TITLE:
Additional Space Dimension in Bound Spaces Created by a Central Object
AUTHORS:
T. V. B. S. Satyanarayana Murthy
KEYWORDS:
Central Object, Bound Space, Gravitational, Charge, Additional Space Dimension, Energy, Mass
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.2,
January
30,
2015
ABSTRACT: Space is a common
entity in any static or dynamic system of objects whether the system is a bound
system or an open system. Space is described by either measured or abstract
dimensions. All motions, momentum and energy transfers take place in space in
any given system of objects. By understanding space we understand many physical
phenomena happening in space. One method is to observe similarities among
phenomena, deduce possible relations and validate the relations through known
results. De Broglie wavelength for matter waves is a typical theorized abstract
dimension existence of which is established through experiments later. In this
paper, the author studies two bound spaces in two bound systems, namely, atomic
bound systems and gravitationally bound systems. Both these bound systems have
similar characteristics; they have inertial masses in motion with constant
kinetic energies for a given orbital distance around the respective central
object. In atomic bound space, the central object is the central positive
charge which plays the role of creating the bound space around it. In
gravitationally bound space, it is the central mass that plays the same role.
Thus for these two bound systems a common constitutive relation between the
energies of inertial masses in kinetic state, their distance from central
object could be present. By noticing the similarities of the two systems, the author
proposes such a relation through introduction of an additional space dimension.
The existence of the proposed additional dimension is proved in this paper by
considering hydrogen atom for atomic bound space and by considering any
gravitational system for gravitationally bound space. Though the magnitude of
the additional space dimension is different in both the situations, the
additional space dimension exists. It is observed that in hydrogen atom the
additional space dimension is a constant for the given positive charge of
hydrogen atom when electron is in any energy state having principal quantum
number of any value from 1 to 5 and with the orbital quantum number zero. For
other quantum numbers additional space dimension exists. In the case of gravitational
bound space, the additional space dimension is constant for a given mass of the
central object for any energy of orbiting inertial mass. The author concludes
that total mass energy of an inertial mass having a constant kinetic energy in
any bound space is related to an additional space dimension defined by the
constitutional property of the central object creating that bound space. As the
relation is generic, it throws opportunity to examine other known similar
macro, micro or quantum bound spaces created by central objects with different
constitutive properties.