Heim theory
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Heim theory is a proposed 'theory of everything', based on the work of the German physicist Burkhard Heim. The theory attempts to resolve incompatibilities between quantum theory and general relativity. The term "Heim theory" is also used for theories which are extensions or generalizations of the original theory proposed by Heim. Most notable are the theoretical generalizations put forth by Walter Droescher, who worked in collaboration with Heim at some length. Their combined theories are also known as "HeimDroescher" theories, although there are no international established standards for naming Heimrelated theories at present. This ambiguity in the term "Heim Theory" has led to some confusion and difficulty over the correct interpretation of the theory. For example, in its original version Heim theory used 6 dimensions, which was sufficient to derive the masses of elementary particles. Droescher first extended this to 8, in order to demonstrate that the quantum electrodynamics and QCD structures of the standard model could be found within this expanded version of the original Heim theory. Later, 4 more dimensions were used in the 12 dimensional version that involves extra gravitational forces one of which corresponds to quintessence . All these theories are often known as "Heim theories". The various dimensional extensions allow one to interpret that branches of established physics can be found in Heim theory, including Maxwell's equations.
Contents[hide] 
Principles
There are some empirical predictions of Heim theory which can in principle be experimentally verified, but this has not been achieved to date. These include
 Predictions for the masses of neutrinos, and
 Predictions for the conversion of photons into the socalled "gravitophotons" resulting in a measurable force
Heim also introduces in his theory a new vocabulary which describes his predicted forces and interactions with matter. As a majority of these terms were originally in German, translation of these into English has resulted in some ambiguity.
Introduction
In order to appreciate the significance of Heim theory and other "theories of everything", it is necessary to briefly discuss the incompatibilities of quantum theory and general relativity. For sufficiently small and bound systems, (say, around the size of atoms and quarks) quantum theory proposes that these systems behave as if certain physical characteristics of them are quantized. For example, only fixed amounts of energy can be exchanged with such systems. For sufficiently large and unbound systems, general relativity proposes that energy and mass are interchangeable, and that systems possess a continuum of energies as particles approach the speed of light. If we consider the situation where small particles move close to the speed of light in a bound system, both theories become problematic in describing the full behaviour of the observed system. This is because discretization of energy proposed by quantum mechanics is apparently incompatible with the continuum of energy proposed by general relativity and its consequences. A similar situation arises when an attempt is made to describe a large quantity of mass or energy confined to a small region of space. In particular, a successful theory which can unify quantum and general relativity theory should be able to explain the lifetimes of particles (how long the particle exists before it decays into energy and disappears), and the reasoning behind the observed quantization of mass in elementary particles.
To resolve this difference, Heim theory attempts to explain the nature of elementary particles, along with their observed lifetimes and discrete mass spectrum using a concept known as quantized geometrodynamics. This concept involves an abstract mathematical object embedded in 12dimensional space. The space occupied by this object is extremely small. In this model, all space consists of many quantized surface elements on the order of 10^{70} m^{2} small. Each quantized surface element is known as a metron (term coined by Heim). The theory is a purely geometrical theory  that is, space is considered quantized and all the nuclear forces arise analogously to gravity in general relativity. Some features of the theory are:
 The reasonable accuracy of the mass formula  The mass formula predicts the masses of 16 elementary particles to a relative accuracy of one part in 10,000. The probability of this being due to chance is on the order of 1 in 10^{64} [(10,000)^{16} = (10^{4})^{16}]. No other established theory of fundamental particles at present have made comparable theoretical predictions to this accuracy. Thus if there were more widespread acknowledgement of the correctness of the mass formula, then perhaps part of the foundations, logic, and consequences of the Heim theory will have to be acknowledged as a possibility. Note also, that although vol.1 of Heim's magnum opus contains several errors that are in need of correction  the Heim theory group members are currently active in that area , vol. 2 was cross checked more thoroughly and is essentially error free  and it is here that the mass formula is derived.
