# Heim theory

Heim theory is a collection of ideas about the fundamental laws of physics proposed by Burkhard Heim[4], [5] and further developed by Walter Dröscher and Jochem Häuser.[6]. Most of their original work and the subsequent theories based on it have not been peer reviewed. 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. Part of the theory is formulated in terms of difference operators; Heim called the mathematical formalism "Selector calculus". [1]

## Overview

The mathematics behind Heim's theory requires extending spacetime with extra dimensions; various formulations by Heim and his successors involve six, eight, or twelve dimensions. Within the quantum spacetime of Heim theory, elementary particles are represented as "hermetry forms" or multidimensional structures of space. Heim has claimed that his theory yields particle masses directly from fundamental physical constants and that the resulting masses are in agreement with experiment. This claim was disputed by physicist John Reed in 2006, who then changed his mind with further research and now thinks there is something to Heim's theory. [2].

For Heim, this composite nature was an expression of internal, six-dimensional structure. 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 [7].

There are some differences between the original "Heim Theory" and the extended versions proposed by his successors. For example, in its original version Heim theory has six dimensions, i.e. the 4 of normal space-time with two extra timelike dimensions. Droescher first extended this to eight and claimed that this yields quantum electrodynamics along with the "particle zoo" of mesons and baryons. Later, four more dimensions were used to arrive at the twelve dimensional version, which involves extra gravitational forces; one of these corresponds to quintessence [8]. All of these extended theories are often called "Heim theories." Heim derived a constraint and upper limit on the number of possible dimensions-- namely 12.

Although it purports to unify quantum mechanics and gravitation, the original Heim theory cannot be considered a theory of everything because it does not incorporate all known experimental data. In particular, it gives predictions only for properties of individual particles, without making detailed predictions about how they interact. The theory also allows for particle states that don't exist in the Standard Model, including a neutral electron and two extra light neutrinos, and many other extra states. Presently, there is no known mechanism for the exclusion of these extra particles, nor an explanation for their non-observation. [9] Although it is claimed that Heim theory can incorporate the modern structure of particle physics [10], the available results predict the masses for composite hadrons rather than quarks and do not include gluons or the W and Z bosons [11], which are experimentally very well-established. [3][4][5] In Heim theory, quarks are interpreted as 'condensation zones' of the six-dimensional internal structure of the particles [12], and the gluons are asserted to be associated with one of the "hermetry forms" [13]; however, no results have been published in which the observed properties of these particles are predicted in detail.

Heim theory, like loop quantum gravity theory but unlike String Theory, is background independent.

## History

The basic theory was developed in near-isolation from the scientific community. Heim became disabled when an explosives-handling accident at age 19 left him without hands and mostly deaf and blind. This led him to prefer isolation to a university environment where communication would be too much of a strain for him. Heim himself had only one publication in a peer reviewed scientific journal, and this only at the insistence of his friends. 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 was made by Häuser, Dröscher 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 [14] and abstract of paper in [15]). 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 [16]). Dröscher claimed to have successfully extended Heim's six-dimensional theory, which had been sufficient for derivation of the mass formula, to an eight-dimensional theory which included particle interactions.

## Claimed predictions of the theory

Predictions claimed to have been derived from first principles that are experimentally testable are:

• Predictions of the masses of neutrinos
• Predictions of new particles
• Predictions of excited states of existing particles
• Predictions for the conversion of photons into the so-called "gravito-photons" resulting in a measurable force.

Heim predicted in the 1980s that neutrinos would have nonzero mass. By that point, however, the prediction of a nonzero mass for the neutrino had been long discussed in theoretical physics as a solution to the solar-neutrino question. At the moment, the mass of neutrinos are not well enough known to verify whether the neutrino mass calculated by Heim is the same as the measured mass. Heim did not predict the observed neutrino oscillation, which is a consequence of the fact that the mass eigenstates do not correspond to the flavor eigenstates. However, Dröscher and Häuser developed the category of non-ordinary matter in 2008 [6] , with the photon as the only mediator between it and ordinary matter. The neutral electron is included in this new class of matter, which would explain its non-observance to date.

