To the God of the universe
Index
Extract
Introduction
Chapter 1
- Space and time is one unit
Chapter 2
2.1. Aristotle
2.2 The Scientific Revolution
2.3 Isaac Newton
2.4 Immanuel Kant
2.5 Gottfried Leibniz
2.5 Einstein space and time
Extract
Relative means connection, relation; absolute means
the opposite idea: pure, without connection, without relation. Space and time are
relative concepts because they cannot be considered in separated form; they are
one unit; they are not independent one of other, therefore they are not
absolute concepts. All the events occur and the things stay simultaneously in a
concrete space and time, that is to say, in a specific place and moment.
Relativity studies the motion of the bodies in the space and time.
Introduction
“Imagination is more important than knowledge. For
knowledge is limited to all we now know and understand, while imagination
embraces the entire world, and all there ever will be to know and understand.”
Albert Einstein.
The unique being that can explain the big mysteries of
the universe is God because He created the universe. Human beings, even the
most advanced minds, only do speculations in the matter. However, sometimes,
God concedes man the key for the comprehension of some aspects of his creation.
For example, He allowed man to know a part of the atomic energy complexity,
which explains essential topics on the origin of life. Atom, space and time are
a part of the mysteries of creation. The big philosophers have studied that
triad of mysteries that shall be forever an essential theme. Notwithstanding of
its difficulty, I have considered to write some reflections about the
relativity of space and time, which are presented in the first chapter of this
work. The point of view of the principal philosophers, in widespread sense, along
the different periods of history is included in the second chapter.
Chapter 1
1. Space and time is
one unit
Today, when a person listen the word time its mind
automatically consider these three options: a) weather, b) past, present and
future and c) the traditional measures of time: seconds, minutes, hours, days,
weeks, months, years and centuries. But since the philosophical point of view the
word time has other connotation. Time is
one infinite dimension inextricably
united to space.
Time does not exist in fractioned form. You cannot cut
time like you cut bread or any other material thing. The measures of time are
invention of the human mind. Seconds, minutes, hours, days, weeks, months,
years and centuries are only creations of man; they really do not exist in
material form but in ideas. The earth motion is what determines the human
concept of time. The idea of time is linked and is a derivation of that motion.
For example, the true age of one people is the number of times that that person
has experienced the earth motion regarding the Sun. Past and future does not
exist. The unique reality is the present, here and now. Past is a simple
reminiscence, a memory of reality; future something that has not happened.
If you stay for a long time in a lonely island or in
the jungle without watch and calendar it is very likely that you lose the traditional
measures of time.
An isolated Eskimo of the North Pole or an Indian of
the Amazon region does not know our concepts of time. They do not realize our
idea of second, minute, hour or year. Nevertheless, they live the same time
that we live because they live the same earth motion than us. This mean that
time ---as infinite dimension --- exists independently of our conscience or
concepts. Time is a strong unavoidable force. Time is relative to the earth
motion and not to our conscience or concepts on time. The proof of this
assertion is that time exert its effects on our bodies and over nature. For
example, we cannot avoid being old; we cannot change the regular cycles of
nature.
We cannot touch, smell, feel, listen or taste time,
numbers or geometric figures. The measures of space and time are only concepts
created by our minds. The mathematics axioms are the most elaborated expressions
of the rationalist thought.
We perceive the regular changes of the physic reality
because they occur in a concrete space and time. Numbers and geometric figures are only
imaginary representations of the things.
Man thought, which is in permanent evolution, is what
change, but space and time is always the same infinite dimensions; they do not
change. The essence of time is always the same: the earth motion regarding the Sun.
But what is essence of things?
Essence is the characteristic that makes the
difference between one thing and other; essence is permanent, it is the quality
that stays in one thing despite of the change.
Each people have its own time and it encompasses past
(memories), present (current reality) and future (which has not happened). Time
of each people concludes when people die. In that moment its human time end.
But life and time, itself, are eternal.
Is time a mathematical dimension?
Time, in essence, is an infinite dimension, but man
has created measures for that infinitude. Time is an inextricable unit with
space. That unit between space and time is the same essence of mathematics,
because the unique number that really exists is one. The other numbers are
derivations of one. Two is two times one; nine is nine times one. Fractions are
also derivations of ones so that one is the unique number that really exists.