 The 8dimensional extension by Droescher gives the interactions  and a group structure as in the Standard Model. It also gives two additional gravity forces  one that has the characteristics called quintessence. The observed apparent acceleration in the expansion of the universe can be rationalized with a combination of Heim and Droescher's theories.
 There are 4 independent variables assumed in the theory  h (Planck's Constant), G (Gravitational constant), vacuum permittivity and permeability. Combinations of these constants in various mathematical functions derived from Heim theory allows one to derive existing particle masses and their lifetimes to within a reasonable experimental error. It also proposes that other particles not discovered at present, are in existence. The Heim theory also proposes that the fine structure constant is dependent on these 4 independent variables.
 Some of the predictions are still outstanding  e.g. the neutrino masses (see selected results in [1]).
 A sign that the theory is perhaps undergoing a renewal of interest is a paper published by the American Institute of Aeronautics and Astronautics in 2005 authored by Droescher and Haeuser. The paper discusses potential aerospace applications of Heim theory. It was decided by the Nuclear and Future Flight Propulsion Technical Committee of the AIAA to acknowledge the publication with a "best paper of the year" award in July 2005. This award attracted much attention, including the cover story for the first 2006 issue of New Scientist [2]
The mass formulae
The mass formulae are perhaps the most important of Heim's theory at the moment. This is because it is the portion of his theory which can be thoroughly analyzed by comparing its numerical results and a standard table of masses for fundamental particles. There are multiple mass formula equations used in succession to compute the entire theoretical "mass spectrum".
The mass spectrum predicts the masses of fundamental particles and their "resonances". It consists of several nested levels of variables, and is described in summary in the paper "Recommendation of a Way to a Unified Description of Elementary Particles" by Burkhard Heim, published in the journal Zeitschrift für Naturforschung. Teil A, Band 32A Heft 17, 1977 Jan.Juli, pg. 233243.
Heim gives the form of the mass spectrum to be
In Heim's 1989 mass formula [3], the expression for the masses is broken down as follows:
 M = μα _{+} [(G + S + F + φ) + 4qα _{−} ]
(see the above link for explanations of the terms in this expression).
The derivation of Heim's 1989 formula relies on the partial result published in 1977. Also, there are specific mass spectrum formulae for charged particles, and uncharged particles. These formulae are based on their respective hermetry forms.
Comparison between theoretical and experimental values
Here are tables comparing the theoretical and experimental or measured particle masses and lifetimes of selected particles:
Particle name  Theoretical mass (MeV/c^{2})  Experimental mass (MeV/c^{2})  Absolute error  Relative error 

Proton  938.27959  938.27231  0.00728  0.00000776 
Neutron  939.57336  939.56563  0.00773  0.00000823 
Electron  0.51100343  0.51099907  0.00000436  0.00000853 
Particle type  Particle name  Theoretical mass (MeV/c^{2})  Measured mass (MeV/c^{2})  Theoretical mean life/10^{8} sec  Measured mean life/10^{8} sec 

Lepton  EleNeutrino  0.381 × 10^{8}  < 5 × 10^{8}  Infinite  Infinite 
Lepton  Mu Neutrino  0.00537  < 0.17  Infinite  Infinite 
Lepton  TauNeutrino  0.010752  < 18.2  Infinite  Infinite 
Lepton  Electron  0.51100343  0.51099907 ± 0.00000015  Infinite  Infinite 
Lepton  Muon  105.65948493  105.658389 ± 0.000034  219.94237553  219.703 ± 0.004 
Baryon  Proton  938.27959246  938.27231 ± 0.00026  Infinite  Infinite 
Baryon  Neutron  939.57336128  939.56563 ± 0.00028  917.33526856 × 10^{8}  (886.7 ± 1.9) × 10^{8} 
 "measured" = Particle Data Group Cern 2002
 "theoretical" = Heimtheory Group 2003
Heim's approach to calculating the mass spectrum requires 4 parameters, of which the gravitational constant G is the least precise. It has an uncertainty of up to 0.001 (see e.g. [4] where it is suggested that uncertainty might even be higher). As a result, relative errors of up to 0.001 are expected. This assumption holds if the mass formula equations are more or less linear with respect to G.
