Author James L. Oschman PhD
EDINBURGH LONDON NEWYORK PHILADELPHIA ST LOUIS SYDNEY TORONTO 2000
by Gerhard W. Bruhn, Dep. of Mathematics, Darmstadt University of Technology
Summary According to J.L. Oschman’s imagination behind the physical world of forces there is a hidden super world of potentials, but we, the physicists, are used to see its projection onto a certain screen, where we see the forces only, while the influence of potentials remains invisible normally. As a counter example he refers to the vector potential A of a magnetic field H. According to his opinion the Aharonov-Bohm-effect (AB-effect) proves that the vector potential A can have a physical meaning too going beyond that one given by the vector field H. Especially J. L. Oschman remarks that while the forces are cancelled by destructive interference nevertheless its potentials remain effective. He calls the remaining potentials of scalar and vector type "scalar waves" and "vector waves" respectively. – This definition of "potential waves" allows us to calculate them explicitly and examine the physical effects combined with them. As a result we can give a representation of all "null potential waves" (φ0,A0) the physical fields of which are cancelled by destructive interference: All "null potential waves" (φ0,A0) are shown to be generated by an arbitrary solution U(x,t) of the wave equation. Applying this to the AB-effect we see that the generating function U in this case remains undetermined by the AB-effect and hence, there is no physical information given by the AB-effect that goes beyond the information contained in the corresponding magnetic vector field H. – A comparison with Meyl’s and Bearden’s "scalar waves" shows that both concepts have nothing in common.
As is well-known from Electrodynamics a large class of EM-processes can be described by means of two potentials, a scalar potential φ and a vector potential A. The couple (φ,A) belongs to Oschman’s super world. What is to be seen on the screen of our "physical world" are electric and magnetic fields and current and electric charge densities. Each of these quantities can be derived from potentials (φ,A) (cf. Appendix A), the magnetic field by
(1) H = curl A ,
the electric field by
(2) E = – grad φ – μAt ,
the current density by
(3) j = 1/c² Att – Δ A
and the density of electric charges by
(4) ρ = 1/c² φtt – Δ φ .
Here the potentials are tied by the additional condition
(5) div A + ε φt = 0 ,
the well-known Lorenz-condition (falsely ascribed to due to H.A. Lorentz). It is easily to be seen (cf. Appendix B) that another couple of potentials (φ',A') will generate identically the same EM-process, if the conditions
(6) A' – A = – grad U
(7) φ' – φ = μUt
are fulfilled, where the function U has to be some solution of the wave equation
(8) 1/c² Utt – Δ U = 0 .
In this way the fields (H, E, j, ρ) generated by the potentials (φ,A) by (1)-(5) can be cancelled by the opposite process (–H, –E, –j, –ρ) due to destructive interference, where the opposite process is generated by the couple (–φ', –A'). Hence
(9) (φ,A) + (–φ', –A') = (φ – φ', A –A') = (–μUt, grad U)
is a couple that generates the "null process"
(10) (H,E,j, ρ) + (–H, –E, –j, –ρ) = (0, 0, 0, 0) .
From this derivation it is easily to be seen that each "null process" can be generated by such a couple
(11) (–μUt, grad U)
where U is an arbitrary solution of the wave equation (8).
By (11) under consideration of (8) we know all potential couples which are called "scalar waves" by J.L. Oschman on p.205 of his book (s. the subscript of Fig. 14.3); somewhat inappropriate as we feel, we would prefer the term "null potential wave" instead of it.
Fig. 14.3 Coils used to emit fields and potentials.
A A standard coil emits electric and magnetic fields in the space around it.
B In the bifilar coil the electric and magnetic fields are cancelled, and electric scalar and magnetic vector waves are produced.
C The torroidal coil has the same effect.
D The Möbius coil produces only scalar waves.
The information on coil properties is from Abraham (1998)
Due to (11)/(8) there is a lot of possibilities to construct null-potential waves:
Let U = f(k·x – ct) where f is an arbitrary function and k be a unit vector. This generates the potentials
φ = – μUt= μ c f ', A = grad U = k f ',
but, of course, the physical quantities H,E,j, ρ generated by this null potential couple using the representation formulas (1)-(4) vanish identically, i.e. the null-potential wave has no physical effect: It doesn’t appear on the physical screen.
