6. Space, Time and Energy

Abstract:

The hypothesis that both the Universe and particles possess four spatial dimensions, together with the quantification of space, allows us to apply the equations of classical macroscopic physics to elementary particles and obtain a four-dimensional spatial particle or atoms of space and time, from which they derive all other particles: electrons, photons, quarks, etc. and their corresponding  antiparticles. Energy is the curvature of space, mass is due to rotation of the particle in four-dimensional space, while the charge is the time or period it takes to go around the fourth dimension. Two rotations, one in space and the other in the fourth dimension, suffice to obtain four different particles, two electrons and two positrons with spins ±1/2. The photon is an atom of space-time, turning only in three-dimensional space.

ARTICLE                                            DONWLOAD PDF 

1. Introduction.

General relativity supposes that space-time is continuum. However there is no experimental evidence of this. Are continuous space and time? Or just are we convinced that continuity as a result of conditioning of education? In recent years physical and mathematical have questioned whether it is possible that space and time are discrete.

“The familiar concept of a “space-time continuum” implies that it should be possible to measure always smaller and smaller distances without any finite limit. Heisenberg, who insisted on expressing quantum mechanical laws in terms of measurable observables, questioned already the validity of this postulate [1]. We should thus treat the ultimate limit a for the smallest measurable length as a yet unknown quantity. Actually, we learned already from the development of relativity and quantum mechanics that Nature can impose restrictions on our measurements because of two universal

constants: the velocity c and the quantum of action h. Could Nature impose a third restriction, resulting from the existence of a universally constant quantum of length a and a universally constant quantum of time a/c?” [2]

Theories related to quantum gravity such as string theory and doubly special relativity and black hole physics predict the existence of a minimal length [3-7]. In 1947 Snyder used a technique that has a minimal lenght quantification in the physics of space-time [8, 9].

In 1962, Wheeler [10] was one of the first physicist to introduce the discrete spacetime to approach the problem of quantum gravity. Ponzano and Regge later [11] propose discrete space-time based on adjacent triangles network, thus achieving an arbitrary curved

surfaces.

Also, G. Jaroszkiewicz and K. Norton, in a series of papers replace the continuum space-time by a discrete space-time. [12-16]. Another modern approach to quantized spacetime is provided by Prugovecki [17, 18].

Heisenberg himself noted that physics must have a fundamental length scale which together with Planck’s constant and the speed of light, permit the derivation of particle masses [19, 20].

The combination of the speed of light c, the quantum of action h and the gravitational constant G, gives the Planck length  lp = (G ℏ / c³ )¹ˡ² , which is considered a limit to the extent the space-time distance [21,24]. It is also assumed that the Planck length is the limit of application of the Newton's nonrelativistic law of gravitation. However, the gravitational interaction has only been tested for distances greater than 1 cm with good accuracy [25-30].

“Considering that the general purpose of physics is to build theories that account for numerical experimental data, the construction of a theory of space-time is a necessity” [31].

In this paper we put forward such a model of discrete space-time curvature in which part of a minimal length and that both the particles and the space itself has four spatial dimensions. It follows natural way:

•  time, due to the expansion of the universe.
•  energy, due to the curvature of space.
• mass, due rotation of the elementary particle.
• electric charge, which is the time it takes for the particle in a spin in the fourth dimension.

“The idea of using extra spatial dimension to unify different forces started in 1914 with Nordstom. In 1919 Kaluza noticed that the 5-dimensional generalization of Einstein theory can simultaneously describe gravitational and electromagnetic interaction [32]”.

Currently to resolve the hierarchy problem of particle physics, theories are also used extra dimensions [33-41]. Pauli declared "the concept of space and time in a very small scales requires a fundamental change”.

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

 11. Conclusions

From the hypothesis by which both particles and space have four spatial dimensions we can deduce the equations of restricted relativity as well as the charge, mass and frequency of the unitary particle, which coincides with the electron and from which all the others are derived.

The mass of the unitary particle or electron (Eq.15) is obtained from the potential of the gravitational field due to the rotation of the Planck bubble, which expands until it reaches the unitary radius (Eq.11). It can also be obtained by keeping constant energy per volume.

Mass, charge, space and time are quantified and are different manifestations of energy.

The energy of the electron can be expressed in terms of its mass, charge (in module), proper time, or wavelength (radius of the flat disk) or distance at which the space and time atoms reach a lineal speed of rotation equal at the speed of light or universe expansion in the fourth dimension or time dimension.

The up quark and down quark masses and their respective electric charges are obtained in terms of unit mass. The mass and electric charge of the proton and neutron can also be obtained in terms of unit mass. The mass difference between proton and neutron is due to the different energies of the constituents (quarks).

The masses of up and down quarks and their respective electric charges are obtained in terms of the unitary mass. The proton and neutron’s mass and charge can also be obtained in terms of the unitary mass. The mass difference between proton and neutron is due to the different energy in the constituent elements (quarks).

a) Electron: We can suppose the electron (particle) to be a unitary spherical volume of space can rotate about x, y, z of the fourth dimension. The mass is then the energy enclosed within this volume 3D, while the electric charge is its spherical surface.

Since the 3D space particles are united (Newton’s law of gravitation), the rotation will also make the surrounding space rotate until the linear rotation speed reaches c=welu, which occurs at a distance of r=𝜆u

Because of the 3D particles are linked (Newton's law of gravitation), the rotation will rotate the atoms of space and time of the 3D space adjacent to the linear speed of rotation is equal to c=𝛚e 𝜆u, and this occurs at a distance r= 𝜆u.

Rotation in the fourth dimension will change the atoms of space and time in observable three-dimensional space, which generates the wave and giving rise to charge and time at rest.

While one rotation is made in three-dimensional space, half a rotation is made in the fourth dimension, which means we see the particle in reverse, with spin ......

Einstein assumed that the electron is the most important particle in the Universe.

b) Photon: In the photon, the spherical volume of space surrounded by a space-time ring that turns in three-dimensional space (we=2pn) gives rise to the observable frequency. As the rotation may have opposite senses , clocwise or anticlockwise, we can have a photon with positive or negative spin. The rotation will rotate the space adjacent to a distance equal to its wavelength, which generates the wave.

c) Space: When both rotations are null we obtain empty space. Therefore space is formed by a series of four-dimensional space bubbles or space-time particles spreading in all directions, which causes the curvature and expansion of the Universe. If we attribute spatial rotation we to empty space it becomes a photon.

When both rotations are zero, we get empty space, so space will consist of a series of 4D space particles or atoms of space-time of four dimensions that extend in all directions, causing the curvature and expansion of the Universe. . If we equip the empty space of the spatial rotation we, becomes a photon. If in addition to the spatial rotation, it takes a second rotation in the fourth dimension, we get the different particles, electrons and quarks of first generation and their corresponding antiparticles. Therefore, the particles are excitation of the medium, this being formed from particles or atoms of four dimensions of space and time.

The old intuition that something has to be in "absolute rest" (the atom of space and time) was correct. A. Messer also part of a minimum length that calls a, and a four-dimensional space. It allows to characterize different types of particles with quantum numbers.

“Although the idea of a minimal length is now more easily acceptable, it is still used in various ways [53]”. “Different types of elementary particles are now characterized by their (ux,uy, uz, uct), quantum numbers, specifying how the associated Y functions vary in space and time at the scale of a/2. In this sense, we can say that particle states correspond to different patterns of excitations of space and time[2]”.