## M.W. Evans' Vacuum Current

### G.W. Bruhn, Darmstadt University of Technology

In a web rebuttal [2] Evans repeats his "proof" of his vacuum current. He writes after some preliminary remarks:

### 2. DERIVATION OF THE VACUUM CURRENT

The equations used in ref.{1} are standard model equations, namely the Ampère-Maxwell law in the vacuum:

Ñ × B1/ E/∂t = 0                                                       (1)

and the scalar and vector potentials defined by:

E = − A/∂tÑ Φ ,         B = Ñ × A                                 (2)

Here B is the magnetic flux density in tesla and E is electric field strength in volts per meter. In any textbook it is found that by using the vector identity:

Ñ × (Ñ × A) = Ñ (Ñ · A) − Ñ² A                                      (3)

a wave equation is obtained by substituting eq.(2) in eq.(1):

(1/ ∂²A/∂t²Ñ²A) + Ñ (1/ Φ/∂t + Ñ · A) = 0 .               (4)

In ref.(1) this wave equation was rewritten as:

∇A = − Ñ (1/ Φ/∂t + Ñ · A)                                           (5)

in order to define the vacuum current

jA := − 1/μo Ñ (1/ Φ/∂t + Ñ · A)                                      (6)

In vector notation and S.I. units the Lorenz condition (1) is:

1/ Φ/∂t + Ñ · A = 0                                                         (7)

So if the Lorenz condition is used we obtain the usual result

∇A = 0 .                                                                           (8)

### So far everything is fine: The opponents Evans and Bruhn agree! Especially I emphasize Evans' consent to the equivalence

(1) Û (5):                 Ñ × B1/ E/∂t = 0         Û         ∇A = − Ñ (1/ Φ/∂t + Ñ · A)         (= μo jA)

### regardless of any gauge condition.

The rest of ref.{1} discusses the vacuum current (6) if the Lorenz condition is not used.

### 3. DELIBERATE DECEPTIONS BY BRUHN

It is unpleasant to have to use the phrase "deliberate deception", but this has become unavoidable. In this case the deceptions are as follows.

1) Bruhn introduces a matter current density j in his eq.(1.1) - this is not used in ref.{1}.

Excuse me, Myron, I could have had some reason to consider inhomogeneous equations instead of your homogeneous equations. It's just the same effort as to show the equivalence (1) Û (5).

2) It is then asserted, in a deliberately false manner, that there is "confusion" in eqs.(1) to (5). If so hundreds of textbooks may be throw away.

That's only your misunderstanding of the situation, Myron. I fully agree with the equations (1) - (5) as was stated above.

3) Deliberately attempts are made to confuse the reader by asserting that there is confusion between "Lorenz gauged and "Lorenz ungauged" (sic). Such a confusion does not exist, the analysis in Section 2 is entirely standard.

And just this "standard" of your Section 2 is what I consider as dubious. Let's have a look at your paper [1] on "Extracting Energy from the Vacuum". On p.514, 2nd column, we read:

Quotation

### ∇A = − Ñ (1/c²∂Φ/∂t + Ñ · A) = μojA                         (10) . . .                 jA = σ EA                                                                   (12) It is shown by Lehnert and Roy [6] that the equations of classical electrodynamics in the vacuum then become:                 Ñ · E = 0 ;                 Ñ × H = σ EA + ∂D/∂t                 (13)

End of quotation

The second equation in (13) is WRONG: It is a misinterpretation of the Lehnert and Roy paper [6] by Evans which contradicts the above equivalence (1) Û (5). By using that equivalence we may conclude:

Eq.(10) (identical with eq.(5)):   ∇A = − Ñ (1/ Φ/∂t + Ñ · A)     Þ(1)Û(5)     Eq.(1):  Ñ × B1/ E/∂t = 0

thus, we obtain the correct (homogeneous) Ampère-Maxwell equation

Ñ × B = 1/ E/∂t         or         Ñ × H = D/∂t                         (13')

i.e. the vacuum current jA = σ EA has to be removed from eq.(13).

### There is no vacuum current jA in the (corrected) Ampère-Maxwell equation (13').

Herewith all confusion of Evans' "rebuttal" should have been removed.

### References

[1] M.W. Evans e.a., Classical Electrodynamics without the Lorentz Condition:
Extracting Energy from the Vacuum
, Phys. Scr. Vol. 61, 513-517, 2000
http://aias.us/documents/mwe/omniaOpera/omnia-opera-563.pdf

[2] M.W. Evans, REBUTTAL OF A PSEUDO-PAPER BY G. BRUHN IN PHYSICA SCRIPTA (2006):
WAVE EQUATION WITH VACUUM CURRENT
(2007),
http://www.atomicprecision.com/blog/wp-filez/aformalrebuttalgbruhnphysscripta2.pdf

[3] G.W. Bruhn, No Energy to be Extracted from the Vacuum, Phys. Scr. Vol. 74, 535-536 , 2006,
see the detailed quote in
http://www2.mathematik.tu-darmstadt.de/~bruhn/misunderstandings.html

[6] B. Lehnert and S. Roy, Extended Electromagnetic Theory, World Scientific Singapore (1998),
online at APEIRON Vol.4 Nr. 2-3, Apr.-July 1997
http://redshift.vif.com/JournalFiles/Pre2001/V04NO2PDF/V04N2ROY.PDF

### Links concerning Evans' Energy from the Vacuum

(09.07.2007) Bo Lehnert Correcting M.W. Evans' Distortions

(05.07.2007) Evans' Misunderstanding of Lehnert's Settlement with Bruhn