PH201/400 – Week 20 Philosophy of the Special Sciences: Space and Time in Newtonian Physics

1. PH201/400 – Week 20 Philosophy of the Special Sciences: Space and Time in Newtonian Physics

3. 1. Introduction What is Philosophy of a Special Science? So far: ‘General’ philosophy of science: address general topics like explanation and use cases from particular sciences as examples. Trend since the late 1970s - Philosophy of special science: address specific questions that arise in a special science.

4. The Project: • Bring a modern scientific theory to bear on traditional philosophical concerns. Examples: relativity and the nature of space and time, quantum mechanics and determinism, … • Analyse the basic concepts a theory uses. Examples: the nature of the wave function in quantum mechanics, the units of selection in evolutionary biology, … • Discuss the methods used in a certain science. E.g. experiments in economics, … • …

5. Examples: • Philosophy of physics (quantum mechanics and action at a distance, the ontology of quantum field theory, the nature of spacetime, …) • Philosophy of biology (the units of selection problem, part-whole relations, big data, …) • Philosophy of Chemistry (the nature of chemical bond, reduction to physics, … • Philosophy of economics (the nature of rational decision making, the use of false models to make predictions, …) • …

6. 2. Newtonian’s Axioms (1) Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. Formally: if F = 0 then a := d2x/dt2 = 0. (2) The change of motion is proportional to the motive force impressed and it is made in the direction in which that force is impressed. Formally: F = ma = m d2x/dt2 (Newton’s equation). (3) To every action there is always opposed an equal reaction: or, the mutual action of two bodies upon each other are always equal, and directed to contrary parts. Formally: F12 = – F21 Note: (1) is a special case of (2). So (1) is redundant.

7. 3. Newton on Space and Time Question: What do x and t in the above expressions mean? Space and time. Yes, but what is exactly does that mean? To highlight the problem notice that implicit in the principle of inertia (axiom 1) is the distinction between objects in constant versus accelerated motion. This is ill defined as everything is at rest in some system and accelerated in another one.

8. Background: The Cartesian association of space with matter: the defining feature of matter is its extension. So space is not just the ‘arena’ in which matter is located. Therefore: true motion is a relational notion

9. Newton denies the Cartesian position: • Space and time are independent entities. • Absolute space is something as real as matter and its existence does not require matter. • Intuitively: space is like a container in which one can place material objects. But as the container does not depend on the objects placed in it, space does not depend on the objects placed in it. Space and the objects it contains are distinct and equally real.

10. For this reason his view has become known as ‘substantivalism’ (some times ‘absolutism’). • The opposite of this doctrine is relationism: it denies the existence of a matter-independent space and instead views space as a system of relations between objects. • This is Leibniz’s position; see below.

11. Newton then describes absolute space and time and contrasts them with relative space and relative time (p.118): Absolute space: ‘Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.’ Relative space: ‘Relative space is some movable dimension or measure of absolute spaces; which our senses determine by its position to bodies […]’

12. Absolute motion: ‘Absolute motion is the translation of a body from one absolute place into another […]’ Relative motion: ‘relative motion [is] the translation from one relative place into another.’ Example:

13. Absolute time: ‘Absolute, true, and mathematical time […] flows equably without relation to anything external.’ Relative time: ‘relative, apparent, and common time, is some sensible and external […] measure of duration by means of motion, which is commonly used instead of true time; such as an hour a day, a month, a year.’

14. Newton’s claim: absolute time/space are not reducible to relative time/space. • These descriptions give us some indications of what Newton has in mind, but they are not definitions. So what then is absolute space? • Space is composed of points, which figure as a kind of ‘building blocks’ for more complex geometrical objects such as lines and surfaces and volumes. • These points exist independently of material objects in two senses:

15. These points exist independently of material objects in two senses: • Locations exist before material bodies occupy them. These space points are possible absolute places for material objects, over and above their relative locations. • Space would exist even if there were no matter.

16. Characteristics of absolute Space: • Immutability: Space is distinct from matter, but in addition to this it is also unaffected by matter (or by anything else). That is, the presence of matter does not change space time points themselves or any of their features. • Absolute space is a three-dimensional (Euclidean) ‘box’ that exists without changing, neither in time nor with matter. Absolute space is like the stage on which the drama is played: it ‘hosts’ the actors but is unaffected by them. • Every point of absolute space is exactly like every other. All points are the same and hence there is no experimental method (not even in principle) to distinguish one absolute place from any other (p. 161).

