for example, from charges, and which should
take responsibility for interactions these charges. We use mathematical
function to provide some calculation, for instance:
F = E (source1, distance12) · source2, (56)
instead using function (51).
7. Velocity Of Light In Relativistic Mechanics.
In relativistic mechanics instead the co-ordinate system
{t, x, y, z}, (57)
where velocity of light is finite and equal:
c = 299,792,458 m/s; (58)
establish four-dimensional space [3, p.23]:
{ ct, x1, x2, x3 } or {xi}. (59)
where i = 0,1,2,3; and x0 = ct, and where define interval:
ds^2 = c^2dt^2 – dx1^2 – dx2^2 – dx3^2, (60)
or:
ds = cdt root( 1 – v^2/c^2) (61)
and four-dimensional velocity:
ui = dxi/ds (62)
or
ui = {1/root(1- v^2/c^2), v/(c. root( 1- v^2/c^2)) } (63)
From definition of interval [3], interval ds for light, and for any
phenomenon with speed c in space (57), equal zero, and a relativistic
velocity of light cr in space (59) will be equal infinity by definition
of velocity (62):
cr = dxi/ds = dxi/0 = ∞, (64)
or from (63) when v = c:
cr = {cri} = {1/root(1- v^2/c^2), v/( c . root(1- v^2/c^2)) }|v=c =
= {1/root(1- c^2/c^2), c/(c . root(1- c^2/c^2))} =
={ 1/0, 1i/0 } = { ∞, ∞i }. (65)
Let’s consider relation between four-velocity and classical
mechanics.
Quotation 13.”The limiting transition from relativistic to classical
mechanics can be produced formally by the transition to the limit c→
∞ in
the formulas of relativistic mechanics.” [3, p.2]. For c = ∞ from
formula (63) we get:
ui = {1/root(1- v^2/∞) , v/ ∞ . root(1- v^2/∞) } = { 1, 0, 0, 0
}, (66)
We have one value of speed (66) only, in other words, it is projection
infinite number of finite value of speeds of classical mechanics into
one value of relativistic speed, and we see that speed has constant
components and acceleration will equal zero in any cases, but that does
not have physical sense or velocity (63) does not bind with classical
mechanics.
Let’s consider four-acceleration w.
wi = d^2xi/ds^2; (67)
wi = { cd^2t/c^2dt^2( 1- v^2/c^2), v^2/c^2( 1 – v^2/c^2 ) } =
= { 1/∞, v^2/∞ } = { 0, 0i }; (68)
We see that four-acceleration (68) does not have sense from mechanics
point of view too.
Let’s note, requirement c = ∞ in “classical” case of
relativistic mechanics looks artificial because classical mechanics is
based
on observations and we observe finite velocity of light, and c = ∞
is not property of classical mechanics but it is a some way to bind new
theory with old one, particularly to get Galileo’s transformation
from Lorentz’ one.
Infinite value of relativistic velocity of light cr show us
contradiction of relativistic mechanics where is declared the principle
of
the invariance of finite speed of light. The relativistic mechanics was
developed to explain results of Michelson-Morley’s experiments [5]
and keep light as disturbance of some kind of medium. Non-potential
property of light should mean that light is not disturbance of a some
kind of medium and the results of the Michelson-Morley’s experiments
we should obtain because light interact with mirrors of
the Michelson’s interferometer as particles, and we should not have
to involve the principle of invariance of speed of light on the
inertial
co-ordinate systems. We can use Galileo’s transformation.
Let’s apply Galileo’s transformation for the Michelson’s
interferometer. The interferometer consists one transparent and two
plain mirrors, transparent mirror locates on the intersection of two
perpendicular axes, and plain mirror locates on each axis on the same
distance L from transparent mirror. Let’s assume that one axis is
congruent with direction of Earth motion, mark this axis by A and mark
perpendicular axis by B, and speed this motion equal v. Also mark time
which photons spend between mirrors: t1 time from transparent
mirror to plain one along axis A in direction of the Earth motion; t2
time in contra direction along axis A; t3 = t4 time which photons spend
along axis B. Now we can write three equation for mention times. If
speed c is congruent with v we have:
( c + v ) t1 = L + vt1; (69)
If speed c and v have contra directions:
( c – v ) t2 = L – vt2; (70)
If speed c and v have perpendicular directions:
( c^2 + v^2 ) t3^2 = L^2 + v^2t3^2; (71)
>From equations (69-70) we have:
t1 = t2 = L/c; (72)
t3 = t4 = L/c; (73)
t1 + t2 = t3 + t4; (74)
>From (74) we see that photons spend the same time along perpendicular
axes. This is reason why we do not observe wave properties of
photons, or interference of light.
