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Email: Amrit Sorli

Unification of Mathematical And Physical Time In Relativity Theory

Dott. Ing. Amrit Sorli, SpaceLife Institute,
Podere Petraiole, 53012 Chiusdino (SI), Italy

In the Theory of Relativity the difference between physical time and mathematical time is obvious. Mathematical time is a fourth coordinate of space-time: X4 = i * t; t indicates the duration of material change, number i is an imaginary number. I squared is -1. Mathematical time is an abstract quantity that can not be observed. Physical time can be observed as a stream of material change in physical space (the concrete space in which stellar objects exist) (1).

To build an adequate model of the world, mathematical time should become a concrete description of physical time, where mathematical time t describes its duration. Unification of mathematical and physical time allows a description of electromagnetic phenomena in inertial system K that is fixed, and inertial system K’ that is in motion as in a Galilean transformation.

Light has the same speed in the inertial system K and in the inertial system K'. The speed of physical time (the speed of material change) is slower in K' and faster in K, the duration of physical time in inertial system K regarding inertial system K' is following:

t = t'

From this point of view the Special Theory of Relativity can be described within three-dimensional Euclidean space. There in no "time dilatation" and "space contraction", but the speed of physical time in inertial system K’ is slower than in the system K. The experiment with clocks on an airplane that is flying in the opposite direction of the earth’s rotation confirms that speed of physical time in the airplane (inertial system K') is slower than on the surface of the earth (inertial system K). We measure duration and speed of physical time with clocks.

The brother that has remained on the earth will become older than his twin that has travelled on a fast space ship because the speed of physical time is slower on the fast space ship than on the earth.

Einstein-Minkowski space-time can not be observed in the universe. It is only a mathematical model of the world and not the world itself. However most of physicists think that space-time is a physical reality. The picture of the world is becoming more real than the world itself. This misunderstanding creates contradictions: hypothetical travel into the past (2).

In Einstein-Minkowski’s space-time, the past exists as a negative space-time. Theoretically one could travel into the past and kill his grandmother. The question arises: If he kills his grandmother how he could be born? The other contradiction appear when one try to catch a missing train. Let’s say that one should part from Milan to Rome at 9 AM. He arrives at the station at 9.15 and misses the train. He jumps into a spaceship, travels through a space-time wrinkle into the past and comes back to the station at 8.45. But the train will still travels towards Rome. It will not stop and travel backwards.

Physical time is irreversible. Change A transforms into change B, B transforms into C and so on. When B is exists, A no longer exists, and when C exists, B does not. Time travel into the past should not be considered even as a hypothetical possibility.

General Relativity: With the unification between mathematical time and physical time in General Relativity, physical space can be described using a three dimensional Riemann space. The speed of physical time depends on the curvature of 3-dimansional physical space. That is, on the strength of the gravitational force in a given volume of physical space. The more physical space is curved, the more slowly physical time passes.

Experiments prove that the speed of clocks at sea level are slower than those on the top of a mountain. This means that the speed of physical time depends on the strength of the gravitational field. It is not that in a stronger gravitational field there is a dilatation of time as a fourth coordinate of space. Riemann space-time is only a mathematical model and not cosmic space itself.

Physical space is A-Temporal. In physical space by itself, physical time does not run as a physical quantity in which material change are made. Material change of itself is physical time. Theoretically, in physical space without material change, physical time does not run.

Gravitational force is carried directly by A-Temporal physical space. No hypothetical gravitational wave or hypothetical gravitons are needed for transmitting gravity. Gravitational force is A-temporal in the sense that no motion of particle or wave (physical time) is needed for it to act.

In his article "Chief Notions and Methods of the Theory of Relativity Presented in its Development" that is kept in the Morgan Library in New York, Einstein says that the general theory of relativity cannot be imagined without gravitational ether which is non-homogeneous, and its state has no autonomous existence, but depends on the field generating matter. Since in the new theory, metric facts can no longer be separated from true physical facts, the concept of space and ether merge together.

