Keywords: Mechanics, Spacetime, Laws of motion, Annihilationcreation
INTRODUCTION
Our goal in
this paper is to advance a modified form of special relativity (i.e., STR). All
current attempts of research along these lines reject or replace one of the two
principles of STR. We consider Einstein’s two principles as well founded
postulates and hence we do not challenge them. One can still modify STR without
rejecting or modifying anyone of these two principles. In order to clear the
attempt to be presented here we need to start with Newtonian mechanics.
A BRIEF SUMMARY OF
NEWTONIAN MECHANICS
Newtonian spacetime
The spatial component of Newtonian spacetime
is a three dimensional Euclidean space that’s rigid and eternal. The temporal
component is a one dimensional time that’s absolute.
Newtonian laws of motion
The first law, i.e., the law of inertia.
Everybody perseveres in its state of being at
rest or of moving uniformly straight forward except insofar it’s compelled to
change its state by an impressed force.
The second law, i.e., the differential law.
F=ma
The third law, i.e., the action reaction law.
All forces occur in pairs, and these two
forces are equal in magnitude and opposite in direction.
A BRIEF SUMMARY OF
SPECIAL RELATIVISTIC MECHANICS
STR spacetime
STR spacetime is Minkowskispace. The spatial
component of STR spacetime is a three dimensional Euclidean space and is rigid
and eternal. The temporal component is one dimensional time and simultaneity is
relative unlike in Newtonian spacetime where it’s absolute. The relativity of
simultaneity is a consequence of the invariance of the speed of light.
STR laws of motion
STR accepts the first and third laws without
any modifications but modifies the second law.
The law of inertia
The second law is modified to
F=γma
Enter our attempt at
modifying STR
In current research STR has been modified to
Doubly STR. This is the impressive work of Pavlopoulos, Giovanni
AmelinoCamelia, Lee Smolin, Ted Jacobson, Joao Magueijo, Grigori Volovik,
James Bjorken and others. All these impressive bodies of research works attempt
to modify or replace one of the two basic postulates of STR. These researchers
postulate an observerindependent Planck energy or Planck length. We attempt to
modify STR without modifying or replacing the two postulates. The postulates
are highly justiﬁed as their adoption allowed for reconciliation of classical
mechanics with classical electrodynamics. So we accept the two postulates
without modifications and modify STR along other lines.
A PRESENTATION OF
OUR MODIFIED STR (i.e., MSTR)
MSTR spacetime
MSTR spacetime’s spatial component is a
nonEuclidean
MSTR laws of motion
In MSTR
material points are immutable, i.e., material points are only capable of
constant velocity motion. The above postulates have as its consequence the idea
that there exists an only inertial system. The transformation rules of MSTR are
not Galilean ones of Newtonian mechanics but are the Lorentzian transformation
rules of STR. MSTR unlike STR does not modify Newtonian mechanics but is a
rejection of it. For MSTR material points have constant velocities and there
exists only inertial systems and frames of reference while in both Newtonian
mechanics and STR there are both inertial and noninertial as in both
frameworks material points are capable of constant velocity motion and
accelerated motion. In MSTR force, acceleration, angular momentum, potential
energy and Newton’s laws of motion are rejected. In our framework MSTR a
material point moves at a constant velocity from its creation to its
annihilation and has only linear momentum given by
In our framework during
mechanical collisions of material points, the material points before collision
are annihilated and those after are new creations.
In Newtonian and STR a material
point can lose or gain energy continuously while in quantum theory it can do so
discontinuously. In our MSTR a material point can neither lose nor gain energy
and thus neither gains nor loses it continuously or discontinuously. The
framework of MSTR has no bound systems as all material points are only capable
of constant velocity motion.
CONCLUDING REMARKS
All
attempts to account for gravity within STR were unsuccessful e.g. those of
Henri Poincare, Albert Einstein, Gunnar Nordstrom and others at STR scalar
theories of gravity. So it seems plausible that gravity cannot be accounted in
any theory that’s Lorentz invariant. Einstein road to general relativity showed
that gravity could only be accounted for in a framework that went beyond STR
and would have STR as a limit case. Our MSTR requires no modifications in order
to account for gravity.
1.
Einstein A (1905) On the electrodynamics of moving
bodies, Annalen der Physik.
2.
Einstein A (1915) The field equations of gravitation.
Koniglich Preassische Akademieder Wissenschaften.
3.
Weinberg S (1995) The quantum theory of fields.
Cambridge University Press.
4.
Pavlopoulos TG (1967) Breakdown of Lorentz invariance.
Phys Rev.
5.
Magueijo J, Smolin L (2001) Lorentz Invariance with an
invariant energy scale.
QUICK LINKS
 SUBMIT MANUSCRIPT
 RECOMMEND THE JOURNAL

SUBSCRIBE FOR ALERTS
RELATED JOURNALS
 Journal of Carcinogenesis and Mutagenesis Research (ISSN: 26430541)
 Journal of Cancer Science and Treatment (ISSN:26417472)
 Journal of Pathology and Toxicology Research
 Journal of Nursing and Occupational Health
 Journal of Allergy Research (ISSN:2642326X)
 Chemotherapy Research Journal (ISSN:26420236)
 BioMed Research Journal (ISSN:25788892)