Inside Out

I'm glad to find out that one of my favorite movies is finally available online.

Font for Counterfactuals

I was cleaning up my old files some time ago and found a truetype font I created over a decade ago to print the symbol used to express counterfactual conditionals. In LaTeX, one does so with $A\boxright C$ using the txfonts package. My file also includes a character for the `might' conditional and a few other characters useful to philosophers who must submit material in MSWord. Hope it is of use to someone.

Conference on Causal and Epistemic Asymmetry

The 2007 Shapiro Conference at Brown on Causal and Epistemic Asymmetry turned out well. I now have the audio available for 3 of the talks. The other 3 talks only have partial recordings because of computer problems.

What I'm Reading

With the Pacific APA approaching, I'm reading through Harvey Brown's Physical Relativity, which contains a good discussion of many attempts to figure out how best to interpret the principle of relativity, the content of special relativity, etc.

It reminds me about a puzzle about the various differences between space and time. In Minkowski spacetime, both spatial length and temporal length are treated in the same way, but spatial length doesn't ever get used in the dynamics (of EM or most other theories) whereas temporal length is used for F=ma and half-lives of unstable particles.

This raises a question. Could there be a theory with some implementation of F=ma but without direct use of a temporal metric, treating the time-like dimension just like the space-like dimensions in special relativity?

Guide to Conditionals

I've posted the work from a graduate seminar on conditionals, which is a guide to some of the philosohical literature on conditionals.

Lectures in Foundations of Quantum Mechanics

My spies inform me of some lectures by David Albert on quantum mechanics.

Some comments: In the October 23rd 2006 lecture, the students seem to have some resistance to the idea that the wave-function, instead of being some imprecise representation of dicrete microscopic properties like spin-in-the-z-direction, is the physical reality itself. I'm not sure exactly what the source of the resistance is, but here is something that one needs to keep clear.

There exists the mathematical entity, called the wave function, and the physical entity, which I call the cosmic goo. (Albert uses the term 'wave function' to refer to both the mathematical object and the goo, and that might be a point of confusion.)

Besides the obvious conceptual difference between a physical object and a mathematical object that represents the physical object, the wave function does not map in a one-one way to the physical object. Any global phase change to psi, e.g. sticking a minus sign in front of it, changes the mathematical object, but so changed it would represent one and the same state of the cosmic goo.

The key point Albert is making is that there are no extra properties like spin-in-the-z-direction in the GRW interpretation. There is just the goo.

Causation

Over the summer, I've been writing on causation and now have arrived at a few conclusions as well as a few new hypotheses. I gave a couple of different talks on the subject in Australia in late July, and you should be able listen to all the talks from the Centre for Time conference in Sydney. The recording of mine is now available. Just for a written summary, I'll point out here what I thought were the most important points of my talk.

The broad goal of the part of causal-theorizing I am interested in is the metaphysical project of identifying the physical structures that make it reasonable in typical circumstances to think of the world as operating according to old-fashioned principles of cause and effect.

I've been involved for a number of years now in developing theories that try to explain the causal asymmetry in terms of a global thermodynamic asymmetry, roughly entropy. But as yet, no one has said what an account of causation would be that is compatible with such a story. And that's what I'm giving.

Claim #1: Something very close to J. S. Mill's account of causation, is the best candidate for a theory of the objective causal structure in the world. The argument for this roughly is that deterministic relations among parts of the fundamental physical state of the world play enough of the constitutive roles of causes and effects that it is reasonable to identify the determination relations as constituting objective causation.

The primary problems with such an account break down into three categories. How is indeterminism handled? How is one to make sense of how causation and determination is connected with ordinary usage of the language of cause and effect? What explains the asymmetry of causation?

I'll omit discussion of indeterminism here to save space.

As for how folk causal concepts connects with objective causation, there is a key point to be made about what needs to be explained.

Claim #2: What does not need a unified explanation are the intuitions people have about what causes what in singular cases.

We can explain all we need to explain about the connection between folk causal intuitions and the underlying objective causation by positing a number of (possibly incompatible) principles that have no clear systematization. This leads one to

Claim #3: The literature developing and criticizing accounts of causation based on how well they account for the phenomena of overdetermination, varieties of preemption, double prevention, etc. is a waste of time.

