On the nature of time
Where does the universe come from? What is the universe made up? And what are space and time?
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| Israel Pérez (1976-) |
For our purposes, we can classify matter in at least two manifestations as it was conservatively realized in the XIX century. There exists ponderable matter, which comprehends all solids, fluids, plasmas and particles (From the perspective of physics this matter corresponds to the set of particles of the standard model); and imponderable matter which is that one that James C. Maxwell discussed in his works. We understand imponderable matter as that primordial matter that constitute a continuum and is the progenitor of ponderable matter and, among other things to be investigated, serves to propagate the interactions (force fields). Some call it the aether, spirit, space; others quantum foam; others the metacontinuum; modern physics call it the quantum vacuum (though currently it is not seen as something material), background, the Higgs field, etc. Here the name is irrelevant, what is important of this is the notion that there is a subtle continuous material entity that makes up the universe.
Moreover,
I support the idea that something cannot be created out of nothingness;
understanding nothingness as the absence of any kind of M. From this
affirmation it follows that it is useless to inquire whether the
universe was created or whether it will vanish. For in such a case, I
would have to ask the cause of the creation or the whereabouts of the
creator falling into an infinite regression. And also I would have to
ask what happen with the M after it has vanished; for it is not possible
for me to conceive that after such event only empty space and time
remained. I believe that it is absurd to think that space exists only as
a container of M without thinking that space itself is made up of some
kind of M. And also for time, time would have no meaning if matter were
not constantly changing. By this I champion Aristotle’s view wherein is
stated that motion precedes time; the cause that we believe in a flow of
time is motion or change of matter. The change of matter relative to
matter itself makes us feel that something that we have called time
flows. We perceive different events (visual, auditive, etc.) and thanks
to our material memory we feel a flow of time because we compare a
current event with a previous one.
Similarly,
our notion of Newtonian space arises in relation to material objects.
For instance, if I remove say an apple from a table, my brain
immediately tells me that moments ago there was something there filling
certain volume and occupying some place or position, because in relation
to the other objects in the room, which still remain in the same
position, there is something missing. Hence, I think that space remains
there but the object not. Now, if we further imagine that we remove all
objects in the room, then even the room, the earth, the stars, galaxies
and so on, all things in the universe, we are left only with space and
time (or nothing if you wish), but how can space (or nothingness) exists
if is not made up of something? How can time flow if nothing changes?
Some
others may argue that motion is referred to space and time. Yes, but
how do we measure space and time? The way we measure time is by motion
or change of matter, and the way we measure space is in relation to
material objects. An electronic clock (or any other kind) is an
instrument that is continually changing; each second is a completion of a
process that is taking place inside the “machinery” whose parts are
made up of matter in motion, if there were no changes in the clock a
process would not be completed and a second in the clock would not be
displayed. Does this imply that time does not flow? Certainly, time
still flows because time is the intrinsic motion and change of the
universe, motion and change can never stop. And a ruler is a material
object we use to compare and delimit a particular length; without
matter, space would be meaningless too, for there would be nothing to
relate the motion. For such reason, space itself should be a material
continuum even if there were no ponderable objects to refer.
Since
nothing can be created out of nothingness, it cannot be empty spaces
where there exists nothing, which implies that the universe and space
are made up of continuous M. Hence, there is no room for material
discontinuity, total emptiness is inconceivable to me. A volume can be
deprived of ponderable matter but not from imponderable matter. Thus,
from here we must also conclude that imponderable matter must constitute
a continuous medium in conjunction with ponderable matter. And also for
the description of physical phenomena imponderable matter might be seen
as an absolute physical reference frame because matter evolves relative
to matter; physicists know that what I have stated may imply the
abandonment of the philosophy of the general relativity though this does
not necessarily force us to give up the covariance of the physical
laws. What I have said simply implies that we are living immersed in a
dynamical material space. To even further support my notion about space
let us consider the following paradox of place as put forward by
Aristotle:
If everything that exists has a place, place too will have a place, and so on ad
infinitum.
The
premise in which the Aristotle’s statement is founded is the assumption
that space exits, but nevertheless, it is implicit that space is not
made up of anything, which is contradictory. For this reason one arrives
at the fallacy that everything that exists, including place, must have
or occupy a place. Now recall that for ancient thinkers, matter meant:
space occupied. Hence the paradox is resolved when one acknowledges that
space is made up of matter, and therefore space cannot have or occupy
space ad infinitum.
I
also hold the position that ideal objects are part of the universe. Of
this kind are mathematics and any other hallucination, dream or idea
created by my own being; because reasoning is the product of the dynamics
of the universe. And although what I think dissipates energy, this does
not entail that what I am thinking ’exists’ or ’is’ in the real (or
measurable) universe. Only the laws of logic as well as the laws of
experience will dictate whether the interpretations that I have
constructed to describe the universe are univocal to it. And again, for
this reason, if space is some physical entity, and therefore exists, it
must be made up of something, otherwise it is an element created by my
imagination with no physical constitution. Of that nature is topology or
Euclidean geometry which epitomizes the Newtonian background of space.
There is neither temporal beginning nor temporal end of the universe
I
think that the universe is, exists, has always been and will exist
indefinitely and infinitely, the universe will never become into
nothingness. I retain the opinion that there was no moment of creation
and it will not be an end. For thinking of the occurrence of these
events simply implies a change from a particular state to a distinct
one, a simple transition. In a similar way to the points of a
circumference in which any arbitrarily chosen point can be the beginning
of the circumference, in the same way occurs with the universe, the
beginning or end is mere convention to delimit two major events. Even
more, each moment can be the beginning or end of a series of events;
this is what is called evolution, where causality is implicit. Hence,
the problem to be resolved is the principle of causality, which demands
an initial cause (initial conditions in mathematical terms) and, at the
same time, leads us to an infinite regression, for we must ask the cause
of the Big Bang (if we believe in this model) and so on and so forth.
Therefore, we should accept that inside the notion of time the dynamics
of the universe is involved, time is the word we use to denote the
changes that the universe suffers and is also the word used to determine
the movements of bodies, its other name is not precisely duration but
rather mutation, material change. Both time and the principle of
causality constitute our second great problem to be studied. Since
material change is the source of the notion of time the big question to
be answered is not merely “what is time?” but rather, “what is
change?”, “why things
change?”. I think that once one has recognized that the universe ’is’ or
’exists’, one must ask: why does the universe evolve on its own? What
motor propels the universe? Was there really an initial cause that
started the motion of the universe?
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The Measure of Time
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| Henri Poincaré (1854-1912) |
By Henri Poincaré, translated by George Bruce
Halsted
In French: Poincaré, Henri
(1898), “La mesure du temps”, Revue de métaphysique et de morale 6: 1-13
English translation: Poincaré, Henri
(1907), “The Measure of Time”, The value of science, New York: Science Press,
pp. 26-36
So long as we do not go outside
the domain of consciousness, the notion of time is relatively clear. Not only
do we distinguish without difficulty present sensation from the remembrance of
past sensations or the anticipation of future sensations, but we know perfectly
well what we mean when we say that, of two conscious phenomena which we
remember, one was anterior to the other; or that, of two foreseen conscious
phenomena, one will be anterior to the other.
When we say that two conscious
facts are simultaneous, we mean that they profoundly interpenetrate, so that
analysis can not separate them without mutilating them.
The order in which we arrange
conscious phenomena does not admit of any arbitrariness. It is imposed upon us
and of it we can change nothing.
I have only a single observation
to add. For an aggregate of sensations to have become a remembrance capable of
classification in time, it must have ceased to be actual, we must have lost the
sense of its infinite complexity, otherwise it would have remained present. It
must, so to speak, have crystallized around a center of associations of ideas
which will be a sort of label. It is only when they thus have lost all life
that we can classify our memories in time as a botanist arranges dried flowers
in his herbarium.
But these labels can only be
finite in number. On that score, psychologic time should be discontinuous.
Whence comes the feeling that between any two instants there are others? We
arrange our recollections in time, but we know that there remain empty
compartments. How could that be, if time were not a form preexistent in our
mind? How could we know there were empty compartments, if these compartments
were revealed to us only by their content?
