Heim theory

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Heim theory is a term used to describe a non-mainstream proposed 'theory of everything', based on the assumptions used by Heim on his work in propulsion and mass calculations. Neither most of his original work nor theories based on his work have been peer reviewed. Burkhard Heim attempted to resolve incompatibilities between quantum theory and general relativity. To meet that goal, he developed a mathematical approach based on quantizing spacetime itself, and proposed the metron as a (two-dimensional) quantum of (multidimensional) space. The mathematics behind Heim's theory requires extending spacetime with extra dimensions; various formulations by Heim and his successors involve 6, 8, or 12 dimensions. Within the quantum spacetime of Heim theory, elementary particles are represented as "hermetry forms" or multidimensional structures of space. In his lifetime, Heim has attempted to use his method to calculate elementary particle masses directly from fundamental physical constants. Most of the resulting masses are in remarkable agreement with experiment. After his death, others have continued with his multi-dimensional "quantum hyperspace" framework. Most notable are the theoretical generalizations put forth by Walter Dröscher, who worked in collaboration with Heim at some length. Their combined theories are also known as "Heim-Droescher" theories. There are some discrepancies between the original "Heim Theory" and the extended versions proposed by his successors. 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. The extended Heim-Dröscher theory also claims to account for the "dark matter" problem of astrophysics.

History

The basic theory was developed in near isolation from the scientific community. Heim's handicaps 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. Heim's original 1977 publication remains the only peer-reviewed publication on Heim theory. A small group of physicists is now trying to bring it to the attention of the scientific community, by publishing and copy-editing 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 conference proceedings by the American Institute of Physics journal in 2005 (see table of contents in [1] and abstract of paper in [2]). 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 20-22, 2001 at the University of Sussex (see list of talks [3]). Droescher was able to extend Heim's 6-dimensional theory, which had been sufficient for derivation of the mass formula, to an 8-dimensional theory which included particle interactions, thus re-producing the structures seen in the standard model.

Principles

Two of the main principles of Heim's theory are his:

Predictions for the masses of neutrinos, and
Predictions for the conversion of photons into the so-called "gravito-photons" resulting in a measurable force.

These are empirical predictions which can in principle be experimentally verified, but have not all been achieved to date. Physicists have confirmed that neutrinos have mass. This is a major finding of the US-based Main Injector Neutrino Oscillation Search (Minos) experiment. The news release of this is found in the "News Items" section.

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 that 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 12-dimensional 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 m² 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. No other established theory of fundamental particles at present have made comparable theoretical predictions to this accuracy.

The 8-dimensional 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 input parameters 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 other constants.

Some of the predictions are still outstanding - e.g. the neutrino masses (see selected results in [4]).

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 [5]

Terminology

Heims theory as any scientific discipline requires strict terminology to be used, even more stringent than in other disciplines due to the complexity and vastness of the theory. This section declares the terms and gives a short explanation:

Corpuscle: A particle such as a photon can be considered a wave or a quanta, and can be described in a materialistic (measuring, weighting etc.) or energetic (as holographic wave interference-patterns) fashion. The term dates back to Newton (Corpuscular theory), and is adapted in a modern way by Heim (someone with proper understanding should update this definition).

The mass formulae

The mass formulae are perhaps the most important aspects 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 1-7, 1977 Jan.-Juli, pg. 233-243.

Heim gives the form of the mass spectrum to be

m=a^{4}\eta _{q}{\sqrt {\frac {2N}{2N-1}}}

In Heim's 1989 mass formula [6], the expression for the masses is broken down as follows:

M=\mu \alpha _{+}[(G+S+F+\phi )+4q\alpha _{-}]

(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 experimental masses and lifetimes of selected particles with the data generated using Heim's non-peer reviewed code:

Particle name	Theoretical mass (MeV/c²)	Experimental mass (MeV/c²)	Absolute error	Relative error
Proton	938.27959	938.27231	0.00728	0.00000776
Neutron	939.57337	939.56563	0.00773	0.00000823
Electron	0.51100343	0.51099907	0.00000436	0.00000853

The mass for the neutron has been predicted by the formula a decade before experimental data existed.

Particle type	Particle name	Theoretical mass (MeV/c²)	Measured mass (MeV/c²)	Theoretical mean life/10^-8 sec	Measured mean life/10^-8 sec
Lepton	Ele-Neutrino	0.381 × 10^-8	< 5 × 10^-8	Infinite	Infinite
Lepton	Mu -Neutrino	0.00537	< 0.17	Infinite	Infinite
Lepton	Tau-Neutrino	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 × 10⁸	(886.7 ± 1.9) × 10⁸

"measured" = Particle Data Group Cern 2002
"theoretical" = Heim-theory 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. [7] 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

\left({\frac {d\phi }{dr}}\right)^{2}+32{\frac {c^{2}}{3}}F\left({\frac {d\phi }{dr}}+F\phi \right)=0,F={\frac {1}{r}}{\frac {h^{2}+\gamma m^{3}r}{h^{2}-\gamma m^{3}r}}.