One, the concept of unit, represents the essence and
diversity of all the things that exist in nature and universe. All the things
are in essence one. One apple is different to one orange. But they have a
common characteristic: its essence that is one. Space and time also is only one
dimension. Space and time are the place and moment where occur all the events
of nature.
One, space, time and nature is an identity. In turn, one,
space, time and nature is only one: God.
So that:
One, space, time, nature = God
One = 1
Space= 1
Time = 1
Nature = 1
God = 1
Equation of the universe harmony
(O, S, T, N) f:
G
O = 1
S = Space
T = Time
N= Nature
G= God
This means that one, which is the essence of space, time
and Nature are mathematical function of God which is infinite and eternal and
embrace all the things that exists in the universe.
Human mind can conceive the concepts of infinitude and
eternity. To say the contrary is only a logic assertion that, nonetheless, is
not truth.
One, the unit, that is God, is the creative power of
universe, the primary energy.
One represents the rationalist thought because
mathematics is a development of reason. In turn, nature is the supreme
expression of practice, the supreme expression of empiricism because nature represents
the material world.
Rationalism and empiricism are opposed and
complementary conceptions; the synthesis of both represents the universe harmony.
The problem for humanity arises when one conception is
imposed and the other is discarded. For example, that is what is happening in
this moment in the European economy, where the rationalist economic conceptions
are affecting the population wellbeing.
Mathematics has a big prestige. People consider
mathematics an exact science. Therefore in man there is a strong trend toward
the application of the mathematical principles to the different aspects of
life. This is especially visible in the economic matter. But not always in
mathematics we can to find the big answers to the big questions of the life.
Chapter II
In this chapter it is presented the point of view of
the main philosophers on space and time; the texts included are in the public
domain, therefore they may be quoted. I have considered that might be useful
for the readers to find in one text like this the most important concepts of
those philosophers on the theme and therefore I have included the quotes in extensive
form.
The ancient thinkers settled the base of knowledge.
For example, concepts like atom were discovered by Democritus, a pre Socratic
wise. Parmenides pronounced for first time the famous phrase “I think, therefore
I exist”, concept attributed to Descartes centuries after. Anaximander taught
the existence of many worlds, idea expressed later by the scientists of the
Quantum Theory.
After of Socrates, considered the father of
philosophy, important philosophers formulated their opinions on the theme.
Plato, for example, told that time arose in the same moment that the heaven
arose and assured that time is measured through the luminaries’ motion.
2.1 Aristotle
He made the first deep and extensive explanation on space
and time. He thought that space and time were absolute. In his book Physics, book 4, part 10 he assures
that:
“Next for discussion after the subjects
mentioned is Time. The best plan will be to begin by working out the
difficulties connected with it, making use of the current arguments. First,
does it belong to the class of things that exist or to that of things that do
not exist? Then secondly, what is its nature? To start, then: the following
considerations would make one suspect that it either does not exist at all or
barely, and in an obscure way. One part of it has been and is not, while the
other is going to be and is not yet. Yet time-both infinite time and any time
you like to take-is made up of these. One would naturally suppose that what is
made up of things which do not exist could have no share in reality.
Further, if a divisible thing is to exist, it is
necessary that, when it exists, all or some of its parts must exist. But of
time some parts have been, while others have to be, and no part of it is though
it is divisible. For what is 'now' is not a part: a part is a measure of the
whole, which must be made up of parts. Time, on the other hand, is not held to
be made up of 'nows'.
Again, the 'now' which seems to bound the past
and the future-does it always remain one and the same or is it always other and
other? It is hard to say.
Again, the 'now' which seems to bound the past
and the future-does it always remain one and the same or is it always other and
other? It is hard to say.
Part 11
But neither does time exist without change; for
when the state of our own minds does not change at all, or we have not noticed
its changing, we do not realize that time has elapsed, any more than those who
are fabled to sleep among the heroes in Sardinia do when they are awakened; for
they connect the earlier 'now' with the later and make them one, cutting out
the interval because of their failure to notice it. So, just as, if the 'now'
were not different but one and the same, there would not have been time, so too
when its difference escapes our notice the interval does not seem to be time.
If, then, the non-realization of the existence of time happens to us when we do
not distinguish any change, but the soul seems to stay in one indivisible
state, and when we perceive and distinguish we say time has elapsed, evidently
time is not independent of movement and change. It is evident, then, that time
is neither movement nor independent of movement.
