When we
speak about structures and forces, we discover functions and scales. Things
are causally interrelated in two ways: among structures within the same scale,
and hierarchically when they are referred to a structure belonging to a higher
scale that contains them or when structures belonging to a lower scale are
referred to them. The complementarity structure-force underlines that all
things are structures, that they contain structures of a lower scales as its
substructures or discrete digital units, coming down to the fundamental
particles themselves, that they are discrete digital units of structures of a
higher scale, and that they generate forces. What makes it universal is that
the complementary force comes from the four fundamental forces known which
operate in the subatomic fundamental structure. The complementarity is valid
from the microscopic world of the subatomic fundamental particles up to the
macroscopic world identified with the universe itself. Indeterminism at any
scale is resolved by statistical determinism at a higher scale.
Introduction
Following Parmenides, Aristotle said thateverything
is one. But for him the one is a transcendental attribute ofeverything. What he
did not said is that everything comprises many things, i.e.,many ones, just as
the one together with the other ones are part of anotherone.
Max Planck’s discovery that fundamental energy is discretely transmitted, together with Max Born´s probabilistic interpretation, led Werner Heisenberg to formulate, in 1927, the hypothesis that the emission of radiations is a statistical phenomenon. Once the condition of a particle is known, it is only necessary to define the probability for its location, since, at the subatomic scale, any actual measurement implies disturbing the measured object. Heisenberg’s “uncertainty principle” affirms the inability simultaneously and accurately to determine the position and the speed of any subatomic particle.
Max Planck’s discovery that fundamental energy is discretely transmitted, together with Max Born´s probabilistic interpretation, led Werner Heisenberg to formulate, in 1927, the hypothesis that the emission of radiations is a statistical phenomenon. Once the condition of a particle is known, it is only necessary to define the probability for its location, since, at the subatomic scale, any actual measurement implies disturbing the measured object. Heisenberg’s “uncertainty principle” affirms the inability simultaneously and accurately to determine the position and the speed of any subatomic particle.
We can, therefore, say that, in a
phenomenological or analog scheme, systems and processes are described in terms
of facts to be directly measurable in a larger scale, while in a quantum or
digital scheme events are particular and need, for their formulation, the use
of the notion of quanta. Statistics are necessary to leap from the quantum
scheme to the phenomenological scheme. But this leap means moving from a lower
scale to a higher scale, i.e., from a set of discrete, separate digital units
to a constant analogical process. Indeterminism happens in all the possible
scales, but its determination is solved at a higher scale by means of
statistics. The problem of quantum mechanics is that at its own scale, the most
fundamental of all, no statistical resolution of quantum phenomena can exist,
since there is no lower scale. This conclusion forces us to assign
indeterminism for particular situations. If the transmission of energy, which
is how the relationship between a cause and its effect takes place, is not a
constant flow, but a flow of quanta or discrete units, in the scale of these
discrete units there is no need that such-and-such a unit should be transmitted
at such-and-such a moment. From the point of view of a higher scale the
transmission of energy is a perfectly analogical process, since it is
statistical.
Structure and Force
as the Two Complementary Sides of Things
The whole universe and its things are
structure and force, which are made up by matter, energy, time and space. Also,
the comprehension of the nature of these essential elements is essential for a
true understanding of reality.
Structure and force are the two faces of
being and constitute a complementarity. They naturally issue from the concepts
of matter and energy, which are the primary manifestations of the universe.
That complementarity constitutes the universal, unifying and ordering principle
of all things. The multiplicity of things acquires unity in this complementarity,
because everything is simultaneously structure and force, everything originates
in matter and energy, and is part of other structures according to progressive
proportions. We perceive that things of the universe mutate and can conclude
that the causal relationship is a force that transforms energy and produces
change, and that the forces that are set free depend on the functionality of
structures according to natural laws that can be known scientifically. In the
course of the evolution of the universe, structures become progressively more
complex and functional in ever higher scales.
