Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] three central misconceptions about relativity

At 1:31 PM -0700 10/13/11, John Denker wrote:

In particular, in some quarters it is fashionable to teach
relativity by introducing "paradoxes" to be analyzed. This
makes absolutely no sense to me.
-- We don't introduce mechanics in terms of mechanical
paradoxes.
-- We don't introduce electrostatics in terms of electrostatic
paradoxes.
-- et cetera ...

I think there are two types of paradoxes that can arise. The first are those raised by the teacher to emphasize the apparent "weirdness" of relativity. In those cases, I agree with JD that it is inappropriate to emphasize the counterintuitive nature of relativity. The second case is the situation that arises when we respond to student questions--often very thoughtful and insightful questions. It is often necessary to show that responding to those questions leads to an apparent paradox that only relativity can resolve. Those often involve the relativity of simultaneity, which is a difficult concept for students who are not yet beyond the concrete thinking stage.

It is also possible that doing this has an effect similar to one I recently read about, when an author wants to take on a popular belief that is false by "debunking the myth." If they start out by stating the myth and then giving the counter argument, this study found that what was stated first was more often remembered better than what followed, so the net effect was quite the opposite from what was intened--the myth becomes more firmly implanted.

Teaching students who are only barely comfortable with two-dimensional geometry and trigonometry about Minkowski diagrams and 4-space is really not too practical. They already have problems with abstractions, so those of us who teach students t that level are pretty much required to look at the differences between Newtonian and Relativistic mechanics, and more or less leave it there. In my classes I teach relativity by starting with Einstein's postulates, and "derive" the space and time dilation formulas using simple geometric arguments, without using the Lorentz transformation matrix. This sometimes makes a derivation more complex (e.g., the velocity addition rules) than it would need to be if the students were more comfortable in 4-dimensional physics, but they are simply not ready for the 4-d stuff at this point.

I take some comfort in this by realizing that if they ever get to the point where they will be learning relativity in the "correct" way, they will have enough knowledge about what results need to be that they will be able to appreciate the great simplicity that the modern approach to relativity brings.

... so why why why do some folks cook up relativity misconceptions
and foist them on students? I'm talking about problems involving
poles in barns, and things like that. The statement of the problem
seems designed to teach people to think about relativity the wrong
way. That is, if you think about relativity the right way, you would
never dream of formulating the problem that way. It's like asking
about a flying unicorn ten miles north of the north pole.

I don't think that we need to create paradoxes in relativity, but when questions arise (and they almost always do) that lead to apparent paradoxes, then showing that only relativity can resolve the paradox is, I think of some value. What we know now, is that paradoxes don't occur in relativity, they occur in Newtonian mechanics when we push its limits of applicability too far. So the emphasis isn't on relativity creating paradoxes, but relativity resolving them.

I know it is bad manners to speculate about other people's motives.
Once upon a time I suspected some people were just bragging about
how tough they were and how smart they were, because they knew
about this incredibly weird and paradoxical theory. However, I
don't think that anymore. I think they just have no clue about
how relativity really works.

I'm sure that there were and probably still are some who understand relativity on this level, and there are others who think it a good approach because that's the way they were taught, and I certainly don't endorse that approach. Unfortunately, they are also not qualified to teach relativity in the manner proposed by JD.

The laws of physics -- when properly stated -- do not contain any
paradoxes, so far as we know. In contrast, if you mis-state the
laws, you can cook up all sorts of paradoxes ... but why would
you want to?

Agreed. That is an important point. Paradoxes arise because of our flawed thinking or flawed application of the laws of physics, and not because of flawed laws of physics.

As I see it, special relativity is not paradoxical. It's not even
weird. It's just the geometry and trigonometry of spacetime.

IMHO it is a tremendous mistake to portray special relativity as
weird and paradoxical. It is a disservice to students.

Agreed also, although weird is clearly in the eye of the beholder. When something the student has "known" for a long time is shown to be not true, the "weird" label will almost always be applied to the new material rather than the old.

We can agree that contracted rulers are weird, and dilated clocks
are weird, and velocity-dependent mass is weird ... but those
things are not part of relativity, and haven't been for more than
100 years. They are as dead as phlogiston.

