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PHL 356 Philosophy of Physics
Week VI
Is Space Absolute or Relational ?
What is the ontological status of space ?
First, what do we mean by “ontology”?
• Ontology is the study of fundamental stuff, the kinds of
things that might exist.
• To ask about the ontology of some theory is to ask about
the basic things the theory assumes to exist.
• Eg., what is the ontology of arithmetic?
– It’s about numbers and operations on them.
• What is the ontological status of numbers?
– Platonist answer: Numbers are independently existing entities,
outside of space and time. Axioms are (purported) true
descriptions of these numbers.
– Anti-realist answer (one of many): Numbers are just words, with no
independent existence. Axioms are just statements that we
accept, like rules in a game; they are not objectively true or false.
What is the ontological status of space ?
• Is space a thing that exists in its own right,
independent of material bodies?
• Is space a substance?
• Is it absolute in any sense? And what does the term
“absolute” mean?
• Or is space merely a system of relations? If so, what
sorts of relations?
• Similar questions can be asked about time and
spacetime.
Some senses of “absolute”
1.
Space exists in its own right. It is objectively real. It is not
dependent in any way on material objects in space. (This view is
often called “substantivalism,” as it holds that space is a substance.
2.
Space is not reducible to a system of relations.
3.
Space is not mind-dependent.
4.
Space is a container, a stage in which material bodies exist.
5.
Space effects matter, but matter does not effect space
6.
Properties of space (eg, metrical or topological) are intrinsic to
space and not dependent on minds or material bodies.
Some historical views on the
different senses of absolute
1.
2.
3.
4.
5.
6.
Aristotle
Yes
Yes
Yes
Yes
Yes
Yes
Newton
Yes
Yes
Yes
Yes
Yes
Yes
Leibniz
No
No
No
No
No
No
Berkeley & No
Mach
No
No
No
No
No
Kant
No
Yes
No
No
No
Yes
Einstein
No
No
Yes
No
No
No
Newton
• Isaac Newton (1642 – 1727)
• Philosophiae Naturalis
Principia Mathematica
published in 1687.
• This book, known simply as
the Principia, is arguably the
single greatest scientific work
ever. (Darwin’s Origin of
Species (1859) is also a
contender for the title.)
Newton
Newton was the great champion of absolute space.
“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...”
(You will find this and the following quote in Scholium to
Def. 8 of the Principia)
Newton’s bucket
“... the surface of the water will at first be
flat, as before the bucket began to move;
but after that, the bucket by gradually
communicating its motion to the water, will
make it begin to revolve, and recede little by
little from the centre, and ascend up the
sides of the bucket, 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 time with the vessel,
it becomes relatively at rest in it.”
I: water flat and at rest wrt bucket
II: water rotating wrt bucket
III: water at rest wrt bucket, but
surface is concave
What is the difference between I
and III that explains the
concave surface?
Conclusion: water must be rotating
wrt space itself
Thus, space is a thing in its own
right.
Newton’s globes in empty space
“It is indeed a matter of great difficulty to discover... the true motions
of particular bodies from the apparent; because the parts of that
immovable space... by no means come under the observation of our
senses. Yet the thing is not altogether desperate... For instance, if
two globes, kept at a distance one from the other by means of a
cord that connects them, were revolved around their common centre
of gravity, we might, from the tension of the cord, discover the
endeavour of the globes to recede from the axis of their motion...
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 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...” (Principia, 12)
Spheres in empty space
Tension in cord
Newton’s absolutism
• Space exists
• It is a container
• It is independent of any matter or any change of matter
• We should not confuse space with its “sensible measure”
• It is the cause/source of inertia
• Inertial motion (true velocity) cannot be observed, but
acceleration can (eg, in the bucket or spheres examples).
(Acceleration is a change of inertial motion.)
Leibniz
• Gottfried Whilhelm Leibniz
(1646 – 1716)
• One of the all-time great
philosophers
• Co-inventor of the calculus
(with Newton, but
independently)
• Leibniz-Clarke
Correspondence was an
exchange with Newton
Leibniz’s Relationalism
“I hold space to be something merely relative, as
time is; that I hold it to be an order of
coexistences, as time is an order of
successions. For space denotes, in terms of
possibility, an order of things which exist at the
same time, considered as existing together;
without enquiring into their manner of existing.
And when many things are seen together, one
perceives that order of things among
themselves.” (Leibniz, Leibniz-Clarke
Correspondence, 25f)
“I say then, that if space was an absolute being,
there would something happen for which it would
be impossible there should be a sufficient reason.