But that is not all; into this
form we wish to put not only the phenomena of our own [27] consciousness, but
those of which other consciousnesses are the theater. But more, we wish to put
there physical facts, these I know not what with which we people space and
which no consciousness sees directly. This is necessary because without it science
could not exist. In a word, psychologic time is given to us and must needs
create scientific and physical time. There the difficulty begins, or rather the
difficulties, for there are two.
Think of two consciousnesses,
which are like two worlds impenetrable one to the other. By what do we strive
to put them into the same mold, to measure them by the same standard? Is it not
as if one strove to measure length with a gram or weight with a meter? And
besides, why do we speak of measuring? We know perhaps that some fact is
anterior to some other, but not by how much it is anterior.
Therefore two difficulties: (1)
Can we transform psychologic time, which is qualitative, into a quantitative
time? (2) Can we reduce to one and the same measure facts which transpire in
different worlds?
The first difficulty has long
been noticed; it has been the subject of long discussions and one may say the
question is settled. We have not a direct intuition of the equality of two
intervals of time. The persons who believe they possess this intuition
are dupes of an illusion. When I say, from noon to one the same time passes as
from two to three, what meaning has this affirmation?
The least reflection shows that
by itself it has none at all. It will only have that which I choose to give it,
by a definition which will certainly possess a certain degree of arbitrariness.
Psychologists could have done without this definition; physicists and
astronomers could not; let us see how they have managed.
To measure time they use the
pendulum and they suppose by definition that all the beats of this pendulum are
of equal duration. But this is only a first approximation; the temperature, the
resistance of the air, the barometric pressure, make the pace of the pendulum
vary. If we could escape these sources of error, we should obtain a much closer
approximation, but it would still be only an approximation. New causes,
hitherto neglected, electric, magnetic or others, would introduce minute
perturbations.
In fact, the best chronometers
must be corrected from time to time, and the corrections are made by the aid of
astronomic observations; arrangements are made so that the sidereal clock marks
the same hour when the same star passes the meridian. In other words, it is
[28] the sidereal day, that is, the duration of the rotation of the earth,
which is the constant unit of time. It is supposed, by a new definition
substituted for that based on the beats of the pendulum, that two complete
rotations of the earth about its axis have the same duration.
However, the astronomers are
still not content with this definition. Many of them think that the tides act
as a check on our globe, and that the rotation of the earth is becoming slower
and slower. Thus would be explained the apparent acceleration of the motion of
the moon, which would seem to be going more rapidly than theory permits because
our watch, which is the earth, is going slow.
IV
All this is unimportant, one
will say; doubtless our instruments of measurement are imperfect, but it
suffices that we can conceive a perfect instrument. This ideal can not be
reached, but it is enough to have conceived it and so to have put rigor into
the definition of the unit of time.
The trouble is that there is no
rigor in the definition. When we use the pendulum to measure time, what
postulate do we implicitly admit? It is that the duration of two identical phenomena is
the same; or, if you prefer, that the same causes take the same
time to produce the same effects.
And at first blush, this is a
good definition of the equality of two durations. But take care. Is it
impossible that experiment may some day contradict our postulate?
Let me explain myself. I suppose
that at a certain place in the world the phenomenon α
happens, causing as consequence at the end of a certain time the effect α'. At
another place in the world very far away from the first, happens the phenomenon
β, which
causes as consequence the effect β'. The phenomena α and β are
simultaneous, as are also the effects α' and β'.
Later, the phenomenon α is
reproduced under approximately the same conditions as before, and simultaneously the
phenomenon β is also
reproduced at a very distant place in the world and almost under the same
circumstances. The effects α' and β' also
take place. Let us suppose that the effect α' happens perceptibly before the effect β'. If experience made us witness
such a sight, our postulate would be contradicted. For experience would tell us
that the first duration αα' is equal to the first duration ββ' and that the second duration αα' is
[29] less than the second duration β'. On the other hand, our postulate would
require that the two durations αα' should be equal to each other, as likewise the two durations ββ'. The
equality and the inequality deduced from experience would be incompatible with
the two equalities deduced from the postulate.
Now can we affirm that the
hypotheses I have just made are absurd? They are in no wise contrary to the
principle of contradiction. Doubt less they could not happen without the
principle of sufficient reason seeming violated. But to justify a definition so
fundamental I should prefer some other guarantee.
V
But that is not all. In physical
reality one cause does not pro duce a given effect, but a multitude of distinct
causes contribute to produce it, without our having any means of discriminating
the part of each of them.
Physicists seek to make this
distinction; but they make it only approximately, and, however they progress,
they never will make it except approximately. It is approximately true that the
motion of the pendulum is due solely to the earth's attraction; but in all
rigor every attraction, even of Sirius, acts on the pendulum.
Under these conditions, it is
clear that the causes which have produced a certain effect will never be
reproduced except approximately. Then we should modify our postulate and our
definition. Instead of saying : 'The same causes take the same time to
produce the same effects,' we should say : 'Causes almost identical take
almost the same time to produce almost the same effects.'
Our definition therefore is no
longer anything but approximate. Besides, as M. Calinon very justly remarks in
a recent memoir:('Etudes sur les diverses grandeurs', Paris, Gauthier-Villars,
1897.)
One of the circumstances of any
phenomenon is the velocity of the earth's rotation; if this velocity of
rotation varies, it constitutes in the reproduction of this phenomenon a
circumstance which no longer remains the same. But to suppose this velocity of
rotation constant is to suppose that we know how to measure time.
Our definition is therefore not
yet satisfactory; it is certainly not that which the astronomers of whom I
spoke above implicitly adopt, when they affirm that the terrestrial rotation is
slowing down.
What meaning according to them
has this affirmation? We can only understand it by analyzing the proofs they
give of their [30] proposition. They say first that the friction of the tides
producing heat must destroy vis viva. They invoke therefore the principle of
vis viva, or of the conservation of energy.
They say next that the secular
acceleration of the moon, calculated according to Newton's law, would be less
than that deduced from observations unless the correction relative to the
slowing down of the terrestrial rotation were made. They invoke therefore
Newton's law. In other words, they define duration in the following way : time
should be so defined that Newton's law and that of vis viva may be verified.
Newton's law is an experimental truth; as such it is only approximate, which
shows that we still have only a definition by approximation.
If now it be supposed that
another way of measuring time is adopted, the experiments on which Newton's law
is founded would none the less have the same meaning. Only the enunciation of
the law would be different, because it would be translated into another
language; it would evidently be much less simple. So that the definition
implicitly adopted by the astronomers may be summed up thus: Time should be so
defined that the equations of mechanics may be as simple as possible. In other
words, there is not one way of measuring time more true than another; that
which is generally adopted is only more convenient. Of two watches, we have no
right to say that the one goes true, the other wrong; we can only say that it
is advantageous to conform to the indications of the first.
The difficulty which has just occupied
us has been, as I have said, often pointed out; among the most recent works in
which it is considered, I may mention, besides M. Calinon's little book, the
treatise on mechanics of M. Andrade.
VI
The second difficulty has up to
the present attracted much less attention; yet it is altogether analogous to
the preceding; and even, logically, I should have spoken of it first.
Two psychological phenomena
happen in two different consciousnesses; when I say they are simultaneous, what
do I mean? When I say that a physical phenomenon, which happens outside of
every consciousness, is before or after a psychological phenomenon, what do I
mean?
In 1572, Tycho Brahe noticed in
the heavens a new star. An immense conflagration had happened in some far
distant heavenly body; but it had happened long before; at least two hundred
years were necessary for the light from that star to reach our earth. This [31]
conflagration therefore happened before the discovery of America. Well, when
considering this gigantic phenomenon, which perhaps had no witness, since the
satellites of that star were perhaps uninhabited, I say this phenomenon is
anterior to the formation of the visual image of the isle of Española in the
consciousness of Christopher Columbus, what do I mean?
A little reflection is
sufficient to understand that all these affirmations have by themselves no
meaning. They can have one only as the outcome of a convention.