Merging of A-Temporal physical space and gravitational ether introduces "non-homogeneous density of physical space" that corresponds to the density of matter. The denser the matter, the denser the physical space. In the General Theory Of Relativity, curvature of space is a mathematical description for the density of physical space. The "areas" of higher density attract each other (3).

One could imagine physical space as an elastic medium that has a tendency to shrink. The more dense the medium, the stronger is the shrinking force. The "shrinking force" is the gravitational force. The strength of the gravitational force in a given volume of an elastic medium depends on the amount of matter in it. Gravitational pulls together the physical space in which the sun and earth are floating and does not act on the sun and earth directly. Centripetal forces act directly on the earth pulling it away from the sun. Gravitational forces and centripetal forces are equal: Fc = Fg.

Density of physical space around a stellar object increases towards its centre. The speed of physical time slows with increasing density. Experiments show that the speed of physical time on a high mountain is faster than at sea level. Physical space is denser at sea level and less dense on the top of the mountain. By going deeper into the earth, the density of physical space increases and the speed of physical time slows. The speed of the clock mechanism on the boat should be greater than the speed of the clock mechanism 6000 meters under the sea.

Light is bending when passing the sun because gravitational force attracts it. It is not that light is bending because of curved cosmic space. The idea that physical space could be curved was born with the discovery of the spherical geometries of Riemann and Lobacevski. There is no experimental evidence for the existence of curved physical space. Imagining that the sun bends physical space as a bowl and that earth moves around the sun on its surface appears imprecise. A-Temporal physical space with its density describes gravitation in a more tangible way.

By throwing a stone in the water, waves will spread. By throwing a stone (supernova explosion) in physical space, only the density of space around the stone increases, but no waves of physical space are created. A hypothetical gravitational wave is here understood as a large increase of density in physical space that travels through space. The change of density of space is directly related to the change of the amount of matter in a given volume of physical space. Matter that is thrown out by the explosion causes only an increase in the density of physical space around it. It is not assumed that a wave of high density can travel through physical space without matter.

It seems that the properties of physical space are so different from the properties of water that they cannot be compared. One cannot suspect that physical space is creating waves as water does. According to the understanding of gravitation, gravitational waves do not exist.

Gravitational waves emanating from the explosion of a supernova have not been detected. Loinger considers that gravitational waves are only fictitious entities generated by purely formal approaches (4).

EPR Experiment This new understanding of time and gravitation brings new light to the experiment of Einstein, Podolsky and Rosen (EPR). This experiment shows that the information between quantum A and quantum B which have been together and then sent into space in opposite directions travels between them instantly. One could predict that in the EPR experiment the information medium between two particles is physical space itself. For information to reach from particle A to particle B no physical time is needed (no travel of particle or wave). Like gravitational force, information between particle A and particle B is also instant and A-Temporal.

Einstein - Rosen Tunnels And Possible Solutions For Cosmic Dynamics

The original idea of the transportation of the energy of matter through a kind of tunnel that connects black holes and white holes is due to Einstein and Rosen. With the introduction of the density of physical space, the disappearance of matter into the centre of black holes has a new interpretation: in the centre of the black hole, physical space is so dense that gravitational force disintegrates all atomic and subatomic particles into physical space itself. With the transformation of matter into space the density of cosmic space increases. This process increases the gravitational forces between galaxies. The speed of expansion of the universe is decreasing. At a certain point the expansion will stop and the universe will start to collapse into an enormous black hole that then explodes into a new big bang. Big bangs are cyclic.

Other possible dynamics between matter and physical space could be the following: astronomical observations show that the Active Galactic Nucleus (AGN) continuously emits fresh gases. Energy cannot be created or destroyed. Matter cannot simply appear in AGN out of nothing. The idea here is that in black holes the energy of matter transforms into the energy of physical space. This process keeps the density of physical space high in the centre of the galaxy (AGN) where the energy of space transforms back into the energy of matter. Here the AGN functions as a white hole.