In contrast to the former result J. L. Oschman claims the Aharonov-Bohm effect (AB-effect) to prove the meaning of a vector potential in the physical world. The reader is referred to the literature for details, e.g.
We shall check this claim:
The AB-effect occurs in the neighbourhood of a magnetic vector field H generated by a vector potential A,
(1) H = curl A .
Evidently the effect depends on the vector potential A, since its value is given by the boundary integral
(12) ∫∂Ω A·dx
around the boundary ∂Ω of a check surface Ω, strangely enough, even when there was no magnetic field H at all along the path ∂Ω of integration (which can be realized by suited experimental configuration).
Indeed the AB-effect described by (12) attracted great attention in the year of its discovery – until people realized that by applying the well-known Stokes’ integral theorem to equation (12) it could be transformed to
(13) ∫∂Ω A·dx = ∫∫Ω curl A ·do= ∫∫Ω H ·do.
But this result means that the AB-effect is calculable by merely knowing the magnetic field H (on the check surface Ω) without taking into account any further "super world properties" of the potential A that are not already contained in the trace H = curl A.
The AB-effect does not depend on "super world" properties of A that are not visible in the physical world – the knowledge of H (on the "physical screen") is sufficient.
We can demonstrate this easily too by means of a null-potential wave, especially by means of its null-vector potential, which due to (11) has the form A0 = grad U: Hence the calculation of the AB-Effect of A0 using (12) yields
(14) ∫∂Ω A0·dx = ∫∂Ω grad U · dx = U(P) – U(P) = 0 ,
if we start the integration at an arbitrary point P of the boundary ∂ Ω and after one cycle of integration along ∂ Ω we stop the integration at P again.
This result (14) shows that the special information contained in a null-vector potential A0 = grad U is just ignored by the AB-effect. Hence the AB-effect doesn’t prove the physical meaning of a vector potential A for the physical world, since its possible part A0 = grad U, which exceeds the information contained in curl A, is always mapped to 0, whatsoever the actual meaning of the function U should be.
J.L. Oschman gives some further statements on his "scalar waves", our null-potential waves:
Scalar waves appear to interact with atomic nuclei, rather than with electrons. Such interactions are described by quantum chromodynamics (Ynduráin 1983).
We doubt that. Schrödinger’s equation and other equations of atomic physics contain scalar potentials V. So at first glance one might believe that here we would have a direct effect of potential on the "physical screen". But the next glance shows that the potential V is restricted by the condition V = 0 at infinity. This means that the additional constant contained in V is fixed, and the information in V is equivalent to that one in grad V, which is a force and hence a quantity of the "physical screen". Therefore we guess that Oschman’s reference might be an over-interpretation or misunderstanding of sources in physical literature.
The waves are not blocked by Faraday cages or other kinds of shielding,
This statement could possibly be fulfilled by choice of the generating function U. But it is physically worthless, since null-potential waves have – as far as we know up to now – no physical effect, no traces on the "physical screen".
they are probably emitted by living systems, and they appear to be intimately involved in healing (see e.g. Jacobs 1997, Rein 1998).
The sources given by J. L. Oschman seem not to be of physical competency.
The scalar potential has a peculiarity: it propagates instantaneously everywhere in space, undiminished by distance.
This property of instantaneous propagation is what null-potential waves can have by no means. Since they are generated by solutions U of the wave equation (8) and are consequently solutions of the wave equations likewise. But according to the theory of partial differential equations the wave equation does not admit superluminal solutions.
Oschman’s "scalar waves" cannot propagate with superluminal velocity.
At the end it could be of interest to compare Oschman’s concepts with other concepts in literature: Ochman’s scalar wave is a potential (like voltage) or a vector potential, while Meyl’s and Bearden’s scalar waves are waves of electric or magnetic field vectors. There is no synthesis possible due to its different units of measurement.
J.L. Oschman’s "scalar wave" concept is not compatible with the "scalar waves" invented by T. Bearden or K. Meyl.