VII
We should first ask ourselves
how one could have had the idea of putting into the same frame so many worlds
impenetrable to each other. We should like to represent to ourselves the
external universe, and only by so doing could we feel that we understood it. We
know we never can attain this representation: our weakness is too great. But at
least we desire the ability to conceive an infinite intelligence for which this
representation would be possible, a sort of great consciousness which should
see all, and which should classify all in its time, as we classify, in our time, the
little we see.
This hypothesis is indeed crude
and incomplete, because this supreme intelligence would be only a demigod;
infinite in one sense, it would be limited in another, since it would have only
an imperfect recollection of the past; and it could have no other, since
otherwise all recollections would be equally present to it and for it there
would be no time. And yet when we speak of time, for all which happens out side
of us, do we not unconsciously adopt this hypothesis; do we not put ourselves
in the place of this imperfect god; and do not even the atheists put themselves
in the place where god would be if he existed? What I have just said shows us,
perhaps, why we have tried to put all physical phenomena into the same frame.
But that can not pass for a definition of simultaneity, since this hypothetical
intelligence, even if it existed, would be for us impenetrable. It is therefore
necessary to seek something else.
VIII
The ordinary definitions which
are proper for psychologic time would suffice us no better. Two simultaneous
psychologic facts are so closely bound together that analysis can not separate
without mutilating them. Is it the same with two physical facts? Is not my
present nearer my past of yesterday than the present of Sirius?
It has also been said that two
facts should be regarded as simultaneous when the order of their succession may
be inverted at will. It is evident that this definition would not suit two
physical facts which happen far from one another, and that, in what concerns
them, we no longer even understand what this reversibility would be; besides,
succession itself must first be defined.
IX
Let us then seek to give an
account of what is understood by simultaneity or antecedence, and for this let
us analyze some examples. I write a letter; it is
afterward read by the friend to whom I have addressed it. There are two facts
which have had for their theater two different consciousnesses. In writing this
letter I have had the visual image of it, and my friend has had in his turn
this same visual image in reading the letter. Though these two facts happen in
impenetrable worlds, I do not hesitate to regard the first as anterior to the
second, because I believe it is its cause. I hear thunder, and I conclude
there has been an electric discharge; I do not hesitate to consider the
physical phenomenon as anterior to the auditory image perceived in my
consciousness, because I believe it is its cause.
Behold then the rule we follow,
and the only one we can follow: when a phenomenon appears to us as the cause of
another, we regard it as anterior. It is therefore by cause that we define
time; but most often, when two facts appear to us bound by a constant relation,
how do we recognize which is the cause and which the effect? We assume that the
anterior fact, the antecedent, is the cause of the other, of the consequent. It
is then by time that we define cause. How save our selves from this petitio
principii? We say now post hoc, ergo
propter hoc; now propter hoc, ergo post hoc; shall
we escape from this vicious circle?
X
Let us see, not how we succeed
in escaping, for we do not completely succeed, but how we try to escape. I execute a voluntary act A and
I feel afterward a sensation D, which I regard as a consequence of the act A;
on the other hand, for whatever reason, I infer that this consequence is not
immediate, but that outside my consciousness two facts B and C, which I have
not witnessed, have happened, and in such a way that B is the effect of A, that
C is the effect of B, and D of C.
But why? If I think I have
reason to regard the four facts A, B, C, D, as bound to one another by a causal
connection, why range them in the causal order A B C D, and at the same time in
the chronologic order A B C D, rather than in any other order?
I clearly see that in the act A
I have the feeling of having been active, while in undergoing the sensation D,
I have that of having been passive. This is why I regard A as the initial cause
and D as the ultimate effect; this is why I put A at the beginning of the chain
and D at the end; but why put B before C rather than C before B?
If this question is put, the
reply ordinarily is: we know that it is B which is the cause of C because we always see B
happen before C. These two phenomena, when witnessed, happen in a certain
order; when analogous phenomena happen without witness, there is no reason to
invert this order.
Doubtless, but take care; we
never know directly the physical phenomena B and C. What we know are sensations
B' and C' produced respectively by B and C. Our consciousness tells us
immediately that B' precedes C' and we suppose that B and C succeed one
another in the same order.
This rule appears in fact very
natural, and yet we are often led to depart from it. We hear the sound of the
thunder only some seconds after the electric discharge of the cloud. Of two
flashes of lightning, the one distant, the other near, can not the first be
anterior to the second, even though the sound of the second comes to us before
that of the first?
XI
Another difficulty; have we
really the right to speak of the cause of a phenomenon? If all the parts of the
universe are interchained in a certain measure, any one phenomenon will not be
the effect of a single cause, but the resultant of causes infinitely numerous;
it is, one often says, the consequence of the state of the universe a moment
before. How enunciate rules applicable to circumstances so complex? And yet it
is only thus that these rules can be general and rigorous.
Not
to lose ourselves in this
infinite complexity let us make a simpler hypothesis. Consider three
stars, for
example, the sun, Jupiter and Saturn; but, for greater simplicity,
regard them
as reduced to material points and isolated from the rest of the world.
The
positions and the velocities of three bodies at a given instant suffice
to
determine their positions and velocities at the following instant, and
consequently at any instant. Their positions at the instant t determine
their positions at the instant t + h as well as their positions at the
instant t
— h.
Even more; the position of
Jupiter at the instant t, together with that of Saturn at the instant t + a,
determines the position of Jupiter at any instant and that of Saturn at any
instant.
The aggregate of positions
occupied by Jupiter at the instant t + e and Saturn at the instant t + a + e is
bound to the aggregate of positions occupied by Jupiter at the instant t and
Saturn at the instant t + a, by laws as precise as that of Newton, though more
complicated. Then why not regard one of these aggregates as the cause of the
other, which would lead to considering as simultaneous the instant t of Jupiter
and the instant t + a of Saturn?
In answer there can only be
reasons, very strong, it is true, of convenience and simplicity.
XII
But let us pass to examples less
artificial; to understand the definition implicitly supposed by the savants,
let us watch them at work and look for the rules by which they investigate
simultaneity. I will take two simple examples,
the measurement of the velocity of light and the determination of longitude.
When an astronomer tells me that
some stellar phenomenon, which his telescope reveals to him at this moment,
happened nevertheless fifty years ago, I seek his meaning, and to that end I
shall ask him first how he knows it, that is, how he has measured the velocity
of light.
He has begun by supposing that
light has a constant velocity, and in particular that its velocity is the same
in all directions. That is a postulate without which no measurement of this
velocity could be attempted. This postulate could never be verified directly by
experiment; it might be contradicted by it if the results of different
measurements were not concordant. We should think ourselves fortunate that this
contradiction has not happened and that the slight discordances which may happen
can be readily explained.
The postulate, at all events,
resembling the principle of sufficient reason, has been accepted by everybody;
what I wish to emphasize is that it furnishes us with a new rule for the
investigation of simultaneity, entirely different from that which we have
enunciated above.
This postulate assumed, let us
see how the velocity of light has been measured. You know that Roemer used
eclipses of the satellites of r, and sought how much the event fell behind its
prediction. But how is this prediction made? It is by the aid of astronomic
laws, for instance Newton's law
Could not the observed facts be
just as well explained if we attributed to the velocity of light a little
different value from that adopted, and supposed Newton's law only approximate?
Only this would lead to replacing Newton's law by another more complicated. So
for the velocity of light a value is adopted, such that the astronomic laws
compatible with this value may be as simple as possible. When navigators or geographers
determine a longitude, they have to solve just the problem we are discussing;
they must, without being at Paris, calculate Paris time. How do they accomplish
it? They carry a chronometer set for Paris. The qualitative problem of
simultaneity is made to depend upon the quantitative problem of the measurement
of time. I need not take up the difficulties relative to this latter problem,
since above I have emphasized them at length.
Or else they observe an
astronomic phenomenon, such as an eclipse of the moon, and they suppose that
this phenomenon is perceived simultaneously from all points of the earth. That
is not altogether true, since the propagation of light is not instantaneous; if
absolute exactitude were desired, there would be a correction to make according
to a complicated rule.
