PHL 356 Philosophy of Physics

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PHL 356 Philosophy of Physics

• Week VI
• Is Space Absolute or Relational ?

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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 or some
  field is to ask about the basic things in it.
• Eg., what is the ontology of arithmetic?
• Its 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 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.

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• 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.

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Some senses of absolute

• Space exists in its own right. It is objectively
  real. It is not dependent in any way on objects
  in space. (This view is often called
  substantivalism, as it holds that space is a
  substance.
• It is not reducible to a system of relations.
• Space is not mind-dependent.
• Space is a container, a stage in which bodies
  exist.
• Space effects matter, but matter does not effect
  space
• Properties of space (eg, metrical or topological)
  are intrinsic to space and not dependent on minds
  or bodies.

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Some historical views on the different senses of
absolute

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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. (Darwins Origin of Species (1859) is also
  a contender for the title.)

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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)

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Newtons 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.

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• 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?
• Conclusion water must be rotating wrt space
  itself
• Thus, space is a thing in its own right.

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Newtons 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)

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Spheres in empty space

Tension in cord
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Newtons 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.)

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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

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Leibnizs 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)

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• 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)

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A Leibniz shift

• U
• U

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• 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)

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Leibnizs Argument

• Suppose Newtons absolute space exists.
• Every point of absolute space is, by def., like
  every other point.
• 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).
• However, God does nothing without a reason
  (Principle of Sufficient Reason).
• Thus, God could not make the universe at any
  place in absolute space.
• But God did make the universe.
• Therefore, (contrary to the initial assumption),
  absolute space does not exist.

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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.

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• 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 Newtons bucket.
• Bucket and rotating globes seem to establish
  absolutism.
• First serious challenge to this was from Mach.

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Clarkes objections

• Clarke objected
• If space is relational, then if God gave the
  universe a jerk, we wouldnt feel it.
• If God made the universe a million years earlier,
  it wouldnt really be earlier.
• Clearly, Clarke badly misunderstands Leibnizs
  view.

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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

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Machs 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 )

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• Newtons 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)

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Machs strategy

• Mach objects to Newtons 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 Newtons thought experiment
• Claims that in an empty universe the balls would
  not act the way Newton says
• Claims that if we could rotate a large mass
  around bucket, water would climb the walls

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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 very plausible.

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The Case for Machs Reply

• Mach proposes a new theory mass is the cause of
  inertial motion.
• No evidence for this
• Motivated by philosophical view empiricism
• However, since this is possible, Mach undermines
  to some extent the degree of belief we had that
  Newtons two balls would maintain tension.
• Machs counter TE may not be as likely as
  Newtons, but it has some plausibility.
• Thus, it is a moderately successful attack on
  Newtons TE hence on absolute space.

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Einstein

• Einstein certainly thought we could do physics
  without Newtons 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.

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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, Machs 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 love us is probably not,
  since we could determine whether the first is
  true or false, but we couldnt tell whether the
  second is true or false.)

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• 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
  Machs 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.

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• 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.

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• 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.

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Summary

• Newton argues for absolute space (and time) using
  bucket thought experiment.
• Leibniz proposes relationalism, citing principle
  of sufficient reason.
• But Leibniz has trouble explaining the bucket
  (ie, his view works well for positions and
  velocities, but not for accelerations).
• Mach (and Berkeley) stress empiricism, claim
  Newtons absolute space is metaphysical nonsense.
• Einstein agrees and uses Machs philosophical
  view to launch General Relativity.
• Today, it remains an open debate. The hole
  argument is currently a focus of much attention.

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Further Reading

• Dainton, Time and Space
• Sklar, Space, Time, and Spacetime
• Earman, World Enough and Spacetime
• Friedman, Foundations of Spacetime Theories
• The first two are introductory, the later two are
  quite advanced texts.

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Assignment for next week

• This is your second short assignment (15). Due
  next week, before class.
• Who won, Newton or Leibniz or Mach?
• Stick to the pre-Relativity situation. You will
  find plenty to read in Huggett.
• As before, your answer should be one page (300
  words), due next week (Wednesday, Feb. 25).
  Note This is a change from the earlier due date
  of one week.
• Submit by email to charissa.varma_at_utoronto.ca