March 18, 2006: E-Mail-discussion appended
                                    March 29, 2006: Reply to Hauser's "rebuttal" appended

Remarks on Burkhard Heim's IGW Successors
J. Hauser and W. Droescher and their Theory

by Gerhard W. Bruhn, Darmstadt University of Technology

1. The IGW (Institute of Border Sciences)

Since 1999 there existed a web site of the Institut für Grenzgebiete der Wissenschaft (IGW) on the server of the Leopold-Franzens-University Innsbruck (Austria).

The indicated owner of that web site was Prof. Dr. Andreas Resch. Under scientific personel were nominated Prof. Dr. Jochem Hauser and Dipl.-Ing. Walter Droescher (originally in German: Häuser and Dröscher).

However, none of the indicated persons belongs to the staff of the Leopold-Franzens-University.

According to his own biographic data A. Resch was Professor for clinical psychology and paranormology at the Accademia Alfonsiana, Pontifical Lateran University Rom from 1969 to 2000. And J. Hauser is professor at the Braunschweig-Wolfenbüttel Fachhochschule at Salzgitter, Germany. Walter Droescher, probably retired now, was a theorist at the Vienna Patent Office in the 80s, when he began to work with B. Heim.

The IGW simply tried to deceive their visitors by wrongly alleging to belong to the Innsbruck University
in order to obtain reputation by devious means.

However, on Jan 27 2006 the Leopold-Franzens-University became aware of the abuse of universitary facilities by the IGW, and the IGW web site was instantly removed.

Typically enough for the ambitions of the IGW, informations on the IGW and the Resch-Verlag can still be found on the pseudo-science web sites

2. The Hauser-Droescher Extension of the Heim Theory

The Heim theory did never pass a rigorous peer reviewing. In 2002 the authors J. Hauser and W. Droescher started to extend the former Heim theory which a reviewer (below) considered to be almost (!?!) error-free. For a version of that new theory they got "the" AIAA research award 2004. That formulation pretends as if there is only one AIAA award a year. However, there are more than 50 kinds of such awards a year. And the award under consideration here is the Best-Paper Award of just that Technical Committee, Nuclear and Future Flight TC, a member of which is J. Hauser himself. In 2005 the TCs of AIAA gave away 21 Best-Paper Awards.

The "best paper of 2004" [2] was replaced by the authors with a revised version [1] which we are referring here to. We consider a basic section where the concept of a so-called poly-metric is introduced:

Quote from [1]:


In GR the metric has the meaning as physical potential for gravitation. As was mentioned before this view is extended to Heim space H8. We now present the most general transformation that is responsible for all physical interactions. Most important is the double transformation as described in Eq. (1). A curve in R4 can be specified by either Cartesian coordinates xm or by curvilinear coordinates ηi. However, since R4 is a subspace of Heim space H8 with so called internal coordinates ηi (Dröscher and Hauser, 2004), there exists a general coordinate transformation xmαi)) from R4 → H8R4 resulting in the metric tensor (this is a major difference to GR)

gik = ∂xm/∂ξα ∂ξα/∂ηi ∂xm/∂ξβ ∂ξβ/∂ηk ,     gik : = Σμ,ν=1 ... 8 gik(μν) ,     gik(μν) = ∂xm/∂ξ(μ) ∂ξ(μ)/∂ηi ∂xm/∂ξ(ν) ∂ξ(ν)/∂ηk ,     (1)

where indices α,β = 1,...,8 and i,m,k = 1,...,4. The Einstein summation convention is used. The above transformation is instrumental for the construction of the poly-metric utilized to describing all possible physical interactions. The metric tensor can be written in the form as expressed in the second term of Eq. (1). Parentheses indicate that there is no index summation. In Dröscher and Hauser (2004) it was shown that 12 hermetry forms can be generated having direct physical meaning, by constructing specific combinations from the four subspaces. The following denotation for the metric describing hermetry form Hl with l = 1,...,12 is used:

gik(Hl) : = Σμ,ν Î Hl gik(μν)                                                                                (2)        

where summation indices are obtained from the definition of the hermetry forms. The expressions gik(Hl) are interpreted as different physical interaction potentials caused by hermetry form Hl, extending the interpretation of metric employed in GR to the poly-metric of H8.