Or else finally they use the
telegraph. It is clear first that the reception of the signal at Berlin, for
instance, is after the sending of this same signal from Paris. This is the rule
of cause and effect analyzed above. But how much after? In general, the
duration of the trans mission is neglected and the two events are regarded as
simultaneous. But, to be rigorous, a little correction would still have to be
made by a complicated calculation; in practise it is not made, because it would
be well within the errors of observation; its theoretic necessity is none the
less from our point of view, which is that of a rigorous definition. From this
discussion, I wish to emphasize two things: (1) The rules applied are exceedingly
various. (2) It is difficult to separate the qualitative problem of
simultaneity from the quantitative problem of the measurement of time; no
matter whether a chronometer is used, or whether account must be taken of a
velocity of transmission, as that of light, because such a velocity could not
be measured without measuring a time.
XIII
To conclude : We have not a
direct intuition of simultaneity, nor of the equality of two durations. If we
think we have this intuition, this [36] is an illusion. We replace it by the
aid of certain rules which we apply almost always without taking count of them.
But what is the nature of these
rules? No general rule, no rigorous rule; a multitude of little rules
applicable to each particular case.
These rules are not imposed upon
us and we might amuse ourselves in inventing others; but they could not be cast
aside without greatly complicating the enunciation of the laws of physics,
mechanics and astronomy.
We therefore choose these rules,
not because they are true, but be cause they are the most convenient, and we
may recapitulate them as follows : "The simultaneity of two events,
or the order of their succession, the equality of two durations, are to be so
defined that the enunciation of the natural laws may be as simple as possible.
In other words, all these rules, all these definitions are only the fruit of an
unconscious opportunism."
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The
Unreality of Time
 |
| John E. Mctaggart (1866-1925) |
by John Ellis McTaggart. The Unreality of Time. Published in Mind: A
Quarterly Review of Psychology and Philosophy 17 (1908): 456-473.
It doubtless seems highly paradoxical to
assert that Time is unreal, and that all statements which involve its reality
are erroneous. Such an assertion involves a far greater departure from the
natural position of mankind than is involved in the assertion of the unreality
of Space or of the unreality of Matter. So decisive a breach with that natural
position is not to be lightly accepted. And yet in all ages the belief in the
unreality of time has proved singularly attractive.
In the philosophy and religion of the
East we find that this doctrine is of cardinal importance. And in the West,
where philosophy and religion are less closely connected, we find that the same
doctrine continually recurs, both among philosophers and among theologians.
Theology never holds itself apart from mysticism for any long period, and
almost all mysticism denies the reality of time. In philosophy, again, time is
treated as unreal by Spinoza, by Kant, by Hegel, and by Schopenhauer. In the
philosophy of the present day the two most important movements (excluding those
which are as yet merely critical) are those which look to Hegel and to Mr.
Bradley. And both of these schools deny the reality of time. Such a concurrence
of opinion cannot be denied to be highly significant -- and is not the less
significant because the doctrine takes such different forms, and is supported
by such different arguments.
I believe that time is unreal. But I do
so for reasons which are not, I think, employed by any of the philosophers whom
I have mentioned, and I propose to explain my reasons in this paper.
Positions in time, as time appears to us prima
facie, are distinguished in two ways. Each position is Earlier than some, and
Later than some, of the other positions. And each position is either Past,
Present, or Future. The distinctions of the former class are permanent, while
those of the latter are not. If M is ever earlier than N, it is always earlier.
But an event, which is now present, was future and will be past.
Since distinctions of the first class are
permanent, they might be held to be more objective, and to be more essential to
the nature of time. I believe, however, that this would be a mistake, and that
the distinction of past, present and future is as essential to time as the
distinction of earlier and later, while in a certain sense, as we shall see, it
may be regarded as more fundamental than the distinction of earlier and later.
And it is because the distinctions of past, present and future seem to me to be
essential for time, that I regard time as unreal.
For the sake of brevity I shall speak of
the series of positions running from the far past through the near past to the
present, and then from the present to the near future and the far future, as
the A series. The series of positions which runs from earlier to later I shall
call the B series. The contents of a position in time are called events. The
contents of a single position are admitted to be properly called a plurality of
events. (I believe, however, that they can as truly, though not more truly, be
called a single event. This view is not universally accepted, and it is not
necessary for my argument.) A position in time is called a moment.
The first question which we must consider
is whether it is essential to the reality of time that its events should form
an A series as well as a B series. And it is clear, to begin with, that we
never observe time except as forming both these series. We perceive events in
time as being present, and those are the only events which we perceive
directly. And all other events in time which, by memory or inference, we believe
to be real, are regarded as past or future -- those earlier than the present
being past, and those later than the present being future. Thus the events of
time, as observed by us, form an A series as well as a B series.
It is possible, however, that this is
merely subjective. It may be the case that the distinction introduced among
positions in time by the A series -- the distinction of past, present and
future -- is simply a constant illusion of our minds, and that the real nature
of time only contains the distinction of the B series --the distinction of
earlier and later. In that case we could not perceive time as it really is, but
we might be able to think of it as it really is.
This is not a very common view, but it
has found able supporters. I believe it to be untenable, because, as I said
above, it seems to me that the A series is essential to the nature of time, and
that any difficulty in the way of regarding the A series as real is equally a
difficulty in the way of regarding time as real.
It would, I suppose, be universally
admitted that time involves change. A particular thing, indeed, may exist
unchanged through any amount of time. But when we ask what we mean by saying
that there were different moments of time, or a certain duration of time,
through which the thing was the same, we find that we mean that it remained the
same while other things were changing. A universe in which nothing whatever
changed (including the thoughts of the conscious beings in it) would be a
timeless universe.
If, then, a B series without an A series
can constitute time, change must be possible without an A series. Let us
suppose that the distinction of past, present and future does not apply to
reality. Can change apply to reality? What is it that changes?
Could we say that, in a time which formed
a B series but not an A series, the change consisted in the fact that an event
ceased to be an event, while another event began to be an event? If this were
the case, we should certainly have got a change.
But this is impossible. An event can
never cease to be an event. It can never get out of any time series in which it
once is. If N is ever earlier than O and later than M, it will always be, and
has always been, earlier than O and later than M, since the relations of
earlier and later are permanent. And as, by our present hypothesis, time is
constituted by a B series alone, N will always have a position in a time
series, and has always had one.{1} That is, it will always be, and has always been,
an event, and cannot begin or cease to be an event.
Or shall we say that one event M merges
itself into another event N, while preserving a certain identity by means of an
unchanged element, so that we can say, not merely that M has ceased and N
begun, but that it is M which has become N? Still the same difficulty recurs. M
and N may have a common element, but they are not the same event, or there
would be no change. If therefore M changes into N at a certain moment, then, at
that moment, M has ceased to be M, and N has begun to be N. But we have seen
that no event can cease to be, or begin to be, itself, since it never ceases to
have a place as itself in the B series. Thus one event cannot change into
another.
Neither can the change be looked for in
the numerically different moments of absolute time, supposing such moments to
exist. For the same arguments will apply here. Each such moment would have its
own place in the B series, since each would be earlier or later than each of
the others. And as the B series indicate permanent relations, no moment could
ever cease to be, nor could it become another moment.
Since, therefore, what occurs in time
never begins or ceases to be, or to be itself, and since, again, if there is to
be change it must be change of what occurs in time (for the timeless never
changes), I submit that only one alternative remains. Changes must happen to
the events of such a nature that the occurrence of these changes does not
hinder the events from being events. and the same events, both before and after
the change.
Now what characteristics of an event are
there which can change and yet leave the event the same event? (I use the word
characteristic as a general term to include both the qualities which the event
possesses, and the relations of which it is a term -- or rather the fact that
the event is a term of these relations.) It seems to me that there is only one
class of such characteristics -- namely, the determination of the event in
question by the terms of the A series.
Take any event -- the death of Queen
Anne, for example -- and consider what change can take place in its
characteristics. That it is a death, that it is the death of Anne Stuart, that
it has such causes, that it has such effects -- every characteristic of this
sort never changes. "Before the stars saw one another plain" the
event in question was a death of an English Queen. At the last moment of time
-- if time has a last moment -- the event in question will still be a death of
an English Queen. And in every respect but one it is equally devoid of change.