Heim's theory also makes several predictions that have not been validated by experiment. The theory predicts several new particles that are not yet observed, but this may be because they fall in the secondary matter class. It apparently predicts a neutral electron [7], although in a popular talk, Heim notes that while a neutral electron is allowed by his theory, it is not required [8]. It would be difficult to reconcile a prediction of a neutral electron with the lack of any observation of the particle [9]. According to the Totalitarian principle that every interaction not forbidden must occur, such a light neutral particle should be the end product of the decay of every known elementary particle [10], and ought to be seen in every experiment involving particle collisions. But these arguments are nullified if, by being a particle of secondary matter, its interactions are extremely weak. Walter Dröscher and J. Hauser, in their latest papers, suggest that this particle may be a candidate for dark matter. They estimate that it is normally not seen as the decay paths leading to it are diverted to more probable reactions such as gravito-photon creation. Only at the Big Bang were energies large enough to form neutral electrons, which then remained as 'fossils' of the Big Bang, to act as Dark Matter.

He also predicts excited states of elementary particles. These predictions do not fully correspond to measured values. Finally, the original theory does not predict permanent substructure to the elementary baryons-- however, though the original 6 dimensional theory does not include quarks, which would apparently be at odds with measurements in experimental high energy physics, the 8 dimensional extension of Heim & Walter Dröscher does have quarks. 6-D Heim theory explains the results of such scattering experiments as due to temporary condensations in the 'configuration zones' of the particle's inner structure. According to Heim, matter consists of an exchange of maxima and minima of condensations of six dimensional fluxes.

Finally, Heim's theory predicts that it should be possible to produce an effective "gravity" force by converting photons into "gravito-photons," a particle which he predicts the existence of but has not yet been directly observed. This is discussed in the section Heim's predictions for a quantum gravity force below.

Empirical confirmation of supersymmetry (for example detecting the hypothetical Lightest Supersymmetric Particle or any other particle predicted by the Minimal Supersymmetric Standard Model) would falsify all existing versions of Heim theory, which are mutually exclusive with supersymmetry. Also, it is not certain whether Heim theory would be able to accommodate the existence of the Higgs boson, the only undiscovered particle expected in the Standard Model, and one which has not been predicted by the published versions of the Heim mass formula. Heim theory is said to be a Higgs-less theory as it is not dependent on the Higgs mechanism for the concept of mass. The ATLAS and CMS experiments at the Large Hadron Collider are likely to discover the Higgs boson in the next several years, if it exists.

### Heim's claimed predictions for particle masses compared with experimental masses

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 standard deviations
Proton 938.27959 938.272029±0.000080 0.00756 0.00000776 94.5
Neutron 939.57337 939.565360±0.000081 0.00801 0.00000853 98.9
Electron 0.51100343 0.510998918±0.000000044 0.00000451 0.00000883 102.5
Neutral electron 0.51617049 Unobserved N/A N/A N/A
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 Neutrino 4 0.021059 Excluded by LEP
(unless > 45000)
Infinite N/A
Lepton Neutrino 5 0.207001 Excluded by LEP
(unless > 45000)
Infinite N/A
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

The predicted masses were claimed to have been derived by Heim using only 4 parameters - h (Planck's Constant), G (Gravitational constant), vacuum permittivity and permeability. This implies that all masses must be dimensionless functions containing no free parameters multiplied by the Planck mass. The ratio of two predicted masses should therefore have no theoretical error caused by uncertainties in the four input parameters. While Heim theory is the only physical theory which has come close to predicting the correct masses of particles, when comparing such ratios using the above table one can see that they are outside the experimental limits.

#### John Reed's Criticism and Retraction

According to a 2006 posting to the "PhysicsOrgForum" by John Reed [11], the apparent success of the Heim theory predicting particle masses may be illusory. Reed argued that Heim's original work, published only in German, has been very difficult to follow, and the masses are derived from Heim's "Matrix A." Reed translated the original German work to find out how Heim's Matrix A was derived, and discovered that the data in Matrix A used "EMPERICAL DATA OF GROUND STATES"-- in other words, experimental values of particle masses were inserted into the theory by hand. Therefore he argues there should be no surprise in simply recovering the experimental data used as an input assumption. Reed goes on to remark that this should not be taken as deliberate fudging by Heim, since Heim himself did not intend this data to be used to predict the elementary particle masses in the first place. Reed commented "Heim was after the excited states, and for this he needed good estimates of the ground states. He used experimental mass values for this." Nevertheless, since the excited states calculated were in fact "useless" (according to Reed), it was unclear whether any other predictions of the Heim theory remain. [12]

In a later posting in August 2007, however, Reed, received the updated 1989 mass formula code from the Heim Theory group, and on the basis of this, withdrew the assertion that both the 1989 and 1982 code almost certainly used quantum numbers based on the A matrix.

