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'''Heim theory''' is a [[physics theory]], initially proposed by a German physicist, the late [[Burkhard Heim]], that attempts to develop a [[theory of everything]]. Heim theory's six dimensional model was later extended to eight and twelve dimensions, in collaboration with W. Dröscher.<ref name=g1/><ref name=g2/><ref name="hpcc-space.de/publications">[http://www.hpcc-space.de/publications/index.html List of Publications]</ref> [[Walter Dröscher]] and Jochem Hauser, professor and former head of the Aero- and Aerothermodynamics Dept. of the [[European Space Agency]]<ref>[http://idw-online.de/pages/en/news111911 AIAA-Forschungspreis für Professor Dr. Jochem Häuser] idw-online.de, 05/11/2005; [http://public.fh-wolfenbuettel.de/~haeuser/ Prof. Dr. Jochem Häuser]@, Ostfalia HaW Campus Suderburg</ref> have attempted to apply it to nonconventional [[space propulsion]] and [[faster than light]] concepts, as well as the origin of [[dark matter]].<ref name="hpcc-space.de/publications"/><ref>T. Auerbach [http://www.scientificexploration.org/journal/jse_06_3_auerbach.pdf Heim’s Theory of Elementary Particle Structures]</ref> Heim theory has been criticized because much of the original work and subsequent theories were not initially [[peer review]]ed.<ref name="Ludwiger">v. Ludwiger, L. (2001, January 28) ''Zum Tode des Physikers Burkhard Heim''. Feldkirchen-Westerham.[http://www.mufon-ces.org/text/deutsch/heim.htm]</ref> Heim eventually published some of his work in 1977<ref>{{cite journal|author=Burkhard Heim|title=Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen (Recommendation of a Way to a Unified Description of Elementary Particles)|journal= Zeitschrift für Naturforschung|year=1977|volume=32a|pages=233–243|bibcode = 1977ZNatA..32..233H }}</ref> and more recently aspects of ''Extended Heim Theory'' have also been submitted to the scientific community's inspection.<ref>Hauser, J., Dröscher, W., ''Emerging Physics for Novel Field Propulsion Science''<br> Paper presented at the Space, Propulsion & Energy Sciences International Forum SPESIF-2010, Johns Hopkins - APL, Laurel, Maryland, 23–25 February 2010,
and published by the [[American Institute of Physics]].
[http://www.hpcc-space.de/publications/documents/AIP2010Hauser.pdf]
</ref>
Heim attempted to resolve incompatibilities between [[Quantum mechanics|quantum theory]] and [[general relativity]]. To meet that goal, he developed a mathematical approach based on quantizing spacetime, and proposed the "metron" as a (two-dimensional) [[quantum]] of (multidimensional) space. Part of the theory is formulated in terms of [[difference operator]]s; Heim called this type of mathematical formalism ''Selector calculus''.<ref>{{Cite book|first=Burkhard |last=Heim |title=Elementarstrukturen der Materie - Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation |publisher=Resch Verlag |origyear=1980 |year=1998 |isbn=3-85382-008-5 |chapter=Chapter 3 |pages=99–172}}</ref> <!-- actually look up metron and Heim - getting many GS hits -->
[[File:Wormhole travel as envisioned by Les Bossinas for NASA.jpg|thumb|right|Artist's conception of a warp drive design. Heim theory proposes [[timelike]] extra dimensions of space to permit [[faster than light travel]].]]

==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 subsequently changed his mind with further research and now thinks there is something to Heim's theory.<ref>J. Reed (2006, 2007); quoted in [http://www.sff.net/people/Geoffrey.Landis/heim_theory.html Rise and Fall of the Heim Theory] . Retrieved 16 June 2007.</ref> In the Physics Forum, Sept. 4 2007, Reed wrote, "I'm more convinced now that there is really something to his theory. I don't understand much of the math yet. It's very complicated and different from anything I'm familiar with. I have a Ph.D. in physics so I know something about physics."