17. Problem: • This characterisation of absolute space makes it hard to understand what absolute space is because the objects we are familiar with are material. • Absolute space and time are not accessible to experience. • But: ‘we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects.’ (p. 120) • Everyday example: You feel pushed towards the front when the bus stops; circular fun fair rides.

18. Newton’s Bucket: Motion of the Water 1 2 3 4 Motion of the bucket Watch the experiment:https://www.youtube.com/watch?v=sjXLHP25OwY

19. Analysis: The reason that the water curves is rotation. But – and this is the salient point – it is not rotation relative to the bucket, as situations 2 to 4 show. In situations 2 and 4 the water rotates relative to the bucket, yet in one situation the water is curved and in the other it is not; in situation 3 the water is at rest relative to the bucket, and yet it is curved.

20. From this Newton concludes that it must be motion with respect to absolute space which brings about the observable effect : ‘This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here [in situation 3] directly contrary to the relative, becomes known, and may be measured by this endeavour.’ (p. 122, emphasis added) But the experiment shows even more, as Newton himself (in the above quote) says: we can experience the effects of absolute space.

21. Newton’s globes F=0 F=5 Situation 1 Situation 2 By assumption the two globes are the only objects in the universe. So there is no difference in the relational properties between the globes in situation 1 and 2; so the globes do not move relatively at all. But yet there is no tension in situation 1 while there is one in situation 2.

22. Conclusion: There is a detectible motion that is not comprehensible as a relative motion. So the effect is due to motion in absolute space. Study question: how can Newton know?

23. Remaining Worries: • Absolute space acts on mass, but not vice versa (by assumption). How does this square with Newton’s third principle? • How to detect the absolute position and velocity of something in absolute space?

24. 4. Relationism Starting point: whenever we deal with space in (scientific) practice, all we need is a an object that serves as a reference point, relative to which the position of an object is determined. In other words, we need a frame of reference, that is, relative space. Example: when we send a satellite in space we use the earth as reference point.

25. Given a frame, we can define relative motion as the change of position relative to the reference body and we can specify unequivocally the location of any object at any time. Reaction: what more can be said? Isn’t this all we need? Why postulate an unobservable absolute space? There simply is no absolute frame of reference!

26. This leads to relationism: ‘I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistence, as time is an order of successions.’ (Leibniz, p. 146; emph. added) Or to put it another way, without matter there would be no relations between things and hence no space! Note: ‘relational’, ‘relationist’, or ‘relative’ as used here are distinct from ‘relativistic’ in the sense of Einstein’s relativity theory.

27. Problem: • This point of view implies that any reference frame is as good as any other. However, it is obvious that not all systems are equal because the law of inertia cannot hold in every relative frame. • Example: a force is acting on a particle and it accelerates (in the laboratory system). Now consider a reference frame that takes the particle itself as reference point. In such a reference frame the law of inertia is false, as there is a force acting on the particle but it does not accelerate. • By definition, the frames in which the law holds are called ‘inertial frames.

28. Question: How can one account for this inequality from a relationist point of view? How do we decide which frames are inertial frames? Study question: How do Newton’s bucket and globe experiments look from a relationist perspective? Note: all these problems recur in the context of modern space time theories (STR and GTR).

30. Appendix: The Leibniz – Clarke Correspondence Historical remark: the correspondence is a series of letters exchanged in the years 1715-1716 between Leibniz and Newton’s spokesman Clark. Leibniz: the principle of sufficient reason (PSR): ‘nothing happens without a reason why it should be so, rather than otherwise.’ (p. 145) Then: ‘… 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.’ (p. 147)

31. And that ‘something’ is the following (p.147): (P0) PSR is true. (P1) Space is absolutely uniform; that is, one point of space does not differ from any other one. [This follows from Newton’s substantivalism.] (P2) If all points of space are the same, then ‘[it is] impossible there should be a reason, why God, preserving the same situation of bodies among themselves, should have places them in space after one certain particular manner, and not otherwise; why everything was not placed the quite contrary way, for instance, by changing East into West.’ (p. 147) (P3) Things are placed in a certain way, and according to the principle of sufficient reason there must be a reason for this. Contradiction! There is and there is no sufficient reason to place a certain collection of object.