“When I first looked into the 1982 version, the A matrix was present in the equations and a suggestion given for its values. Only in reading Heim's books did I learn the source of the values. Heim said that he had to fix the values to obtain correct ground state masses. I assumed that in the following work this hadn't changed. Apparently that assumption is incorrect. It looks like Heim made further progress and found a way to derive masses without the A matrix, so the A matrix should no longer be part of the discussion.” [13].

On September 4th, Reed reported on results obtained by the updated 1989 formula:

“I've completed my programming of Heim's unpublished 1989 equations to derive the extra quantum numbers (n, m, p, sigma) that I thought were coming from the A matrix. I can now say for certain that the A matrix is not involved with this new version. In addition, I can derive particle masses with only the quantum numbers k, Q, P, kappa and charge without the A matrix. This is what I had hoped to be able to do. These results agree with Anton Mueller's results. I'm able to get accurate masses for the 17 test particles I have tried this program on. The worst mass comparisons with experimental data are the neutron, 939.11 vs 939.56 experimental and the eta, 548.64 vs 547.3 experimental. All the others are closer, sometimes agreeing to 6 digits.” [13]

#### Derivation of the Mass Formula

There exists a preliminary version of this derivation available on-line [14] . This version still may contain some errors, and the authors, the Heim Theory Group, are in the process of checking and amending it [15].

### Heim's predictions for a quantum gravity force

In the 1950s, Heim had predicted what he termed a 'contrabary' effect whereby photons, under the influence of a strong magnetic field in a certain configuration, could be transformed into 'gravito-photons', which would provide an artificial gravity force. This idea caused great interest at the time [17]. A recent series of experiments by Martin Tajmar et al., partly funded by ESA, may have produced the first evidence of artificial gravity [18] (about 18 orders of magnitude greater than what General Relativity predicts). As of late 2006, groups at Berkeley and elsewhere were attempting to reproduce this effect. By applying their 'gravito-photon' theory to bosons, Dröscher and Häuser were able to predict the size and direction of the effect [16]. A further prediction of Heim-Dröscher theory shows how a different arrangement of the experiment by Tajmar et al. could produce a vertical force against the direction of the Earth's gravity. However, in July 2007, a group in Canterbury, New Zealand, said that they failed to reproduce Tajmar et al's effect, concluding that, based on the accuracy of the experiment, any such effect, if it exists, must be 21 times smaller than that predicted by the theory proposed by Tajmar in 2006.[17] Tajmar et al., however, interpreted a trend in the Canterbury data of the order expected, though almost hidden by noise. They also reported on their own improved laser gyro measurements of the effect, but this time found 'parity breaking' in that only for clockwise spin did they note an effect, whilst for the Canterbury group there was only an anti-clockwise effect [18]. In the same paper, the Heim-Theory explanation of the effect is, for the first time, cited as a possible cause of the artificial gravity. Tajmar has recently found additional support from Gravity Probe B results [19] .

## Selector calculus

Selector calculus is a form of calculus, employed by Burkhard Heim in formulating his theory of physics.

Selector calculus is similar to finite element methods in that it uses difference operators instead of differential operators to calculate analogues to derivatives and line integrals. The motivation is that the limit of distance going to zero does not make sense, because there exists a smallest unit of measure in Heim theory, called the metron.

The discretization of selector calculus was used as an approach to model the observed quantized nature of fundamental particles. The use of this method by Heim results in a theory of particles which does not have infinities. Infinities sometimes arise in the widely-accepted model of particle physics, the Standard Model, but can be renormalized to finite quantities in a mathematically rigorous way, which is strictly required in order for the theory to remain physically sensible.

### Difference and summation operators

The differencing operator is intended to be analogous to taking derivatives of functions.

$\eth$ (which Heim calls Metrondifferential in German) is defined to be the same as $\nabla$ in difference operator.

The summation operator is intended to be analogous with integration. Instead of using the integral sign, Heim substitutes a bold italicised capital S for the typical integral sign. In this case

$S^{n_2}_{n_1} \phi \eth n = S^{n_2}_{n_1} \eth \psi = \sum_{n=n_1}^{n_2} \left ( \psi(n) - \psi(n-1) \right ) = \psi(n_2) - \psi(n_1 - 1).$

Note that $\phi \eth n = \eth \psi$.

