1. PHL 356 Philosophy of Physics
Week VI
Is Space Absolute or Relational ?

2. 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.

3. 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.

4. Some senses of “absolute”
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.
Space is not reducible to a system of relations.
Space is not mind-dependent.
Space is a container, a stage in which material 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 material bodies.

5. Some historical views on the different senses of absolute1. 2. 3. 4. 5. 6.
Aristotle
Yes
Newton
Leibniz No
Berkeley & Mach
Kant
Einstein

6. 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.)

7. 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)

8. 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.”

9. 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.

10. 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)

11. Spheres in empty space
Tension in cord

12. 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.)

13. 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

14. 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)

15. “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)

16. A Leibniz “shift” U

17. “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)

18. Leibniz’s Argument Suppose Newton’s 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.

19. 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.

20. 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.

21. 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.

22. 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

23. 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 )

24. “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)

25. 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

26. 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.

27. 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.

28. 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.

30. 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.)

31. 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.”

32. 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.”

33. 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.”

34. Summary
Newton argues for absolute space (and time) using the 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 Newton’s absolute space is metaphysical nonsense.
Einstein agrees and uses Mach’s philosophical view to launch General Relativity.
Today, it remains an open debate. The “hole argument” is currently a focus of much attention (next class).

35. Further Reading Dainton, Time and Space
Sklar, Space, Time, and Spacetime
Earman, World Enough and Spacetime
The first three are introductory, the last is quite advanced.