Prof. Robert d'E Atkinson Probably the first exploration of Euclidean relativity in history.
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(!)).
Does not yet use proper time
 as fourth spatial
dimension because it only deals with general relativity with stationary
mass particles.
Dr. R. G. Newburgh, Dr. T. E. Phipps US Air Force research paper.
A Space-Proper Time Formulation of Relativistic Geometry (Air Force Cambridge Research Laboratories, Office of Aerospace Research,
U.S. Air Force, 1969)
Seems like the first proposal to use proper time
as fourth spatial
dimension. See also
this document for a complete listing and biography of Dr.
Phipps.
Drs.
Hans Montanus Introduces the
difference between Relative and Absolute Euclidean space-times (REST versus AEST).
He favors the latter (my own articles build on REST).
Special relativity in an absolute Euclidean Space-Time (Physics
Essays, vol 4, nr 3, 1991)
The
Fizeau experiment in an absolute Euclidean Space-time
(Physics Essays, vol 5, nr 4, 1992)
A new concept of
time (Physics Essays, vol 6
nr 4, 1993)
General relativity in an absolute Euclidean space-time
(Physics Essays, vol 8, nr 4, 1995)
Electrodynamics
in an absolute Euclidean space-time
(Physics Essays, vol 10, nr 1, 1997)
Arguments against
the general theory of relativity and for a flat alternative
(Physics Essays, vol 10 nr 4, 1997)
Compton scattering, pair annihilation, and Pion decay in an absolute
Euclidean space-time (Physics Essays, vol 11, nr 2, 1998)
A Geometrical Explanation for the Deflection of Light
(Physics Essays, vol 11, nr 3, 1998)
Hyperbolic Orbits in an Absolute Euclidean Space-time (Physics Essays, vol 11 nr
4, 1998)
Proper Time Physics (PDF
5MB) (Hadronic
J.22:625-673,1999)
Galactic Rotation and Dark Matter in an Absolute Euclidean Space-time (Physics Essays, vol 12 nr
2, 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)
Talk at the
IARD conference 2004.
Prof.
Jose Almeida 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.
An alternative to Minkowski space-time
(arXiv:gr-qc/0104029, 2001)
4-Dimensional optics, an alternative to relativity
(arXiv:gr-qc/0107083, 2001);
A theory of mass and gravity in 4-dimensional optics
(arXiv:physics/0109027, 2001)
K-calculus in 4-dimensional optics
(arXiv:physics/0201002, 2002)
Prospects for unification under 4-dimensional optics
(arXiv:hep-th/0201264, 2002)
Unification of classic and quantum mechanics
(arXiv:physics/0211056 ,2002)
Maxwell's equations in 4-dimensional Euclidean space
(arXiv:physics/0403058, 2004)
Euclidean formulation of general relativity
(arXiv:physics/0406026, 2004)
The null subspace of G(4,1) as source of the main physical theories
(arXiv:physics/0410035, 2004)
Talk at the Moscow conference Number Time Relativity 2004
Talk at
the PIRT IX conference Londen 2004.
Choice of the best geometry to explain physics
(arXiv:physics/0510179, 2005)
Monogenic functions in 5-dimensional spacetime used as first principle: gravitational dynamics, electromagnetism and quantum mechanics
(arXiv:physics/0601078, 2006)
How much in the Universe can be explained by geometry?
(arXiv:0801.4089, 2008)
Prof. Alexander Gersten
Uses the term 'Mixed Space' to refer to the space where time t
and proper time
have changed place. Probably the first one to recognize the value of Montanus' work.
Talk at the
IARD conference 2002.
Euclidean Special Relativity (PDF file) (Found. Phys. 33, 2003, Pages 1237-1251)
Carl Brannen Emphasis on the geometry and mathematics
(geometric or Clifford algebra) that could be used as a basis for
Euclidean relativity.
The Proper Time Geometry (pdf, ver 1.0 10/19/2004)
Phase Velocity of de Broglie Waves (pdf, ver 1.0 11/20/2004)
The Geometry of Fermions (pdf, ver 1.01, 10/21/2004)
The Geometric Speed of Light (pdf, ver 1.0 11/07/2004)
Nonlinear Waves on the Geometric Algebra (pdf, ver 1.1 12/02/2004)
Homepage of Carl with various other papers on particle physics.
Dr. Giorgio Fontana Summarizes the results of Montanus, Gersten and
Almeida in his first article and extends this with some more speculative
thoughts
The Four
Space-times Model of Reality (arXiv.org, physics/0410054A)
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))
On the foundations of Gravitation Inertia and Gravitational Waves (Scribd)
Extending Maxwell's equations to Euclidean relativity in 5D
Towards an Unified Engineering Model for Long (and short?) Range Forces and Wave Propagation (Powerpoint presentation)
Homepage of Giorgio
Fontana.
Dr.
Anthony Crabbe
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.
Alternative conventions and geometry for Special Relativity (Annales
de la Fondation Louis de Broglie Vol 29 no 4, 2004)
The Limitations of the
Minkowski Model of Space-time,
talk at the 13th Triennial
Conference of the International Society for the Study of Time,
(Monterery, CA July 28-Aug 3 2007)
Dr. Phillips V. Bradford
Characteristic elements of Euclidean relativity, using proper time and
universal velocity
c for all objects in space-time.
Alternative ways of
looking at physics,
with amongst others
A space-time,
geometric interpretation of the beta factor in Special Relativity.
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
as fourth dimension.
Richard D. Stafford Ph.D.,
Resolution of the
Relativity/Quantum Mechanics Conflict
(on
Web Archive) Uses Euclidean
space-time with
as fourth dimension to solve a
common problem with the perception of reality.
Subramaniam Kanagaraj,
Euclidean Special
Relativity
Personal website, presenting articles
based on a Euclidean interpretation of special relativity. A velocity
vector 4-Euclidean Space-Time (EST) geometrical model governed by the
functions of a circle is formulated with the (++++) Euclidean signature.
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
Propulsion without propellant using four-momentum of photons in Euclidean
special relativity
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
as invariant, yet uses a (++++)
metric. The approach falls outside the scope of this page. |
|
Hans Montanus' visualization
of the relation between Minkowski and Euclidean diagrams (From: Proper Time
Physics, Hadronic Journal 22, 625-673, 1999) |
.
.