8. Contradiction Of Einstein’s Postulates.
From mathematical point of view postulate is statement, which be
accepted without proof, and which is used to build a theory
does not conflicting with this postulate. From physical point of view
any math model is considered as approximation of physical reality,
and we can discuss as model itself as more assumptions which precede
this model.
Let’s consider the Einstein’s postulates from physical point of
view.
Quotation 14. “… the same laws of electrodynamics and optics will
be valid for all frames of reference for which the equations of
mechanics
hold good. We will raise this conjecture (the purport of which will
hereafter be called the “Principle of Relativity”) to the status of
a postulate,
and also introduce another postulate, which is only apparently
irreconcilable with the former, namely, that light is always propagated
in
empty space with a definite velocity c which is independent of the
state of motion of the emitting body.”[5,pp.37,38]
Now consider two properties of light, which follow from those
postulates:
1) “…light is always propagated in empty space with a definite
velocity c which is independent of the state of motion of the emitting
body.”
2) The velocity of light is constant in all inertial systems of
reference. Let’s note that constancy is form of dependency: v = c.
>From physical point of view any physical body can be a system of
reference, include and emitting body or source of light. If speed of
source
of light is constant to a some inertial system of reference, then the
source is the inertial system of reference too. This means that
the Einstein’s postulate declare independency and dependency of light
from one body in the same time: independency because it is source
of light, and dependency because it is the inertial system of
reference.
Simultaneous independency and dependency does not have sense from
physical point of view.
9. Conclusions.
In work [1,2] Maxwell develops the theory of electromagnetism and the
electromagnetic hypothesis of light on the basement of the potential
theory, and unites the static and the kinetic electricity, magnetic
phenomenon and light into one electromagnetic world.
This work is based completely on the Maxwell’s work [1,2], in
particular:
- on the importance of dimensions of values [1, p.2 ];
- on the Maxwell’s definition of kinetic electricity [1,2 ] as motion
two kind – positive and negative, charges, unlike static electricity
bind with one kind of charges;
- on the Maxwell’s description of the Neumann’s potential theory
of light [2] as description of “physical” properties of the
potential
theory;
- on the description property of light [2] – independence from
properties destination body, which we call as non-potential property
of light because this property is not satisfy requirements of
application of the potential theory.
We showed that Maxwell had reasons to abandon the electromagnetic
hypothesis of light, namely:
- equivalency of speed electromagnetic disturbance and light is not
enough to make decision about nature of phenomenon;
- Maxwell’s theory does not explain contradiction for electrolyte:
“true nature current with non-true conduction”;
- Using Maxwell’s definition of kinetic charges for displacement
current shows us that speed of electromagnetic disturbance is less
then speed of light in 2 = 1.414 times, and, by Maxwell, the
electromagnetic hypothesis of light should be excluded;
- If we apply Maxwell’s argument against Neumann’s theory to
Maxwell’s theory, we should not use potential theory to describe
light, and should abandon the electromagnetic hypothesis of light;
- If we take to consideration differences between static and kinetic
charges, we cannot write equation of electrical displacement (7),
this means we cannot obtain wave equation and the electromagnetic
hypothesis of light.
Detail analysis of the Maxwell’s electromagnetic hypothesis of light
brings followed results:
- Modern Maxwell’s equations for “source-free” space are pure
mathematical theory which written on a some kind of analogy to
electromagnetic equations, because still do not establish by experiment
analogy of E, H and (23 - 26) for “source-free” space.
- The electrical displacement even in static state is kinetic
phenomenon because it is measured by charges in kinetic meaning.
The displacement of electricity into medium does not change charges
this medium in whole as in any parts.
- Static and kinetic charge cannot be combine in the same equation
even they consist the same nature particles, and have
the same dimensions, because these charges are calculated into
different way.
