THE REUNION THEORY

THE REUNION THEORY – The expression E=mc² tells us that, in the distant past, there were several explosions that propelled atoms outward from a common environment.

 

INTRODUCTION

Some years ago, we published an essay titled: “The expression E=mc² tells us that, in the distant past, there were several explosions that propelled atoms outward from a common environment.” As the reader may notice, the phrase “The Reunion Theory” was missing from that title.

Although that essay touched upon the subject of our “Reunion Theory,” its significant role within the study’s thesis remained rather unclear. A reader’s questions of interpretation brought this shortcoming to our attention. For this reason, we have presented this new essay, aiming to approach the subject in as pedagogical a manner as possible.

 

THE REUNION THEORY

 

We have termed our analysis the “REUNION THEORY.” It examines the associations and links that must exist between the physical variables involved in the following process: an explosion, the journey of an atom, and the final manifestation of energy, as expressed by the equation E=mc².

For instance, we associate the variable “force” with the mass (m) upon which it acts, and with the acceleration (a) that it imparts to that mass. It should be understood that we are discussing “associations,” not “quantitative evaluations.”

The Reunion Theory will help us decipher how a single variable, such as the speed of light (c), can recur and appear as a squared term within the same expression.

 

EQUIVALENCES AND TRANSFORMATIONS IN THE REUNION THEORY

Throughout the journey of an atom, from the distant past to the

present day, we shall identify the interactions occurring between the relevant variables as follows:

EQUIVALENCE RELATIONSHIPS:

We define as EQUIVALENT those concepts that describe the same PHYSICAL QUALITY or situation.To clarify, consider the following examples:

VELOCITY: Within this concept, the VELOCITY (v) of a body's mass and the VELOCITY (c) of light are considered EQUIVALENT.

ENERGY: Within this concept, potential ENERGY and kinetic ENERGY are considered EQUIVALENT.

SPACE: In the context of stellar distances, the speed of light (c) is used as a unit of measurement for space. Thus, we can establish an EQUIVALENCE between a spatial distance (e) and the speed of light (c).

 

THE CONCEPT OF TRANSFORMATION

Alongside the concept of EQUIVALENCE, we must also consider the concept of TRANSFORMATION, which occurs between physical variables.

In a TRANSFORMATION, one physical variable acts as the cause of another—that is, we are dealing with a cause-and-effect relationship, which is NOT the case for EQUIVALENCE.

As an example, consider POTENTIAL ENERGY (Ep) and the physical concept of WORK (T). We can express this as follows:

 

This demonstrates a capacity for transformation; we recognize this as a transformation.

Another transformation occurring between physical variables—perhaps more difficult to discern because it requires a specific type of reasoning—is as follows:

We define the variable Force (F) as: F = m.a

where (m) is the mass variable and (a) is the acceleration variable.

However, we can also TRANSFORM it into:

 F = m·c

where (c) is the speed of light.

This assertion requires further justification on our part:

Acceleration (a) is expressed as: a = ∂v/∂t, where (v) is the velocity acquired by the atom due to the action of force (F),

where (t) is the elapsed time.

Furthermore, we know that the variation in velocity (v) resulting from that force can be described by the formula:

                                                 

where (v) is the final velocity intended to be reached during time (t), between the initial (i) and final (f) points of application of the aforementioned force. We must also assume that this time interval was infinitesimal.

However… we must bear in mind THAT THE FINAL POINT (F) IS LOCATED AT THE POSITION WHERE (V) REACHES THE SPEED OF LIGHT (c), as this is THE LIMITING VALUE FOR VELOCITIES. Therefore, the acceleration between the initial point (i) and the final point (f)—that is, the increase in velocity between (i) and (f)—is limited by the speed of light.

                                      

In other words, the limit to this increase in velocity is the speed of light (c). Thus, the acceleration (a) of the mass (m) is constrained.

Therefore, we can consider that the aforementioned primordial FORCE (F), which acted infinitesimally upon the particle, CAUSED ITS MASS TO TRAVEL AT THE SPEED OF LIGHT (C).

F = mc

We can also interpret this change as a TRANSFORMATION.

  

SYMBOLISM FOR USE WITHIN THE FRAMEWORK OF THE “REUNION THEORY”

This symbolism is well-suited for representing the connections among variables—even a variable’s connection to itself, as in the case of the speed of light (c), which can be expressed as: (

If we wish to assess its impact, we would consider the value (c).

In the theory under discussion, it should be noted that we refer to the physical variables involved in an atom’s movement in terms of "actions" rather than mere quantities. In an empirical analysis—or an experimental trial—we can observe the specific contribution of each variable.

For instance, the variable Force (F) is expressed as:

F = m · a

In our symbolic language, we apply the following notation:

 

 

Through this symbolism, we indicate that the UNION (∪) of the variable mass (m) and the variable acceleration (a) constitutes the resulting variable, Force (F). Similarly, we can symbolically represent the variable Work (T) as the UNION (∪) of a Force and a distance (e).

      

                                

In other words, we have moved from POTENTIAL ENERGY to WORK, and now we move from WORK to the EXPRESSION OF ITS COMPONENTS.

The work (T)—which, according to the aforementioned expression, THE ATOM IS CAPABLE OF PROVIDING—IS STORED WITHIN THE ATOM, RECORDED AS THE COMBINATION OF THE PRIMORDIAL FORCE (F) WE DISCUSSED AND THE DISTANCE (E) TRAVERSED BY THE MASS DURING THE EVENTS IN QUESTION.

Let us recall that, at the scale of physical units we are considering, distances are measured in units of LIGHT-SPEED (UVL); thus, the particle in question, propelled by the force (F), reached a speed equal to the speed of light (c).

By expressing the distance (e) in units of light-speed (uvl), we can establish the EQUIVALENCE:

 

Therefore, we can write:

                                          

Here, (c) represents space measured in light units.

To demonstrate that the expression  represents POTENTIAL ENERGY, we propose the following reasoning:

As we have:  and as we have obtained

The result is:

What is the expression we were investigating?

  

HOW CAN THE EQUALITY REPRESENTED BY THE EXPRESSION E=mc² BE THEORETICALLY JUSTIFIED?

We know that this expression has already been empirically demonstrated; therefore, we accept its validity.The task that remains is to justify its validity from a theoretical perspective.

To this end, we will draw upon our “Reunion Theory,” utilizing the symbolism established for its variables. We need only examine the expression of the aforementioned formula, in symbolic form, which we derived in the preceding paragraph while highlighting the grouping of the two variables involved.

 

FORCE SPACE