(End of quote)

We pointed out by email to the authors that already the first equation in (1) cannot be true: We have

∂xm/∂ξμ ∂ξμ/∂ηjj = ∂xm/∂ξμμ = dxm

and thus

gjkjk = Σm (dxm)2 > 0 for each dx0,

since each dxm is real due to the assumption x = (x1, x2, x3, x4) Î R4 = R×R×R×R, where R denotes the well-known set of all real numbers. This shows that the matrix (gjk) is positive definite while in GR the matrix (gjk) must be indefinite like the Minkowski-matrix diag(1, 1, 1, −1).

The detected error is already contained in Hauser's and Dröscher's first paper [3; Section 3.2].

Jochem Hauser replied:

With regard to your Objections 1, 2 it must be said that R4 only stands for an abbreviation that has the following meaning in GR:

a manifold M with the following characteristcs:
4-dimensional curvilinear space which is locally Minkowskian,
i.e. gik = nonconstant in general

We answered with:

R4 cannot denote a manifold which is used in GR:
Your "manifold M" (= R4) is such that you can identify its points with the quadrupels (x1,x2,x3,x4) where the coordinates are numbers such that you can define the metric (gik) by

gjkjk = (dx1)2 + (dx2)2 + (dx3)2 + (dx4)2.

This is nothing but the space R4, on the one hand with Euclidian rectilinear coordinates xm (m=1,2,3,4), where on the other hand you introduce curvilinear coordinates ηj (j=1,2,3,4) by means of the coordinate transform xm = xmαj)).

N.B. The coefficients gjk being nonconstant is a necessary but no sufficient condition for the nonflatness of the manifold.

Counter examples

(1) One can introduce polar coordinates in the (flat = Euclidean) plane which - as is well-known - have nonconstant metric coefficients gjk though its curvature is zero; cf also the 3D-example in S.M. Carroll [5; p.48, (2.30-32) and [6; p.41, (2.41-43)].

(2) S.M. Carroll considers the surface of the two-sphere in R3 as a simple example of a non-Euclidean manifold

ds2 = (dη1)2 + sin2η1 (dη2)2     (= dθ2 + sin2θ2     in Carroll's notation),

the curvature of which is 1 [5; p.48, (2.33) and [6; p.71, (2.45)].

The curvature of the "manifold M" is - as is well known - independent of the coordinates used.

However, with respect to the x-coordinates the "manifold M" has zero curvature, i.e. your "manifold M" is flat, so also with respect to the curvilinear coordinates ηj (j=1,2,3,4).

A coordinate transform on a manifold is without effect on its curvature.

The calculation of the curvature with respect to the x-coordinates is trivial and yields zero, while the calculation w.r. to the curvilinear coordinates would take a lot of trouble to yield the same zero result at the end. This is the reason why tensor calculus is used in multidimensional differential geometry.

If you like to construct a manifold (locally) Minkowski, then you must give up the assumption x = (x1,x2,x3,x4) ÎR4 and modify it to x4Î iR. Setting x4 = i ct we start with the Minkowskian metric

gjkjk = (dx1)2 + (dx2)2 + (dx3)2 − (cdt)2

This defines a metric locally Minkowski - however, this metric is even globally Minkowski, i.e. the defined manifold M is flat again.

Such a flat manifold M is too special to be useful in GR or its extensions.

Thus, J. Hauser and W. Droescher erroneously take a flat spacetime M instead of the curved spacetime of GR as a basis of their extended Heim-theory [1 - 4], which, of course, is not sufficient and should be revised by the authors - if possible at all. That requires alterations the reviewer doesn't intend to prescribe.


[1]     Walter Droescher, Jochem Hauser: Heim Quantum Theory for Space Propulsion Physics, 2005,
          URL presently unknown,
          (available also at or ???)

[2]     Walter Droescher, Jochem Hauser: Guidelines for a Space Propulsion Device Based on Heim's Quantum Theory,
          AIAA 2004-3700, AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Ft. Lauderdale, FL,
          July 2004, 28 pp.,
          (available also at or ???)