We must take this as our starting-point and try
to discover-since we wish to know what time is-what exactly it has to do with
movement.
Now we perceive movement and time together: for
even when it is dark and we are not being affected through the body, if any
movement takes place in the mind we at once suppose that some time also has
elapsed; and not only that but also, when some time is thought to have passed,
some movement also along with it seems to have taken place. Hence time is
either movement or something that belongs to movement. Since then it is not
movement, it must be the other.
But what is moved is moved from something to
something, and all magnitude is continuous. Therefore the movement goes with
the magnitude. Because the magnitude is continuous, the movement too must be
continuous, and if the movement, then the time; for the time that has passed is
always thought to be in proportion to the movement.
The distinction of 'before' and 'after' holds
primarily, then, in place; and there in virtue of relative position. Since then
'before' and 'after' hold in magnitude, they must hold also in movement, these
corresponding to those. But also in time the distinction of 'before' and
'after' must hold, for time and movement always correspond with each other. The
'before' and 'after' in motion is identical in substratum with motion yet
differs from it in definition, and is not identical with motion.
But we apprehend time only when we have marked
motion, marking it by 'before' and 'after'; and it is only when we have
perceived 'before' and 'after' in motion that we say that time has elapsed. Now
we mark them by judging that A and B are different, and that some third thing
is intermediate to them. When we think of the extremes as different from the
middle and the mind pronounces that the 'nows' are two, one before and one
after, it is then that we say that there is time, and this that we say is time.
For what is bounded by the 'now' is thought to be time-we may assume this.
When, therefore, we perceive the 'now' one, and
neither as before and after in a motion nor as an identity but in relation to a
'before' and an 'after', no time is thought to have elapsed, because there has
been no motion either. On the other hand, when we do perceive a 'before' and an
'after', then we say that there is time. For time is just this number of motion
in respect of 'before' and 'after'.
Hence time is not movement, but only movement in
so far as it admits of enumeration. A proof of this: we discriminate the more
or the less by number, but more or less movement by time. Time then is a kind
of number. (Number, we must note, is used in two senses-both of what is counted
or the countable and also of that with which we count. Time obviously is what
is counted, not that with which we count: there are different kinds of thing.
Just as motion is a perpetual succession, so also is time. But every
simultaneous time is self-identical; for the 'now' as a subject is an identity,
but it accepts different attributes. The 'now' measures time, in so far as time
involves the 'before and after.
The 'now' in one sense is the same, in another
it is not the same. In so far as it is in succession, it is different (which is
just what its being was supposed to mean), but its substratum is an identity:
for motion, as was said, goes with magnitude, and time, as we maintain, with
motion. Clearly, too, if there were no time, there would be no 'now', and vice
versa. just as the moving body and its locomotion involve each other mutually,
so too do the number of the moving body and the number of its locomotion. For
the number of the locomotion is time, while the 'now' corresponds to the moving
body, and is like the unit of number.
Time, then, also is both made continuous by the
'now' and divided at it. For here too there is a correspondence with the
locomotion and the moving body. For the motion or locomotion is made one by the
thing which is moved, because it is one-not because it is one in its own nature
(for there might be pauses in the movement of such a thing)-but because it is
one in definition: for this determines the movement as 'before' and 'after'.
Here, too there is a correspondence with the point; for the point also both
connects and terminates the length-it is the beginning of one and the end of
another. But when you take it in this way, using the one point as two, a pause
is necessary, if the same point is to be the beginning and the end. The 'now'
on the other hand, since the body carried is moving, is always different.
Hence time is not number in the sense in which
there is 'number' of the same point because it is beginning and end, but rather
as the extremities of a line form a number, and not as the parts of the line do
so, both for the reason given (for we can use the middle point as two, so that
on that analogy time might stand still), and further because obviously the
'now' is no part of time nor the section any part of the movement, any more
than the points are parts of the line-for it is two lines that are parts of one
line.
In so far then as the 'now' is a boundary, it is
not time, but an attribute of it; in so far as it numbers, it is number; for
boundaries belong only to that which they bound, but number (e.g. ten) is the
number of these horses, and belongs also elsewhere.
It is clear, then, that time is 'number of
movement in respect of the before and after', and is continuous since it is an
attribute of what is continuous.” End of the quotes.