But in one respect it does change. It began by being a future event. It became
every moment an event in the nearer future. At last it was present. Then it
became past, and will always remain so, though every moment it becomes further
and further past.
Thus we seen forced to the conclusion
that all change is only a change of the characteristics imparted to events by
their presence in the A series, whether those characteristics are qualities or
relations.
If these characteristics are qualities,
then the events, we must admit, would not be always the same, since an event
whose qualities alter is, of course, not completely the same. And, even if the
characteristics are relations, the events would not be completely the same, if
-- as I believe to be the case -- the relation of X to Y involves the existence
in X of a quality of relationship to Y.{2} Then there would be two alternatives
before us. We might admit that events did really change their nature, in
respect of these charseteristics, though not in respect of any others. I see no
difficulty in admitting this. It would place the determinations of the A series
in a very unique position among the characteristics of the event, but on any
theory they would be very unique characteristics. It is usual, for example, to
say that a past event never changes, but I do not see why we should not say,
instead of this, "a past event changes only in one respect -- that every
moment it is further from the present than it was before". But although I
see no intrinsic difficulty in this view, it is not the alternative I regard as
ultimately true. For if, as I believe, time is unreal, the admission that an
event in time would change in respect of its position in the A series would not
involve that anything really did change.
Without the A series then, there would be
no change, and consequently the B series by itself is not sufficient for time,
since time involves change.
The B series, however, cannot exist
except as temporal, since earlier and later, which are the distinctions of
which it consists, are clearly time-determinations. So it follows that there
can be no B series where there is no A series, since where there is no A series
there is no time.
But it does not follow that, if we
subtract the determinations of the A series from time, we shall have no series
left at all. There is a series -- a series of the permanent relations to one
another of those realities which in time are events -- and it is the
combination of this series with the A determinations which gives time. But this
other series -- let us call it the C series -- is not temporal, for it involves
no change, but only an order. Events have an order. They are, let us say, in
the order M, N, O, P. And they are therefore not in the order M, O, N, P, or O,
N, M, P, or in any other possible order. But that they have this order no more
implies that there is any change than the order of the letters of the alphabet,
or of the Peers on the Parliament Roll, implies any change. And thus those
realities which appear to us as events might form such a series without being
entitled to the name of events, since that name is only given to realities
which are in a time series. It is only when change and time come in that the
relations of this C series become relations of earlier and later, and so it
becomes a B series.
More is wanted, however, for the genesis
of a B series and of time than simply the C series and the fact of change. For
the change must be in a particular direction. And the C series, while it
determines the order, does not determine the direction. If the C series runs M,
N, O, P, then the B series from earlier to later cannot run M, O, N, P, or M,
P, O, N, or in any way but two. But it can run either M, N, O, P (so that M is
earliest and P latest) or else P, O, N, M (so that P is earliest and M latest).
And there is nothing either in the C series or in the fact of change to
determine which it will be.
A series which is not temporal has no
direction of its own, though it has an order. If we keep to the series of the
natural numbers, we cannot put 17 between 21 and 26. But we keep to the series,
whether we go from 17, through 21, to 26, or whether we go from 26, through 21,
to 17. The first direction seems the more natural to us, because this series
has only one end, and it is generally more convenient to have that end as a
beginning than as a termination. But we equally keep to the series in counting
backward.
Again, in the series of categories in
Hegel's dialectic, the series prevents us from putting the Absolute Idea
between Being and Causality. But it permits us either to go from Being, through
Causality, to the Absolute Idea, or from the Absolute Idea, through Causality,
to Being. The first is, according to Hegel, the direction of proof, and is thus
generally the most convenient order of enumeration. But if we found it
convenient to enumerate in the reverse direction, we should still be observing
the series.
A non-temporal series, then, has no
direction in itself, though a person considering it may take the terms in one
direction or in the other, according to his own convenience. And in the same
way a person who contemplates a time-order may contemplate it in either
direction. I may trace the order of events from the Great Charter to the Reform
Bill or from the Reform Bill to the Great Charter. But in dealing with the time
series we have not to do merely with a change in an external contemplation of
it, but with a change which belongs to the series itself. And this change has a
direction of its own. The Great Charter came before the Reform Bill, and the
Reform Bill did not come before the Great Charter.
Therefore, besides the C series and the
fact of change there must be given -- in order to get time -- the fact that the
change is in one direction and not in the other. We can now see that the A
series, together with the C series, is sufficient to give us time. For in order
to get change, and change in a given direction, it is sufficient that one
position in the C series should be Present, to the exclusion of all others, and
that this characteristic of presentness should pass along the series in such a
way that all positions on the one side of the Present have been present, and
all positions on the other side of it will be present. That which has been
present is Past, that which will be present is Future.{3} Thus to our previous
conclusion that there can be no time unless the A series is true of reality, we
can add the further conclusion that no other elements are required to
constitute a time-series except an A series and a C series.
We may sum up the relations of the three
series to time as follows: The A and B series are equally essential to time,
which must be distinguished as past, present and future, and must likewise be
distinguished as earlier and later. But the two series are not equally
fundamental. The distinctions of the A series are ultimate. We cannot explain
what is meant by past, present and future. We can, to some extent, describe
them, but they cannot be defined. We can only show their meaning by examples.
"Your breakfast this morning," we can say to an inquirer, "is
past; this conversation is present; your dinner this evening is future."
We can do no more.
The B series, on the other hand, is not
ultimate. For, given a C series of permanent relations of terms, which is not
in itself temporal, and therefore is not a B series, and given the further fact
that the terms of this C series also form an A series, and it results that the
terms of the C series become a B series, those which are placed first, in the
direction from past to future, being earlier than those whose places are
further in the direction of the future.
The C series, however, is as ultimate as
the A series. We cannot get it out of anything else. That the units of time do
form a series, the relations of which are permanent, is as ultimate as the fact
that each of them is present, past, or future. And this ultimate fact is
essential to time. For it is admitted that it is essential to time that each
moment of it shall either be earlier or later than any other moment; and these
relations are permanent. And this -- the B series -- cannot be got out of the A
series alone. It is only when the A series, which gives change and direction,
is combined with the C series, which gives permanence, that the B series can
arise.
Only part of the conclusion which I have
now reached is required for the general purpose of this paper. I am endevouring
to base the unreality of time, not on the fact that the A series is more
fundamental than the B series, but on the fact that it is as essential as the B
series -- that the distinctions of past, present and future are essential to
time and that, if the distinctions are never true of reality, then no reality
is in time.
This view, whether it is true or false,
has nothing surprising in it. It was pointed out above that time, as we
perceive it, always presents these distinctions. And it has generally been held
that this is a real characteristic of time, and not an illusion due to the way
in which we perceive it. Most philosophers, whether they did or did not believe
time to be true of reality, have regarded the distinctions of the A series as
essential to time.
When the opposite view has been
maintained, it has generally been, I believe, because it was held (rightly, as
I shall try to show later on) that the distinctions of present, past and future
cannot be true of reality, and that consequently, if the reality of time is to
be saved, the distinction in question must be shown to be unessential to time.
The presumption, it was held, was for the reality of time, and this would give
us a reason for rejecting the A series as unessential to time. But of course
this could only give a presumption. If the analysis of the notion of time
showed that, by removing the A series, time was destroyed, this line of
argument would be no longer open, and the unreality of the A series would
involve the unreality of time.
I have endeavoured to show that the
removal of the A series does destroy time. But there are two objections to this
theory, which we must now consider.
The first deals with those time-series
which are not really existent, but which are falsely believed to be existent,
or which are imagined as existent. Take, for example, the adventures of Don
Quixote. This series, it is said, is not an A series. I cannot at this moment
judge it to be either past, present or future. Indeed I know that it is none of
the three. Yet, it is said, it is certainly a B series. The adventure of the
galley-slaves, for example, is later than the adventure of the windmills. And a
B series involves time. The conclusion drawn is that an A series is not
essential to time.
The answer to this objection I hold to be
as follows. Time only belongs to the existent. If any reality is in time, that
involves that the reality in question exists. This, I imagine, would be
universally admitted. It may be questioned whether all of what exists is in
time, or even whether anything really existent is in time, but it would not be
denied that, if anything is in time, it must exist.