[3]     Walter Droescher, Jochem Hauser: Physical Principles of Advanced Space Transportation based on Heim's Field Theory,
          AIAA/ASME/SAE/ASE, 38th Joint Propulsion Conference & Exhibit, Indianapolis, Indiana,
          7-10 July, 2002, AIAA 2002-2094, 21 pp.,
          URL presently unknown,
          (available also at or ???)

          IGW Innsbruck 2003

[5]     Sean M. Carroll: Lecture Notes on General Relativity,
          Addison Wesley 2004, ISBN 0-8053-8732-3

[6]     Sean M. Carroll: Spacetime and Geometry,
          Addison Wesley 2004, ISBN 0-8053-8732-3

Quote from

Up to this point, Heim had not yet confided in other theoretical physicists on the details of the mass formula derivation. Hence, the DESY results were not widely published and disseminated for academic scrutiny. Fortuitously in the same year, Walter Droescher, a theorist at the Vienna Patent Office, began to work with Heim. The first result of their collaboration cumulated into the second volume of Heim's major work, appearing in 1984. It is almost(!?!) error-free, in contrast to the first volume which was not reviewed to this extent.



3. Further Discussion

Though the authors J. Hauser and W. Droescher were repeatedly informed by email about the above objections, there was no further reply till February 04, 2006. The discussion will be continued when we receive further contributions.

E-Mail Discussion

I received two longer emails from J. Hauser with no contributions to the question under consideration. Especially J. Hauser gave no equations or proofs to correct his criticized article or my objections above.

Hugh Deasy wrote on March 18, 2006:

You say:

"R4 cannot denote a manifold which is used in GR:

Your "manifold M" (=R4) is such that you can identify its points with the quadrupels (x1,x2,x3,x4) where the coordinates are numbers such that you can define the metric (gik) by

        gjkjk = (dx1)2 + (dx2)2 + (dx3)2 + (dx4)2.

This is nothing but the space R4, on the one hand with Euclidian rectilinear coordinates xm (m = 1,2,3,4),"

But in

Heim says
"Extending the ideas of Einstein, Kaluza, Klein and Jordan the theory described in this report shows how to geometrize in principle not only the gravitational field but the other force fields as well. They appear as geometrical structures of spacetime, R4 (a Minkowski space with x4 = ict) subject to the usual conservation laws, and lead to a general non-Hermitian geometry in R4"

So this is not a flat real space.


Hugh Deasy

G.W. Bruhn replied:

First of all: When physicists are using the language of mathematics then they have to notice the precise mathematical definitions of the symbols in use. If someone thinks that he can give own meanings to the symbols then he should not complain the confusions and misunderstandings that arise by that way.

Example: R denotes the set of all real numbers. R4 is the set of all quadrupels (x1,x2,x3,x4) of REALS xm. Thus, the Minkowski space M, where x4 = ict is imaginary, is not R4.

It is less complicated to introduce the Minkowski space M as R4 in mathematical sense but equipped with the (pseudo-)metric (since indefinite)

        ds2 = (dx1)2 + (dx2)2 + (dx3)2 − (dx4)2 = γmndxmdxn

where (γmn) denotes the Minkowski-matrix diag(1,1,1,−1).

It is well-known that M is flat. The reason is that all derivatives of the Minkowski metric coefficients vanish. This implies that the Ricci tensor Rmn vanishes. Hence we have the curvature R = Rmn γmn = 0, which means that M is flat.

We now come to Hauser's paper. His equation (1) is equivalent to

(*)         ds2 = (dx1)2 + (dx2)2 + (dx3)2 − c2 dt2 = gijij

where the coordinates xm and the "curvilinear" coordinates ηj are linked by a smooth coordinate transform xm = xmj).

NB. Both sides of (*) define the metric of the same manifold M referring to different coordinates. That does not change the curvature: Let Rij denote the Ricci tensor relative to the eta-coordinates and Rmn the Ricci tensor relative to the x-coordinates, then we obtain the curvature from

(**)         R = Rij gij = Rmn γmn = 0 γmn = 0.