[[File:Baryon-decuplet-small.svg|thumb|300px|
Combinations of three u, d or s quarks forming baryons with a spin-{{frac|3|2}} form the ''[[Eightfold way (physics)|uds baryon decuplet]].'' Heim theory utilizes complex particles like [[baryons]] to explain [[quintessence (physics)|quintessence]].]]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-Dröscher" theories or Extended Heim theory.<ref name="igw-resch-verlag.at">[http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band3.html igw-resch-verlag.at/resch_verlag/burkhard_heim/band3.html]</ref>

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. Dröscher first extended this to eight and claimed that this yields [[quantum electrodynamics]] along with the "particle zoo" of [[meson]]s and [[baryon]]s. Later, four more dimensions were used to arrive at the twelve dimensional version, which involves extra gravitational forces; one of these corresponds to [[quintessence_(physics)|quintessence]].<ref name="igw-resch-verlag.at"/>
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 particle|neutral]] [[electron]] and two extra light [[neutrino]]s, 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.<ref>[http://www.heim-theory.com/downloads/G_Selected_Results.pdf Introduction to Heim's Mass Formula. Selected Results]</ref> Although it is claimed that Heim theory can incorporate the modern structure of particle physics,<ref name="igw-resch-verlag.at"/> the available results predict the masses for composite [[hadron]]s rather than [[quark]]s and do not include [[gluon]]s or the [[W and Z bosons]],<ref>Walter Dröscher, Jochem Hauser [http://www.americanantigravity.com/documents/AuerbachJSE.pdf Coupled Gravitational Fields. A New Paradigm for Propulsion Science]</ref> which are experimentally very well established.<ref>{{Cite journal| author= R. Brandelik et al. ([[TASSO]] collaboration)|title=Evidence for Planar Events in e<sup>+</sup>e<sup>-</sup> Annihilation at High Energies|journal=Phys. Lett. B| year=1979|volume=86|pages=243–249|doi=10.1016/0370-2693(79)90830-X|bibcode = 1979PhLB...86..243B| issue= 2 }}</ref><ref>{{Cite journal| author= G. Arnison et al. ([[UA1]] collaboration)|title=Experimental Observation of Isolated Large Transverse Energy Electrons with Associated Missing Energy at <math>\sqrt{s}</math> = 540 GeV|journal=Phys. Lett. B|year=1983|volume=122|pages=103–116|bibcode = 1983PhLB..122..103A |doi = 10.1016/0370-2693(83)91177-2 }}</ref><ref>{{Cite journal| author= S. Eidelman et al.|title= Review of Particle Properties|journal=Phys. Lett. B|year=2004|volume=592|page=1|doi= 10.1016/j.physletb.2004.06.001|arxiv = astro-ph/0406663 |bibcode = 2004PhLB..592....1P|url=http://pdg.lbl.gov}}</ref> In Heim theory, quarks are interpreted as 'condensation zones' of the six-dimensional internal structure of the particles,<ref>{{cite web|url = http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band3.html
| title = IGW Research| author = Burkhard Heim|language = German}}</ref> and the gluons are asserted to be associated with one of the "hermetry forms".<ref>Walter Dröscher and Jochem Hauser [http://www.hpcc-space.de/publications/documents/ExtendedHeimTheory.pdf Extended Heim Theory, Physics of Spacetime, and Field Propulsion], 10 April 2006</ref>

==History==
<!--somewhere a timeline should be provided so that readers can follow the development of the theory, since it is very confusing without providing the context in which everything in Heim theory was derived-->