The universe is not the container of
things in a space-time referent, nor is the space-time field of causality. The
universe consists mainly of the interaction of structures and forces that
produce the organization of matter while developing space-time. The dimensional
parameters of time and space are understood precisely by the two terms of this
complementarity.
The empirical basis to establish that
force and structure are the two complementary, universal, constitutive, and
transforming aspects of the universe lies in the distinction between matter and
energy. For matter (as mass) and energy, Albert Einstein discovered their
convertibility and equivalence, which he expressed in the famous equation E = m
c ². And as in the case of mass, the equivalence with energy in electrical
loads has been established.
Structure
To understand the concept “structure,”
one has to first analyze the notion “mass.” This notion was introduced by Isaac
Newton [4] to explain both gravity and Galileo’s principle of inertia.
Abstraction and simplification is necessary to describe physically the
phenomena of force and change, but this interferes with a true understanding of
matter. In spite of being evident that a set of mass points that conforms a
body has volume, we would not advance much if mass is only seen in its ability
to occupy places in spaces by belonging to bodies.
Even though a structure can be conceived
as a material point without any extension, as in the theory of the gravitation,
the location of a gravity centre, the distance to another body, and the amount
of mass, are also properties of matter. A structure is a determined organized
matter, and reciprocally, matter does not exist unless it constitutes a
structure. One might imagine that a structure is a cluster of massive points
without extension, occupying a determined space at a certain moment of time, in
pre-existing space-time. But this image is wrong. The significant issue is that
no matter how small a corpuscle, it is functional and has aptitude to relate to
other corpuscles in the same scale. The relationship of two or more corpuscles
generates a structure as well as a particular space-time.
Although a structure, in the perspective
of dynamics, is reduced to mass and from the point of view of mass we do not
find anything else than mass, the basic energy is condensed into matter that
contains mass and other properties. All this produces an extraordinary
functionality that allows the spatial distribution of the structure in diverse
degrees of functionality and complexity starting up from the fundamental
particles. These properties are extension, volume, electric load, and a
composite of diverse types of subatomic particles. Each of these particles
possesses spin. Most have the form of corpuscle and also of wave, and are
related to other particles through at least a specific type of the four forces.
They subsist in time if they are not undergoing change. As simple the structured mass can be, it
generates space-time and possesses some type of functionality through which it
is capable to be a cause or to be an effect, of being the source or the
recipient of forces, and of containing, accepting or yielding energy.
A structure is fundamentally the
relation or the causal link that is established between two or more structures
that, besides other specific functions, are functional to each other and vice
versa, and becoming the substructures of a higher scale structure. In addition,
the said structure acquires its own functionality by virtue of the
functionality of its substructures and the relationship that the said
substructures establish among them. For example, two atoms of hydrogen and one
of oxygen relate because of some of their respective functions, producing the
structure of a typical water molecule, which possesses also its own functions,
among these having specific weight, gravity and so on.
Due to its functionality, matter has the
capacity to assembly itself, to be ordained, to be constructed and to be
organized, i. e., to be structured. When we think about the notion “structure,”
we shall understand also the ideas of group, constitution, order, assembly,
construction and organization, disposition, arrangement, system, distribution,
scheme, etc., which constitute synonymous of the possibilities of matter, and
refer to constitutive parts of lower
scales and are included in units of higher scales.
A structure should not be seen as rigid,
as a building, or as anything geometric, as a molecule, or as anything static
and permanent. A structure includes the more intangible things of nature, such
as perceptions and ideas. In the same way, a structure is capable of generating
force, and force is capable of structuring mass and electrical load. The
mass-electric load operated by force acquires the quality of structure.
