17a (Matthews 139-146) [I]n philosophical disquisitions, we
ought to abstract from our senses, and consider things themselves, distinct
from what are only sensible measures of them. –
In 1748 the great
Swiss mathematician and physicist, Leonhard Euler, published a paper in the Mémoires de l’académie des sciences de
Berlin entitled, “Réflexions sur l’espace et le tems,” (Reflexions on
space and time). In it he observed
that the principles of Newtonian mechanics had proven to be so useful for
explaining the phenomena of nature as to be beyond doubt, and he cited two
principles in particular that had achieved that status: that a body once at
rest will remain at rest forever unless acted upon by some outside force, and
that a body once set in motion in a certain direction will continue in that
same direction with that same speed unless acted upon by some outside
force. In effect, bodies will resist
efforts to change their state of motion and rest. Having made this
observation Euler proceeded to ask a question: what is it with reference to
which a body acts to resist efforts to change its state of motion? Alternatively, what is it with respect to
which a body preserves in its state of motion? Or, yet again, what is it that governs the
inertial behaviour of bodies? Is it something real
that does this? Or is it something
merely imaginary — something that human beings have cooked up merely as a way
of organizing and classifying things and that they could have made in any of
a number of different ways, like our varying ways of classifying things into
groups? The answer to this
question may seem so obvious that it would be absurd even to have bothered to
ask it. Obviously, something merely
imaginary could not be what bodies move with reference to or what causes them
to resist certain kinds of motion while persisting in others. But sometimes obvious
answers to obvious questions can have disquieting results. Euler was writing at a
time when a significant proportion of the natural philosophers of continental
Europe, a group Euler referred to collectively as the “metaphysicians,” had gathered
behind Leibniz in opposition to the English “mathematical philosophy” of But then what about
the inertial properties of bodies? If
we say that a body resists changes in motion, do we merely mean to say that
it resists being moved away from those bodies that immediately surround
it? That can’t be right. Consider a ship in still water. The ship is at rest relative to the water
particles that surround it. Now
consider what happens if the water starts to move. At first the ship stays where it is and it
is only gradually, as the water particles continue to hit it, that it begins
to move with the stream and it takes some time for it to take on the full
speed of the water particles.
Why? We think it is because of
the ship’s inertia. The ship, once at
rest (or once moving in a certain direction at a certain speed) resists any
changes to that state of motion so that it takes some force from the
continually impacting water particles to make it move. But if that is what is
going on then it means that the ship’s inertial state cannot be determined
with reference to the immediately surrounding bodies. If it were, then as soon as the immediately
surrounding bodies started to move, the ship would move along with them,
since the principle of inertia says that it strives to say in its state of
motion, and if its state of motion is defined relative to the immediately
surrounding bodies, then when they move it must strive to move along with
them. Far from it taking a force to
speed the ship up to the speed of the water, it ought to take a force to hold
it back. But just the opposite occurs. So let’s return to our
question. What determines the inertial
behaviour of bodies? If it is not the
immediately contiguous bodies might it be some more remote ones, considered
as being at rest? But which ones would
those be? If all motion is ultimately
relative and we merely stipulate which bodies we are going to treat as the
landmarks relative to which others are moving, then we make the inertial
behaviour of bodies depend on something merely imaginary, because we can
imagine any bodies we want to be the fixed ones relative to which others are
moving. And, manifestly, that is an
incorrect way of looking at things, because we can pick certain bodies as the
ones we want to consider to be at rest and then discover that the inertial
behaviour of bodies does not follow in accord with our stipulations. Sitting by the window of a train I see
another train pass by, and I stipulate that I must therefore be at rest and
it in motion. But then I look down at
the floor and see a bottle rolling down the aisle towards me at the same
speed the train is passing by outside — even though the bottle was lying
there motionless a moment ago. I am
not going to say that some occult cause gave the bottle a push. I am going to say that the fact that I
stipulated that my train car is at rest is merely the way I was imagining
things and if I want to get the facts right I had better start to imagine
that I and the train car have started to move in the opposite direction and
that bottle and the outside train are preserving in their inertial state. But if the inertial
state of bodies is not governed by their motion or rest relative to the
immediately surrounding bodies and not governed by what bodies I choose to
imagine them to be moving or resting with respect to, then what is it
governed by? Very remote bodies like
the fixed stars? It would be a strange
thing, however, if bodies that are so many trillions of miles away from us
should govern the inertial behaviour of bodies here on Earth. — And a particularly strange thing for
“metaphysical” natural philosophers to maintain, given their otherwise
adamant rejection of action at a distance!