Regarding the causal asymmetry, there are a number of details that have yet to be worked out, but I think the following distinction between influence and promotion constitutes an important advance. I will just illustrate with an ordinary case of forward causation. Because (we can guess) the weather is chaotic enough in just the right ways, whether there is a storm 10 years from now sensitively depends on the exact motion of your finger right now. For simplicity consider two coarse-grained macrostates, finger-up and finger-down. Each macrostate can be implemented with a wide variety of microscopic configurations. Let 'influence' be the name for the dependence of the world on the non-actual finger-macrostate measured with respect to the actual world (microstate) history. Let 'promotion' be the name for the dependence of the world on the non-actual finger-macrostate measured with respect to the actual finger-macrostate. To see the difference, suppose that my finger is in some finger-up state and that there will be a storm exactly 10 years from now. Because storms are relatively rare, the probability that there would have been a storm had I had my finger down is low. This gives us good reason to say that I am having a strong influence on the storm coming about. In causal terms, I am an important partial cause of the future storm. If, instead of comparing the probability of the storm given finger-down to the 100% probability of the storm occurring given the totality of facts about the actual world, we compare the probability of the storm given finger-down to the probability of the storm given finger-up, then it might be that the finger being in one position does not raise the probability of the storm. In such a case, one can say that the finger's position does not promote or inhibit the storm.

Claim #4: The goal in explaining causal asymmetry is to explain the promotion asymmetry, not the influence asymmetry.

I also hypothesize the following.

Claim #5: There is nothing more to explaining the causal asymmetry beyond explaining the promotion asymmetry.

That having been said, I think that to some extent explaining the promotion asymmetry is explaining it away.

Mass

I have been following up on the issue of whether it is better to think of relativistic mass as invariant or not. There are a couple of recent papers, "The Newtonian Limit of Relativity Theory and the Rationality of Theory Change", "There is no really good definition of mass." I find "Does mass really depend on velocity, dad?" more useful and to the point, but I think the issue can be simplified a bit more.

The heart of the issue is how we should align our concepts with the physical facts and laws. Relativistic particles respond to force in the same way as classical particles, by way of an equation F=ma. The question is, "Do the letters in the equation correspond to the same thing (or close enough) in the relativistic and classical theories?" In both Newtonian physics and relativistic physics, acceleration is absolute in the sense of not being relational (i.e., relative to the positions or velocities or other properties of other physical objects). Acceleration geometrically corresponds to the curvature of a particle's world line. In both Newtonian physics and relativistic physics, this curvature is invariant under all spacetime symmetries, including boosts, which allegedly affect mass in the relativistic theory. One can also, in both theories take the mass to be invariant as well. This is a good way to think of F=ma, because the referents of all the variables are then independent of any arbitrary coordinate system or reference frame.

The proponent of relativistic mass believes that mass should be identified with the velocity-dependent quantity (rest mass * gamma). Acceleration should be defined as the change in ordinary three-dimensional velocity v as measured by the passage of coordinate time t. On this definition, the acceleration a, velocity v, and coordinate time t are all quantities that only make sense given some (necessarily arbitrary) reference frame. The dependence of a on v and t is such that the curvature of a particle's world line is gamma * a. Thus, the equation of motion of classical mechanics F=ma=intrinsic mass * curvature becomes F=ma=(rest mass * gamma) * (curvature / gamma).

I suggest that it is needlessly complicated to associate mass with (rest mass * gamma) and acceleration with (curvature / gamma). This is because (1) it makes both the mass and the acceleration frame-dependent quantities and (2) the gamma's cancel out once the mass and acceleration are multiplied together--which is the only law where they appear.

Better to associate mass with the intrinsic mass (i.e., rest mass) so that it is by itself invariant, and the acceleration with the curvature so that it is invariant as well. Thus, the law of motion F=ma directly relates invariant quantities in nature. Unless there is some countervailing reason, it is conceptually clearer to align the referents of the variables used in expressions of the fundamental laws with convention-free quantities that can be thought of directly as physical properties.

