Heim theory

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 Droescher, who worked in collaboration with Heim for some length. Their combined theories are also known as "Heim-Droescher" theories, although there are no international established standards for naming Heim-related theories at present. This ambiguity in the term "Heim Theory" has lead to some confusion and difficulties 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 QED 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. This includes Maxwell's equations.

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 amount of energy can be exchanged with such systems. For sufficiently large and unbound systems, general relativity proposes that energy and mass are interchangable, 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 12-dimensional space. This space is extremely small, and consists of many quantized surface elements on the order of 10^-70 m² small. Each quantized surface element is known as a metron (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 on the order of 1 in 10⁶⁴ [(10,000)¹⁶ = (10⁴)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 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 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 has been 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.

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 sucession 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

<math>m = a^4 \eta_q \sqrt{\frac{2N }{2N-1}} <math>

In Heim's 1989 mass formula [2], the expression for the masses is broken down as follows:

<math>M = \mu \alpha_+ [(G + S + F + \phi) + 4 q \alpha_- ]<math>

(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:

(where 'measured' = Particle Data Group Cern 2002 ( [3] ) and 'theoretical' = Heim-theory Group 2003 [4] )

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

<math> \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}.<math>

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

<math>r_c = \frac{h^2}{\gamma m^3}. <math>

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 identially 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

1. a non-linear operator whose matrix representation C consists of 4 submatricies
   • These submatricies are generated with the 4 non-linear operators indexed as C_a
2. 64 state functions ψ indexed with three independent labels ψ_abc

The three indicies run from 1 to 4, resulting in 64 different eigenvalue equations

<math>\,\! \hat C_a \psi_{abc} = \lambda_{abc} \psi_{abc} \Rightarrow

           \hat C_a \left | abc \right \rangle = \lambda_{abc} \left | abc \right \rangle<math>

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

<math>\,\! C = \left \langle abc \right | \hat C_d \left | def \right \rangle.<math>

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

<math> 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} <math>

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. If the eigenvectors are normalized, they 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}.

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 of them are "unphysical". They are usually interpreted as auxillary 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 = T₁∪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 results in a theory which describes the physical world in terms of an increasing number of dimensions. These extra dimensions (which are auxillary 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 auxillary coordinates occuring as a mathematical tool in the theory. It introduces symmetry into Heim Theory which simplifies its expression and manipulation. The phenomena descibed in these auxillary 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 sqaured |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

The theory shares a similar physical picture, namely a quantized spacetime, with the recently published loop quantum gravity theory (LQG) by L. Smolin, A. Ashtektar, C. Rovelli, M. 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 intital stages and is nowhere near producing preditions such as a mass spectrum.

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 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 that the actual electron. In additon, the selection rules for Heim-Theory 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 copy-editing Heim's work and by checking and expanding the relevant calculations. Recently a series of presentaions of Heim theory were made by Haeuser, Droescher and Von Ludwiger. A paper based on the former was published in a peer-reviewed 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 20–22, 2001 at the University of Sussex (see list of talks [7]). 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.