## Evans' Misunderstanding of Lehnert's Settlement with Bruhn

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

Bo Lehnert wrote to M.W. Evans here:

Concerning the point on the gauge process made by Gerhard Bruhn on the work by Sisir and myself, I had at that time a discussion with Bruhn. His point was due to a misunderstanding, and the discussion was settled at the beginning of Section 2 in his paper of Physica Scripta 74(2006)535.

### Hence Lehnert refers to Section 2 of that paper [3] as the basis of a settlement with Bruhn.

The essential phrases are:

### The authors of [2] refer to a former paper [1] where two of them had described the gauge process quite correctly not differing from the textbooks. However, as we shall see, the leading author of [2] has made a wrong use of the equations in [1] by confusing the above cases (a) and (b).

The authors of [1] were Bo Lehnert and Sisir Roy, the leading author of [2] was Myron W. Evans.

Quotation from the Physica Scripta paper [3] 74(2006)535, Section 2:

## No Energy to be Extracted from the Vacuum . . .

(a) The ‘Lorenz-free’ case: Without Lorenz gauge (1.3) the Ampère–Maxwell equation Ñ × H = j + Dt is equivalent to equation

(1.1)                 1/ Att − ΔA + Ñ (Ñ·A + 1/ Φt) = μo j .

(b) The case of Lorenz gauge: With Lorenz gauge (1.3) the Ampère–Maxwell equation Ñ × H = j + Dt is equivalent to equation

(1.4)                 1/ Att − ΔA = μo j .

. . .

### 2. The Flaw of Thinking in [2]

The authors of [2] refer to a former paper [1] where two of them had described the gauge process quite correctly not differing from the textbooks. However, as we shall see, the leading author of [2] has made a wrong use of the equations in [1] by confusing the above cases (a) and (b).

He is intending to treat the vacuum case, where no charge and no current is present, of ‘classical electrodynamics without the Loren(t)z condition’, i.e. he considers case (a). So he starts with the reduced ‘Lorenz free’ equation (1.1) with j = 0, with the equation

1/ Att − ΔA + Ñ (Ñ·A + 1/ Φt) = 0 ,                                                                 (2.1)

and, having in mind the Lorenz gauged version (1.4), he defines a ‘vacuum current’ jA by his equation

− (Ñ·A + 1/ Φt) =: μo jA.                                                                                 [2;(10)]

Therewith equation (2.1) takes the form

1/ Att − ΔA = μo jA.                                                                                             (2.2)

Now we come to the magic trick: our author remembers equation (2.2) to belong to the Ampère–Maxwell equation and so he concludes

Ñ × H = jA + Dt ,                                                                                                 [2;(20)]

ignoring that this is true only under Lorenz gauge (case (b)) while he had decided to consider the Lorenz-free case (a).

### Therefore equation [2;(20)] is wrong.

For the way back to the Ampère–Maxwell equation the Lorenz term (1.3) is essential and must be ‘reimbursed’, i.e. correctly we have to start with the Lorenz-free version of equation (2.2), i.e. with

1/ Att − ΔA + Ñ (Ñ·A + 1/ Φt) = μo j := μo jA + Ñ (Ñ·A + 1/ Φt)                   (2.3)

to obtain the Ampère–Maxwell equation Ñ × H = j + Dt . However, due to equation (2.3) and the definition [1; (10)] of the vacuum current jA we have

μo j = μo jA + Ñ (Ñ·A + 1/ Φt) = 0,                                                                     (2.4)

thus, the correct calculation yields the ZERO vacuum current j = 0.

### References

[1] Lehnert B and Roy S 1997 Extended Electromagnetic Theory...; APEIRON vol 4, no 2–3, online at
http://redshift.vif.com/JournalFiles/Pre2001/V04NO2PDF/V04N2ROY.PDF

[2] Evans M W 2000 Classical electrodynamics without the Lorentz condition:
extracting energy from the vacuum Phys. Scr. 61 513–7 online at
abstract: http://www.physica.org/ xml/article.asp?article=v061a00513.xml and
PDF full text: http://www.physica.org/asp/document.asp? article=v061p05a00513
http://aias.us/documents/mwe/omniaOpera/omnia-opera-563.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

End of Quotation

### 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

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