Tuesday, February 4, 2020

Einstein, relative rest, and invariance in physics

Well, my 21st century writing about relativity finally did get published, on the "Voices" page of the Arkansas Democrat-Gazette, on November 3, 2007, almost exactly seven years after I started working on it and tried to interest the NY Times and Harper's magazine, without success. Publication on the Voices page meant there was no payment involved. It was really just a long letter to the editor labeled a "Guest Column." Here it is, slightly edited for clarity that was lacking in the published version:


Once upon a time, in the fall of 1977, I had the perfect job. I was a night watchman at the Old State House, usually working the 4 p.m. to midnight shift. My job was to make rounds through the building every hour. The job was perfect because I was a full-time student at UALR, and making a round took only ten minutes. In theory, I had 50 minutes out of each hour for studying.

In practice, I tended to read whatever interested me and to put off working on my homework as long as possible. I also had the luxury of being able to explore the Old State House all by myself whenever I felt like it. Procrastination, of course, is not an uncommon activity among college students. My happy situation was that I was getting paid for it—with a portion of your Arkansas tax dollar.

Or maybe it was your parents’ or grandparents’ dollar. Whatever the case may be, I’d like to now offer a little in the way of a return on that 30-year investment. I’d like to pass along a little bit of scientific knowledge.

During the fall of 1977, I was taking a beginning class in relativity and quantum mechanics. A good deal of my extracurricular reading during the evenings at the Old State House involved those subjects. Among other things, I was trying to find out if relativity really should be associated with the saying “It’s all relative.” I’d read that statement in a newspaper article about the virtuoso violinist and former child prodigy Yehudi Menuhin, who was asked what he’d learned from his acquaintance with Albert Einstein. Menuhin claimed to have learned from Einstein the same thing everyone else had learned, namely that “everything is relative.”

What I’ve learned over the years is that Einstein’s theory means the opposite of what it sounds like it means. When I started teaching physics about ten years ago, I came up with a way of paraphrasing the usual textbook description of the two ideas Einstein used in creating his theory. The ideas, or postulates, can be stated as 1) the laws of physics are not relative, and 2) the speed of light is not relative.

Those are the requirements that went into relativity. In actually finding equations for laws that satisfy these ideas, Einstein rewrote Newton’s laws of motion, simplified the laws of electricity and magnetism, and discovered several new laws, the most well known of which is the equivalence of energy and mass, E = mc2.

Besides the laws themselves, other mathematical entities are invariant in relativity. In particular, space, time, and the speed of light combine together in a simple equation for an invariant quantity called “proper time.” (This is a mistranslation from the French word propre, meaning “own”.) Proper time is the time you read on your own watch. Since you and your watch never move relative to each other, you never observe your own watch to speed up or slow down--contrary to the popular misconception of time slowing down the faster you travel. The slowing down of time is only valid when you compare your time to the time of the clocks in another rest frame, such as the one you left when you went moving off on your own. "Moving on your own," however, is just like not moving at all. That is the real message of relativity.

Relativity is not the name Einstein chose for his theory. He would have preferred it to be called the theory of invariants. This misnaming can be blamed on several of Einstein’s older contemporaries, including the French mathematician Henrí Poincaré and the German physicist Max Planck. Einstein unfortunately in his first relativity paper in 1905 used the accepted terminology of the time and called his first postulate "the principle of relativity". He later objected to his entire theory being called relativity, but he acquiesced to common usage among physicists in 1915 when he named his theory of gravity the general theory of relativity.

Gerald Holton, the grand old man of Einstein studies and an emeritus professor of physics at Harvard, wrote something of an off-the-beaten-path book published in 1996 called “Einstein, History and Other Passions.” Holton neatly summarizes the relative/relativity name confusion: “The cliché became, erroneously, ‘everything is relative’; whereas the point is that out of the vast flux one can distill the very opposite: ‘some things are invariant.’”

So, “everything is relative” may be a balm of hurt minds, but physicists are looking for those things in the universe that are invariant. Invariance, by the way, is related to symmetry, but you’ll have to look that up for yourself.



Update March 14, 2012, Einstein’s 133rd birth anniversary:

Relativity is more about relative rest than relative motion. The question is, can you put yourself in any situation where you can actually say you're NOT at rest? In other words, can you do experiments that will show you are moving?

Constant velocity, with which we are all quite familiar, is just like not being in motion, and so is constant acceleration, as long as it’s either  straight line acceleration or centripetal acceleration (such as going around a curve in a car, or being on an orbiting planet or, in your imagination, on an orbiting electron). The forces we feel during either type of acceleration are, in general relativity, attributable to an equivalent acceleration due to a gravitational field.

There is one type of motion that can’t be considered equivalent to being at rest.  If you had the proper equipment you could do measurements right now that would tell you you’re moving. Yes, being “at rest” on the surface of the earth is the exact type of motion that can’t be considered rest, because Earth is rotating. Earth’s revolving around the sun is relative motion, but earth’s rotation isn’t.  It can be measured by a Foucalt pendulum.  (The large pendulums you see in some science museums are Foucalt pendulums—okay, you could say “pendula” if you insist. They swing in one plane of motion while the earth rotates under them.  Their pivots must be as friction-free as possible to keep them swinging with the same amplitude for a long time.)

Some physicists think (and write and calculate) that even rotation is covered by general relativity as a case of being at rest. I’ll have to get back to you on that, due to my relative ignorance on the subject.