Office hours for the remainder of the term:

• Thursday, 6 December, 2pm-3pm
• Friday, 7 December, 10am-12pm
• Monday, 10 December, 11am-12pm and 1pm-2pm
• Thursday, 13 December, 2pm-4pm

What is the nature of space and time? This class will address this metaphysical question and survey the classic debates in the philosophy of space and time. These debates are inextricably linked with developments in fundamental physics, in particular Newtonian mechanics, statistical mechanics, special and general relativity. We will try to understand how the metaphysical issues concerning space and time interact with foundational issues in spacetime physics.

Prerequisites: Upper-division standing or permission of instructor.

How much technical background is needed for this course? The course is self-contained in the sense that all the physics necessary for doing well in the course will be taught in class. Many humanities majors, for instance, have excelled in earlier versions of this course.

Course materials such as lecture notes, handouts, etc will be made available as they will be used in class.

• Syllabus
• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Midterm Paper Assignment (due 6 November 2007)
• Lecture 9
• Lecture 10
• Lecture 11
• Lecture 12
• Lecture 13
• Lecture 16
• Lecture 17
• Lecture 18

The following articles are from the Stanford Encyclopedia of Philosophy, edited by Ed Zalta:

• Chris Mortensen: Change
• Craig Callender: Thermodynamic asymmetry in time
• Robin LePoidevin: The experience and perception of time
• Nick Huggett and Carl Hoefer: Absolute and relational theories of space and motion
• Robert Rynasiewicz: Newton`s views on space, time, and motion
• Robert DiSalle: Space and time: inertial frames
• Steven Savitt: Being and becoming in modern physics
• John D Norton: The hole argument

Michel Janssen`s survey article on special relativity is also freely availale on the internet. You should also read the relevant topics in the Internet Encyclopedia of Philosophy's entry on time as we go along.

The following articles will be available from e-reserves by the beginning of the term:

• Donald C Williams, "The myth of passage," Journal of Philosophy 48 (1951), 457-472.
• Ned Markosian, "How fast does time pass?" Philosophy and Phenomenological Resarch 53 (1993), 829-844.
• David Lewis, "The Paradoxes of Time Travel," American Philosophical Quarterly 13 (1976), 145-52.
• David Deutsch and Michael Lockwood, "The quantum physics of time travel," Scientific American 270/3 (March 1994), 68-74.
• Lee Smolin, "Atoms of space and time," Scientific American 290/1 (January 2004), 56-65.

Link to this course`s e-reserves page

Quiz 1

Quiz 2

Question 1

Many forgot to state that the entropic asymmetry is fundamental and that this means that all other temporal asymmetries are grounded in the entropic one.

Question 2

I expected you to mention the entropy of a physical system. Furthermore, it is not the case that according to Boltzmann a decrease of entropy should never happen. It can, it`s just rare.

Question 3

Importantly, this is a question about predication, but about truth-making!

Question 4

Generally well solved.

Question 5

This one is about truth and truth conditions for statements, not about knowledge we can or cannot have.

Quiz 3

Question 1

Either you knew it or you didn`t.

Question 2

This thesis is about the phenomenology of temporality, not anything else. Also, you should just state the thesis, not go into details about how detensers explain the experience of temporality.

Question 3

Importantly, this experimental discovery undermines the inference from our subjective experience of the moving now to an objectively existing present.

Question 4

The grandfather paradox is not an ontological paradox, look it up! I still gave half credit if you correctly resolved the paradox you stated.

Question 5

Again, either you knew it or you didn`t.

Midterm Paper

Quiz 4

Question 1

I have accepted a wide range of answers of what the ship mast experiment was supposed to show, from "refutation of tower argument" to "rock partaking in ships`s motion" or "demonstration of inertia" to "circular inertia" and "Newton`s first law".

Question 2

This was sort of a trick question. Of course, Newton thinks that relative motion exists, as he makes clear in the passages from the Scholium cited by Dainton. He just thinks that absolute motion is ontologically prior.