Abraham G 1998 Potential shields against electromagnetic pollution: Synchroton Scalar Synchronizer. Optimox Corporation, PO Box 3378, Torrance, CA 90510-3378.Tet: 800-U3-1601
Afilani T L 1998 Device and method using dielectrokinesis to locate entities. US Patent 5,748,088
Ynduráin FJ 1983: Quantum chromodynamics: An Introduction ... Springer-Verlag
Appendix A: Potential representations of the fields of Electrodynamics
Under the assumption of constant material coefficients the electrical charge density ρ(x,t), the current density j(x,t), the electric field vector E(x,t) and the magnetic field vector H(x,t) have to fulfil the "inhomogeneous" Maxwell-equations
(A1) curl E = – μ Ht ,
(A2) curl H = ε Et + j ,
(A3) ε div E = ρ ,
(A4) div H = 0 .
(A4) yields the existence of a vector potential A such that:
(A5) H = curl A .
Inserting this into (A1) gives
(A6) curl (E + μ At) = 0 ,
which proves the existence of a (local) potentials φ such that
(A7) E = – grad φ – μ At.
In order to fulfil (A2) also we have to assume a relation between the potentials φ, A. >From (A2) we obtain by using (A5) and (A7):
j = curl H – ε Et
(A8) = curl curl A – ε (–μ Att – grad φ)
= grad (div A + ε φt) – (ΔA – 1/c² Att) .
If we couple the potentials φ, A by the Lorenz-condition (falsely ascribed to due to H.A. Lorentz)
(A9) div A + ε φt = 0
(which means that we prescribe the sources of A in addition to prescribing its curl by (A5), which is permissible therefore), we obtain the vector potential representation of the current density
(A10) j = 1/c² Att – Δ A .
Similarly (A3) and (A9) yield the potential representation of the charge distribution ρ:
(A11) ρ = ε div E = ε (1/c² φtt – Δφ).
Altogether taking (A5) = (1), (A7) = (2), (A10) = (3) and (A11) = (4) we have the desired potential representations of the physical field quantities E, H, j and ρ.
Appendix B: Null-Potential-Waves ("Scalar Waves")
Null-potential waves, J. L. Oschman’s "scalar waves", are defined as potential couples (φ0,A0), the generated physical fields of which are completely cancelled by destructive interference. Hence we have
(B1) H0 = curl A0 = 0 ,
(B2) E0 = – grad φ0 – μ A0 t = 0 ,
(B3) j0 = 1/c² A0 tt – Δ A0 = 0 ,
(B4) ρ0 = 1/c² φ0 tt – Δ φ0 = 0 .
Additionally we have to fulfil the Lorenz-condition (falsely ascribed to due to H.A. Lorentz)
(B5) div A0 + ε φ0 t = 0 .
(B6) A0 = grad V
where V is some scalar function. Then (B2) yields
grad (φ0 + μ Vt) = 0 ,
(B7) φ0 = – μ (Vt + χ·(t))
with some function χ(t).
But due to grad U = grad V for U = V + χ we obtain
(B6') A0 = grad U
(B7') φ0 = – μ Ut
Using the Lorenz-condition (falsely ascribed to due to H.A. Lorentz) (B5) yields the necessary condition for U, the wave equation:
(B8) 1/c² Utt – Δ U = 0 .
Conversely (B8) is sufficient to establish the representations (B1)-(B4) by using (B6') and (B7'):
The solutions U of the wave equation (and these only) generate null-potential waves.
The wave equation is one of the best-known equations in the Theory of Partial Differential Equations. An important theorem says that signal propagation cannot exceed the speed of light c.
The wave equation has no superluminal solutions, hence no superluminal
null-potential waves are possible.
The Lorenz condition stems from
Lorenz, L. "On the Identity of the Vibrations of Light with Electrical Currents." Philos. Mag. 34, 287-301, 1867.
van Bladel, J. "Lorenz or Lorentz?" IEEE Antennas Prop. Mag. 33, 69, 1991.
Whittaker, E. A History of the Theories of Aether and Electricity, Vols. 1-2. New York: Dover, p. 268, 1989.