A small group of physicists is now trying to bring the theory to the attention of the scientific community, by publishing and copy-editing Heim's work, and by checking and expanding the relevant calculations. Recently,{{when|date=December 2012}} a series of presentations of Heim theory was made by Hauser, Dröscher and von Ludwiger. Papers based on the former were published in conference proceedings by the [[American Institute of Physics]] journal in 2005 and 2010 (see table of contents in <ref>{{cite web |url=http://proceedings.aip.org/proceedings/confproceed/746.jsp |title=Heim theory presentation |author=Hauser, Dröscher, and von Ludwiger |date= |work= |publisher= American Institute of Physics journal|accessdate=6 November 2010}}</ref>)<ref> [http://adsabs.harvard.edu/cgi-bin/basic_connect?qsearch=walter+dr%C3%B6scher&version=1 Walter Droescher] @ [[Astrophysics Data System]] adsabs.harvard.edu</ref> One article has won a prize for the best paper received in 2005 by the [[American Institute of Aeronautics and Astronautics|AIAA]] Nuclear and Future Flight Technical Committee.<ref> [https://www.aiaa.org/Search/ Walter Dröscher] @ Electronic Library; The American Institute of Aeronautics and Astronautics, aiaa.org</ref><ref> [http://pdf.aiaa.org/preview/CDReadyMJPC2004_946/PV2004_3700.pdf pdf.aiaa.org]</ref> Von Ludwiger's presentation was to the First European Workshop on Field Propulsion, January 20–22, 2001 at the University of Sussex. 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. Marc Millis, former head of the [[Breakthrough Propulsion Physics Program]] mentioned the Dröscher/Heim concepts in an 2010 [[International Astronautical Federation]] conference contribution  as "''Not yet rigorously articulated''".<ref>[http://www.grc.nasa.gov/WWW/bpp/MillisBio.html Bio: Marc Millis] grc.nasa.gov; [http://arxiv.org/abs/1101.1063 pdf] p.5. Table 1</ref><ref>Marc G. Millis, Erik W. Davis  ''Frontiers of propulsion science.'' American Inst. of Aeronautics and Astronautics, Reston 2009, ISBN 978-1-56347-956-4, p.218-221</ref><ref>[http://www.centauri-dreams.org/?p=504 Marc Millis on Hyperspace Propulsion] & [http://www.centauri-dreams.org/?p=501 Hyperdrive to Epsilon Eridani?] centauri-dreams.org, 01/2006</ref>

==Predictions==
Dröscher and Hauser developed the category of non-ordinary matter in 2008.<ref>Hauser, J., Private communication to H. Deasy, July 2008.</ref>
Heim theory predicts a neutral electron,<ref>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 [http://www.americanantigravity.com/documents/AuerbachJSE.pdf]</ref> although in a popular talk, Heim notes that while a neutral electron is allowed by his theory, it is not required.<ref>See end of chapter 9.2 (p. 73) of Heim's [http://www.engon.de/protosimplex/downloads/02%20heim%20-%20mbb%201.2en.pdf MBB presentation] (1976)</ref> It would be difficult to reconcile a prediction of a neutral electron with the lack of any observation of the particle <ref>Abraham Seiden, ''Particle Physics: A Comprehensive Introduction'', Addison Wesley (2004); ISBN 978-0-8053-8736-0</ref>{{Verify source|date=October 2007}}. According to the [[Totalitarian principle]] that every interaction not forbidden must occur, such a light neutral particle should be one of the possible end products of the decay of every known elementary particle,<ref>B. R. Martin and G. Shaw ''Particle Physics'', Wiley (2nd edition, 1997) ISBN 978-0-471-97285-3</ref> and so theoretically has a small probability of occurring in every experiment involving particle collisions.

===Predictions for experimental masses===
{|class="wikitable"
|-
! 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 particle|Neutral]] electron
| 0.51617049
| Unobserved
| N/A
| N/A
| N/A
|}

{|class="wikitable"
|-
! Particle type
! Particle name
! Theoretical mass (MeV/c²)
! Measured mass (MeV/c²)
! Theoretical mean life/10<sup>−8</sup> sec
! Measured mean life/10<sup>−8</sup> sec
|-
| Lepton
| [[Neutrino|Ele-Neutrino]]
| 0.381 × 10<sup>−8</sup>
| < 5 × 10<sup>−8</sup>
| Infinite
| Infinite
|-
| Lepton
| [[Neutrino|Mu -Neutrino]]
| 0.00537
| < 0.17
| Infinite
| Infinite
|-
| Lepton
| [[Neutrino|Tau-Neutrino]]
| 0.010752
| < 18.2
| Infinite
| Infinite
|-
| Lepton
| Neutrino 4
| 0.021059
| Excluded by [[LEP]]<br>(unless > 45000)
| Infinite
| N/A
|-
| Lepton
| Neutrino 5
| 0.207001
| Excluded by [[LEP]]<br>(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 × 10<sup>8</sup>
| (886.7 ± 1.9) × 10<sup>8</sup>
|}
* "measured" = [http://pdg.lbl.gov Particle Data Group Cern 2002]
* "theoretical" = [http://www.heim-theory.com/downloads/G_Selected_Results.pdf Heim-theory Group 2003]