Moreover, the problem simply recurs when we ask about the inertial
state of bodies in close proximity to the fixed stars. Is it reciprocally governed by motion
relative to the Earth? For Euler there was
only one sensible answer to the question.
The inertia of bodies — whether or not they exhibit effects of
inertial force — is not governed by whether or not bodies are moving relative
to other bodies, be those other bodies near or remote. It is governed by whether or not they are
accelerating relative to space itself. Space must accordingly
be a thing in its own right, even if a radically different kind of thing from
body. The principles of inertia cannot
be sustained in concert with a purely relativistic account of space and
motion. There must be an absolute
space existing independently of body as the ultimate reference frame for
inertial motion. QUESTIONS ON THE
1. Under what notions do
common people conceive space and time?
2. Does it make sense to
say that an hour could take more or less time to pass?
3. List the properties of
absolute space.
4. How is relative space
determined?
5. How can absolute and
relative space be the same in figure and magnitude, but different
numerically?
6. How does absolute
motion differ from relative motion?
7. Why is it absurd that
the parts of absolute space should move or change position relative to one another?
8. Why do we consider
relative places and motions instead of absolute ones?
9. Why should we not rest
content with relative places and motions in philosophical disquisitions? 10.
How can we distinguish absolute rest and motion from
relative rest and motion? 11.
Why can true and absolute motion not be determined by
motion relative to surrounding bodies taken to be at rest? 12.
What are the causes by which true motions are
distinguished from relative motions? 13.
How can a true motion be preserved when the relative
remains unaltered, and the relative preserved when the true alters? 14.
What are the effects that distinguish relative from
absolute motion? 15.
What does the ascent of the water up the sides of the
spinning bucket prove? 16.
Why can true circular motion not be determined by rotation
relative to any ambient bodies? 17.
What is wrong with Descartes claim that the planets are at
rest in their vortices even though the vortices are in motion around the Sun? 18.
Why is it a matter of great difficulty to tell true
motions apart from apparent? NOTES ON THE However compelling the
reasons for recognizing that pure space is a thing that exists in its own
right, independently of anything else, there are equally compelling reasons
for denying that there could be any such thing. People have long thought that whatever
exists must either be a thing, or a property or relation of a thing, and they
accordingly have treated space as either a property of things (their
extension) or at least a relation between things (a relation of distance
between bodies presumed to be at rest and taken as defining positions). And so
let us suppose that all bodies were destroyed and brought to nothing. What is
left they call absolute space, all relation arising from the situation and
distances of bodies being removed together with the bodies. Again, that space
is infinite, immoveable, indivisible, insensible, without relation and
without distinction. That is, all its attributes are privative or negative.
It seems therefore to be mere nothing. The only slight difficulty arising is
that it is extended, and extension is a positive quality. But what sort of
extension, I ask, is that which cannot be divided nor measured, no part of
which can be perceived by sense or pictured by the imagination? … From
absolute space then let us take away now the words of the name, and nothing
will remain in sense, imagination, or intellect. Nothing else then is denoted
by those words than pure privation or negation, i.e. mere nothing. [de
Motu, art. 53] However, none of these
wilder speculations make it into Opening definitions.
I. First, II. Second, Absolute space is to be distinguished from relative space, which is
space defined relative to sensible objects considered to serve as
landmarks. “Relative spaces” can be
numerically identical with a portion of absolute space, but they can also be
in motion through absolute space, if the landmark objects are in motion. III. Third, Relative place, in contrast, is the part of relative space a body
takes up and its position is determined relative to sensible landmark
objects. IV. Finally, Conceptual arguments
for the existence of absolute space and time. Having laid down these definitions, First, turning to absolute time, But a motion could hardly speed up or slow down over time if time just is what is measured by that motion. In our very way of thinking and speaking, therefore,
we recognize the existence of something else: an ultimate time that passes
uniformly independently of any sensible process. Turning to space, But it is conceptually impossible that any part of space itself could
move. That is because motion just is
change of place. If a part of space
changed its place, there would have to be some place that stays behind and is
immobile so that the part can be conceived as moving out of it. If that can’t be then no place can
move. On the other hand, if we think
it could be, then a place would have to move out of itself and come to be in
two places at once. But one place
cannot be two places. So, either way
no place can move. There must be
absolute places. And so there must be
absolute space, which is just the sum of the collection of absolute places. We have failed to appreciate these conceptual points, Counterarguments. There are counterarguments to
these two arguments. In response to In response to Newton’s further claim that there must be an immobile
and hence absolute space because motion is change of place and it is absurd
that any place could move out of itself the relativist could reply that
motion is not change of place. It is
change of place relative to certain
sensible landmark objects. So
where there are no bodies there can be no motion just for that reason. And where it is not obvious which bodies to
take to be the landmarks, we can make various stipulations and then the
places determined by those stipulations will likewise be immobile, even
though under other stipulations those same places would move. Again, if we are worried about making the
inertial properties of bodies depend on our arbitrary will and choice in
making a stipulation, we can always let our choice be guided by background
theories about what moving forces are operating on bodies and pick those that
our science tells us are not being accelerated by any known forces. Finally, Properties, causes,
and effects.