Force
In nature energy cannot exist in itself:
either it is “condensed” in matter as mass and electric charge or it
participates in the causal link between two or more structures (as gravity,
electromagnetic radiation, etc.). It therefore needs the intermediation of
matter. Energy is a power that a structure possesses, and no structure can
exist nor act without energy. Every structure can yield or acquire energy. In
this action, it needs of at least another structure, and the relation that they
establish is that of a cause and its effect. When a structure yields energy,
one speaks about cause; when the structure acquires energy, one speaks about
effect. But the energy that a structure acquires, while it is an effect, can be
so large that the structure itself can be destroyed. Every transmission of
energy changes both, the structure cause and the structure effect.
As physics understands it, energy is the
capacity a body has to realize work. This capacity depends on the speed and the
mass of a body –also on its electric load–. According to its definition, energy
is the maximum work that a body is capable of and is half of its mass
multiplied by the square of its speed. Thus we see that the energy of the body
increases with the square of its speed. On the other hand, the speed of a body
does not have an absolute frame of reference; it must be necessarily referred
to at least a second body and has validity only with regard to this second
body.
Structure and Scale
In the course of the history of the
universe, whose origin was an infinite quantity of energy contained in an
infinitely no-space point, it is possible to suppose that the big bang produced
an enormous condensation of energy into matter. After this singular event and
while, from the point of view of the big bang, matter –not space– remains
expanding at the speed of light from the big bang, the net profit is that
matter has been undergoing an increasing ‘structuration’, containing scales
increasingly higher. As a consequence, if matter is the way of condensing
energy, the increasingly structured matter takes advantage of energy in an
increasingly efficient manner.
To understand the causal relationship between
structures due to force, one should introduce the concept of “function”. Any
structure is functional because it exerts force or because it obtain forces.
Function is what allows a structure to be a cause or an effect. It is the
specific combination of forces of a particular structure, that is to say, this
structure is particularly functional because it is cause or effect of a
specific combination of forces. A function of any structure of our universe
exerts weight, since all structures are composed of massive particles, though a
structure can have other most decisive functions that distinguish it, like the
logical relation of ideas.
In the same way a structure is affected
in a determined mode by a particular force, a structure has a particular way to
exercise force and thus be a cause. Force is not an entity that exists
independently of structure, because both are complementary. If every force is
necessarily linked to some structure, the force is exercised according to the
functionality of that particular structure. Force acts according to the way its
complementary structure works. Similarly, the force acts on another structure
according to its particular configuration for which is functional as effect.
Function can be defined as the specific
way that a structure has of either being a cause or being an effect, i.e. the
specific capacity to interact with the way other structures exist. The causal
relationship is established by the pre-determination of the functionality of
both structures that intervene in the transfer of energy by means of the action
of force. A structure is functional in the sense that it is capable of
generating energy as well as of receiving energy. The force belongs to the
functionality of the structure’s cause as well as to the functionality of the structure’s effect. Without the
functionality of both structures there can no be transfer of energy. If
emission and reception of energy does not exist in a given time, the causal
relationship does not take place. A causal relationship needs at least of a
structure that functions as cause and of a structure that functions as effect.
If this does not happen, the functionality will be only potential. The degree
of functionality of a structure depends on the efficiency in the use of energy,
and a structure will have better possibility of surviving if it is more
functional. Functionality is imperfect in most causal relationships that are
more complex.
The causal relationship is deterministic
and works in the same way in all the situations where the conditions are the
same. The base for the existence of the natural laws is precisely the fact that
all beings or things of the universe are simultaneously structures and forces.
The specific function or the way of a particular behavior of a structure is the
basis for the existence of a certain natural law.
The
stability of a structure depends not only on the stability of its structural
components, i.e., its substructures, but mainly on the balance and inner
harmony and the environment. The
degree of equilibrium is inversely related to the complexity of the structure.
The change that is always present is, on the one hand, the natural effect of
both the inherent instability and imbalance and means distructuration. But on
the other hand, change is the effect of the structuring capacity through
aggregation and structural interaction, and means structuration, and evolution.