Now what is existent in the adventures of
Don Quixote? Nothing. For the story is imaginary. The acts of Cervantes' mind
when he invented the story, the acts of my mind when I think of the story --
these exist. But then these form part of an A series. Cervantes' invention of
the story is in the past. My thought of the story is in the past, the present,
and --I trust -- the future.
But the adventures of Don Quixote may be
believed by a child to be historical. And in reading them I may by an effort of
the imagination contemplate them as if they really happened. In this case, the
adventures are believed to be existent or imagined as existent. But then they
are believed to be in the A series, or imagined as in the A series. The child
who believes them historical will believe that they happened in the past. If I
imagine them as existent, I shall imagine them as happening in the past. In the
same way, if any one believed the events recorded in Morris's News from Nowhere
to exist, or imagined them as existent, he would believe them to exist in the
future or imagine them as existent in the future. Whether we place the object
of our belief or our imagination in the present, the past, or the future, will
depend upon the characteristics of that object. But somewhere in our A series
it will be placed.
Thus the answer to the objection is that,
just as a thing is in time, it is in the A series. If it is really in time, it
is really in the A series. If it is believed to be in time, it is believed to
be in the A series. If it is imagined as in times it is imagined as in the A
series.
The second objection is based on the
possibility, discussed by Mr. Bradley, that there might be several independent
time-series in reality. For Mr. Bradley, indeed, time is only appearance. There
is no real time at all, and therefore there are not several real series of
time. But the hypothesis here is that there should be within reality several
real and independent time-series.
The objection, I imagine, is that the
time-series would be all real, while the distinction of past, present, and
future would only have meaning within each series, and could not, therefore, be
taken as ultimately real. There would be, for example, many presents. Now, of
course, many points of time can be present (each point in each time-series is a
present once), but they must be present successively. And the presents of the
different time-series would not be successive, since they are not in the same
time. (Neither would they be simultaneous, since that equally involves being in
the same time. They would have no time-relation whatever.) And different
presents, unless they are successive, cannot be real. So the different
time-series, which are real, must be able to exist independently of the
distinction between past, present, and future.
I cannot, however, regard this objection
as valid. No doubtt, in such a case, no present would be the present -- it
would onlt be the present of a certain aspect of the universe. But then no time
wined be the time -- it would only be the time of a certain aspect of the universe.
It would, no doubt, be a real time-series, but I do not see that the present
would be Iess real than the time.
I am not, of course, asserting that there
is no contradiction in the existence of several distinct A series. My main
thesis is that the existence of any A series involves a contradiction. What I
assert here is merely that, supposing that there could be any A series, I see
no extra difficulty involved in there being several such series independent of
one another, and that therefore there is no incompatibility between the
essentiality of an A series for time and the existence of several distinct
times.
Moreover, we must remember that the
theory of a plurality of time series is a mere hypothesis. No reason has ever
been given why we should believe in their existence. It has only been said that
there is no reason why we should disbelieve in their existence, and that
therefore they may exist. But if their existence should be incompatible with
something else, for which there is positive evidence, then there would be a
reason why we should disbelieve in their existence. Now there is, as I have
tried to show, positive evidence for believing that an A series is essential to
time. Supposing therefore that it were the case (which, for the reasons given
above, I deny) that the existence of a plurality of time-series was
incompatible with the essentiality for time of the A series, it would be the
hypothesis of a plurality of times which should be rejected, and not our
conclusion as to the A series.
I now pass to the second part of my task.
Having, as it seems to me, succeeded in proving that there can be no time
without an A series, it remains to prove that an A series cannot exist, and
that therefore time cannot exist. This would involve that time is not real at
all, since it is admitted that, the only way in which time can be real is by
existing.
The terms of the A series are
characteristics of events. We say of events that they are either past, present,
or future. If moments of time are taken as separate realities, we say of them
also that they are past, present, or future. A characteristic may be either a
relation or a quality. Whether we take the terms of the A series as relations
of events (which seems the more reasonable view) or whether we take them as
qualities of events, it seems to me that they involve a contradiction.
Let us first examine the supposition that
they are relations. In that case only one term of each relation can be an event
or a moment. The other term must be something outside the time-series.{4} For
the relations of the A series are changing relations, and the relation of terms
of the time-series to one another do not change. Two events are exactly in the
same places in the time-series, relatively to one another, a million years
before they take place, while each of them is taking place, and when they are a
million years in the past. The same is true of the relation of moments to each
other. Again, if the moments of time are to be distinguished as separate
realities from the events which happen in them, the relation between an event
and a moment is unvarying. Each event is in the same moment in the future, in
the present, and in the past.
The relations which form the A series
then must be relations of events and moments to something not itself in the
time-series. What this something is might be difficult to say. But, waiving
this point, a more positive difficulty presents itself.
Past, present, and future are
incompatible determinations. Every event must be one or the other, but no event
can be more than one. This is essential to the meaning of the terms. And, if it
were not so, the A series would be insuflicient to give us, in combination with
the C series, the result of time. For time, as we have seen, involves change,
and the only change we can get is from future to present, and from present to
past.
The characteristics, therefore, are
incompatible. But every event has them all. If M is past, it has been present
and future. If it is future, it will be present and past. If it is present, it
has been future and will be past. Thus all the three incompatible terms are
predicable of each event which is obviously inconsistent with their being
incompatible, and inconsistent with their producing change.
It may seem that this can easily be
explained. Indeed it has been impossible to state the difficulty without almost
giving the explanation, since our language has verb-forms for the past,
present, and future, but no form that is common to all three. It is never true,
the answer will run, that M is present, past and future. It is present, will be
past, and has been future. Or it is past, and has been future and present, or
again is future and will be present and past. The characteristics are only
incompatible when they are simultaneous, and there is no contradiction to this
in the fact that each term has all of them successively.
But this explanation involves a vicious
circle. For it assumes the existence of time in order to account for the way in
which moments are past, present and future. Time then must be pre-supposed to
account for the A series. But we have already seen that the A series has to be
assumed in order to account for time. Accordingly the A series has to be
pre-supposed in order to account for the A series. And this is clearly a
vicious circle.
What we have done is this -- to meet the
difficulty that my writing of this article has the characteristics of past,
present and future, we say that it is present, has been future, and will be
past. But "has been" is only distinguished from " is" by
being existence in the past and not in the present, and " will be "
is only distinguished from both by being existence in the future. Thus our statement
comes to this -- that the event in question is present in the present, future
in the past, past in the future. And it is clear that there is a vicious circle
if we endeavour to assign the characteristics of present, future and past by
the criterion of the characteristics of present, past and future.
The difficulty may be put in another way,
in which the fallacy will exhibit itself rather as a vicious infinite series
than as a vicious circle. If we avoid the incompatibility of the three
characteristics by asserting that M is present, has been future, and will be
past, we are constructing a second A series, within which the first falls, in
the same way in which events fall within the first. It may be doubted whether
any intelligible meaning can be given to the assertion that time is in time.
But, in any case, the second A series will suffer from the same difficulty as
the first, which can only be removed by placing it inside a third A series. The
same principle will place the third inside a fourth, and so on without end. You
can never get rid of the contradiction, for, by the act of removing it from
what is to be explained, you produce it over again in the explanation. And so
the explanation is invalid.
Thus a contradiction arises if the A
series is asserted of reality when the A series is taken as a series of
relations. Could it be taken as a series of qualities, and would this give us a
better result? Are there three qualities -- futurity, presentness, and
pastness, and are events continually changing the first for the second, and the
second for the third?
It seems to me that there is very little
to be said for the view that the changes of the A series are changes of
qualities. No doubt my anticipation of an experience M, the experience itself,
and the memory of the experience are three states which have different
qualities. But it is not the future M, the present M, and the past M, which
have these three different qualities. The qualities are possessed by three
distinct events -- the anticipation of M, the experience M itself, and the
memory of M, each of which is in turn future, present, and past. Thus this
gives no support to the view that the changes of the A series are changes of
qualities.