However, in both models the Dynamic Equilibrium between matter and physical space is a basic universal law. The universe is a "perpetual" system with a permanent transformation of energy "matter - physical space - matter - physical space". The Universe does not need energy to move with. It cannot be compared to the machines created by man where "for some work to be done some energy is needed". The second law of thermodynamics cannot be applied to describe universal dynamics. It is valid only for machines. The total energy of the universe and of a single active galaxy sums to zero. An increase in the entropy of gas being produced in the big bang or in an AGN does not influence its total entropy.

Also for the movement of a stellar object, no energy is needed. For example, the force of attraction between physical spaces of the earth and moon is equal to the centripetal force, which pulls the moon from the earth [ F attraction (Fa) = F centripetal (Fc) ]. For the movement of the Moon around the earth, no energy is needed [ Fa - Fc = 0 ]. By moving the stars and planets the universe does not get "tired".

Movement is an intrinsic property of the universe, physical time (material change) has no beginning and will have no end. There was no creation of the universe and there will be no end.

A-Temporal Physical Space And Evolution Of Life

In the universe, one can observe only the entropy of matter. There is no experimental evidence for entropy of physical space. Physical space does not follow the second law of thermodynamics, it has no entropy.

Several experiments show that the functioning of living organisms is directly related to the gravitational force of physical space (5, 6).

Experiment with earthworms shows that the density of physical space around a living organism is higher than around the same dead organism. The weight of a living organism is larger than its weight in death (7).

Research done by Penrose and Hameroff suggests that the force of quantum gravity acting on the mass of neurones within the brain may be responsible for the emergence of consciousness. The process is fundamentally related to the influence of quantum gravity on microtubule networks within the neurones (8,9). Human consciousness is directly related to physical space.

Physical space plays an active role in the functioning of living organisms and in the development of life as well. Matter has an intrinsic tendency to develop into life because it is contained in physical space that has no entropy. The evolution of life is a negentropic process that is growing towards a non entropic state of physical space.

Basic organic molecules needed for the development of life have been discovered in the whole of observable physical space. Universal physical space is in the phase of chemical evolution (10). One can predict that on planets similar to ours chemical evolution has developed into biological evolution. Maybe we are not alone in this vast universe.


The theater or "stage" of the universe is A-Temporal Physical Space. Gravitational force is carried directly by physical space. Matter and physical space are in a permanent dynamic equilibrium. The evolution of life and of human beings is a consistent part of cosmic dynamics.


I thank Roger Gouin for the helpful discussion on the AGN


1. Sorli A. (2004) Mathematical Time And Physical Time In The Theory Of Relativity, GSJ,

2. Sorli A, Sorli I. (2004). A-temporal Gravitation, EJTP, Vol 1, Num 2

3. Davies P. (2002). How To Build The Time Machine. Penguin

4. Loinger A. (2004). The gravitational waves are fictitious entities

5. Krasnov IB.(1994). Institute of Biomedical Problems, Moscow, Russia. "Gravitational neuromorphology",

Advances in Space Biology and Medicine 4: 85-110.

6. US Army (1993). Madigan Army Medical Centre, Tacoma, Washington " Cerebral blood velocity and other cardiovascular responses to 2 days head down tilt. Journal of Applied Physiology. 74 (1): 319-25.

7. Sorli A. (2001). Additional Roundness of Space-Time and Unknown Vacuum Energies in Living Organisms. Frontier Perspectives, Vol 10, Num 2

8. Penrose R. (1994). 'Shadows of the Mind' (Oxford), 377-391.

9. Hameroff S. (1994). 'Quantum Coherence in Microtubules: A Neural Basis for Emergent Consciousness?' Journal of Consciousness Studies 1 (1), 91-118.

10. Mason S. (1991). Chemical Evolution: Origin of the Elements, Molecules, and Living Systems, Oxford University Press