2.2 The
Scientific Revolution
Between the centuries XVI and XVII humankind
experienced a deep transformation. The inflexibility concepts of the Middle Age
progressively were replaced by new scientific ideas and a moderate attitude
toward religion.
The most important work of that historic stage was the
book On the Revolutions of the Celestial
Spheres (1543) of Nicholas Copernicus (1473-1543), who provoked an unprecedented
change, assuring that earth was not the center of the universe like was the
common thought of the scientists and the Catholic Church. Galileo Galilei (1564-1642)
defended years later the ideas of Copernicus which was considered a heresy and
prohibited.
Galileo has been named also the father of science by
his important contributions to the scientific thought, among them, the first
ideas on the relativity of motion.
2.3 Isaac Newton
Isaac Newton (1642-1727) reviewed the scientific
knowledge accumulated in the previous centuries and proposed a set of ideas
that were accepted during 200 years, until the decades of the 20th
century. He pointed out that space and time are absolute concepts. In his book Mathematical Principles of the Natural
Philosophy, (1687) Isaac Newton says:
“Scholium
Hitherto I have laid down the definitions of such
words as are less known, and explained the sense in which I would have them to
be understood in the following discourse. I do not define time, space, place
and motion, as being well known to all. Only I must observe, that the vulgar
conceive those quantities under no other notions but from the relation they
bear to sensible objects. And thence arise certain prejudices, for the removing
of which, it will be convenient to distinguish them into absolute and relative,
true and apparent, mathematical and common.
1. Absolute, true, and mathematical time, of itself, and
from its own nature flows equably without regard to anything external, and by
another name is called duration: relative, apparent, and common time, is some
sensible and external (whether accurate or unequable) measure of duration by
the means of motion, which is commonly used instead of true time; such as an
hour, a day, a month, a year.
2. Absolute space,
in its own nature, without regard to anything external, remains always similar
and immovable. Relative space is some movable dimension or measure of the
absolute spaces; which our senses determine by its position to bodies; and
which is vulgarly taken for immovable space; such is the dimension of a
subterraneaneous, an æreal, or celestial space, determined by its position in
respect of the earth. Absolute and relative space, are the same in figure and
magnitude; but they do not remain always numerically the same. For if the
earth, for instance, moves, a space of our air, which relatively and in respect
of the earth remains always the same, will at one time be one part of the
absolute space into which the air passes; at another time it will be another
part of the same, and so, absolutely understood, it will be perpetually
mutable.
3. Place is a part of space which a body takes up, and is
according to the space, either absolute or relative. I say, a part of space;
not the situation nor the external surface of the body. For the places of equal
solids are always equal; but their superficies, by reason of their dissimilar
figures, are often unequal. Positions properly have no quantity, nor are they
so much the places themselves, as the properties of places. The motion of the
whole is the same thing with the sum of the motions of the parts; that is, the
translation of the whole, out of its place, is the same thing with the sum of
the translations of the parts out of their places; and therefore the place of
the whole is the same thing with the sum of the places of the parts, and for
that reason, it is internal, and in the whole body.
4. Absolute motion is the translation of a body from one
absolute place into another; and relative motion, the translation from one
relative place into another. Thus in a ship under sail, the relative place of a
body is that part of the ship which the body possesses; or that part of its
cavity which the body fills, and which therefore moves together with the ship:
and relative rest is the continuance of the body in the same part of the ship,
or of its cavity. But real, absolute rest, is the continuance of the body in
the same part of that immovable space, in which the ship itself, its cavity,
and all that it contains, is moved. Wherefore if the earth is really at rest,
the body, which relatively rests in the ship, will really and absolutely move
with the same velocity which the ship has on the earth. But if the earth also
moves, the true and absolute motion of the body will arise, partly from the
true motion of the earth, in immovable space; partly from the relative motion
of the ship on the earth; and if the body moves also relatively in the ship;
its true motion will arise, partly from the true motion of the earth, in
immovable space, and partly from the relative motions as well of the ship on
the earth, as of the body in the ship; and from these relative motions will
arise the relative motion of the body on the earth. As if that part of the
earth, where the ship is, was truly moved toward the east, with a velocity of
10010 parts; while the ship itself, with fresh gale, and full sails, is carried
towards the west, with a velocity expressed by 10 of those parts; but a sailor
walks in the ship towards the east, with 1 part of the said velocity; then the
sailor will be moved truly in immovable space towards the east, with a velocity
of 10001 parts, and relatively on the earth towards the west, with a velocity
of 9 of those parts.
