From the Oscillating Universe to Relativistic Energy: A Review

Abstract

We hypothesize a closed Universe belonging to the oscillatory class. More precisely, we postulate a Universe that evolves following a simple harmonic motion whose pulsation is equal to the ratio between the speed of light and the mean radius of curvature. The existence of at least a further spatial dimension is contemplated. Although the space we are allowed to perceive is curved, since it is identifiable with a hypersphere whose radius depends on our state of motion, the Universe in its entirety, herein assimilated to a four-dimensional ball, is to be considered as being flat. All the points are replaced by straight line segments: In other terms, what we perceive as being a point is actually a straight line segment crossing the center of the above mentioned four-dimensional ball. In the light of these hypotheses, we can easily obtain the identity that represents the so called relativistic energy. In this paper we discuss, more thoroughly than elsewhere, the deduction of the so called mass-energy equivalence. Moreover, by carrying out a simple comparison with the way in which we perceive a bi-dimensional surface, the noteworthy concept of dimensional thickness is introduced.

A Short Discussion on the Gravitational Redshift in the Light of an Alleged Local Variability of the Planck Constant

“…We have elsewhere introduced the concept of dimensional thickness [4]. It has been previously claimed that the Universe we are allowed to perceive, when we are at rest, may be assimilated to a hypersphere (a three-dimensional curved space).…”

“…The evolution of the hypothesized Universe may be evidently characterized by four consecutive phases: an accelerated expansion, a decelerated expansion, a decelerated contraction, an accelerated contraction (as a consequence, it is quite evident how the Hubble parameter [3] may have assumed in the past, and could The existence of at least a further spatial dimension is contemplated [4]. Although the space we are allowed to perceive, when we are at rest, is curved, since it is identifiable with a hyper-sphere whose radius depends on our state of motion, the Universe in its entirety, herein assimilated to a four-dimensional ball, is to be considered as being flat.…”

On the Schwarzschild Solution: a Review

“…All the points are replaced by straight line segments: in other terms, what we perceive as being a point is actually a straight-line segment crossing the centre of the 4-ball. [4] At the beginning (no singularity), we hypothesize that the Universe, whose radius equates the Schwarzschild Radius, is homogeneously filled with matter [6].…”

On the Absoluteness of Time

“…More precisely, we postulate a Universe that approximately evolves following a simple-harmonic motion, whose pulsation is equal to the ratio between the speed of light and the value of the mean radius, taken as reference (Cataldo, 2017b(Cataldo, , 2017c. In spite of this, we consider the variations of cosmological distances as being exclusively metric: in other terms, we postulate that the amount of space between whatever couple of points remains the same with the passing of time.…”

“…All the models we have elsewhere discussed (Cataldo, 2016a(Cataldo, , 2016b(Cataldo, , 2017a(Cataldo, , 2017b(Cataldo, , 2017c(Cataldo, , 2017d) start from hypothesizing a closed Universe, homogeneous and isotropic, belonging to the so-called oscillatory class (O 1 type in the Harrison classification) (Harrison, 1967). More precisely, we postulate a Universe that approximately evolves following a simple-harmonic motion, whose pulsation is equal to the ratio between the speed of light and the value of the mean radius, taken as reference (Cataldo, 2017b(Cataldo, , 2017c.…”