Which is against my axiom. And I prove it thus.
Space is something absolutely uniform; and,
without the things placed in it, one point of space
does not absolutely differ in any respect
whatsoever from another point of space. Now
from hence it follows, (supposing space to be
something in itself, besides the order of bodies
among themselves,) that 'tis impossible there
should be a reason, why God, preserving the
same situations of bodies among themselves,
should have placed them in space after one
certain particular manner, and not otherwise; why
every thing was not placed the quite contrary way,
for instance, by changing East into West.” (ibid.
26)
A Leibniz “shift”
U
U
“But if space is nothing else, but that order
or relation; and is nothing at all without
bodies, but the possibility of placing them;
then those two states, the one such as it
now is, the other supposed to be the quite
contrary way, would not at all differ from
one another. Their difference therefore is
only to be found in our chimerical
supposition of the reality of space in itself.
But in truth the one would exactly be the
same thing as the other, they being
absolutely indiscernible; and consequently
there is no room to enquire after a reason
of the preference of the one to the other.”
(Leibniz, ibid. 26)
Leibniz’s Argument
1.
2.
Suppose Newton’s absolute space exists.
Every point of absolute space is, by def., like every
other point.
3. Thus, there can be no reason for God to make the
universe at one place in space rather than another (as
long as internal relations are maintained).
4. However, God does nothing without a reason
(Principle of Sufficient Reason).
5. Thus, God could not make the universe at any place
in absolute space.
6. But God did make the universe.
-----------------------------------------------Therefore, (contrary to the initial assumption), absolute
space does not exist.
Leibniz on time
Leibniz gives a similar argument against absolute
time.
– God could have no reason for making the universe at
time t rather than some other time.
– Thus, absolute time does not exist.
– Events do not happen in an independently existing
time; rather time just is the order of events.
– Time began with the creation of the universe.
Leibniz vs Newton
• Apparent fact: Position and velocity are not
detectable, but acceleration is.
• Leibniz makes a strong case against Newton so
long as we ignore accelerations.
• Leibniz had no reply to Newton’s bucket.
• Bucket and rotating globes seem to establish
absolutism.
• First serious challenge to this was from Mach.
Clarke’s objections
• Clarke objected:
– If space is relational, then if God gave the universe a
jerk, we wouldn’t feel it.
– If God made the universe a million years earlier, it
wouldn’t really be earlier.
• Clearly, Clarke badly misunderstands Leibniz’s
view.
Ernst Mach
• 1838-1916
• Austrian physicist-philosopher
• Strong empiricist
• “mach I, mach II,...”
• The Science of Mechanics is a great
book, covering history and philosophy
of mechanics
• Great influence on Einstein and on
Vienna Circle
Mach’s reply
“If we think of the Earth at rest and the other
celestial bodies revolving around it, there is no
flattening of the Earth ... at least according to our
usual conception of the law of inertia. Now one
can solve the difficulty in two ways; either all
motion is absolute, or our law of inertia is
wrongly expressed ... I [prefer] the second. The
law of inertia must be so conceived that exactly
the same thing results from the second
supposition as from the first.” (History and Root
of the Principle of the Conservation of Energy,
1872 )
“Newton’s experiment with the rotating
water bucket teaches us only that the
rotation of water relative to the bucket walls
does not stir any noticeable centrifugal
forces; these are prompted, however, by its
rotation relative to the mass of the Earth and
the other celestial bodies. Nobody can say
how the experiment would turn out, both
quantitatively and qualitatively, if the bucket
walls became increasingly thicker and more
massive and eventually several miles thick.”
(Mach, Science of Mechanics 1883)
Mach’s strategy
• Mach objects to Newton’s non-empirical (ie,
non-observable), absolute space.
• He proposes a new theory: the source of inertia
is NOT space, but rather is distant mass.
• He rejects Newton’s thought experiment
– Claims that in an empty universe the spheres would
not act the way Newton says
– Claims that if we could rotate a large mass around the
bucket, water would climb the walls
The Case for Newton
• We have seen water climb the walls of the
rotating bucket and we have felt the tension in a
string holding a rock that is spinning around us.
• The two globes TE (thought experiment)
assumes they would act the same in empty
space.
• This seems plausible.
The Case for Mach’s Reply
• Mach proposes a new theory: mass is the cause of
inertial motion.