The author J. Hauser has the misconception that the transformation of the x-coordinates of the Minkowski space M into curvilinear coordinates would change the curvature. This is erroneous as the example of the introduction of polar coordinates in the Euclidian R2 demonstrates.


(I) The Minkowski spacetime M is flat. See [5; p.1 ff.]

(II) The curvature R does not change under coordinate transforms. See [5; p.81]

(III) Hauser's transformed M is flat.


[5]     S. M. Carroll, Lecture Notes in Relativity", arXiv [math-ph/0411085]


Remarks on Hauser's "rebuttal" [7] of my objections

The topics 1., 2., 4. ... 9. do not concern my objections. So I have to reply to topic 3. only:

3. Therefore, spacetime is assumed to be a differentiable 4-dimensional manifold, M4, as long as quantum effects are not considered. This manifold comprises a collection of points where each point is specified by a set of four real numbers and has the same local topology as R4, i.e., it is locally but not globally (as you wrongly assume) like R4. This is why we refer to this spacetime sometimes as R4, but from the physics context its meaning is always clear, see Figs. 1 and 2 on pages 3 and 4 of AIAA 2005-4521. A different question is the embedding of 4D spacetime in an Euclidean space. In GR there exist 10 independent components of the metric tensor, and thus a R10 would be needed. Your example is for embedding a 2D manifold that is, a surface of a sphere, in R3. But this is not relevant for the construction of the poly-metric tensor.

As I have repeatedly pointed out above my criticism refers to your equation (1)

gik = ∂xm/∂ξα ∂ξα/∂ηi ∂xm/∂ξβ ∂ξβ/∂ηk ,     gik : = Σμ,ν=1 ... 8 gik(μν) ,     gik(μν) = ∂xm/∂ξ(μ) ∂ξ(μ)/∂ηi ∂xm/∂ξ(ν) ∂ξ(ν)/∂ηk ,     (1)

which using the rules of calculus can be written in the form

(*)         gjkjk = Σm (dxm)2.

That would be a positiv definite metric and would not fulfil the requirements even of SRT, much less that ones of GR, if one assumes (x1, x2, x3, x4) in R4 as you did.

So something in your definitions must be changed.

We could replace x4 → i x4 = i ct where x4 = ct is real, i.e. we could define an indefinite metric on the real space R4 by

        ds2 = (dx1)2 + (dx2)2 + (dx3)2 − (dx4)2 = γmndxmdxn

where (γmn) denotes the Minkowski-matrix diag(1,1,1,−1). Then we have the metric equation

(**)        gjkjk = γmndxmdxn .

This defines a manifold M that is locally Minkowskian indeed. As can be seen from [5; p.1 ff.] it is Minkowskian even globally. In addition, the metric equation (**) enables us to calculate its curvature R [5; p.81], which is coordinate independent. And the representation of M by means of the coordinates xm yields R = 0 because all derivatives of the metric coefficients γmn vanish, hence the Ricci tensor Rmn as well to obtain R = Rmn γmn = 0. The same result would turn out for any other coordinates ηj specified by Equ. (**).

Thus, this M is flat and therefore of no use for the purposes of GR or any extension of GR.

Concerning the question of embedding:

The spacetime manifold of GR is usually defined without referring to any embedding, see [5; p.31]. Possibly you have misunderstood my remarks: What you are doing by your equation (1) is an embedding of M into the space R4 equipped with an Euclidean or Minkowskian metric respectively. By that way the manifold inherits the metric of the surrounding space, and that is no way to the situations in GR.

Possibly, the whole discussion arises from your not well formulated definitions. If so, there are several good textbooks available where correct methods of definitions of manifolds can be found. Your Equ. (1) e.g. is not compatible with the method described in [5]. So my proposal is that you think over the whole issue and try it with a better formulated theory.


[5]     S. M. Carroll, Lecture Notes in Relativity", arXiv [math-ph/0411085]

[7]    Jochem Hauser and Walter Dröscher: Rebuttal: Critiscm of a Flat Metric by Prof. Bruhn,
        Technical University of Darmstadt, Germany