32. Leibniz’s conclusion: (P1) has to be rejected and with it Newton’s substantivalism. Moreover, Leibniz claims that relationism evades the problem: ‘But if space is nothing else, but that order of relation; and is nothing at all without bodies […] 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.’ (p. 147) Clarke’s reply: ‘[M]ere will, without any thing external to influence it, is alone that sufficient reason.’ (p.147) – That is, God does not need any reason other than his will!

33. So: Clarke accepts the PSR, but has a rather different understanding of it. Leibniz’s argument depends on knowing the kind of reasons for action that God might find compelling. Clarke, however, has a different conception of God’s decision making: that God wants something, for whatever reason, is a sufficient reason. Neither of these lines of argument seems promising because they depend on theological subtleties. So let’s turn to something more promising. Study question: Is the PSR plausible? Should we accept it?

34. Clarke then puts forward the following arguments against the relationist view: (1) The static shift: ‘Different places are really different or distinct one from another, though they be perfectly alike. And there is an obvious absurdity in supposing space not to be real […] if the earth and sun and moon had been placed where the remotest stars now are […] it would not only have been […] la même chose […], which is very true: but it would also follow, that they would have been in the same place, as they are now: which is an express contradiction.’ (p. 148)

35. (2) The kinematic shift: Imagine God moves the entire universe with constant velocity along a straight line through space. On the relationist view, (a) the universe would always be at the same place, and (b) nothing would receive a shock should the motion be stopped suddenly. The first claim is absurd, the second wrong. (p. 148) Leibniz’s reply turns these arguments around and uses them against absolute space. In both cases he argues, contrary to Clarke’s view, that, as the shifts in both cases do not make any practical difference, there simply is no difference. So for the relationist such shifts indeed do not make any difference at all because, by definition, they leave the relations constant.

36. In greater detail, Leibniz’s argument is based on the so-called principle of the identity of indiscernibles (PII). This principle asserts that no two separate individual things can differ only numerically, that is, resemble one another in all their properties and yet not be one and the same thing. In terms of second-order logic the principle reads: For all F (Faiff Fb) a=b. It is worthwhile noting that this is equivalent to: a=b There exists an F so that (Fa & ¬Fb). In words: if a and b are not equal, then there exists a property F such that a has F but b does not. It is this form of the PII that will mainly be used in what follows.

37. Note: The converse of the law, the so-called ‘Principle of the Indiscernibiliy of Identicals’ is unproblematic: a=b For all F (Fa  Fb). Now Leibniz uses this principle to rebut Clarke: The original and the shifted universe cannot be told apart; so according to PII they are the same. But if absolute space did exist, then they would have different locations (or velocities). For this reason, the existence of absolute space is incompatible with PII. Given that we accept PII, we have to reject absolute space.

38. Clarke’s reply: There are motions that differ from one another without being detected. E.g. inside a dark room in a ship it is not possible to tell whether you are at rest or travelling at constant speed. The situation with regard to absolute space is exactly analogous. Leibniz’s reply: It is not actual detection of a difference that matters; what matters is that one could possibly tell the difference in motion. This is so in the case of the ship, but not in the case of absolute space. So whether or not the ship moves is not indiscernible; but whether or not something moves with respect to absolute space is indiscernible.

39. Study question: Why should we accept PII? What becomes of Leibniz’s arguments when we deny it? Problem: These arguments only refute Clarke’s arguments using static and kinematic shifts. But what about acceleration? Imagine the same scenario as above just with the following difference: the universe is not moved with constant velocity but with constant acceleration (dynamic shift). In the accelerated universe new inertial effects would appear, making it discernible from the one that is at rest or in constant motion. How can Leibniz cope with this? Leibniz does not seem to give a satisfactory answer to this problem. So the question remains: how can a relationist account for these inertial effects? Exercise: Most of the arguments so far have been concerned with space. Carry the above points over to the case of time.