– No evidence for this
– Motivated by popular philosophical view: empiricism
• However, since this is possible, Mach undermines to
some extent the degree of belief we had that Newton’s
two spheres would maintain tension.
• Mach’s counter TE may not be as likely as Newton’s, but
it has some plausibility.
• Thus, it is a moderately successful attack on Newton’s
TE; hence on absolute space.
Einstein
• Einstein certainly thought we could do physics without
Newton’s absolute space. In the opening pages of his
paper on General Relativity (1916) he clearly endorses
the Berkeley-Mach point of view.
• He begins with the remark that in classical mechanics
there is an “epistemological defect...pointed out by Ernst
Mach.” (The Principle of Relativity, 112)
• Einstein then describes a TE with two globes that are in
observable rotation with respect to one another. One is a
sphere, the other an ellipsoid of revolution.
Some key terms
It may be useful to define (again) some key terms
– Epistemology is the study of knowledge, or a theory of knowledge.
Eg, Mach’s epistemology is a strict brand of empiricism.
– Empiricism is the doctrine that all knowledge is based on sensory
experience. Liberal versions allow indirect experience (eg, tracks in
a cloud chamber as evidence of electrons); stricter versions require
direct observation.
– Verificationism is the doctrine that a proposition is meaningful (true
or false) if and only if it can be tested by means of empirical
experience. (Eg, “Bob took the money” is meaningful but “God loves
us” is probably not, since we could determine whether the first is
true or false, but we couldn’t tell whether the second is true or
false.)
Einstein asks “What is the reason for the difference in
the two bodies?”
He then sets empiricist -- indeed, verificationist -conditions on any acceptable answer. His
verificationism leads directly to Mach’s principle
and the principle of general co-variance.
“No answer can be admitted as epistemologically
satisfactory, unless the reason given is an
observable fact of experience. The law of causality
has not the significance of a statement as to the
world of experience, except when observable facts
ultimately appear as causes and effects.”
Einstein then declares that classical physics is not up to
proper epistemological standards. That is, it does not
comply with a strict Machian empiricism.
“Newtonian mechanics does not give a satisfactory
answer to this question. It pronounces as follows: -- The
laws of mechanics apply to the space R1, in respect to
which the body S1 is at rest, but not to the space R2, in
respect to which the body S2 is at rest. But the privileged
space R1 of Galileo, thus introduced, is a merely
factitious cause, and not a thing that can be observed. It
is therefore clear that Newton's mechanics does not
really satisfy the requirement of causality in the case
under consideration, but only apparently does so, since it
makes the factitious cause R1 responsible for the
observable difference in the bodies S1 and S2.”
Einstein then goes on to say how things should be properly
viewed, introducing both Mach's principle and the principle of
general co-variance.
“The only satisfactory answer must be that the physical system
consisting of S1 and S2 reveals within itself no imaginable cause to
which the differing behaviour of S1 and S2 can be referred. The
cause must therefore lie outside this system. We have to take it
that the general laws of motion, which in particular determine the
shapes of S1 and S2, must be such that the mechanical behaviour
of S1 and S2 is partly conditioned, in quite essential respects, by
distant masses which we have not included in the system under
consideration. These distant masses and their motions relative to
S1 and S2 must then be regarded as the seat of the causes (which
must be susceptible to observation) of the different behaviour of
our two bodies S1 and S2. They take over the role of the factitious
cause R1. Of all imaginable spaces R1, R2, etc., in any kind of
motion relatively to one another, there is none which we may look
upon as privileged a priori without reviving the above-mentioned
epistemological objection. The laws of physics must be of such a
nature that they apply to systems of reference in any kind of
motion.”
Summary
1.
Newton argues for absolute space (and time) using the bucket thought
experiment.
2.
Leibniz proposes relationalism, citing principle of sufficient reason.
3.
But Leibniz has trouble explaining the bucket (ie, his view works well for
positions and velocities, but not for accelerations).
4.
Mach (and Berkeley) stress empiricism, claim Newton’s absolute space is
metaphysical nonsense.
5.
Einstein agrees and uses Mach’s philosophical view to launch General
Relativity.
6.
Today, it remains an open debate. The “hole argument” is currently a
focus of much attention (next class).
Further Reading
Dainton, Time and Space
Sklar, Space, Time, and Spacetime
http://plato.stanford.edu/entries/spacetimetheories/
Earman, World Enough and Spacetime
The first three are introductory, the last is quite
advanced.