Archive for: August, 2012

A muddled article on Relativity in the Oberlin alumni magazine

My wife graduated from from Oberlin college in 1992, and as such she gets the Oberlin alumni magazine. The summer 2012 issue includes a one-page article entitled "The Entirety of Relativity", which I find to be a very unfortunate presentation of Relativity. (As a pedantic point, it's only talking about Special Relativity (SR), and doesn't address General Relativity (GR) at all, but that really is a pedantic point. When a physicist says "Relativity", she likely means GR (especially given that SR is a subset of GR, so nothing is lost), but when presented publicly we often use "Relativity" as a shorthand for SR.)

The basic problem with the article is that it presents the theory as if its nature were the way that SR has been taught to students for a long time. The article starts with three things that are correct as far as they go: moving clocks run slow, a moving rod is short, and moving clocks aren't synchronized. Where the article loses me, however, is on point number 4, "That's All There Is To It.".The brief text after this says that the first three points are the basis of relativity, and the rest of the article claims that all of SR is a consequence of these three points. This is at the very least a perverse way of describing the theory.

A lot of texts at both the high school and college level present Relativity by first presenting these three points. You're given formulae for each of these consequences; parts of them resemble each other, but they're each presented as if they were a fundamental formula that couldn't be derived from anything else, for you to memorize (or, in a more modern way of thinking about it, look up) and use. However, this is a back-assward way of presenting SR, and I would argue that stating that the rest of SR is a consequence of these three observations is not just back-assward, but in fact wrong.

In fact, these three points are themselves consequences of the theory of Relativity. The formulae for them can be derived from more fundamental considerations. They're no more fundamental than all of the various kinematic formulae you memorize or look up (such as da2) when you do a non-calculus Newtonian mechanics class; those kinematic formulae themselves are just results of the definition of velocity and acceleration as, respectively, the rate of change of position and the rate of change of velocity, together with Calculus. Those definitions are the fundamental thing, not all the various kinematic equations you learn to use if you take a non-Calculus physics class. I could start with da2, take a couple of derivatives, and say, "hey, acceleration is the rate-of-change of the rate-of-change of position, and that's a consequence of this kinematic equation". That would be back-assward and indeed wrong, and it's just as wrong to say that everything else in Relativity is a consequence of moving clocks running slow, separated moving clocks not being synchronized, and moving rods being short.

Special Relativity itself starts with just two very simple postulates— "simple" in the sense of "not complex", not in the sense of "easy to understand". Those postulates are:

  • The laws of physics are the same for every freely-falling observer
  • The speed of light is one of those laws of physics; every freely-falling observer will measure the speed of light in a vacuum to be 2.998×108 meters per second.

Everything else in SR— including moving clocks running slowly, separated moving clocks not being synchronized, and moving rods being short, as well as other things (such as the Doppler shift, focusing of light emitted by a moving object in the direction of motion, an apparent rotation of a moving object) are consequences of these two postulates.

I should note that both of these postulates do require more explanation to be truly precise. For the first postulate, you have to carefully define "freely-falling observer". You get it basically right if there are no net external forces other than gravity acting on that observer. (However, if you allow gravity to be around, things can get a little subtly complicated. It doesn't ruin the postulates, but you have to be careful in treating the consequences.) For the second postulate, in fact it's not the speed of light that's absolute, it's the speed of any object that both carries energy and is massless. Light just happens to be the thing that we think about the most that works like this, and thus we call the cosmic speed limit "the speed of light", even though we really ought to call it "the speed of spacetime" (at least in the context of Relativity).

One of the most interesting consequences of these two postulates it that you have to change the way you think about time. Most of us live our lives with a Galilean/Newtonian view of time: it's an absolute, that advances at the same rate and is the same for everybody. However, you can't maintain that idea and have the speed of the same bit of light be measured at the same rate by everybody regardless of how they're moving. Galileo and Newton would say that the latter is wrong; Einstein's postulate, from which all of Relativity springs, was that in fact it's this speed of massless objects that is absolute, and as such we just have to give up on the idea of absolute time. Some of the consequences of this are that separated moving clocks aren't synchronized and moving clocks run slow... as well as other things.

I'm fond of the way that Thomas Moore's Six Ideas That Shaped Physics presents Special Relativity. (This is the book series that I currently use when teaching introductory calculus-based physics.) His Book R of the series is written for college-level physics who have had Calculus (and indeed have had some Calculus-based Newtonian physics). It presents SR not in the old-fashioned and unfortunate pedagogical way that the Oberlin article does— by starting with the consequences such as time dilation and with their formulae, and only later getting to the fundamental structure of spacetime implied by Einsteins postulates— but rather by starting with the fundamental structure of spacetime implied by Einstein's postulates, and then developing the consequences out of that

Yes, it's easier to just learn the formulae and do calculations about time dilation and so forth, and presents fewer difficult abstract conceptual challenges to students coming across this for the first time. However, if you learn it this way, you're given a warped perspective of what the theory of Special Relativity really is. My beef with this Oberlin alumni article is that it presents Relativity as if the theory itself is based and structured in the way that it has often been taught.

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