Absolute time, in astronomy, is distinguished
from relative, by the equation or correlation of the vulgar time. For the
natural days are truly unequal, though they are commonly considered as equal
and used for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions. It may be, that there is no
such thing as an equable motion, whereby time may be accurately measured. All
motions may be accelerated and retarded, but the true, or equable, progress of
absolute time is liable to no change. The duration or perseverance of the
existence of things remains the same, whether the motions are swift or slow, or
none at all: and therefore, it ought to be distinguished from what are only
sensible measures thereof; and out of which we collect it, by means of the
astronomical equation. The necessity of which equation for determining the
times of a phenomenon, is evinced as well from the experiments of
the pendulum clock, as by eclipses of the satellites of Jupiter.
As the order of the parts of time is immutable,
so also is the order of the parts of space. Suppose those parts to be moved out
of their places, and they will be moved (if the expression may be allowed) out
of themselves. For times and spaces are, as it were, the places as well of
themselves as of all other things. All things are placed in time as to order of
succession; and in space as to order of situation. It is from their essence or
nature that they are places; and that the primary places of things should be
moveable, is absurd. These are therefore the absolute places; and translations
out of those places, are the only absolute motions.
But because the parts of space cannot be seen,
or distinguished from one another by our senses, therefore in their stead we
use sensible measures of them. For from the positions and distances of things
from any body considered as immovable, we define all places; and then with
respect to such places, we estimate all motions, considering bodies as
transferred from some of those places into others. And so, instead of absolute
places and motions, we use relative ones; and that without any inconvenience in
common affairs; but in philosophical disquisitions, we ought to abstract from
our senses, and consider things themselves, distinct from what are only
sensible measures of them. For it may be that there is no body really at rest,
to which the places and motions of others may be referred.” End of the quotes.
2.4 Immanuel Kant
Immanuel Kant (1724-1804) says that space and
time are creations of the man mind. In his book Critique of the Pure Reason, section I on The Transcendental
Aesthetic, he says the following:
Space, Metaphysical Exposition of this Concept
By means of outer sense, a property of our
mind, we represent to ourselves objects as outside us, and all without
exception in space. In space their shape, magnitude, and relation to one
another are determined or determinable.
What, then, are space and time? Are they real
existences? Are they only determinations or relations of things, yet such as
would belong to things even if they were not intuited?
Or is space and time such that they belong
only to the form of intuition, and therefore to the subjective constitution of
our mind, apart from which they could not be ascribed to anything whatsoever?
In order to obtain light upon these questions, let us first give an exposition
of the concept of space.
1.
Space is not an empirical concept, which has been derived from outer
experiences.
2.
Space is a necessary a priori
representation, which underlies all outer intuitions. We can never represent to
ourselves the absence of space, though we can quite well think it as empty of
objects. It must therefore be regarded as the condition of the possibility of
appearances, and not as a determination dependent upon them. It is an a
priori representation, which necessarily underlies outer appearances.
3.
Space is not a discursive or, as we say, general concept of relations of
things in general, but a pure intuition. For, in the first place, we can
represent to ourselves only one space; and if we speak of diverse spaces, we
mean thereby only parts of one and the same unique space. Space is essentially one;
the manifold in it, and therefore the general concept of spaces, depends solely
on [the introduction of] limitations. Hence it follows that an a priori,
and not an empirical, intuition underlies all concepts of space. For kindred
reasons, geometrical propositions, that, for instance, in a triangle two sides
together are greater than the third, can never be derived from the general
concepts of line and triangle, but only from intuition, and this indeed a
priori, with apodictic certainty.
4.
Space is represented as an infinite given magnitude. Space is
represented as an infinite given magnitude.
A general concept of space, which is found
alike in a foot and in an ell, cannot determine anything in regard to
magnitude.
If there were no limitlessness in the
progression of intuition, no concept of relations could yield a principle of
their infinitude.
The Transcendental Exposition of the Concept
of Space
I understand by a transcendental exposition the
explanation of a concept, as a principle from which the possibility of other a
priori synthetic knowledge can be understood.
