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General background and other sources on Euclidean relativity

The common elements in Euclidean relativity are the Euclidean (++++) metric as opposed to the traditional Minkowski (+---) or (-+++) metric, and the universal velocity c for all objects in 4D space-time, which is sometimes suggested in classical relativity as well (e.g. Brian Greene's "The Elegant Universe").  The Euclidean metric is derived from the Minkowski metric by rewriting
     (cdt )2=(cdt)2-dx2-dy2-dz2
into the fully equivalent
     (cdt)2=dx2+dy2+dz2+(cdt )2.
The roles of time t and proper time t  have switched so that proper time t  takes the role of the coordinate for the 4th spatial dimension. This approach should not be mixed up with the so called "Wick rotation" or complex Euclidean relativity, which is different. In Wick rotation, time t is replaced by it, which also leads to a positive definite metric but it maintains proper time t as the Lorentz invariant value whereas in Euclidean relativity t  becomes a coordinate.

Individual authors subsequently apply and extrapolate this basis to various topics, like quantum mechanics, optics, particle physics and so on. Many Euclidean interpretations, with the exception of  Jose Almeida's more recent work, introduce time t as a parameter for tracking velocity and change instead of a dimension. My preference is to treat it as a real fifth dimension x5. This is worked out in "Mass particles as bosons in five dimensional Euclidean gravity" where it is used to show the hierarchy between gravity, electromagnetism and possibly the two other forces.
 

Yahoo's discussion group on Euclidean Relativity (Founded by Prof. J. Almeida). Some authors of articles below are a member of this group.
Prof. Robert d'E Atkinson, General Relativity in Euclidean Terms (Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 272, Issue 1348, pp. 60-78, 02-1963(!)). Probably the first exploration of Euclidean relativity in history.
Hans Montanus, Special relativity in an absolute Euclidean Space-Time (Physics Essays, vol 4 nr 3, 1991);  A new concept of time (Physics Essays, vol 6 nr 4, 1993);  Arguments against the general theory of relativity and for a flat alternative (Physics Essays, vol 10 nr 4, 1997); Proper Time Physics (PDF 5MB) (Hadronic J.22:625-673,1999);  Proper-Time Formulation of Relativistic Dynamics (Found. Phys. 31, Issue 9, Sep 2001, Pages 1357 - 1400);  Flat Space Gravitation (Found. Phys. 35, Issue 9, Sep 2005, Pages 1543 - 1562).
Montanus introduces the difference between Relative and Absolute Euclidean space-times (REST versus AEST). He favors the latter (my own article builds on REST).
Prof. Jose Almeida, 5-dimensional space-time (website with links to arXiv.org for most articles). An Euclidean extrapolation to general relativity, explaining geodesic motion of objects as a result of a 4D refractive index, hence the alternative name '4D Optics'. Almeida considers 4D space-time as a Euclidean null-subspace of a 5D space-time with metric (-++++). The approach allows a treatment of  mass particles in 4D equivalent to photons in 3D, which is supplemented by considering particle worldlines as normals to wavefronts.
Prof. Alexander Gersten, Euclidean Special Relativity (PDF file) (Found. Phys. 33, 2003, Pages 1237-1251). Uses the term 'Mixed Space' to refer to the space where time t and proper time t have changed place. Probably the first one to recognize the value of Montanus' work.
Carl Brannen, Papers on Proper Time Geometry and the Geometry of Fermions. Website with various papers on particle physics. In the middle of this web page are links to Carl's papers on Euclidean relativity. Emphasis on the geometry and mathematics (geometric or Clifford algebra) that could be used as a basis for Euclidean relativity.
Dr. Giorgio Fontana, The Four Space-times Model of Reality (arXiv.org, physics/0410054A). Summarizes the results of Montanus, Gersten and Almeida and extends this with some more speculative thoughts; Hyperspace for Space Travel, Video of presentation at the STAIF 2007 by Dr. Eric Davis (American Institute of Physics, C.P. 880, pp. 1117-1124); Gravitational Waves in Euclidean Space (Excerpt from AIP Conference Proceedings 969, 1055 (2008)); Homepage of Giorgio Fontana.
Anthony Crabbe, Alternative conventions and geometry for Special Relativity (Annales de la Fondation Louis de Broglie Vol 29 no 4, 2004). As an alternative to the traditional Minkowski hyperbolic geometry the author uses 'Circular Function Geometry' (CFG), which is natural for many Euclidean interpretations of special relativity.
Dr. Phillips V. Bradford, Alternative ways of looking at physics, with amongst others A space-time, geometric interpretation of the beta factor in Special Relativity. Characteristic elements of Euclidean relativity, using proper time and universal velocity c for all objects in space-time.
Dr. Witold Nawrot, Is the space-time reality Euclidean? Another Euclidean interpretation, comparing Four-dimensional Euclidean Reality (FER) with Lorentzian space-time. Again a similar approach with t  as fourth dimension.
Richard D. Stafford Ph.D., Resolution of the Relativity/Quantum Mechanics Conflict  Uses Euclidean space-time with t  as fourth dimension to solve a common problem with the perception of reality.
Rob van Linden (i.e., my own work), Dimensions in special relativity theory (Galilean Electrodynamics Vol 18 nr 1, Jan/Feb-2007). A Euclidean interpretation of special relativity. Mass particles as bosons in five dimensional Euclidean gravity. Extending the ideas of the previous article to gravity. Minkowski versus Euclidean 4-vectors. Associating 4-vectors with geometric properties in Euclidean space-time. See also the homepage of this site.
Note on articles by Dr. Frans-Guenter Winkler (website, arXiv): although the same terms Euclidean special and general relativity are used, the geometry of the model is different. It maintains t as fourth dimension and t  as invariant, yet uses a (++++) metric. The approach falls outside the scope of this page.