The errors indicated in the table are approximately 100 times lower than this value. This indicates that the theory is either:
 Nonlinear in G;
 The value of G fortuitously produces these results.
A more precise estimate of the expected error due to G from the theorists would be required to determine which case this is, but this has apparently not yet been produced. As a result, no error bars have been computed for the theoretical values.
Gravitation
Heim theory assumes that a gravitational potential arises from the gradient of a field φ(r). Position dependent mass is the function m(r), and r is the radial distance from a quanta of a point mass.
A differential equation used to describe the basis is
If this equation is nondimensionalized the characteristic length of the system is
The characteristic length is the distance from a point mass for which the field φ(r)=0. It is also the case that the field attains its absolute minimum. Hence, the gravitational force is identically zero at this distance.
The solution to the differential equation has the curve φ(r) concave up. The gravitational potential that arises from this field can be positive, negative or zero.
Further technical details
The 8 dimensions of Heim theory is the result of two mathematical objects
 a nonlinear operator whose matrix representation C consists of 4 submatrices
 These submatrices are generated with the 4 nonlinear operators indexed as C_{a}
 64 state functions ψ indexed with three independent labels ψ_{abc}
The three indices run from 1 to 4, resulting in 64 different eigenvalue equations
The resulting matrix representation for the four C operators is a 64 by 64 matrix defined by
This large matrix is entirely zero with the exception of 24 elements on the main diagonal. The 64 elements on the main diagonal represent the components of an energy density tensor. The 64 elements can be arranged in an 8 by 8 matrix T such that
The nonzero elements T_{ij} are equal to the appropriate eigenvalue which has been mapped into this matrix. This matrix has 8 eigenvalues (and thus 8 eigenvectors) which can be grouped into 4 unique groups based on their degeneracy. If the eigenvectors are normalized, they span a coordinate space called R_{8}. This space has coordinates x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, which can be grouped as {x_{1}, x_{2}, x_{3}}, {x_{4}}, {x_{5}, x_{6}}, and {x_{7}, x_{8}}.
Note also that if we take the basic number of physically existing dimensions to be 6, corresponding to the 6x6 nonzero submatrix of T, then we can use Heim's formula relating this number, P, to the maximum possible number of dimensions, n, i.e.:
 n = 1 + sqrt(1 + p(p − 2)(p − 1))
to give n = 12 for p = 6. This explains the 6 'extra' dimensions of the fully extended theory.
Interpretation
These groupings are labeled respectively

 R_{3}, representing the typical cartesian state space
 T_{1}, representing the time coordinate
 S_{2}, representing the "entelechial" and "aeonic" coordinates
 I_{2}, representing the coordinates which govern the probability state space
The last 4 coordinates have various different interpretations, of which many are "unphysical". They are usually interpreted as auxiliary coordinates which project into the spaces R_{3} and T_{1} through special operators.
As an aside, in the original theory of Heim, the tensor T is only a 6 by 6 matrix. In this HeimDroescher extension, the tensor is an 8 by 8 matrix. The theory of Heim is typically extended by redefining the operator C to have more components. Hence, the generalization of Heim's theory is usually done in this manner. The operator C arises from an indexing of state functions and tensors.
Focussing on only the elements of the 6 by 6 tensor, it can be interpreted as a coupling between two sets of coordinate systems. The elements T_{11} to T_{33} represent the Cartesian coordinates. The elements T_{11} to T_{44} represent the cartesian coordinates plus the time coordinate. These 16 elements are the constituents of Einstein's tensor representing spacetime.
An extension by Droescher to 12 dimensional theory allows some aspects of quantum mechanics to result from Heim theory.