However, while the relativists would not have been silenced by Newton proceed to observe that while absolute space and time cannot be
seen or distinguished by our senses, the same is not the case with absolute
rest and motion. Absolute rest and
motion may be distinguished from relative rest and motion, he claimed, by
their properties, causes, and effects.
If this is true, it would pose an even more serious challenge to the
relativist position. If there is
absolute motion and rest, there must be an absolute space and time in which
the motion and rest takes place.
Sensible evidence for absolute motion and rest would accordingly give
us more than a merely conceptual argument for the existence of absolute space
and time. Properties. Beginning with properties, However, This may seem perplexing.
Having claimed that absolute motion may be distinguished from relative
motion by its properties, causes, and effects, Causes. Turning to causes, But here again there is a problem because it is a question how to
determine what the moving forces are, and where they are acting. We can’t turn around and take merely apparent
motions as proof of the existence of impressed forces. A body can seem to move, not because some
force is acting on it, but rather because some force is acting on its
surroundings to push them in the opposite direction. Likewise, a body can seem to be at rest
even though both it and its surroundings are mutually being moved by some
impressed force. We might think that
we might ourselves be in something of a privileged position in this regard
because we can at least sense when we are putting out an effort to move
something and so ought to be able to tell what forces we are impressing on
bodies to make them really move. But
we are ourselves often carried around by other forces that make our best
efforts produce the opposite of any motion.
Think of trying to paddle a canoe upstream. Our efforts would only be a guide to
determining which bodies have forces acting on them if we only ever acted on
bodies that did not already have other forces acting on them, and that is not
the case. Again we seem to have drawn a blank.
But again it would be premature to infer that causes can never be used
to distinguish true from apparent motions. Effects. Finally In any revolving body, Newton claimed, a real circular motion of the
body — arising from the body really changing place in absolute space — can be
distinguished from a merely relative circular motion — arising from its
surroundings changing position with regard to it — by the effect of the parts
of the body endeavouring to recede from the axis of rotation. Here we do not draw a blank.
Where we see a spinning body throwing off parts in all directions, we
can be sure it is really spinning. On
the other hand, if the body has no rigidity or cohesion, like a
merry-go-round piled high with old, discarded boots, and we see it spinning
around with none of its contents flying out of it even though they are the
sorts of things that are not stuck together, then we can be sure that the
motion is merely apparent and it is rather the surroundings that are turning. Stage 1: The bucket cord is
wound up and the bucket held. We see
the water in the bucket to have a flat surface. The water is at rest relative to the sides
of the bucket. Stage 2: The bucket is released
and the cord unwinds, spinning the bucket.
Though the bucket spins, its motion is not immediately communicated to
the water. At this stage, the surface
of the water is still flat. However,
the water is in high motion relative to the sides of the bucket. Stage 3: As time passes, the
spinning bucket communicates its motion to the water. As this happens, the water comes to rest
relative to the sides of the bucket.
However, something else happens as well. The surface of the water is no longer flat,
but concave. Because the water is
spinning, its parts are trying to recede from the axis of rotation and the
water is heaving up the sides of the bucket as it tries to do so. So though we have rest relative to the
sides of the bucket, as we did at stage one, everything is not the same as
before. There is a force effect
present that shows the true circular motion of the water, notwithstanding its
rest relative to the sides of the bucket. Stage 4. Though Taken in sum the four stages of the experiment show that there can be
true motion or true rest irrespective of whether there is relative motion or
rest. The latter does not determine
the former. Instead, the former is
indicated by the presence of force effects.