Thus, to the natural and inevitable disintegration of all structures, it
opposes the tendency of a progressive structuration and evolution.
The things of the universe are
structures that are hierarchically ordained in scales according to space and
complexity. From the fundamental particles and up to include the totality of
the universe, any structure is a substructure of some structure and contains in
turn substructures. Thus the things of the universe are organizations of many
scales of very diverse sizes, some being contained inside others, so that every
scale is successively enclosing the lower scales. So we can understand that every
structure, exempting the fundamental particles, is constituted by substructures
as its discrete (or digital) units, while the structure itself is the analog
scheme for them, determining their individual conduct by means of statistics.
If a number of structures within the same scale form part of a viable and
subsistent structure, the new constituted structure is functional.
The
substructures of the immediately lower scale are the discrete units of a
structure, and are in turn structures since they are equally composed by
discrete units in a lower scale. A
structure is composed by the discrete units of the immediately lower scale, and
these are composed by the discrete units of the scale successively lower, down
the way that reaches the fundamental units, supposedly the substructures of the
absolutely lowest scale. These relate and organize the fundamental particles.
The structure of the highest possible scale is the same universe, since it is
the only existing structure that contains the totality of structures. The
structures are ordered in progressive and hierarchic modes according to the
dimension or complexity of the scales. A structure is greater that its
substructures, since it contains them. Also, a structure is more complex than
its substructures, since, besides possessing the functions of its
substructures, it possesses its own functionality.
If one takes an evolutionary point of
view into account, two processes may be distinguished. The first one is the
functionality of the substructures, which allows for the existence of
structures of higher scales, and which they integrate. The second one is the
functionality of a structure that allows both its own subsistence and the
creation of an environment for its own substructures. These two reciprocal processes
make possible the explanation of evolution: on one hand, the functionality
allows the leap into a larger scale when two or more structures of a given
scale are related, giving rise to a structure of a larger scale; on the other,
the super-structural functionality makes the existence of structures possible
at lower scales. In a wider perspective, the environment of the universe allows
‘structuration’ in any scale, providing that the lower scales have already been
structured.
Two types of hierarchic orders may be
distinguished within the structure of the universe. First, from the spatial
(quantity) point of view, the structures, including human beings, can occupy a
determined place between the smallest structures of all, which are the
fundamental particles, and the largest structure of all, the universe itself.
Secondly, every structure occupies a place according to its degree of
functionality and complexity. In consequence, while the universe, as structure,
has been expanding, containing in itself an increasingly diversity of
structures, matter has become more complex in the course of time by structuring
things with more degrees of functionality.
The structures of all the possible
scales of the universe are basically constituted by fundamental particles, as
the bricks of a building. And buildings also have walls, roofs and floors. The
things of the universe are composed by finite sets of fundamental particles
combined in particular manner. The basic functionality of the fundamental
particles, characterized by the capacity to exert force, allows for the
particular structure’s own functionality, regardless of its scale. All the
forces known in the universe come from the fundamental particles, and a
function is nothing but that a particular combination of the basic forces.
The fact that all the structures of the
universe are composed by the same type of fundamental particles has threefold
significance. First, it is the foundation that grounds the unity of the whole
universe; the fundamental particles have the same behavior in the universe as a
whole, which allows for the discovery of the universal natural laws. Second,
the four fundamental forces that explain the functioning of all the things of
the universe come from the fundamental particles. Third, it is the foundation
what allows us to explain the mutability of things; things transform into other
things, because its components in the fundamental scale can interact some with
others and also generate structures of higher scales.