Matter and forces
In Albert Einstein's theory of General Relativity, gravitation is interpreted in a geometrical way; it is a consequence of the curvature of spacetime. Heim Theory expands this approach to all forces, so all physical phenomena, even matter itself, are a consequence of the structure of spacetime. As it was stated before, Heim Theory uses an 8dimensional space. Different subsets of R_{8}, that Heim called "hermetries", give rise to all the known particles and interactions:

 H_{1} = R_{3}∪I_{2}: gluons
 H_{2} = R_{3}∪T_{1}∪I_{2}: color charges
 H_{3} = R_{3}∪T_{1}∪S_{2}∪I_{2}: W bosons
 H_{4} = R_{3}∪S_{2}∪I_{2}: Z bosons
 H_{5} = T_{1}∪S_{2}∪I_{2}: photons
 H_{6} = H_{6} (T_{1}∪I_{2}) * H_{7} (T_{1}∪S_{2}): weak charge
 H_{8} = R_{3}∪S_{2}: neutral particles with mass
 H_{9} = R_{3}∪T_{1}∪S_{2}: particles with electric charge and mass
 H_{10} = I_{2}: probability field
 H_{11} = S_{2}∪I_{2}: gravitophoton
 H_{12} = S_{2}: graviton
Note that, according to Heim, either S_{2} or I_{2} (or both) is always necessary for interactions to take place. It's worth noting that Heim Theory predicts the existence of all the known 4 forces, along with 2 new gravitationallike forces:

 H_{1} predicts gluons, carriers of the strong nuclear force.
 H_{3} and H_{4} predicts the W bosons and Z boson, carriers of the weak nuclear force.
 H_{5} predicts photons, carriers of the electromagnetic force.
 H_{10} predicts quintessence, a weak gravitationallike repulsive force that would cause the expansion of universe.
 H_{11} predicts gravitophotons, as yet unobserved particles that would, theoretically, allow the conversion of an electromagnetic field into a gravitationallike field.
 H_{12} predicts gravitons, carriers of gravity.
These force carriers together also allow one to predict novel forms of space travel. Whether this holds true in practice remains controversial.
Misnomers
The method of extending Heim Theory to higher dimensions than the four known, results in a theory which describes the physical world in terms of an increasing number of dimensions. These extra dimensions (which are auxiliary to length, width, height, and time) are often liberally associated with notions such as "consciousness", "spirit", "thought", and the vedic sciences. This is probably due to Heim's interest later in his life to provide a framework for such perceptions and experiences.
It should be noted that it is convenient to label the additional dimensions, but this only serves as a tool for organization. The additional dimensions need not necessarily correspond to physical reality and be interpreted literally. This is because the labelling is arbitrary, and it serves to provide a name for a particular property of the equations in Heim Theory. This is analogous to quantum chromodynamics where quarks are assigned properties named after different colours. Particle physicists are not suggesting that quarks have "colour", rather, that they have an important property for which an arbitrary label has been applied.
These extra dimensions in Heim Theory should be considered auxiliary coordinates occurring as a mathematical tool in the theory. It introduces symmetry into Heim Theory which simplifies its expression and manipulation. The phenomena described in these auxiliary coordinates of Heim theory are projected into real coordinate space which then describe the physics of fundamental particles and the universe.
As an analogy, in Max Born's interpretation of quantum mechanics, the wavefunction ψ itself has no physical meaning, but its magnitude squared ψ^{2} has physical meaning corresponding to probability density. Likewise, the additional coordinates in Heim theory have no physical meaning  only when they are combined together in some mathematical manner does the result have any meaningful physical result.
Relation to other Theories
Quantum theory
The theory is consistent with quantum mechanics, as it is a quantised form of General Relativity (GR). Also, the 8dimensional theory of Dröscher & Heim reproduces the group structure of the standard model (SU(3)xSU(2)xU(1)).
Electromagnetism
In HeimTheory, electromagnetism is explained in the same geometrical way as Gravity in General Relativity.
Relativity
The theory is consistent with General Relativity (GR), as it is a quantised form thereof. The results of this quantisation lead to HeimTheory being an extension of GR to higher dimensions.