Question 3

The answer is the intrinsic conception. If you forgot what this is, you should probably go and look it up.

Question 4

Here I expected people to describe all four phases of the experiment, something that seems simple enough yet many didn`t do it properly.

Question 5

The statement doesn`t make sense in neo-Newtonian spacetime. Go look it up in Dainton, p186.

Quiz 5

Question 1

Mach came up with an alternative explanation of inertial effects, particularly the concave shape of the water`s surface. His explanation included only relative motion: the water`s surface curves because of the relative rotation of the water to the shell of distant masses. For Mach, whether the water or the shell of distant masses rotates has exactly the same effects, viz. the concavity. For Newton, in the latter case the water`s surface will not be concave.

Question 2

Here it was important that you tell me about inertial transformations and how they show that absolute motion in undefined in neo-Newtonian spacetime, as per the question.

Question 3

Almost nobody told me what the general concept of a symmetry is in the context of spacetime theories. A symmetry is a transformation that leaves the structure of the spacetime unchanged. For the second part of the question, it`s important to note that I am asking only about the symmetries of the spatial hypersurfaces, which are rotation, reflection, and translation.

Question 4

Many forgot to tell me what a geodesic was and why this is important here. A geodesic is the shortest path between two points, a sort of generalisation of the notion of a straight line but for spaces or arbitrary dimension and curvature. If you are tracing out a triangle in order to measure its internal angles, the sides must be "straight", i.e. they must be geodesics.

Question 5

The answer is given on the slides 15 and 16 of Lecture 13. It has nothing to do with dimensionality (except perhaps that it should be at least two-dimensional as otherwise the notion of parallels doesn`t make sense).

Quiz 6

Question 1

Go look it up if you didn`t get it!.

Question 2

The hypothesis tested for was "The light speed relative to an observer depends on the observer`s motion through the medium/aether", and not really "The aether exists". Also, you should have discussed the set-up of the experiment.

Question 3

Generally well solved. It`s of course that two inertial observers at relative velocity to one another in general don`t agree as to which distant events are simultaneous with the "here-now". You really need to understand this, it`s arguably the most important result from physics for all of philosophy of time.

Question 4

Important: this is more than just the relativity of simultaneity, although it crucially depends on that. Please give me the full argument if I ask you to!

Question 5

Light cone presentism is the position according to which all events and only those events on the surface of the past light cone are "present" and therefore real. It`s a response because it depends only on the invariant structure of Minkowski spacetime, i.e. the structure on which all inertial observers agree.

Instructions for Final Exam

You will need a blue book. The readings covered will be all those on the syllabus, except Chs 14, 15, 19, 20 from Dainton and the SEP entry on the hole argument.

There will be three types of questions. First, short identification questions (such as "Presentism") where you will have to give a one-sentence description of what the term given means. Second, one- to two-paragraph answers where you have to explain something rather specific, e.g. "Describe Newton`s bucket experiment. Why did he believe that it established substantivalism? What was Mach`s relationist response to the thought experiment?" I think the quizzes will serve as a great wa to prepare for these questions. Third, you will have to write one or two essays which synthesize material from the course. You might be asked e.g. to defend a position against an objection or formulate an objection yourself and then defend the position against it. You will likely be given some choice here, such as write two essays on the following three topics.

Final exam

The class average was 23.9 points.

Identifications (worth one point each):

Question 2

Many did not know this. Boltzmann used this hypothesis to anchor the low-entropy initial state of the universe.

Question 7

Spacetime symmetries are transformations that leave the spacetime structure invariant.

Short answers (worth three points each):

Question 2

Closed timelike curves permit travelling into the past in the context of GR and consistency constraints render the grandfather paradox impotent in prohibiting this possibility. The twin paradox occurs in the context of special relativity.

Question 4

This was not about the rotating disc as encountered when we discussed length contraction in the context of special relativity. Perhaps worst solved of all questions.

Long answers (worth seven points each)

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