The fact that there is a structural
hierarchy of complexity indicates that an ever progressive order exists with
respect to the higher scale. In this manner, the structure of a quark is
composed by fundamental particles; that of a nucleon, by quarks; that of an
atomic nucleus, by nucleons; that of an atom, by nucleus and electrons; that of
a molecule, by atoms; that of an acid or salt, by molecules; and if we proceed
in the way of biology, that of a protein, by amino-acids; that of the cellular
organs, by proteins; that of a cell, by cellular organs; that of fabrics and
fluids, by cells; that of an organ, by fabrics and fluids; that of apparatus
and physiological systems, by organs; that of a living organism, by
physiological systems; that of a social group, by living individuals; that of a
biological species, by social groups; that of an ecosystem, by biological
species, and so on. If we consider the scale “living organism”, we can reach up
to the maximum known complexity, namely the human being.
Space-time
The following are basic propositions on
time and space. The dimension of these parameters is related to quantity, since
both can be measured and both can be used as measures. Both are the
measurements of the movement of matter, and through movement time relates to
space. Time is what takes a body to move at a certain speed in space. A clock,
which is an analog instrument that indicates us the time that is flowing, has
this capacity because its gears rotate at a constant speed, and the spaces
covered by every cog in every gear are similar. The regularity of this movement
is given by the pendulum, which is determined by the constant of gravity. Time
seems to flow at a constant rate. But its flow is determined by change which
varies according to energy. Water evaporates at a constant rate if heat input
remains constant.
The interaction of two bodies creates a
distance. Three bodies create a triangle found in a two-dimensional plane. Four
bodies interacting and not coincidental in the same plane generate four planes,
shaping a three-dimensional space. In the universe this particular space is
common to all its things that relate somehow to the mentioned bodies. Their
capacity to interact is possible because these causally related bodies belong
to a common present that corresponds to the same space-time relative to their
common origin in the big-bang. The speed of light is the maximum possible speed
in the interaction of two bodies. If the speed of light were infinite, time
would be null and void and the interaction between structures would be
instantaneous.
Since Einstein we know that absolute
time cannot exist in space. In the universe, things move in relation to an
observer from zero up to the speed of light. Space and time are universal
measurements for any movement, and both are framed by the speed of light as its
absolute reference. Since the magnitude of the maximum possible movement in the
universe has an absolute limit, namely the speed of the photon, Einstein
concluded that space and time are relative, i. e. both parameters are
correlative with regard to this movement with absolute value. He introduced the
concept “space-time” as two relative parameters that are related between them
and have the speed of light as their absolute reference.
At the far end of the scale, the minimal
distance between two particles, the smallest that can exist, is the number of
Planck. Consequently, time and space are not infinitely small, as it has been
generally supposed. Both parameters begin to exist starting from the mentioned
quantity. Neither infinitesimal time nor infinitesimal space is possible. In
the universe there is a lowest limit and a top limit for causality. The lowest
limit is the dimension of energy given by Planck’s constant, which determines
the lowest scale possible for the existence of the causal relationship. The top
limit for this relationship refers to the maximum speed that movement can have,
which is the speed of light.
What underlies all movement is change,
the origin of movement. Movement is the visible and measurable side of change.
Therefore, both time and space are the measures of the extension and the
duration of a process. In both cases time and space measure a cause in relation
to its effect. On the one hand, time measures how long it takes a cause to
affect something and how long a change takes as it happens. In this sense the
duration can last for a brief instant, or can last much more, according to the
rule of natural laws. On the other hand, space measures the distance between
the position of a cause and the position of its effect. When change is measured
through the causal relationship, time becomes irreversible, because there is
energy expense and energy regain, the ‘structuration’ of something, and the
generation of force. Time cannot be identified with becoming, as Heraclitus
assumed. Becoming is proper to movement. But movement is a particularity of
change. Change is behind time, since it refers to the complete thermodynamic
process where there is movement, but also transformation. A thing changes in a
way so typical that we can infer a universal law, which makes a causal
relationship be deterministic. Still, any single change possesses a fundamental
indetermination.
