Sunday, June 17, 2007

Inertia and Determinism

For one reason or another, I often find myself driving the Taconic State Parkway at night (which, if you've ever done that, you know what I'm saying). On one of these trips I was heading back up to Vermont after a dinner meeting in New York. It was already late when I left the city, and out on the dark road I was keeping myself awake by thinking of some fiendish physics problems to give to my students. (Such are the revenge fantasies of physics professors.) I thought of this one:

A particle moving in one dimension has the trajectory x(t) = t^4.

(a) What is the velocity of the particle at time t=0?
(b) What is the net force acting on the particle at time t=0?
(c) In view of (a) and (b), why does the particle move at all?


I ran through the answers in my mind: (a): The particle is at rest at time t=0. (b): There is no net force on the particle at time t=0. (c): (c): (c):

My grip on the wheel loosened, and my eyes focused on the far distance, as I realized that I didn't really know the answer to part (c) myself!

The Taconic is basically a giant deer park, especially in the middle of the night, so for safety's sake I had to drop the problem and get back to scanning the verges. But over the next year I thought about the problem from time to time, struggling to clarify my thinking on some subtle issues. Finally I wrote up some of the results, and the resulting article, entitled "Inertia and Determinism," has been accepted for publication in
The British Journal for the Philosophy of Science.

I continue to reflect on the curious trajectory of this project - from its whimsical origins in my teaching practice, to its fruition as a published research paper. And meanwhile, my Year of Isaac Newton continues: this summer I'm writing the solutions for the end-of-chapter problems in my manuscript on Newton's Laws. Hopefully I'll know how to answer my own questions this time....

***

Just for the sake of interest, I'll end by excerpting some of the less mathematical material from the paper; for references, see the PDF:

From J. Zimba, "Inertia and Determinism," to appear, Brit. J. Phil. Sci.:

"Beginning in the 19th Century with Ernst Mach and Rouse Ball, and continuing on to more recent times, commentators on Newtonian mechanics have universally asserted that the Law of Inertia follows immediately from the Second Law. Does it? If we are willing to insist, as an axiom on a par with the Laws of Motion themselves, that non-Lipschitz forces do not belong to the theory, then the answer is yes. But if we do not wish to make this a priori restriction on the kinds of forces that may appear in the theory, then we can say two things. First, the Law of Inertia itself stands incomplete, or at least ambiguous, until a specific approach to [[problems like the x(t) = t^4 problem]] is selected. And, second, whatever approach is selected, the completed Law of Inertia will no longer follow mathematically from the Second Law. The Law of Inertia would instead act as a boundary condition, selecting the physical trajectory from among the many mathematical solutions to the Second Law differential equation."

...

"Within the community of mathematicians and physicists, it is often taken for granted that Newtonian mechanics has a deterministic structure. At times, this is even made a matter of definition. Arnold defines classical mechanics as the study of 'the motion of systems whose past and future are uniquely determined by the initial positions and initial velocities of all particles of the system.' Landau and Lifshitz go beyond mere definition, claiming that determinism is in fact an observed feature of classical systems. But such observations could only apply to the small class of non-chaotic systems. And for that matter, to the best of our knowledge, our world is not, in fact, deterministic; so the claim that determinism has ever been observed is open to dispute.

"Mathematicians like Arnold probably want to impose smoothness conditions because doing so makes theorems easier to prove. Then, having imposed the smoothness condition, they don't want to feel that they are leaving out any interesting behaviors; so they define classical mechanics to be the very mathematical object they are studying. Maybe the mathematicians are correct that their theorems are not leaving out any interesting behaviors. But I don't think they can be correct in saying that the smoothness conditions of their treatises are mandated by observed facts about determinism."

...

"One response to this example might be to attempt to repair [the Law of Inertia], or to strengthen it, leading to a conception of the Law of Inertia so strong that it ensures determinism in all possible situations. But it is unclear whether such a program is mathematically possible. Another approach would be to give up the attempt to complete the Laws of Motion, and simply conclude - despite the prejudices of history - that Newtonian mechanics is, and always has been, an indeterministic picture of the universe."

Sunday, June 3, 2007

This Time, It's Personal

Tomorrow morning I'm flying to Detroit. I'll be returning to Vermont the very next day on a chartered plane. With me on the charter will be some crew members, some medical personnel, and both of my parents, who'll be secured in gurneys for the flight. After we land at the Bennington regional airport, an ambulance will carry my parents and me to the Prospect House nursing home, which stands at the edge of the campus where I teach.