But we need not go further into this
question. If the characteristics of the A series were qualities, the same
difficulty would arise as if they were relations. For, as before, they are not
compatible, and, as before, every event has all of them. This can only be
explained, as before, by saying that each event has them successively. And thus
the same fallacy would have been committed as in the previous case.{5}
We have come then to the conclusion that
the application of the A series to reality involves a contradiction, and that
consequently the A serles cannot be true of reality. And, since time involves
the A series, it follows that time cannot be true of reality. Whenever we judge
anything to exist in time, we are in error. And whenever we perceive anything
as existing in time -- which is the only way in which we ever do perceive
things -- we are perceiving it more or less as it really is not.
We must consider a possil)le objection.
Our ground for rejecting time, it may be said, is that time cannot be explained
without assuming time. But may this not prove -- not that time is invalid, but
rather that time is ultimate? It is impossible to explain, for example,
goodness or truth unless by bringing in the term to be explained as part of the
explanation, and we therefore reject the explanation as invalid. But we do not
therefore reject the notion as erroneous, but accept it as something ultimate,
which, while it does not admit of explanation, does not require it.
But this does not apply here. An idea may
be valid of reality though it does not admit of a valid explanation. But it
cannot be valid of reality if its application to reality involves a
contradiction. Now we began by pointing out that there was such a contradiction
in the case of time -- that the charasteristics of the A series are mutually
incompatible and yet all true of every term. Unless this contradiction is
removed, the idea of time must be rejected as invalid. It was to remove this
contradiction that the explanation was suggested that the characteristics
belong to the terms successively. When this explanation failed as being
circular, the contradiction remained unremoved, and the idea of time must be
rejected, not because it cannot be explained, but because the contradiction
cannot be removed.
What has been said already, if valid, is
an adequate ground for rejecting time. But we may add another consideration.
Time, as we have seen, stands and falls with the A series. Now, even if we
ignore the contradiction which we have just discovered in the application of
the A series to reality, was there ever any positive reason why we should
suppose that the A series was valid of reality?
Why do we believe that events are to be
distinguished as past, present and future? I conceive that the belief arises
from distinctions in our own experience.
At any moment I have certain perceptions,
I have also the memory of certain other perceptions, and the anticipation of
others again. The direct perception itself is a mental state qualitatively
different from the memory or the anticipation of perceptions. On this is based
the belief that the perception itself has a certain characteristic when I have
it, which is replaced by other characteristics when I have the memory or the
anticipation of it -- which characteristics are called presentness, pastness,
and futurity. Having got the idea of these characteristics we apply them to
other events. Everything simultaneous with the direct perception which I have
now is called present, and it is even held that there would be a present if no
one had a direct perception at all. In the same way acts simultaneous with
remembered perceptions or anticipated perceptions are held to be past or
future, and this again is extended to events to which none of the perceptions I
now remember or anticipate are simultaneous. But the origin of our belief in
the whole distinction lies in the distinction between perceptions and
anticipations or memories of perceptions.
A direct perception is present when I
have it, and so is what is simultaneous with it. In the first place this
definition involves a circle, for the words "when I have it," can
only mean "when it is present". But if we left out these words, the
definition would be false, for I have many direct presentations which are at
different times, and which cannot, therefore, all be present, except
successively. This, however, is the fundamental contradiction of the A series,
which has been already considered. The point I wish to consider here is
different.
The direct perceptions which I now have
are those which now fall within my "specious present". Of those which
are beyond it, I can only have memory or anticipation. Now the "specious
present " varies in length according to circumstances, and may be
different for two people at the same period. The event M may be simultaneous
both with X's perception Q and Y's perception R. At a certain moment Q may have
ceased to be part of X's specious present. M, therefore, will at that moment be
past. But at the same moment R may still be part of Y's specious present. And,
therefore, M will be present, at the same moment at which it is past.
This is impossible. If, indeed, the A
series was something purely subjective, there would be no difficulty. We could
say that M was past for X and present for Y, just as we could say that it was
pleasant for X and painful for Y. But we are considering attempts to take time
as real, as something which belongs to the reality itself, and not only to our
beliefs about it, and this can only be so if the A series also applies to the
reality itself. And if it does this, then at any moment M must be present or
past. It cannot be both.
The present through which events really
pass, therefore, cannot be determined as simultaneous with the specious
present. It must have a duration fixed as an ultimate fact. This duration
cannot be the same as the duration of all specious presents, since all specious
presents have not the same duration. And thus an event may be past when I am
experiencing it as present, or present when I am experiencing it as past. The
duration of the objective present may be the thousandth part of a second. Or it
may be a century, and the accessions of George IV. and Edward VII. may form
part of the same present. What reason can we have to believe in the existence
of such a present, which we certainly do not observe to be a present, and which
has no relation to what we do observe to be a present?
If we escape front these difficulties by
taking the view, which has sometimes been held, that the present in the A
series is not a finite duration, but a mere point, separating future from past,
we shall find other difficulties as serious. For then the objective time in
which events are will be something utterly different from the time in which we
perceive them. The time in which we perceive them has a present of varying
finite duration, and, therefore, with the future and the past, is divided into
three durations. The objective time has only two durations, separated by a
present which has nothing but the name in common with the present of
experience, since it is not a duration but a point. What is there in our
experience which gives us the least reason to believe in such a time as this?
And so it would seem that the denial of
the reality of time is not so very paradoxical after all. It was called
paradoxical because it seemed to contradict our experience so violently -- to
compel us to treat so much as illusion which appears prima facie to give
knowledge of reality. But we now see that our experience of time -- centring as
it does about the specious present -- would be no less illusory if there were a
real time in which the realities we experience existed. The specious present of
our observations -- varying as it does from you to me -- cannot correspond to
the present of the events observed. And consequently the past and future of our
observations could not correspond to the past and future of the events
observed. On either hypothesis -- whether we take time as real or as unreal --
everything is observed in a specious present, but nothing, not even the
observations themselves, can ever be in a specious present. And in that case I
do not see that we treat experience as much more illusory when we say that
nothing is ever in a present at all, than when we say that everything passes through
some entirely different present.
Our conclusion, then, is that neither
time as a whole, nor the A series and B series, really exist. But this leaves
it possible that the C series does really exist. The A series was rejected for
its inconsistency. And its rejection involved the rejection of the B series.
But we have found no such contradiction in the C series, and its invalidity
does not follow from the invalidity of the A series.
It is, therefore, possible that the
realities which we perceive as events in a time-series do really form a
non-temporal series. It is also possible, so far as we have yet gone, that they
do not form such a series, and that they are in reality no more a series than
they are temporal. But I think -- though I have no room to go into the question
here -- that the former view, according to which they really do form a C
series, is the more probable.
Should it be true, it will follow that in
our perception of these realities as events in time, there will be some truth
as well as some error. Through the deceptive form of time, we shall grasp some
of their true relations. If we say that the events M and N are simultaneous, we
say that they occupy the same position in the time-series. And there will be
some truth in this, for the realities, which we perceive as the events M and N,
do really occupy the same position in a series, though it is not a temporal
series.
Again, if we assert that the events M, N,
O, are all at different times, and are in that order, we assert that they
occupy different positions in the time-series, and that the position of N is
between the positions of M and O. And it will be true that the realities which
we see as these events will be in a series, though not in a temporal series, and
that their positions in it will be different, and that the position of the
reality which we perceive as the event N will be between the positions of the
realities which we perceive as the events M and O.
If this view is adopted, the result will
so far resemble those reached by Hegel rather than those of Kant. For Hegel
regarded the order of the time-series as a reflexion, though a distorted
reflexion, of something in the real nature of the timeless reality, while Kant
does not seem to have contemplated the possibility that anything in the nature
of the noumenon should correspond to the time order which appears in the
phenomenon.
But the question whether such an
objective C series does exist, must remain for future discussions. And many
other questions press upon us which inevitably arise if the reality of time is
denied. If there is such a C series, are positions in it simply ultimate facts,
or are they determined by the varying amounts, in the objects which hold those
positions, of some quality which is common to all of them? And, if so, what is
that quality, and is it a greater amount of it which determines things to
appear as later, and a lesser amount which determines them to appear as
earlier, or is the reverse true? On the solution of these questions it may be
that our hopes and tears for the universe depend for their confirmation or
rejection.
