Technical Paper

March 2002

1. INTRODUCTION

The standard model of particle physics asserts that the building blocks of physics are a certain set of fundamental particles from which the composite particles seen in experiments are constructed. The story of the construction of the standard model is one of a dialogue between experiment and theory, where experiment sometimes led in forcing the theorists to postulate new particles in order to explain the fact that certain reactions occur, whereas other apparently similar ones do not.

On the other hand, the standard model explains some but not all of the features of its list of particles, being the task of current research in unified theories to explain exactly why matter should be formed from ingredients that are ordered in the particular way as we well known. The task of GUTs ( Grand Unified Theories ) is to provide some explanation for the form of the standard model, which has many features that it would be nice to explain, rather than assume arbitrarily.

The most important achievement of the last two decades is not just to have established that our world is made of quarks, leptons, and gauge bosons, but to have brought is toward a new frontier where even more exciting questions can be raised. These speculations do inevitably include the possibility that quarks and leptons are themselves composite.

2. THE PROTON DECAY

As it is well known, GUTs are theories that explicitly violate conservation of baryon number, allowing the interesting new possibility of proton decay

According to the Ghassemi’s theory when the proton decays, it melts in space – time.

3. A NEW THEORY

3.1 Topology:

We shall be interested on topological ideas such as continuity of geometrical shapes and how they are going to change in certain processes. In relation to this, it will be necessary the concept of gaussian curvature of a two-dimensional surface which will be changed according to the topological changes and also according to the fluctuations of certain parameters. In this sense it will be possible to obtain some mathematical relations such as equations.

3.2 On the new theory.

I depart from the fact in observing a piece of matter and taking into account the following ordinary fact:

To each piece of matter there corresponds its proper space at which it is contained.

Now, taking into account symmetry considerations I set up similarly:

It is impossible to talk of a mathematical empty space in physics.

From this statements it must be inferred that mass and space are to be the same. But space and time are inherent from special relativity, then we would have space-time-mass in a similar way to the Ghassemi’s theory.

At this step arise the question, how space-time is to be mass and reciprocally? To answer this question, it is necessary to give some structure to space-time and being so I set up the following hypothesis:

There are only two kinds of elementary particles being the building blocks of space-time: The first one, whose topological structure has positive gaussian curvature and the second one whose topological structure has negative gaussian curvature.

According to this, from such building blocks matter is to be made. Say, if we take a container and remove everything from inside it – every atom, every photon - there will be the topological particles postulated above. If we want to remove such topological particles, it will be impossible since they define the structure of space- time itself. It will only be possible to shrink or stretch via compactification or decompactification processes. There are no gaps between our topological particles since it is assumed that it is impossible to talk of a mathematical empty space in physics.

3.3 On the gaussian curvature and topological structure.

We can choose as a topological structure with positive gaussian curvature a sphere with radius and curvature

( 1 )

satisfying the wave equation

( 2 )

with solution

( 3 )

where ( 4 )

From ( 1 ) and ( 3 ) we have

( 5 )

and then

( 6 )

In a similar way we can choose a topological structure with negative gaussian curvature a piece of the torus there where is negative, then

( 7 )

From this we can obtain

( 8 )

Also we suppose that satisfies the wave equation ( 2 ), and then

( 9 )

where ( 10 )

From ( 6 ) , ( 8 ) and ( 9 ) we obtain

( 11 )

If a change in topology and annihilation process is going to occur, then there must be . It means that

= 0

then

( 12 )

and ( 13 )

so we have from ( 12 ) and ( 13 )

( 14 )

This last relation implies that , which means that the topological particles are in a sort of resonance and a first compactification process have occurred.

From ( 4 ) or ( 10 ) we can put

, ( 15 )

Taking the first of the relations ( 15 ), and putting , where is the light velocity, we have

( 16 )

as it is well known. This means that is the slope of the linear relation . So we can understand as drawing the frontier between our “ space-time ” ( filled with topological particles ) and particles with virtual masses and ordinary masses all them inside our space – time – mass, in the plane. See figure 1.

Figure 1

3.4 About the electric charge of proton and electron .

We know that forces between like electric charges ( two protons or two electrons ) repel each other and forces between unlike electric charges ( one proton and one electron ), they attract each other.

From the viewpoint of this theory protons and electrons are characterized by their values and that they have reached during the compactification processes and for each proton of the group of protons the pair must be different in such a way they can not experiment a compactification process as we can infer from ( 14 ), say, they repel each other. But all they must have the same number of compactifications in order they have the same mass. In similar way it happens for the electrons.

In the case of one electron and one proton, they must have the same pair of values in such a way they attempt to reach a compactification process , but they only differ in the number of compactifications.

3.5 The Invariance of the speed of light .

From current theories we know that photons are particles with zero rest mass and they all have the same velocity in different inertial frames. According to my theory, photons must be the result of topological changes successively ( say, particles that have not experimented compactification processes properly ) which is the manifestation of their movement. Since mass appears when compactification processes have occurred and remains stable, photons only have sense when they are under movement ( in the sense of topological changes ). This explains why there are no photons at rest. Being so, this type of topological changes for photons is not affected by uniform velocities.

3.6 About the unstable elementary particles.

It is explained by compactifications processes, which don’t reach stability. In terms of resonance of the topological particles, such resonance is unstable.

At this step arise the questions:

- What is the size of the gaussian curvature for the topological particles?

- What is the number of compactifications for the protons and electrons?

References

1. Do Carmo, M ( 1976 ) Differential Geometry of Curves and Surfaces. Prentice- Hall, Inc.

2. Halzen, F., and Martin, A. ( 1984 ) Quarks and Leptons. John Wiley & Sons, Inc.

3. Peacock, John A. ( 1999 ) Cosmological Physics. Cambridge University Press.

4. http://www.space-time-mass.com/