### References

• Burkhard Heim, Elementarstrukturen der Materie - Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation, Resch Verlag, (1980, 1998) ISBN 3-85382-008-5. Selector calculus is covered in chapter 3 (pages 99-172).

### First publication in a peer reviewed scientific journal

• Burkhard Heim:
Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen
(Recommendation of a Way to a Unified Description of Elementary Particles),
Zeitschrift für Naturforschung (Max Planck Society), 1977, Vol. 32a, pp. 233-243.
Available online here

### Bibliography

• Burkhard Heim:
Elementarstrukturen der Materie: Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation, Band 1
(Elementary structures of matter: Unified structural quantum field theory of matter and gravitation, Volume 1);
Resch-Verlag, Innsbruck (Austria); 3rd corrected edition 1998;
ISBN 3-85382-008-5, ISBN 978-3-85382-008-7; in German. [19]
Book´s Introduction available here in English.
• Burkhard Heim:
Elementarstrukturen der Materie: Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation, Band 2
(Elementary structures of matter: Unified structural quantum field theory of matter and gravitation, Volume 2);
Resch-Verlag, Innsbruck (Austria); 2nd edition 1996;
ISBN 3-85382-036-0, ISBN 978-3-85382-036-0; in German. [20]
• Walter Dröscher, Burkhard Heim:
Strukturen der physikalischen Welt und ihrer nichtmateriellen Seite
(Structures of the physical world and its immaterial aspect);
Resch-Verlag, Innsbruck (Austria); 1st edition 1996;
ISBN 3-85382-059-X, ISBN 978-3-85382-059-9; in German. [21]
• Walter Dröscher, Burkhard Heim, Andreas Resch:
Einführung in Burkhard Heim: Einheitliche Beschreibung der Welt
(Introduction to Burkhard Heim: Unified description of the world);
Resch-Verlag, Innsbruck (Austria); 1st edition 1998;
ISBN 3-85382-064-6, ISBN 978-3-85382-064-3; in German. [22]

### References

1. ^ Heim, Burkhard (1998) [1980]. "Chapter 3". Elementarstrukturen der Materie - Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation. Resch Verlag. pp. 99-172. ISBN 3-85382-008-5.
2. ^ J. Reed (2006, 2007); quoted in Rise and Fall of the Heim Theory (accessed 16 June 2007).
3. ^ R. Brandelik et al. (TASSO collaboration) (1979). "Evidence for Planar Events in e+e- Annihilation at High Energies". Phys. Lett. B 86: 243–249. doi:10.1016/0370-2693(79)90830-X.
4. ^ G. Arnison et al. (UA1 collaboration) (1983). "Experimental Observation of Isolated Large Transverse Energy Electrons with Associated Missing Energy at $\sqrt{s}$ = 540 GeV". Phys. Lett. B 122: 103-116.
5. ^ S. Eidelman et al. (2004). "Review of Particle Properties". Phys. Lett. B 592: 1. doi:10.1016/j.physletb.2004.06.001.
6. ^ Häuser, J., Private communication to H. Deasy, July 2008.
7. ^ T.Auerbach and I. von Ludwiger, "Heim ́s Theory of Elementary Particle Structures, Journal of Scientific Exploration,Vol. 6, No. 3, pp. 217-231, 1992; available here
8. ^ reference is the end of chapter 9.2 (page 73) of Heim's MBB presentation (1976)
9. ^ Abraham Seiden, Particle Physics: A Comprehensive Introduction, Addison Wesley (2004); ISBN 978-0805387360
10. ^ B. R. Martin and G. Shaw Particle Physics, Wiley (2nd edition, 1997) ISBN 978-0471972853
11. ^ John Reed, Understanding Heim Theory, 12-26-2006, posted to sci.physics.research
12. ^ G. Landis, "Heim Theory" 2007 (accessed 13 Sept 2007)
13. ^ a b PhysOrgForum Science, Physics and Technology Discussion Forums -> Burkhard Heim's Particle Structure Theory
14. ^ [1]
15. ^ [2]
16. ^ [3]
17. ^ http://www2.phys.canterbury.ac.nz/~physrin/papers/SuperFrameDragging2007.pdf
18. ^ Search for Frame-Dragging-Like Signals Close to Spinning Superconductors
19. ^ http://arxiv.org/abs/0707.3806