Loop quantum gravity
The theory shares a similar physical picture, namely a quantized spacetime, with the recently published loop quantum gravity theory (LQG) by Lee Smolin, Abhay Ashtekar, Carlo Rovelli, Martin Bojowald et al. LQG, if proved correct, would stand for a major revision of current physics, while HQT (Heim Quantum Theory) would cause a revolution therein.
Solitons
Note also that a recent theory by Klaus Hasselmann also used a 'metron' to work towards a unified field theory that in principle should give the particle mass spectrum, fine structure constant etc. However, in Hasselmann's theory the Metron is a soliton solution to a version of Einstein's equations, and the theory is in its initial stages and is nowhere near producing predictions such as a mass spectrum.
Unresolved inconsistencies with current physical theory
Neutral electron
Despite making many accurate predictions about subatomic particles, HeimTheory makes at least one prediction that does not seem to agree with the current state of knowledge in this area, namely that there should be a neutral electron with almost the same mass as the normal electron. Experiments have been done to detect a neutral electron, but they may have focussed more on far higher mass ranges than the actual electron. In addition, the selection rules for HeimTheory are not complete  thus it may still turn out that this particle is forbidden.
History
The basic theory was developed in near isolation from the scientific community. Heim's handicap led him to prefer this isolation as the effort of communication in a university environment was too much of a strain for a handless, essentially deaf and blind physicist. Heim himself only had one publication in a peer reviewed journal, and this only at the insistence of his friends, as he himself did not see the need for publication until his theory was complete, even if that should take up to 50 years to be realised. A small group of physicists who learned of Heim's work and studied it in sufficient detail to recognise its potential is now trying to bring it to the attention of the scientific community, by publishing and copyediting Heim's work and by checking and expanding the relevant calculations. Recently a series of presentations of Heim theory were made by Haeuser, Droescher and Von Ludwiger. A paper based on the former was published in a peerreviewed American Institute of Physics journal in 2005 (see table of contents in [5] and abstract of paper in [6]). This article has won a prize for the best paper received in 2004 by the AIAA Nuclear and Future Flight Technical Committee. Von Ludwiger's presentation was to the First European Workshop on Field Propulsion, January 2022, 2001 at the University of Sussex (see list of talks [7]). Droescher was able to extend Heim's 6dimensional theory, which had been sufficient for derivation of the mass formula, to an 8dimensional theory which included particle interactions, thus reproducing the structures seen in the standard model.
External links
Theoretical links
Searches for neutral electrons
 http://pdg.lbl.gov
 http://pdg.lbl.gov/2004/listings/s077.pdf
 Searches for unstable neutral leptons  [8]
 DYNAMICAL ROLE OF LIGHT NEUTRAL LEPTONS IN COSMOLOGY  [9]
Conference proceedings
 http://proceedings.aip.org/proceedings/confproceed/746.jsp
 http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=746&Issue=1
Propulsion physics
 http://www.aiaa.org/content.cfm?pageid=406&gTable=Paper&gID=18840
 http://www.grc.nasa.gov/WWW/bpp/
 http://www.mufonces.org/docs/heimphysics.pdf
 http://www.hpccspace.de/publications/index.html Publications on space applications
 http://www.hpccspace.de/publications/documents/aiaa20043700letter.pdf
 http://www.hpccspace.de/publications/documents/aiaa20034990Talk_Huntsville.pdf
 http://www.hpccspace.de/publications/documents/PrinciplesOfAdvancedSpacePropulsionAIAApaper20024094.pdf
 Droscher, W and Hauser, J, "Guidelines for a Space Propulsion Device Based on Heim's Quantum Theory," AIAA Paper 20043700, 2004 AIAA Best Paper (pdf)
 Droscher, W and Hauser, J, "Heim Quantum Theory for Space Propulsion Physics," Log No 021, STAIF, American Institute of Physics, 2005 (pdf)
News item
 January 5, 2006, Propulsion theory being considered for test by USA government