And, again, is the series of appearances
in time a series which is infinite or finite in length? And how are we to deal
with the appearance itself? If we reduce time and change to appearance, must it
not be to an appearance which changes and which is in time, and is not time,
then, shown to be real after all? This is doubtless a serious question, but I
hope to show hereafter that it can be answered in a satisfactory way.
Notes
{1} It is equally true, though it does
not concern us on the hypothesis which we are now considering, that whatever is
once in an A series is always in one. If one of the determinations past,
present, and future can ever be applied to N, then one of them always has been
and always will be applicable, though of course not always the same one.
{2} I am not asserting, as Lotze did,
that a relation between X and Y consists of a quality in X and a quality in Y
-- a view which I regard as quite indefensible. I assert that a relation Z
between X and Y involves the existence in X of the quality "having the
relation Z to Y" so that a difference of relations always involves a
difference in quality, and a change of relations always involves a change of
quality.
{3} This account of the nature of the A
series is not valid, for it involves a vicious circle, since it uses "has
been" and "will be" to explain Past and Future. But, as I shall
endeavour to show later on, this vicious circle is inevitable when we deal with
the A series, and forms the ground on which we must reject it.
{4} It has been maintained that the
present is whatever is simultaneous with the assertion of its presentness, the
future whatever is later than the assertion of its futurity, and the past
whatever is earlier than the assertion of its pastness. But this theory
involves that time exists independently of the A series, and is incompatible
with the results we have already reached.
{5} It ii very usual to present Time
under the metaphor of a spatial movement. But is it to be a movement from past
to future, or from future to past? If the A series is taken as one of
qualities, it will naturally be taken as a movement from past to future, since
the quality of presentness has belonged to the past states and will belong to
the future states. If the A series is taken as one of relations, it is possible
to take the movement either way, since either of the two related terms can be
taken as the one which moves. If the events are taken as moving by a fixed
point of presentness, the movement is from future to past, since the future
events are those which have not yet passed the point, and the past are those
which have. If presentness is taken as a moving point successively related to
each of a series of events, the movement is from past to future. Thus we say
that events come out of the future, but we say that we ourselves move towards
the future. For each man identifies himself especially with his present state,
as against his future or his past, since the present is the only one of which
he has direct experience. And thus the self, if it is pictured as moving at
all, is pictured as moving with the point of presentness along the stream of
events from past to future.
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By Isaac Newton. Scholium to the Definitions in Philosophiae Naturalis Principia
Mathematica, Bk. 1 (1689); trans. Andrew Motte (1729), rev.
Florian Cajori, Berkeley: University of California Press, 1934. pp.
6-12.
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 common people 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.
I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation 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.
II. Absolute space, in its own nature, without relation 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 commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, 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 continually changed.
III. 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 surfaces, 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 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 as the sum of the places as the parts, and for that reason, it is internal, and in the whole body.
IV. 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 the 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 towards the east, with a velocity of 10010 parts; which the ship itself, with a 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.
V. Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the apparent 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 that they may measure the celestial motions by a more accurate time. 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 flowing of absolute time is not liable to any 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 this duration ought to be distinguished from what are only sensible measures thereof; and from which we deduce it, by means of the astronomical equation. The necessity of this 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.
VI. 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 movable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions.
VII. 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 [definimus] 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.
VIII. But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know [scire], from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined [definiri] from the position of bodies in our regions.
IX. It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes. For all the parts of revolving bodies endeavor to recede from the axis of motion; and the impetus of bodies moving forwards arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined [definiri] by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise, all included bodies besides their translation from near the surrounding ones, partake likewise of their true motions; and though that translation were not made, they would not be really at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell.
X. A property, near akin to the preceding, is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body, which is moved from a place in motion, partakes also of the motion of its place. Upon which account, all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out of its place; and so on, until we come to some immovable place [locum immotum], as in the before-mentioned example of the sailor. Wherefore, entire and absolute motions can be no otherwise determined [definiri] than by immovable places [loca immota]; and for that reason I did before refer those absolute motions to immovable places [loca immota], but relative one to movable places. Now no other places are immovable [immota] but those that, from infinity to infinity, do all retain the same given position one to another; and upon this account must ever remain unmoved [immota]; and do thereby constitute immovable [immobile] space.
XI. The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist [consistit]. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Thus, true motion by no means consists [consistit] in such relations.
XII. The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; thereupon, by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain [plana], as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascent to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows [indicat] its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known [innotescit], and may be measured [mensuratur] by this endeavor. At first, when the relative motion of the water in the vessel was greatest, it produced no endeavor to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain [plana] surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved [indicabat] its endeavor to recede from the axis; and this endeavor showed [monstrabat] the real circular motion of the water continually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavor does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined [defineri] by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavoring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truely at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavor to recede from the axis of their motions.
XIII. Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined [definiendae] by their use, then by the names time, space, place, and motion, their measures [mensurae sensibilies] are properly to be understood; and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities with their relations and sensible measures [vulgaribus mensuris].
XIV. It is indeed a matter of great difficulty to discover [cognoscere], and effectually to distinguish [actu discriminare], the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses [incurrent in sensus]. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.
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Newton's Scholium on Space, Time, Place and Motion
 |
| Isaac Newton (1642-1727) |
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 common people 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.
I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation 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.
II. Absolute space, in its own nature, without relation 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 commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, 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 continually changed.
III. 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 surfaces, 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 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 as the sum of the places as the parts, and for that reason, it is internal, and in the whole body.
IV. 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 the 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 towards the east, with a velocity of 10010 parts; which the ship itself, with a 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.
V. Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the apparent 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 that they may measure the celestial motions by a more accurate time. 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 flowing of absolute time is not liable to any 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 this duration ought to be distinguished from what are only sensible measures thereof; and from which we deduce it, by means of the astronomical equation. The necessity of this 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.
VI. 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 movable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions.
VII. 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 [definimus] 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.
VIII. But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know [scire], from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined [definiri] from the position of bodies in our regions.
IX. It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes. For all the parts of revolving bodies endeavor to recede from the axis of motion; and the impetus of bodies moving forwards arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined [definiri] by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise, all included bodies besides their translation from near the surrounding ones, partake likewise of their true motions; and though that translation were not made, they would not be really at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell.
X. A property, near akin to the preceding, is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body, which is moved from a place in motion, partakes also of the motion of its place. Upon which account, all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out of its place; and so on, until we come to some immovable place [locum immotum], as in the before-mentioned example of the sailor. Wherefore, entire and absolute motions can be no otherwise determined [definiri] than by immovable places [loca immota]; and for that reason I did before refer those absolute motions to immovable places [loca immota], but relative one to movable places. Now no other places are immovable [immota] but those that, from infinity to infinity, do all retain the same given position one to another; and upon this account must ever remain unmoved [immota]; and do thereby constitute immovable [immobile] space.
XI. The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist [consistit]. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Thus, true motion by no means consists [consistit] in such relations.
XII. The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; thereupon, by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain [plana], as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascent to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows [indicat] its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known [innotescit], and may be measured [mensuratur] by this endeavor. At first, when the relative motion of the water in the vessel was greatest, it produced no endeavor to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain [plana] surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved [indicabat] its endeavor to recede from the axis; and this endeavor showed [monstrabat] the real circular motion of the water continually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavor does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined [defineri] by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavoring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truely at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavor to recede from the axis of their motions.
XIII. Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined [definiendae] by their use, then by the names time, space, place, and motion, their measures [mensurae sensibilies] are properly to be understood; and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities with their relations and sensible measures [vulgaribus mensuris].
XIV. It is indeed a matter of great difficulty to discover [cognoscere], and effectually to distinguish [actu discriminare], the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses [incurrent in sensus]. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.
very intersting here this blog on time. what we discover recently, time has only a mathematical, universe is timeless as predictedby Kurt Godel http://link.springer.com/search?query=amrit+sorli+
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