-In relativistic mathematics the velocity of light equal infinity, and
four-velocity and four-acceleration does not bind with classical
mechanics.
-We should rediscover light and radio-waves as non-potential objects
without the principle of the invariance of the velocity of light.
Let’s consider ten points, which connect to two subjects: the
Maxwell’s electromagnetic hypothesis of light, and the relativistic
mechanic.
1. The potential theory very well describes wave properties of
phenomenon in some kind of medium.
2. Maxwell developed the potential theory of electromagnetic
phenomenon.
3. Maxwell proposed the electromagnetic hypothesis of light in a
dielectric vacuum.
4. Michelson and Mourly realized experiment, and did not observe an
expecting interference of light.
5. Fitzgerald and Lorentz explained the result of the
Michelson-Mourly’s experiments by contraction of length and time with
conception of a dielectric ether.
6. Einstein formulated postulates of relativity and constancy of light
velocity in vacuum[5] to obtain Lorentz-like transformation
of coordinate and speed.
7. Einstein’s postulates were declared as “law of Nature” to
exclude ether.
8. Existing of ether was reason to involved the Lorentz transformations
and Einstein’s postulates, to keep usage Einstein’s theory,
field was declared as physical reality.
9. In short words, the wave theory had been developed, the wave device
– interferometer of Michelsom, had been realized, and we
could expect a wave picture – interference of light, but it did not
happen.
10. Fitzgerald, Lorentz and Einstein had explained behavior one
physical object – light, by theory which rebuilt whole physics and
“whole
Nature”.
From result this work we can propose alternative approach to each
mention points. Let’s begin from the ending.
1a. To explain behavior of light in the Michelson-Mourly experiments
without rebuilding whole Nature, we should assume that light interact
with mirror of interferometer as particles – Newton’s corpuscles,
or Plank’s quanta, or Einstein’s photons, and use well-known
Galileo’s
transformation of speed.
2a. From experiments we know that light has wave properties and
properties of particles, and fact was that light behaves as
particles when we expected wave behavior. It is not enough to rebuild
whole physics because our expectation was wrong.
3a. We shown that the electromagnetic field (18 – 21) are pure
mathematical model without experimental establishment of
functions and equations. The fact is: we still did not discover some
kind of physical object as mediator between charges, which can be
separated from charges and which can take responsibilities for
interaction these charges.
4a. Einstein’s postulates [5] have inside physical contradiction.
5a. We found in relativistic mechanic that velocity of light express by
infinite. It is contradiction to the principle of the invariance of the
finite
velocity of light, and to observation of finite velocity of light.
6a. Fitzgerald-Lorentz’ transformation could involve conception of a
dielectric ether, but we still did not observe any charges or currents
into
light.
7a. In Michelson-Mourly’s experiments particles of light satisfy the
Galileo’s transformation, and particles arrived in the same place
synchronously – this is reason why we did not observe wave properties
these particles. The Michelson-Mourly’s experiments shown
that we should consider light as particles which have wave properties,
and should not as medium or field which can be quantized.
8a. We do not have reason to accept the Maxwell’s electromagnetic
hypothesis of light.
9a. We shown differences between static and kinetic charges, and we
cannot combine them into the same equation.
10a. The potential theory has properties which limit it expansion, and
we have consider each case it application from physical point of view.
We cannot use the potential theory for static charges, because there
are very strong local interactions of static charges. We can use
the potential theory for kinetic charges, because the kinetic charges
very well balanced from static charges point of view.
We should rediscover light and radio-waves as non-potential objects
– in meaning dependences from source and independence
from properties of destination body, as objects which move in space
without difference some kind of potential.
References:
1. Maxwell J. C. A Treatise On Electricity & Magnetism. Vol. 1, Dover,
1954, pp. 506.
2. Maxwell J. C. A Treatise On Electricity & Magnetism. Vol. 2, Dover,
1954, pp. 500.
3. Landau L.D., Lifshitz E.M., The Classical Theory of Fields. Vol. 2.
2002, pp. 428.
4. Encyclopedic Dictionary of Mathematics. Second Edition. Vol. 2. The
MIT Press 1996, pp. 2148.
5. Lorentz H.A., Einstein A., Minkowski H., Weyl H. The Principle of
Relativity., 1923, Dover, 1952, pp. 216.