If this equation is nondimensionalized the characteristic length of the system is

r_{c}={\frac {h^{2}}{\gamma m^{3}}}.

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 non-linear operator whose matrix representation C consists of 4 submatrices
- These submatrices are generated with the 4 non-linear 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

\,\!{\hat {C}}_{a}\psi _{abc}=\lambda _{abc}\psi _{abc}\Rightarrow {\hat {C}}_{a}\left|abc\right\rangle =\lambda _{abc}\left|abc\right\rangle

The resulting matrix representation for the four C operators is a 64 by 64 matrix defined by

\,\!C=\left\langle abc\right|{\hat {C}}_{d}\left|def\right\rangle .

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

T={\begin{bmatrix}T_{11}&T_{12}&T_{13}&T_{14}&0&0&0&0\\T_{21}&T_{22}&T_{23}&T_{24}&0&0&0&0\\T_{31}&T_{32}&T_{33}&T_{34}&0&0&0&0\\T_{41}&T_{42}&T_{43}&T_{44}&T_{45}&T_{46}&0&0\\0&0&0&T_{54}&T_{55}&T_{56}&0&0\\0&0&0&T_{64}&T_{65}&T_{66}&0&0\\0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0\\\end{bmatrix}}

The non-zero 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. The eigenvectors span a coordinate space called R₈. This space has coordinates x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, which can be grouped as {x₁, x₂, x₃}, {x₄}, {x₅, x₆}, and {x₇, x₈}.

Note also that if we take the basic number of physically existing dimensions to be 6, corresponding to the 6x6 non-zero sub-matrix of T, then we can use Heim's formula relating this number, P, to the maximum possible number of dimensions, n, in a containing 'hyperspace'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. Note that the above equation only has low integer solutions (p,n) = (4, 6) or (6, 12). The next highest solution is (57, 420). After that solutions are space by appoximately 1,000,000 or more. Additional considerations rule out the higher dimensional variations, leaving only the lower two as unique solutions.

Interpretation

These groupings are labeled respectively

R₃, representing the typical cartesian state space
T₁, representing the time coordinate
S₂, representing the "entelechial" and "aeonic" coordinates
I₂, 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 R₃ and T₁ through special operators.

As an aside, in the original theory of Heim, the tensor T is only a 6 by 6 matrix. In this Heim-Droescher 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 T₁₁ to T₃₃ represent the Cartesian coordinates. The elements T₁₁ to T₄₄ 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 space-time. Heim Theory expands this approach to all forces, so all physical phenomena, even matter itself, are a consequence of the structure of space-time. As it was stated before, Heim Theory uses an 8-dimensional space. Different subsets of R₈, that Heim called "hermetries", give rise to all the known particles and interactions:

H₁ = R₃∪I₂: gluons
H₂ = R₃∪T₁∪I₂: color charges
H₃ = R₃∪T₁∪S₂∪I₂: W bosons
H₄ = R₃∪S₂∪I₂: Z bosons
H₅ = T₁∪S₂∪I₂: photons
H₆ = H₆ (T₁∪I₂) * H₇ (T₁∪S₂): weak charge
H₈ = R₃∪S₂: neutral particles with mass
H₉ = R₃∪T₁∪S₂: particles with electric charge and mass
H₁₀ = I₂: probability field
H₁₁ = S₂∪I₂: gravito-photon
H₁₂ = S₂: graviton

Note that, according to Heim, either S₂ or I₂ (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 gravitational-like forces:

H₁ predicts gluons, carriers of the strong nuclear force.
H₃ and H₄ predicts the W bosons and Z boson, carriers of the weak nuclear force.
H₅ predicts photons, carriers of the electromagnetic force.
H₁₀ predicts quintessence, a weak gravitational-like repulsive force that would cause the expansion of universe.
H₁₁ predicts gravito-photons, as yet unobserved particles that would, theoretically, allow the conversion of an electromagnetic field into a gravitational-like field.
H₁₂ 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", etc. This, however, is a misinterpretation of Heim, as he always associated x5 and x6 only with organisation and nothing more. This misunderstanding 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 8-dimensional theory of Dröscher & Heim reproduces the group structure of the standard model (SU(3)xSU(2)xU(1)).

