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Re: [Phys-l] how to explain relativity



I've been thinking about this subject some more.

I keep coming back to emphasizing the point that relativity is
*not* weird, paradoxical, or obscure.

There seems to be a multi-decade tradition in the introductory
physics courses of emphasizing how counter-intuitive or even
paradoxical relativity is ... but IMHO this is false physics,
horrid history, and pathetically poor pedagogy.

I changed the Subject: line from "prove" relativity to _explain_
relativity, since non-experts don't really want proofs; usually
they would much rather have an explanation.

When it comes time to explain relativity, I imagine a dialog
along the following lines:

Simplicio: If the principle of relativity is so important,
why wasn't it discovered in like, you know, the early 1600s?

Salvatio: It was!
Relativity was explicitly explained in Galileo's
_Dialogue Concerning the Two Chief World Systems_ (1632).

Let me start by reminding you, Simplicio, of something you
already know, namely that the laws of physics look the same
relative to a uniformly-moving reference frame e.g. in a
ship, train, or aircraft.

Anything that purports to be a law of physics but does not
uphold Galileo's principle of relativity is a defective
law, and needs to be reformulated.

This is a well-known result, but it is highly nontrivial.
Note that it applies only to uniform straight-line motion.
This is in contrast to uniform rotation, which does change
the laws of physics, by introducing centrifugal and Coriolis
terms. This means that the philosophical remark "everything
is relative" does not apply to physics; some things are
relative, but some things are not.

In my writings over the years, there have been numerous mentions
of Galileo's principle of relativity. Every so often somebody
sends in a "correction" informing me that I meant to say "Einstein's
principle of relativity". Well, no, actually I meant what I said.

And leaving aside the details of the history, we have the vastly
more important pedagogical point that when trying to explain
relativity we should start by explaining the well-known, non-weird,
non-paradoxical, everyday aspects of relativity. I call this
"first-order" relativity. We should cover that before (or instead
of!) delving into the obscure higher-order correction terms.

The dialog continues:

Simplicio: If relativity is particularly important to electricity
and magnetism, why was this not appreciated during the earliest
days of electromagnetic theory?

Salvatio: It was!
Maxwell's equations are relativistically correct to all orders,
and have been since Day One (1865).

This, too, is a notrivial result. It predicts that light will
propagate through a vacuum. This is quite different from other
waves, such as sound, that propagate through a material medium.
This in turn suggests that the speed of light will be the same
for all observers, independent of the observers' state of motion
... which is spectacularly different from other waves such as
sound. The speed of sound is different going upwind versus
going downwind.

This also predicts that if you have an electron beam, i.e. a
stream of electrons moving relative to the lab frame, that is
considered a current, and the current will produce a magnetic
field ... whereas in a reference frame comoving with the
electrons there would not be a magnetic field.

Simplicio: So, what's the big deal about relativity? Everybody
knows that you can play catch inside a moving airplane, and
the dynamics is the same, no matter how fast or slow the
airplane is moving. And everybody knows that light can go
through a vacuum. And everybody knows that an electrical
current produces a magnetic field.

Salvatio: That's just my point. Almost all of relativity is a
collection of well-known prosaic results.

Simplicio: Is that all there is to it?

Salvatio: No. If you look into it closely, you find there are
quite a few obscure, hard-to-observe effects. These effects
must be there, in order to make Galilean relativity consistent
with the other principles of physics.

However, my point remains: These effects are obscure not because
relativity is intrinsically obscure, but because you have already
accepted the non-obscure parts and have explicitly chosen to
look into the obscure corners.

Simplicio: Maybe I should go read Einstein's 1905 paper.

Salvatio: No, you should not ... and you should not read Maxwell's
1865 paper either, for the same reason.

Simplicio: Why not?

Salvatio: Electromagnetism is best understood in terms of vectors
(actually bivectors). Alas, Maxwell initially explained it without
using vectors, because vectors had not been invented yet. As a
result, his explanation is vastly more complicated and less useful
than a modern explanation.

Similarly, relativity is best understood in terms of the geometry
and trigonometry of spacetime. (If you don't yet know what spacetime
is, that's OK. A major purpose of this dialog is to get you interested
in spacetime.) Alas, Einstein initially explained relativity without
using spacetime, because spacetime had not been invented yet. As a
result, his explanation is vastly more complicated and less useful
than a modern explanation.

There is proverb that says you must crawl before you walk, but it
is not actually true. If you know how to walk, you can walk across
an open field, even if it's a field you've never visited before.

Pedagogy need not recapitulate phylogeny.
Figure-of-speech reference:
http://en.wikipedia.org/wiki/Recapitulation_theory

Simplicio: Well, then, what do people mean by Einstein's principle
of relativity?

Salvatio: Basically, you can think of it as Einstein's realization
that
a) Galilean relativity had been right all along;
b) Maxwellian electrodynamics had also been right all along; and
c) this required subtle changes to several of the other pre-1905
laws of physics, in order to maintain consistency.

Simplicio: Didn't Einstein introduce the idea of a four-dimensional
space-time continuum?

Salvatio: Nope. That was Minkowski, _Raum und Zeit_ (1908).

If you want to understand relativity, spacetime is where you start.
Relativity is just the geometry and trigonometry of spacetime.

Spacetime depends on just two very simple ideas, namely the idea
that time is the fourth dimension, and that the fourth dimension
behaves almost (but not quite) the same as the other three. These
ideas have at least a dozen major consequences. The first-order
consequences (with one exception) are large, prosaic, and well-known.
The second-order consequences are, naturally enough, more obscure.
Spacetime provides a simple, elegant, unified view of all these
phenomena.

* Spacetime unifies space and time.
* Spacetime unifies momentum and energy.
* Spacetime unifies electricity and magnetism.
* Spacetime explains rest energy: m c^2
-- as observed in matter/antimatter annihilation;
-- which is connected to low-speed kinetic energy: .5 p v,
-- and also connected to photon energy: 1.0 p c.
* Spacetime unifies rotations and boosts.
* Spacetime unifies odometers and clocks in motion.
* Curved spacetime explains stationary clocks in a gravitational field.
* Curved spacetime explains the ordinary gravitational acceleration.

et cetera.