For this purpose it is required (1) that such
knowledge does really flow from the given concept, (2) that this knowledge is
possible only on the assumption of a given mode of explaining the concept.
Geometry is a science which determines the
properties of space synthetically, and yet a priori. What, then, must be
our representation of space, in order that such knowledge of it may be
possible? It must in its origin be intuition; for from a mere concept no
propositions can be obtained which go beyond the concept -- as happens in
geometry (Introduction, V). Further, this intuition must be a priori,
that is, it must be found in us prior to any perception of an object, and must
therefore be pure, not empirical, intuition. For geometrical propositions are
one and all apodictic, that is, are bound up with the consciousness of their
necessity; for instance, that space has only three dimensions. Such
propositions cannot be empirical or, in other words, judgments of experience,
nor can they be derived from any such judgments (Introduction, II).
How, then, can there exist in the mind an
outer intuition which precedes the objects themselves, and in which the concept
of these objects can be determined a priori?
Manifestly, not otherwise than in so far as
the intuition has its seat in the subject only, as the formal character of the
subject, in virtue of which, in being affected by objects, it obtains immediate
representation, that is, intuition, of them; and only in so far,
therefore, as it is merely the form of outer sense in general.
Our explanation is thus the only explanation
that makes intelligible the possibility of geometry, as a body of a
priori synthetic knowledge. Any mode of explanation which fails to do this,
although it may otherwise seem to be somewhat similar, can by this criterion be
distinguished from it with the greatest certainty.
Conclusions from the above Concepts
(a) Space does not represent any property of
things in themselves, nor does it represent them in their relation to one
another. That is to say, space does not represent any determination that
attaches to the objects themselves, and which remains even when abstraction has
been made of all the subjective conditions of intuition. For no determinations,
whether absolute or relative, can be intuited prior to the existence of the
things to which they belong, and none, therefore, can be intuited a priori.
(b) Space is nothing but the form of all
appearances of outer sense. It is the subjective condition of sensibility,
under which alone outer intuition is possible for us. Since then, the
receptivity of the subject, its capacity to be affected by objects, must
necessarily precede all intuitions of these objects, it can readily be
understood how the form of all appearances can be given prior to all actual
perceptions, and so exist in the mind a priori, and how, as a pure
intuition, in which all objects must be determined, it can contain, prior to
all experience, principles which determine the relations of these objects.
It is, therefore, solely from the human
standpoint that we can speak of space, of extended things, etc.
Transcendental Aesthetic
Section II, Time
Metaphysical exposition of the Concept of Time
1. Time is not an empirical concept that has
been derived from any experience. For neither coexistence nor succession would
ever come within our perception, if the representation of time were not
presupposed as underlying them a priori. Only on the presupposition of
time can we represent to ourselves a number of things as existing at one and
the same time (simultaneously) or at different times (successively).
They are connected with the appearances only
as effects accidentally added by the particular constitution of the sense
organs. Accordingly, they are not a priori representations, but are
grounded in sensation, and, indeed, in the case of taste, even upon feeling
(pleasure and pain), as an effect of sensation. Further, no one can have a
priori a representation of a color or of any taste; whereas, since space
concerns only the pure form of intuition, and therefore involves no sensation
whatsoever, and nothing empirical, all kinds and determinations of space can
and must be represented a priori, if concepts of figures and of their
relations are to arise. Through space alone is it possible that things should
be outer objects to us.
2. Time is a necessary representation that
underlies all intuitions. We cannot, in respect of appearances in general, remove
time itself, though we can quite well think time as void of appearances. Time
is, therefore, given a priori. In it alone is actuality of appearances
possible at all. Appearances may, one and all, vanish; but time (as the
universal condition of their possibility) cannot itself be removed.
3. The possibility of apodictic principles
concerning the relations of time, or of axioms of time in general is also grounded
upon this a priori necessity. Time has only one dimension; different
times are not simultaneous but successive (just as different spaces are not
successive but simultaneous).
These principles cannot be derived from
experience, for experience would give neither strict universality nor apodictic
certainty.
Time is not a discursive, or what is called a
general concept, but a pure form of sensible intuition. Different times are but
parts of one and the same time; and the representation that can be given only
through a single object is intuition.
5. The infinitude of time signifies nothing
more than that every determinate magnitude of time is possible only through limitations
of one single time that underlies it. The original representation, time,
must therefore be given as unlimited.