As Thomas Kuhn pointed out, phlogiston was not a dumb idea in its
day. However, its day ended a long time ago.

Well, if we talk about about contracted rulers and dilated clocks, we are going to confuse students even more than they are already. A dilated clock makes about as much sense as one by Dali. But I think it is fair to talk about perceptions, which can be real. We can argue that space and time in *our* inertial rest frame are what counts to us, but that reality may appear differently to those in another inertial frame.

That brings us to another misconception, namely the idea that the
development of special relativity began and ended with Einstein's
1905 paper.

Every so often, somebody casually mentions Galileo's principle
of relativity, and some nitwit corrects him: "You meant Einstein's
principle of relativity". That really makes my hair stand on end.
The fact is, Galileo enunciated the principle of relativity with
magnificent clarity in 1632. That gives him 273 years of priority.
I'm also quite sure that Einstein wasn't the first to discuss
Lorentz contractions. (For that matter, Lorentz wasn't either.)

As of 1901, Poincaré and Lorentz knew more about relativity than
Galileo ever did. As of 1905, Einstein knew more about relativity
than Poincaré and Lorentz did. As of 1908, Minkowski knew more
about relativity than Einstein did. This is how science works.
Newton said he stood on the shoulders of giants.

There are a lot of people (including some on this list) who
advocate using the history of science to motivate and organize
the teaching of science. They say history is important. Well,
I say history is sufficiently important that when you tell the
story, you should tell what really happened, not some fractured
fairy tale.

This has direct pedagogical consequences: Just because Einstein
used contracted rulers and dilated clocks in 1905 doesn't mean
that is a good idea. In fact it is a terrible idea. Every minute
spent learning about such things is at least two minutes wasted,
because you will have to unlearn it before you can achieve any
real understanding of relativity.

This also has consequences that extend outside the classroom
... consequences that are (for most people) far more serious
than anything having to do with relativity per se. Let me
explain:

I have spent many years as a manager. This includes helping to
set up collaborations. As you might imagine, it is hard to get
a not-so-famous person to collaborate with a famous person, if
the expectation is that no matter what happens, the famous
person will get all the credit. This is a big problem, and it
hurts the big shots as well as the little shots, and hurts the
organization as a whole, by making it hard to set up collaborations.

Any big-shot with any sense will be ultra-scrupulous to give
credit to collaborators, but it's never enough. I have personally
experienced this problem from the big-shot point of view, from
the little-shot point of view, and from the bystander / manager
point of view. I guarantee you, it is nasty all around.

This is really a Big Deal for me. When I invite somebody to
give a colloquium on the subject of quasars, you can be sure
I invite Jocelyn Bell.

I beg all of you, please, don't mess this up. Most people don't
really need to know much about special relativity, but they do
need to know how to collaborate.

Well said. This is a big problem, and has been perpetrated by many, up to and including the Nobel committees. I'm sure we can all think of at least a half-dozen prizes that should have been given to someone else, either instead of or in addition to the named recipients. Jocelyn Bell is only one of many. Lise Meitner and Ralph Alpher also pop to mind. Rosalind Franklin is also a possibility, but we'll never know about her since she died before the importance of the double helix was fully understood.

Unfortunately, a reticence to give credit where it is due is too often a factor in a competitive world. It's also often counterproductive, as JD has pointed out.

Collaboration is more important than manufacturing paradoxes, but paradoxes often arise spontaneously, and when they do, they must be dealt with, but it is important that their origin be attributed to where it belongs, and, so far at least, relativity in not that place.

Hugh

PS, I apologize for the delay in this response (several other responses may have overtaken this one by now). I have been travelling and, while I can receive e-mail, my ISP doesn't let me send it through a "foreign" server--at least I haven't figured out how to make it work. They also won't let me send e-mails from any of my other addresses through their server. Not what I had hoped when I relocated, but my previous ISP didn't offer coverage at the new location, so i was forced to change.

H^2
--

Hugh Haskell
mailto:hugh@ieer.org
mailto:haskellh@verizon.net

It isn't easy being green.

--Kermit Lagrenouille