There are circumstances that make it seem natural to say the mass of an object increases with its speed. If you have a black box N containing a non-spinning hollow cylinder of mass, and another black box S of identical construction with very quickly spinning hollow cylinder of mass, then the spinning cylinder will appear to have a higher mass by a factor of gamma. This will reveal itself if you put S on a scale or if you put it on a balance or if you try to accelerate it along its axis of rotation. Nevertheless, this can be explained not by positing that the mass has increased, but that time has slowed down for the particles on the surface of the cylinder. Since the particles in S experience a temporal duration that is (1/gamma) times what is experienced by the particles in N. If you are trying to hold them up with a force, you will need to apply some force F to N, but a force F*gamma to S. Because the force on S doesn't have as much time to do the same amount of work, it needs to be stronger by a factor that will cancel the factor by which time is shortened.

Color

Over January, I have been researching color quite a bit. I have found Hazel Rosotti's Colour very useful for a science of color that allows quick answers to questions like, "How do various animals get a blue color?" Also, very good is the C.L. Hardin classic, Color for Philosophers.

Inertia

I've read Donald Lynden-Bell's article "Inertia" which sketches a relationist theory of inertia starting out with a treatment of classical mechanics and concluding that in a cosmological model with "hyperspherical topology," presumably S^3xR, Mach's Principle is fulfilled.

There are a number of features that are standard for relationist treatments of classical mechanics, e.g., a prediction that the angular momentum of the universe is zero. What isn't clear to me is how he can explain Newton's bucket experiment. The article includes an interesting section where he extends the analogy between the Newtonian law of gravitation and the Coulomb force law to suggest that there should be a gravomagnetic force analogous to the magnetic force on a moving charge. In the case of the non-rotating bucket, the rest of the universe is not rotating and we get no interaction. In the case of the rotating bucket, we can take the bucket to be at rest and the rest of the universe to be rotating around the bucket at say 20 revolutions/minute. This creates a gravomagnetic field which is equal to what we ordinarily call the Coriolis force. The question is, if the bucket was taken to be at rest, how does it couple to this gravomagnetic field. In electromagnetism, the magnetic field impresses a force proportional to the velocity of the charged particle. But the bits of water in the bucket are by hypothesis not moving, so how are they affected by the circulating galaxies?

A related article is "Classical Mechanics without Absolute Space" with J. Katz.

F=ma

I've just read a series by Frank Wilczek in Physics Today on the classical idea of force, "Whence the force of F=ma?" parts 1, 2, and 3. One question he raises at the end of part 1 is "why force was--and usually still is--introduced in the foundations of mechanics, when from a logical point of view energy would serve equally well, and arguably better." He then goes on to suggest two reasons, first, that net forces are observable by their changes on momentum and second, that forces seem to accord closely with our "sensory experience of exertion."

I think from a foundational standpoint we can give a better justification of a force-oriented approach to classical mechanics, and relativity as well. First, accelerations are absolute unlike velocities and positions which are only relative to other material bodies. (This assumes that we are working with the spacetime best adapted to classical mechanics, Galilean spacetime.) The fact that accelerations are absolute can in some sense be read straight off of ma=F_1+F_2+.... Second, accelerations can be characterized intrinsically, so that they are reference-frame independent and coordinate independent quantities. Accelerations are given by the covariant derivative of the tangent to any particle's world line along that world line.

Energy, in contrast, is a reference-frame dependent concept. If we describe the motion of some particles in one reference frame, they will have some kinetic energy E. This same system redescribed from a Galilean boosted frame will have some other energy E'. Energy is also not an absolute concept as it is given by mv^2/2, which uses a relational quantity v.

Post-Modernism

When I was recently asked to explain what post-modernism is, I immediately punted, knowing that there are a number of ideas that are tossed together, and I have never had enough patience to sort through them. Fortunately Keith DeRose has written a nice overview, "Characterizing a Fogbank: What Is Postmodernism, and Why Do I Take Such a Dim View of it?" with good links to more extensive discussion.

Spin

I have been reading Levy-Leblond (1967) "Nonrelativistic particles and wave equations," that tries to show that the g=2 result , g being the gyromagnetic ratio, that physicist textbooks routinely say only comes from a relativistic treatment of spin. For example, Sin-Itiro Tomonaga argues in The Story of Spin that the g=2 result comes when we use Lorentz transformations to represent the revolution of electrons around the nucleus. Leblond seems in part to be on track with some of his claims about how the Dirac equation can be treated in a non-relativistic spacetime, but I think the geometry can be expressed better some other way.