Conclusions from these Concepts
(a) Time is not something that exists of
itself, or which inheres in things as an objective determination, and it does not,
therefore, remain when abstraction is made of all subjective conditions of its
intuition.
(b) Time is nothing but the form of inner sense,
that is, of the intuition of ourselves and of our inner state. It cannot be a determination
of outer appearances; it has to do neither with shape nor position, but with
the relation of representations in our inner state.
c) Time is the formal a priori
condition of all appearances whatsoever. Space, as the pure form of all outer
intuition, is so far limited; it serves as the a priori condition only
of outer appearances. But since all representations, whether they have for
their objects outer things or not, belong, in themselves, as determinations of
the mind, to our inner state; and since this inner state stands under the formal
condition of inner intuition, and so belongs to time, time is an a priori
condition of all appearance whatsoever.
Time is therefore a purely subjective
condition of our (human) intuition (which is always sensible, that is, so far
as we are affected by objects), and in itself, apart from the subject, is
nothing.” End of the quotes.
2.5 Gottfried
Leibniz
This German thinker made an important
contribution to the comprehension of the concepts of space and time. He taught
that matter is integrated by an essential component that he called monads.
Monads have a program that determines its behavior during its existence.
Therefore casualty and causality do not exist. All the processes of matter are
part of a perfect program that works in space and time.
2.6 Einstein
space and time
Albert Einstein (1879-1955) assures that space
and time are relative concepts. In his book Relativity, 1954 he said:
Relativity and the problem
of space
It is characteristic of
Newtonian physics that it has to ascribe independent and real existence to
space and time as well as to matter, for in Newton's law of motion the idea of
acceleration appears. But in this theory, acceleration can only denote
"acceleration with respect to space". Newton's space must thus be
thought of as "at rest", or at least as "unaccelerated", in
order that one can consider the acceleration, which appears in the law of
motion, as being a magnitude with any meaning. Much the same holds with time,
which of course likewise enters into the concept of acceleration.
Newton himself and his most
critical contemporaries felt it to be disturbing that one had to ascribe
physical reality both to space itself as well as to its state of motion; but
there was at that time no other alternative, if one wished to ascribe to
mechanics a clear meaning.
It is indeed an exacting
requirement to have to ascribe physical reality to space in general, and
especially to empty space. Time and again since remotest times philosophers
have resisted such a presumption. Descartes
argued somewhat on these lines: space is identical with extension, but
extension is connected with bodies; thus there is no space without bodies and hence
no empty space. The weakness of this argument lies primarily in what follows.
It is certainly true that the concept extension owes its origin to our
experiences of lying out or bringing into contact solid bodies. But from this
it cannot be concluded that the concept of extension may not be justified in
cases which have not themselves given rise to the formation of this concept.
Such an enlargement of concepts can be justified indirectly by its value for
the comprehension of empirical results.
The assertion that
extension is confined to bodies is therefore of itself certainly unfounded. We
shall see later, however, that the general theory of relativity confirms Descartes'
conception in a roundabout way.
What brought Descartes to
his remarkably attractive view was certainly the feeling that, without
compelling necessity, one ought not to ascribe reality to a thing like space,
which is not capable of being "directly experienced".
The psychological origin of
the idea of space, or of the necessity for it, is far from being so obvious as
it may appear to be on the basis of our customary habit of thought. The old
geometers deal with conceptual objects (straight line, point, surface), but not
really with space as such, as was done later in analytical geometry. The idea
of space, however, is suggested by certain primitive experiences. Suppose that
a box has been constructed.
The
concept of space as something existing objectively and independent of things
belongs to pre-scientific thought, but not so the idea of the existence of an
infinite number of spaces in motion relatively to each other.
This
latter idea is indeed logically unavoidable, but is far from having played a
considerable role even in scientific thought.
But
what about the psychological origin of the concept of time? This concept is
undoubtedly associated with the fact of "calling to mind", as well as
with the differentiation between sense experiences and the recollection of
these. Of itself it is doubtful whether the differentiation between sense experience
and recollection (or simple re-presentation) is something psychologically
directly given to us. Everyone has experienced that he has been in doubt
whether he has actually experienced something with his senses or has simply
dreamt about it. Probably the ability to discriminate between these
alternatives first comes about as the result of an activity of the mind
creating order.
