Euclidean Relativity
(a.k.a. 'proper
time physics' or 'proper time geometry')
The Minkowski hyperbolic framework is
often hard to grasp for those who get involved in relativity theory. Euclidean relativity
proposes an intuitive circular geometry as alternative that uses proper time
t as
the fourth spatial dimension. Other 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 spacetime.
The Euclidean metric is derived from the
Minkowski metric by rewriting
into the equivalent
.
The roles of time t and proper time
have switched so that proper time
takes the role of the coordinate for the 4th spatial dimension. The universal
velocity c
appears from the regular time derivative
.
The approach
should not be mixed up with the "Wick rotation"
or complex Euclidean relativity. Wick rotation replaces time t by it, which
also yields a positive definite metric but it maintains proper time
as the Lorentz invariant value whereas in Euclidean relativity
becomes a coordinate.
The Euclidean geometry is consistent with
Minkowski based relativity in two reference frames. The hyperbolic
Minkowski geometry turns into a rotation in 4D circular geometry where length contraction and time
dilation result from the geometric projection of 4D properties to our 3D space. In three
reference frames, some interpretations produce a different velocity addition formula, also
affecting other formulas that depend on the velocity addition formula. The
inconsistency does so far not imply known contradictions with experimental data.
This may be due to the uncommon conditions that are required to show measurable
deviations.
The Euclidean approach makes relativity
accessible in an intuitive way and inspires further development and speculation.
Individual authors apply and extrapolate it to various topics, like
quantum mechanics, optics, particle physics and so on. Many Euclidean
interpretations introduce time
t as a
parameter
for tracking velocity and change. In Jose Almeida's and my own work it is
treated as a fifth dimension.
Below are a
number of references to articles on Euclidean relativity published by various
authors, including my own (see Van Linden). Each author approaches the topic in his own way and
individual interpretations were often developed independently without knowledge of the
other authors. First fundamental work came from the Dutch mathematician Hans Montanus in the beginning of the 90's.
During the last 510 years other authors
have begun to find each other and have published their articles, initiating an
innovative trend in relativity.
References:
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. 6078, 021963(!)).
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 SpaceProper 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 spacetimes (REST versus AEST).
He favors the latter (my own articles build on REST).
Special relativity in an absolute Euclidean SpaceTime (Physics
Essays, vol 4, nr 3, 1991)
The
Fizeau experiment in an absolute Euclidean Spacetime
(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 spacetime
(Physics Essays, vol 8, nr 4, 1995)
Electrodynamics
in an absolute Euclidean spacetime
(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 spacetime (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 Spacetime (Physics Essays, vol 11 nr
4, 1998)
Proper Time Physics (PDF
5MB) (Hadronic
J.22:625673,1999)
Galactic Rotation and Dark Matter in an Absolute Euclidean Spacetime (Physics Essays, vol 12 nr
2, 1999)
ProperTime
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 spacetime as a Euclidean nullsubspace of a 5D spacetime
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 spacetime
(arXiv:grqc/0104029, 2001)
4Dimensional optics, an alternative to relativity
(arXiv:grqc/0107083, 2001);
A theory of mass and gravity in 4dimensional optics
(arXiv:physics/0109027, 2001)
Kcalculus in 4dimensional optics
(arXiv:physics/0201002, 2002)
Prospects for unification under 4dimensional optics
(arXiv:hepth/0201264, 2002)
Unification of classic and quantum mechanics
(arXiv:physics/0211056 ,2002)
Maxwell's equations in 4dimensional 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 5dimensional 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 12371251)
Carl Brannen MSc. 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
Spacetimes 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. 11171124)
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 Spacetime,
talk at the 13^{th} Triennial
Conference of the International Society for the Study of Time,
(Monterery, CA July 28Aug 3 2007)
Dr. Phillips V. Bradford
Characteristic elements of Euclidean relativity, using proper time and
universal velocity
c for all objects in spacetime.
Alternative ways of
looking at physics,
with amongst others
A spacetime,
geometric interpretation of the beta factor in Special Relativity.
Dr. Witold Nawrot,
Is the
spacetime reality Euclidean? Another Euclidean interpretation,
comparing Fourdimensional Euclidean Reality (FER) with Lorentzian
spacetime. 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
spacetime 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 4Euclidean SpaceTime (EST) geometrical model governed by the
functions of a circle is formulated with the (++++) Euclidean signature.
Rob F.J. Van Linden BSc. (i.e., my own work, also accessible
through the buttons in the navigation menu)
Dimensions in special relativity
theory
(Galilean
Electrodynamics Vol 18 nr 1, Jan/Feb2007); A Euclidean interpretation of special relativity
providing arguments for a
geometrical unification of gravity and electromagnetism in five
dimensions.
Mass particles as bosons in five dimensional Euclidean gravity
(web, May 2007);
Extending the ideas of the previous article to gravity, proposing
to regard mass particles themselves, instead of gravitons, as bosons
following null geodesics in 5D gravity.
Minkowski versus
Euclidean 4vectors
(web, feb 2006);
Associating 4vectors with geometric properties in Euclidean spacetime.
Propulsion without propellant using fourmomentum of photons in Euclidean
special relativity
(web, apr 2008); describing an alternative method to accelerate
particles or objects, using principles of 4D momentum that follow
from Euclidean special relativity.
Relativity Simplified;
Simplified and popularized description of
of the essentials of Euclidean relativity.
The Universe as a MultiDimensional Fractal;
Speculations on a
fractallike universe,
based on the geometry of Euclidean relativity. It suggests a hierarchical ordering
of the four forces of
Nature together with
their fermions and bosons through their number of
dimensions.
Note on articles by Dr. FransGuenter 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. 


3D graph of classical equation for relativistic addition of velocities


3D graph of new equation for relativistic addition of velocities as derived by Van Linden
(Dimensions in special relativity theory, Galilean
Electrodynamics Vol 18 nr 1, Jan/Feb2007)

Hans Montanus' visualization
of the relation between Minkowski and Euclidean diagrams (From: Proper Time
Physics, Hadronic Journal 22, 625673, 1999)


5D
SpaceTimeMatter 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
CampbellMagaard embedding theorem.
A quote from an article of Paul Wesson,
In Defense of Campbell's Theorem as a Frame for New Physics
(arXiv.org grqc/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.
Accredited Online Colleges A list of online colleges with academic and
professional resources in the area of theoretical physics.
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 nonmainstream physics.
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, Moscow 2011)
Yearly conference on alternative ways to interpret relativity.
Wikipedia: Special relativity (alternative formulations)
A collection of alternative formulations for special relativity.
Alternative
Relativity links in the dmoz Open Directory Project The Open Directory is an attempt to build a global catalogue of the web.
Updated september 28th, 2012