High relative motion can be due to the motion of the surroundings
rather than the contents (as at stage 2), in which case the contents do not
really move, and high absolute motion can occur even when there is zero
relative motion, as at stage 3 where both the contents and the surroundings
are in absolute motion. Questions. Though the bucket experiment
may seem to shatter the view that all motion is relative, commentators
continue to be divided over exactly what it proves. Is the bucket experiment an experiment or
just an illustration? If it is an
experiment is it an empirical experiment, intended to produce an observation
that confirms a theory, or a thought experiment — one that cannot actually be
performed but that appeals to our intuitions about what would happen in some
contrary to fact case? But then, what exactly does the bucket experiment prove? It can’t plausibly prove that when we see
the water move up the sides of the bucket we are seeing the true motion of
the water in absolute space. It can’t
prove this because we know that the Earth is moving relative to the fixed
stars, and therefore that the whole Earth and everything on it, including the
bucket and water are very likely in some state of absolute motion (granting
that it is implausible that the Earth is the only body in the universe that
is truly at rest). So the true or
absolute motion of the water in the bucket could not only be its rotation about its axis in the bucket. It would have to be some combination of
that rotary motion with other motions, not revealed by the experiment. On standard interpretations, the point of the bucket experiment is not
to fix the true, absolute state of motion of the water. The bucket experiment only suffices to
establish a point of principle: that not all motions are merely relative;
there are such things as real or true or absolute motions, even if we may not
know in any given case exactly what they are.
But, it is argued, we don’t need to know this for any given case. All we need to know is that for sure there
are some components of observed motions that are unquestionably due to
absolute motion. If there are absolute
motions, there must be an absolute space.
And thus, the bucket experiment constitutes a kind of empirical
confirmation of the existence of absolute space. On this understanding, But not everyone has been satisfied with the argument considered in
these terms — or, consequently, willing to attribute precisely this version
of it to A problem with this argument is that it does not actually prove that
there is absolute space. It only
proves that there are absolute motions (those indicated by force
effects). It is a bit of a leap to say
that because there are force effects that therefore there must be motion in
absolute space, especially given that we don’t see motion in absolute space. What we do see is, ultimately, motion
relative to the fixed stars. And
perhaps that is all that the bucket experiment proves: that when bodies move
relative to the fixed stars there are force effects that aren’t there when
they are at rest relative to the fixed stars. Newtonians like Euler claimed that it would be an odd thing if the
fixed stars were to direct the inertial properties of bodies here on
Earth. But One response to this line of criticism on the part of defenders (or
reinterpreters) of It is not implausible that Newton would have wanted us to think along
these lines and reach the conclusion that even in an otherwise empty
universe, the water would still rise up the sides of the bucket as it starts
to rotate — or that even in our universe, it would remain flat if the heavens
and all of the rest of the universe were rotating around it, rather than it
rotating within them. That would
certainly scuttle any attempt to argue that inertial forces might be
determined by reference to the fixed stars.
The point of the experiment would be to get us to see that this is not
plausible because intuitively, even if there were no fixed stars there would
still be inertial forces, and even if there were motion relative to the fixed
stars, there might be no inertial forces. But then the “experiment” is not an empirical proof of the existence
of absolute space, but a further conceptual argument in the grand old
Cartesian style — or perhaps just an illustration of what it means to say
that real motion is distinguished by force effects. Perhaps that is all From effects to causes
to properties.
Earlier I alluded to the fact that while To show how this might be done, We could go a step further. We
could take the amount of tension in the cord to be a measure of the degree of
relative motion. Now comes the second stage.
From having determined what we can by reference to the effects of
absolute motion, we turn to the causes:
We deliberately apply a moving force to opposite faces of the two
globes and see whether the tension in the cord increases or decreases. If it increases, we know that the globes
were all along rotating in the direction of the forces we applied. If it decreases, we know they were moving
in the opposite direction. (Keep in
mind that we are in an otherwise empty universe, so this is the only way to
determine the direction of rotation.) At this point we have determined both the speed and the direction of
rotation of the globes. Now imagine the universe filled with bodies and look for some
circumambient objects that appear to be preserving their distance from the
globes and from one another while rotating in the opposite direction. These bodies can be considered to be at
rest in absolute space (because where they rotating they would recede from
one another), and their positions can define positions in absolute space, so
that the absolute state of motion of all other bodies can be determined
relative to them. Thus we really do end up being, at least in principle, able to use
causes and properties as well as effects in order to discriminate absolute
motions. Rejoinders. Two final objections are worth
mentioning. The first is that So we can’t tell what bodies are in absolute motion or at absolute
rest after all. All we can do is say
what bodies are in motion relative to what other bodies. The notion of absolute space is
inapplicable and might as well be abandoned. A final objection reiterates a point made earlier. If the arguments for the existence of
absolute space are all purely conceptual, how does that fit with the
inductivist scientific methodology ESSAY
QUESTIONS AND RESEARCH PROJECTS
1.
2. Leibniz engaged in a
critical correspondence with
1. George Berkeley considered
absolute space and time to be “abstract ideas” that have been invented by
philosophers and that do not reflect anything that could possibly exist. He was unpersuaded by Newton’s bucket
experiment and attempted to respond to it both in his Principles of Human Knowledge 101-117 and in his De Motu 52-66. Explain and assess |