In the previous paragraphs
we have attempted to describe how the concepts space, time and event can be put
psychologically into relation with experiences. Considered logically, they are
free creations of the human intelligence, tools of thought, which are to serve
the purpose of bringing experiences into relation with each other, so that in
this way they can be better surveyed.
Science has taken over from
pre-scientific thought the concepts space, time, and material object (with the
important special case "solid body") and has modified them and
rendered them more precise. Its first significant accomplishment was the development
of Euclidean geometry, whose axiomatic formulation must not be allowed to blind
us to its empirical origin (the possibilities of laying out or juxtaposing
solid bodies). In particular, the three-dimensional nature of space as well as
its Euclidean character is of empirical origin (it can be wholly filled by like
constituted "cubes").
The subtlety of the concept
of space was enhanced by the discovery that there exist no completely rigid
bodies.
All bodies are elastically
deformable and alter in volume with change in temperature. The structures,
whose possible congruence’s are to be described by Euclidean geometry, cannot
therefore be represented apart from physical concepts. But since physics after
all must make use of geometry in the establishment of its concepts, the
empirical content of geometry can be stated and tested only in the framework of
the whole of physics.
In this connection atomistic
must also be borne in mind, and its conception of finite divisibility; for
spaces of sub-atomic extension cannot be measured up.
Atomistic also compels us
to give up, in principle, the idea of sharply and statically defined bounding
surfaces of solid bodies. Strictly speaking, there are no precise laws, even in
the macro-region, for the possible configurations of solid bodies touching each
other.
In spite of this, no one
thought of giving up the concept of space, for it appeared indispensable in the
eminently satisfactory whole system of natural science.
Mach, in the nineteenth
century, was the only one who thought seriously of an elimination of the
concept of space, in that he sought to replace it by the notion of the totality
of the instantaneous distances between all material points. (He made this
attempt in order to arrive at a satisfactory understanding of inertia).
The
Field
In Newtonian mechanics, space
and time play a dual role. First, they play the part of carrier or frame for
things that happen in physics, in reference to which events are described by
the space co-ordinates and the time. In principle, matter is thought of as
consisting of "material points", the motions of which constitute
physical happening. When matter is thought of as being continuous, this is done
as it were provisionally in those cases where one does not wish to or cannot
describe the discrete structure. In this case small parts (elements of volume)
of the matter are treated similarly to material points, at least in so far as
we are concerned merely with motions and not with occurrences which, at the
moment, it is not possible or serves no useful purpose to attribute to motions
(e.g. temperature changes, chemical processes).
The second role of space and time was that of
being an "inertial system". From all conceivable systems of
reference, inertial systems were considered to be advantageous in that, with
respect to them, the law of inertia claimed validity.
In this, the essential thing is that
"physical reality", thought of as being independent of the subjects
experiencing it, was conceived as consisting, at least in principle, of space
and time on one hand, and of permanently existing material points, moving with
respect to space and time, on the other. The idea of the independent existence
of space and time can be expressed drastically in this way: If matter were to
disappear, space and time alone would remain behind (as a kind of stage for
physical happening).
What is the position of the special theory of
relativity in regard to the problem of space? In the first place we must guard
against the opinion that the four-dimensionality of reality has been newly
introduced for the first time by this theory. Even in classical physics the
event is localized by four numbers, three spatial co-ordinates and a time
co-ordinate; the totality of physical "events" is thus thought of as
being embedded in a four-dimensional continuous manifold. But on the basis of
classical mechanics this four-dimensional continuum breaks up objectively into
the one-dimensional time and into three-dimensional spatial sections, only the
latter of which contain simultaneous events. This resolution is the same for
all inertial systems. The simultaneity of two definite events with reference to
one inertial system involves the simultaneity of these events in reference to
all inertial systems. This is what is meant when we say that the time of
classical mechanics is absolute. According to the special theory of relativity
it is otherwise.”
And regarding time Einstein
assure:
“Since there exists in this
four-dimensional structure [space-time] no longer any sections that represent
"now" objectively, the concepts of happening and becoming are indeed
not completely suspended, but yet complicated. It appears therefore more
natural to think of physical reality as a four dimensional existence, instead
of, as hitherto, the evolution of a three dimensional existence.” End of the
quotes.
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