When we get to the nursing home, an aide and I will wheel both of my parents into my dad's room. My mom will want to see where her husband will be staying. Next I'll wheel my mom into her room, so she can meet her roommate. I'll hang some family pictures on the walls of both rooms. I'll make a list of what their rooms will need in order to be comfortable. Then I'll wheel my dad over to visit with my mom in her room. Later, my wife will come over from work, and she and I will sit with my parents for dinner. When dinner is over, my parents will each go back to their rooms and sleep among strangers in strange beds.

Apparently, my dad was quite a traveler in his day. I've seen pictures of him that were taken in rural Mexico during the 1960's, and he's told stories of a trip to California back in 1955. (He hired a farmer to fly him around Orange County in a cropduster, back when it was all farmland there.) When my sister and I were three or four years old, he brought us back some souvenirs from a trip to Morocco. But that trip in 1973 or thereabouts was apparently the last hurrah. In the 1970's the bottom started dropping out of Detroit, and the restaurant my parents operated began losing money. In 1985, after years of struggle, my dad finally sold the business and the land it was on - land that had once been pasture on his father's farm.

By 1999 my parents were doing better, thanks to the income my dad was earning as a screw machine operator. A strong man, and a hard worker ever since his childhood on the farm, he was now (at the age of 72) working sixty-hour weeks in a hot factory. I know how hot it was, because I worked with him there back in the summer of 1992, when I was between terms at Oxford. My dad and I were both on second shift. As a Rhodes Scholar/Night Janitor, I was responsible for cleaning the front offices, as well as the shop floor and bathrooms. (Let me tell you sometime about the hazing rituals that factory workers have for new college-boy janitors. For now, I'll just say that one of them involves playfully permuting the functions of various bathroom fixtures.)

That summer my dad and I both reported to the night foreman, who was an asshole named Hugh, but everybody called him Baby Huey when he wasn't around. One night I got some kind of food poisoning, and I was lying flat on my back out on the oily shop floor, moaning and holding my stomach. Huey came by and saw me lying next to my mop bucket, and he said, "What's wrong?" I said, "I'm sick." He said, "You know, your dad works." (His tone added a parenthetical, "Unlike you.")

In 1999 I had found more agreeable work as a doctoral student in physics at Berkeley. On the academic schedule I had plenty of free time, and my mom and I thought it would be nice if my dad could do some traveling, like when he was young. So I planned a trip to Istanbul and Rome. I flew from Oakland to Detroit, where I picked up my dad, and together we flew from Detroit to Istanbul for the first leg of the trip.

When I saw him, the first thing I noticed was that he was walking on his tiptoes with an odd shuffling motion. When I mentioned it, he said that he'd been healing slowly from his hernia operation. (He had finally gotten around to having an operation for a hernia that he got while working construction back in 1985 - his first job after selling the restaurant.) This made sense, so I didn't think much of it.

That shuffling gait was the onset of a neurodegenerative disease, one that resembles Parkinsons in its symptoms, while not responding to Parkinsons treatments. Today my dad is in bed almost 24 hours a day. Apart from the motor control and related issues, he's in fairly good health. He's just completely helpless.

When I graduated from Williams College in 1991, my whole family came out for the commencement ceremonies. During the weekend, we took a side trip to Mount Equinox in southern Vermont. My mother, who grew up in Chattanooga living amidst the Smoky Mountains, pronounced Vermont to her liking. She said that if there were anyplace she would ever go to live besides back to Chattanooga, it would be Vermont.

Were she born in a different time and place, my mother would have been a senator. Though uneducated, she has an iron will and rare qualities of intellect. As recently as six months ago she was enjoying her usual pastimes, which include correcting the poker players' mistakes on ESPN, reading 50 books a month, and doing the Sunday Times crossword with fearful automaticity.

Then in January she came down with pneumonia and septicemia, spending the next month in and out of the hospital. The doctors also diagnosed her with emphysema and a heart condition. (It had been decades since she'd had a physical.) Her illnesses have aged her: dulled her wits, left her weak. Since February she's been mostly confined to her bed at home, breathing compressed oxygen.

My half-brother Wayne, who lives in my parents' basement and who is frankly a little slow, has been my dad's primary caregiver these past several years. As long as my mom was healthy, things were stable. The situation had its drawbacks, but it kept my parents in their home, which is what was most important to them.

But since February, when my mom returned home from the hospital, my parents have both needed care 24 hours a day from home health aides, to the tune of $24,000 per month. As my parents' attorney-in-fact, I have been signing the checks. From the start, simple arithmetic said they would have to move.

None of my parents' options were good. My brothers and sisters and I have chosen as well as we could for them. On Tuesday, my mom will see the green hills of Vermont again, and my dad will have one more plane ride.