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Re: [Phys-l] Paradoxes, or not. (Was: invariant mass...)



On 02/26/2008 02:13 PM, Hugh Haskell wrote:

I think it depends on how you do it.

Agreed.

If you lead the students to
think that you have stated the problem correctly, then you do confuse
the students, but if you put the problem out in the form of how
different observers see the same situation, then it becomes an
"apparent paradox," which, when the problem is properly stated, goes
away. So using this technique enables students to realize just what
you said--a correctly stated problem cannot lead to a paradox.

Treating it as an "apparent paradox" is better than treating
it as a paradox. That's a step in the right direction. But
why not take one more step in that direction, and reverse the
pedagogical sequence, so that the correct way of thinking is
taught first???

In my use of apparent paradoxes in the classroom, the emphasis is on
what the different observers see and why that shouldn't be surprising
if you describe the situation correctly.

That emphasis sounds fine. Given that emphasis, who needs
paradoxes (apparent or otherwise)? The goal should be for
students to realize that relativity is not weird, surprising,
or paradoxical.

I also use the idea of
apparent paradox to establish why relativity works only along the
line of motion and not transverse to it.

Huh? I cannot imagine what that's trying to say.

Relativity is just the geometry and trigonometry of spacetime.
It works just fine, transverse to the motion or otherwise.

Spacelike rotations don't commute with boosts, but there is nothing
surprising about that. Rotations don't even commute with rotations
in D=3, so we shouldn't expect them to commute in D=4.


==========================================
On 02/26/2008 02:27 PM, Rauber, Joel wrote in part:

When I discuss these examples, I try to really downplay the
"paradoxical" part of it and discuss it as an example, [1]

Exactly! Yes yes yes!

In small defence of some discussion of paradoxes (not as a general
method of pedagogy!)

Some paradoxes are so well known and so in the public reservoir of
general knowledge, that to avoid their discussion strikes me as almost
pedagogically negligent.

OK. But wouldn't it be better to replace the word "paradox" with
"example", in accordance with principle [1] above?

These are very far and few between IMO. The
canonical example IMO, is the twin paradox. Perhaps the "Pole and the
Barn".

Indeed, those are two good examples to analyze. They can be
analyzed just fine without involving any paradoxes or even
apparent paradoxes.

where I might
mention as an aside that some folks may finds aspects of these problems
paradoxical. Or at least that what I try to do. I wouldn't go any
farther in the defence of paradoxes. (The above isn't in our
introductory course, but in our third semester "modern" physics course.)
And I use the above two examples *more* as a vehicle for drawing careful
space-time diagrams to aid the interpretation of problems rather than as
examples of paradoxes.

Total agreement.

The introductory course plays by different rules, different from
the advanced course.

| The correctly-stated laws of physics do not lead to paradoxes.
| The incorrectly-stated laws of physics are full of paradoxes.
| Why should we give the students practice misstating the laws
| of physics?
|

Amen

| One of the guys who taught me relativity said that his goal
| was to get us to the point where we couldn't even state a
| paradox ... since a correctly-stated description of any
| situation is non-paradoxical.
|

I like that guy :-)

He has a good attitude.

:-)