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 (electromagnetism)|permeability]].

==Criticism==
Physicist Gerhard Bruhn has criticized Heim theory for not having been properly peer reviewed.
<!-- "Physicist Gerhard Bruhn has criticized Heim theory for having a flat M metric." -->
<!--maybe, but this quote says nothing of the kind (flat M metric).
{{Quotation|The Heim theory did never pass a rigorous peer reviewing. In 2002 the authors J. Hauser and W. Dröscher 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.-''Gerhard Bruhn, on www.mathematik.tu''}}-->
<ref name="bruhn">[http://www.mathematik.tu-darmstadt.de/~bruhn/IGW.html Remarks on Burkhard Heim's IGW Successors J. Hauser and W. Droescher and their Theory], Gerhard W. Bruhn, Darmstadt University of Technology, March 29, 2006</ref>

<!-- this rebuttal was of the flat M metric, which appears not to be right, so hiding this for now ...
Heim theorists responded with a rebuttal.
{{Quotation| ...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...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.-''Hauser and Dröscher's Rebuttal on www.hpccspace.de''<ref>[http://www.hpcc-space.de/news/RebuttalProfBruhnTUD.pdf Rebuttal: Critiscm of a Flat Metric] re: Prof. Bruhn, Technical University of Darmstadt, Germany, March 7, 2006</ref>
}}
-->

According to a 2006 posting to the "PhysicsOrgForum" by John Reed,<ref>John Reed, [http://www.physicsforums.com/showthread.php?p=1197916 ''Understanding Heim Theory'', 12-26-2006, posted to sci.physics.research]</ref> the apparent success of the Heim theory predicting particle masses may be illusory. 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.<ref>G. Landis, "[http://www.sff.net/people/geoffrey.landis/Heim_theory.html Heim Theory]" 2007 . Retrieved 13 Sept 2007.</ref>

In a later posting in August 2007, 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.
{{Quotation| “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.”.<ref name=autogenerated1>[http://forum.physorg.com/index.php?showtopic=4385&st=1680 PhysOrgForum Science, Physics and Technology Discussion Forums -> Burkhard Heim's Particle Structure Theory<!-- Bot generated title -->]</ref>}}

On September 4, Reed reported on results obtained by the updated 1989 formula:
{{Quotation|"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.”
<ref name=autogenerated1 />}}

There exists a preliminary version of this derivation available on-line.<ref>[http://chsunier.ch/Books/Themata/beitraege/RESCH/D_Zur_Herleitung_Der_Heimschen_Massenformel.pdf Zur Herleitung der Heimschen Massenformel]</ref> This version still may contain some errors, and the authors, the Heim Theory Group, are in the process of checking and amending it.<ref>[http://www.heim-theory.com/Inhalt/Einfuhrung_in_die_Heimsche_Mas/einfuhrung_in_die_heimsche_mas.html Einführung in die Heimsche Massenformel]</ref>

More recently, Reed said:
{{Quotation|"I think I have some idea of what Heim did now. There is much talk in his book about "empirical data". He took the particle mass data and cooked up his equations to make them correct. It certainly was a lot of work for him, but I don't think it has much to do with physics. I'm sorry to say I wasted a lot of time on this but I hope I can save someone else some work.”
<ref>John Reed, [http://www.physforum.com/index.php?showtopic=4385&st=2955&#entry487786 ''Burkhard Heim's Particle Structure Theory'', 06-27-2011, posted to Physforum]</ref>}}