The previous reasoning shows that the
existence of time and space depends on the interaction of structures, which is
the basis of change. The following step is to show that neither time nor space
pre-exist things. Time and space do not exist prior to matter and energy, but
develop or express themselves in every interaction of material bodies. If
matter and energy manifest themselves in structure and force, neither time nor
space can exist independently, but their existences depend on the existence of
the complementarity structure-force. Time and space not only depend on
structure and force, but they are temporarily and naturally a posteriori. Time
is the rate at which energy is transferred between structures in the causal
relationship. Space is the place configured by the structures that interact,
now as the substructures of their causal relationship.
In the first instant, at the beginning
of time and when space was not even compressed into the infinitely small, only
primeval and infinite energy existed. From this first instant, in what has come
to be known as the “big bang,” when this primeval energy began to be
“condensed” into matter, and fundamental structures – mass and electric load –
that exert force starting at the quantum scale, the becoming of matter, the
development of time and the extension of space became possible. This development
and this extension were not then, nor are they now independent from the
conversion of energy into mass and electric load. The fundamental particles
responsible for these two properties are highly functional and generate their
own spatial fields of force within which they can interact causally.
The primeval energy, which contained the
codes of all the laws of nature, has given rise to the subsequent
‘structuration’ of matter from its first condensation into fundamental
particles and into intelligence, in an act of creation that does not have any
known conclusion. Just as the structure of matter shapes space (space is
inconceivable if not a part of a structure), the functionality of the
structures that transforms energy into force makes time possible (time is
generated by the causal relationship). So, just as structure generates space,
force generates time.
If force is defined in terms of the
alteration of the movement of matter in space-time, and matter is defined as
its ‘structuration’ according to the spatial coordinates, then force will have
to define time. In this equation force becomes free from space, since space is
annulled for being on both sides of this equation. Inversely, this means not
only that time depends on force, but that force develops time. We saw that
energy pre-exists force. The energy that comes from a cause is always future
time, is potentially existent. When it enters the spatial parameter, energy,
mediated by the complementarity structure-force, turns into force, and time
develops.
This idea is understandable if we think
that force, which carries specified or differentiated energy, is the necessary
inter-structural link between the cause and its effect; it is the meeting point
between the structure cause and the structure effect. In order for an effect to
happen it is necessary that its cause be mediated by a force if both the cause
and the effect are to be identified by functional structures. In the causal
relationship the cause generates a force that the effect consumes and, in this
action, both are modified somehow. The force generates the causal relationship
when the transfer of energy is actualized.
Since in any causal relationship a
temporary sequence takes place, the force is the instance that intervenes
between the “before” and the “after” of the event; it constitutes the “now” of
the event that irreversibly modifies the structure. In any change there is a
transfer of energy according to the first law of thermodynamic; any change is
irreversible, according to its second law. Therefore, we can underline that
force generates becoming and develop time.
An isolated event, a sole cause and
effect relationship, does not say us much about space-time. It just manages to
tell us that an event separates the before from the after in some place. The
space-time dimension is the set of the multiple particular events that are
successively related because they are being actualized at a certain time, which
is the present for a certain place in space. But this dimension cannot be
linear. Time is not independent from space. The succession of events is not
given only in a spatial point. It includes an interdependent fabric of
different and infinite events whose correlation is a matter of the position in
space not just of the observer, who is a particular reference, but of the big
bang, which is the absolute reference of the whole universe. The universe is
the array of the causal interrelationships that originated in the big bang. And
because of this common origin, the universe has unity and its natural laws are
fulfilled for all time and place.
I have tried to show that space is
related to structure, and time is related to force. The universe is not the
space-time field where forces and structures play, but the game itself is the
space-time developed by the interaction structure-force. If the primeval origin
was infinite energy contained in a non-space, its evolution in the course of
time has followed the path of a constant and increasingly complex
‘structuration’, which has continuously gone develops space and consumes
energy.
Bibliography:
Patricio
Valdes-Marin, Geometry of Very High Velocities. http://www.metrocosmos.blogspot.com/.