 

Relation between Minkowski and Euclidean diagrams
Hans Montanus' visualization of the relation between Minkowski and Euclidean diagrams (From: Proper Time Physics, Hadronic Journal 22, 625-673, 1999)

 

5D Space-Time-Matter consortium, coordinated by Prof. Paul Wesson. Not so much identifiable as Euclidean relativity but proposals very similar to mine regarding the application of a fifth dimension, based on the Campbell-Magaard embedding theorem.
A quote from an article of Paul Wesson, In Defense of Campbell's Theorem as a Frame for New Physics (arXiv.org gr-qc/0507107, July 25th 2005) reflects one of the key elements of my own article, "Mass Particles as Bosons in Five Dimensional Euclidean Gravity" :

"The implication of this for particles is clear: they should travel on null 5D geodesics. This idea has recently been taken up in the literature, and has a considerable future. It means that what we perceive as massive particles in 4D are akin to photons in 5D."



Suggestions for additional sources are welcome.


Other interesting science/physics/math links:
How to become a good theoretical physicist? By Nobel laureate Prof. Gerard 't Hooft.
MIT Open Courseware Study on your own. Learning at a distance.
Eric Weisstein's World of Physics An encyclopedia for Physics and Mathematics.
Einstein archives online Many original texts and scans of handwritings.
Walter Babin's page on special relativity and theoretical physics A place to publish non-mainstream physics.
What is the Role of an Amateur Scientist? By G. Habrovski, president of Madison Area Science and Technology (MAST).
Math, Physics and Engineering Applets A collection of visualizations of various Physics and Math topics by Paul Falstad.
Andrew Hamilton's homepage Curved spacetime visualized. Watch yourself falling into a black hole.
Physical Interpretations of Relativity Theory (PIRT X, London 2006) Yearly conference on alternative ways to interpret relativity.
PIRT Budapest 7-9 september 2007 Initiated by Prof. Duffy, organizer of the PIRT London. Discussing the usual PIRT themes with emphasis on the philosophical aspects.
Alternative Relativity links in the dmoz Open Directory Project The Open Directory is an attempt to build a global catalogue of the web.

Updated March13th, 2008
 
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