==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.<ref>[http://www.newscientist.com/article/mg18925391.200-testing-heims-theories.html Testing Heim's theories], Newscientist</ref> A recent series of experiments by [[Martin Tajmar]] et al., partly funded by [[European Space Agency]], may have produced the first evidence of artificial gravity <ref>[http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html esa.int]</ref> (about 18 orders of magnitude greater than what [[General Relativity]] predicts). {{As of|2006|alt=As of late 2006}}, groups at [[University of California, Berkeley|Berkeley]] and elsewhere were attempting to reproduce this effect. By applying their 'gravito-photon' theory to [[bosons]], Dröscher and Hauser were able to predict the size and direction of the effect. 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.<ref name=graham>{{cite journal|author=R.D. Graham, R.B. Hurst, R.J. Thirkettle, C.H. Rowe, P.H. Butler|title=Experiment to Detect Frame Dragging in a Lead Superconductor |doi=10.1016/j.physc.2007.11.011|year=2008|pages=383|volume=468|journal=Physica C: Superconductivity|url=http://www2.phys.canterbury.ac.nz/~physrin/papers/SuperFrameDragging2007.pdf|bibcode = 2008PhyC..468..383G|issue=5 }}</ref> 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 .<ref>[http://arxiv.org/abs/0707.3806 Search for Frame-Dragging-Like Signals Close to Spinning Superconductors]</ref> 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.<ref>[http://arxiv.org/abs/0707.3806 [0707.3806&#93; Search for Frame-Dragging-Like Signals Close to Spinning Superconductors]. Arxiv.org. Retrieved on 2010-10-17.</ref>

==Selector calculus==
'''Selector calculus''' is a form of [[calculus]], employed by [[Burkhard Heim]] in formulating his theory of physics.
The differencing operator is intended to be analogous to taking derivatives of functions.

:<math>\eth</math> (which Heim calls ''Metrondifferential'' in German) is defined to be the same as <math>\nabla</math> 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

:<math>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). </math>

Note that <math>\phi \eth n = \eth \psi</math>.
<ref>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 (pp. 99–172).
</ref>

==See also==
* [[United States gravity control propulsion research (1955 - 1974)]]
* [[Kaluza-Klein theory]], a five-dimensional extension of general relativity unifying [[gravitation]] and [[electromagnetism]].
* [[Mass formula]]
* [[Eugene Podkletnov]], allegedly observed gravity shielding effects of rotating [[superconductor]]s in 1992.

==Further reading==
===First and second publication in a peer reviewed scientific journal===
* {{cite journal|author=Burkhard Heim|title=Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen (Recommendation of a Way to a Unified Description of Elementary Particles)|journal= Zeitschrift für Naturforschung|year=1977|volume=32a|pages=233–243|bibcode = 1977ZNatA..32..233H }}
* Hauser, J., Dröscher, W., ''Emerging Physics for Novel Field Propulsion Science''<br> Paper presented at the Space, Propulsion & Energy Sciences International Forum SPESIF-2010, Johns Hopkins - APL, Laurel, Maryland, 23–25 February 2010, published by the [[American Institute of Physics]]. [http://www.hpcc-space.de/publications/documents/AIP2010Hauser.pdf]