Electromagnetism

In Heim-Theory, 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 Heim-Theory being an extension of GR to higher dimensions.

Loop quantum gravity and string theory

The theory shares a similar physical picture with LQG, namely a quantized spacetime, i.e. 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.

Table: Comparisons between LQG, String and Heim theories

Properties and features	String theory	Quantum geometry (LQG)	Heim-Theory
Description area	space-time R4	R4	R6
Fundamental objects	Space, time, strings & branes	Spin network, spin-foam	Surface quanta (metrons)
Number of spatial dimensions	9 or 10	3 (more possible)	3
Number of imaginary dimensions	1	1	3 (or 5)
space-time as a background metric	yes	no	no
Modification of general relativity	yes	yes	yes
Modification of quantum theory	yes	yes	no
Conceptual Fusion of quantum theory and general relativity	no	yes	no (or possible)
new physical principles needed	yes	no	no
Nature of matter	Excitation states of strings/branes	States of the spin networks	Cyclic exchange processes of maxima of structure compressions
Explanation of standard model of matter	only tentative	not required, not possible	with extension to 8 Dimensions
Unknown elementary particles predicted	yes	no	neutral electron
Explanation for dark matter in the universe	maybe	no	probably
infinity problems in the formalism	no (?)	no (?)	no
unification of quantization	not of space and time	yes	(under development)
Unification of the forces of nature	yes	no , but allowed	Electromagnetism and gravitation
Super-symmetry required and presupposed	yes	no	no
Uniqueness	no (many string vacua)	no (ambiguity in Hamilton operator)	yes
Existence of many other universes	possible	uncertain	yes
Explanation possible for beginning of universe	Big Bang model	Big Bang model	Zero Matter origin model
Explanation for entropy of black holes	limited	yes	not yet examined
Explanation possible for cosmic Inflation	possible	possible	not necessary
Description of scattering experiments	yes	not yet achieved	not yet calculated
Explanation of fundamental physical constants	no	no	yes
Contact with low energy physics (everyday world)	only tentative	only tentative	fully
Verifiable predictions	only tentative, partly falsified	only tentative	Masses and lifetimes of elementary particles and resonances

extended table (von Ludwiger, 2006, private communication) after R. Vaas: The duel: Strings versus loops, in "Bild der Wissenschaft", 4, 2004

Unresolved inconsistencies with current physical theory

Neutral electron

Despite making many accurate predictions about sub-atomic particles, Heim-Theory makes at least one prediction that does not seem to agree with the current state of knowledge in this area, namely that there might be a neutral electron with almost the same mass as the normal electron, however HT does not demand the existence of a neutral electron. Experiments have been done to detect a neutral electron, but they may have focused more on far higher mass ranges than the actual electron. In addition, the selection rules for Heim-Theory are not complete - thus it may still turn out that this particle is forbidden.

External links

Theory

A site which alleges to offer an explanation of Heim theory:

http://www.heim-theory.com

Various Implementations of Heim theory mass formula

Thread about Burkhard Heim's Particle Structure Theory on Physorg Forum In this thread on the Physorg Forum, the mass formula is under discussion and investigation. Several implementations in Java, C, C#, Pascal, Excel, Maxima and Mathematica have been developed.

Project Heim-Theory on Sourceforge has source code of those various implementations.

Heim Mass Calculator The Java implementation as an applet (runs directly in the web browser).

Protosimplex The Protosimplex site was among the first to offer a popularized introduction of Heim theory in both German and English. The Excel Worksheet Heim Mass Calculator is available there.

Neutral electron searches

Conference proceedings

Propulsion physics

Papers by Walter Dröscher and Jochem Häuser at HPCC-Space GmbH
- Guidelines for a Space Propulsion Device Based on Heim's Quantum Theory 2004 AIAA Best Paper (pdf: A4, US letter)
  - same document at aiaa.org (requires subscription)
- Physical Principals of Advanced Space Propulsion Based on Heim's Field Theory 2002
- Future Space Propulsion Device Based on Heim's Field Theory 2003 presentation
The Physics of Burkhard Heim and its Applications to Space Propulsion by Illobrand von Ludwiger 2001
NASA Breakthrough Propulsion Physics (BPP) Project

News items

Welcome to Mars express: only a three hour trip, The Scotsman, 2006-01-05
Take a leap into hyperspace, New Scientist, 2006-01-05
Spaceships of the future to take humans to Mars in 2.5 hours, Pravda, 2006-02-16
Light shed on mysterious particle - Neutrino, BBC, 2006-03-31