===Bibliography===
* Burkhard Heim: ''Elementarstrukturen der Materie: Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation'', Band 1 <ref>(Elementary structures of matter: Unified structural quantum field theory of matter and gravitation, Volume 1)</ref>; Resch-Verlag, Innsbruck; 3rd corrected ed. 1998; ISBN 3-85382-008-5, ISBN 978-3-85382-008-7; in German.<ref name=g1>[http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band1.html Burkhard Heim: Elementarstrukkturen der Materie 1 - IGW]. Igw-resch-verlag.at. Retrieved on 2010-10-17.</ref>  [Burkhard Heim [http://www.engon.de/protosimplex/elementary_structures.pdf Introduction]
* Burkhard Heim: ''Elementarstrukturen der Materie: Einheitliche strukturelle Quantenfeldtheorie der Materie und Gravitation'', Band 2 <ref>(Elementary structures of matter: Unified structural quantum field theory of matter and gravitation, Volume 2)</ref>; <br>Resch-Verlag, Innsbruck; 2nd ed. 1996; ISBN 3-85382-036-0, ISBN 978-3-85382-036-0; in German.<ref name=g2>[http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band2.html Burkhard Heim: Elementarstrukkturen der Materie 1 - IGW]. Igw-resch-verlag.at. Retrieved on 2010-10-17.</ref>
* Walter Dröscher, Burkhard Heim: ''Strukturen der physikalischen Welt und ihrer nichtmateriellen Seite'' <ref>(Structures of the physical world and its immaterial aspect)</ref>; Resch-Verlag, Innsbruck; 1996; ISBN 3-85382-059-X, ISBN 978-3-85382-059-9; in German.<ref>[http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band3.html Burkhard Heim: Elementarstrukkturen der Materie 1 - IGW]. Igw-resch-verlag.at. Retrieved on 2010-10-17.</ref>
* Walter Dröscher, Burkhard Heim, Andreas Resch: ''Einführung in Burkhard Heim: Einheitliche Beschreibung der Welt'' <ref>(Introduction to Burkhard Heim: Unified description of the world)</ref>; Resch-Verlag, Innsbruck; 1998; ISBN 3-85382-064-6, ISBN 978-3-85382-064-3; in German.<ref>[http://www.igw-resch-verlag.at/resch_verlag/burkhard_heim/band4.html Burkhard Heim: Einführung in Burkhard Heim - IGW]. Igw-resch-verlag.at. Retrieved on 2010-10-17.</ref>

===References===
{{reflist|colwidth=30em}}

==External links==
{{external links|reason=Very Excessive|date=January 2012}}

Sites offering explanations of and discussions about Heim theory related topics:
* [http://www.heim-theory.org Heim Theory], Wiki site and discussion forum
* [http://www.heim-theory.com Website of the research group Heim Theory]
* [http://www.engon.de/protosimplex/ Protosimplex – Ideen von Burkhard Heim] The Protosimplex site was among the first to offer a popularized introduction of Heim theory in both German and English.
* [http://sourceforge.net/projects/heim-theory Project ''Heim-Theory'' on ''Sourceforge''] offers source code of some of the recent implementations.
* [http://www.daimi.au.dk/~spony/HeimMassFormula/HeimCalculator/ Heim Mass Calculator] The Java implementation as an applet (runs directly in the web browser).
* [http://news.scotsman.com/spacescience/Welcome-to-Mars-express-only.2739585.jp Welcome to Mars express: only a three hour trip], The Scotsman, 2006-01-05
* [http://www.newscientist.com/article/mg18925331.200-take-a-leap-into-hyperspace.html Take a leap into hyperspace], ''New Scientist'', 2006-01-05
* [http://english.pravda.ru/science/tech/16-02-2006/76045-0 Spaceships of the future to take humans to Mars in 2.5 hours], Pravda, 2006-02-16
* [http://www.newscientist.com/article.ns?id=mg18925391.200 Testing Heim's theories], ''New Scientist'', 2006-02-18
* [http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html Towards a new test of general relativity?], (M.Tajmar gravimagnetic field experiment) European Space Agency News, 2006-03-23
* [http://www.sciencedaily.com/releases/2006/03/060325232140.htm Anti-gravity Effect? Gravitational Equivalent Of A Magnetic Field Measured In Lab], Science Daily article about [[Martin Tajmar|M. Tajmar's]] work, 2006-03-26
* [http://news.bbc.co.uk/1/hi/sci/tech/4862112.stm Light shed on mysterious particle - Neutrino], BBC, 2006-03-31
* [http://www.newscientist.com/article/mg19225771.800 Gravity's secret], ''New Scientist'', Article about gravitomagnetic experiments performed by [[Martin Tajmar|M.Tajmar]] and de Matos, 2006-11-11

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