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Along JD's lines I will share the following experience. In converting
our introductory physics classes from a traditional lecture/lab to a
so-called lecture-studio format, we consolidated a portion of modern
physics topics into the regular mechanics semester. This meant special
relativity, and we made a conscious decision to depart from the
"traditional" approach and adopted almost a pure spacetime approach.
Since our textbook had no reference whatsoever to spacetime diagrams, we
had to create our own material, which consisted of worksheets and group
problem solving. We also created our own introductory reference
document. Between 3 faculty and maybe 5 grad students, we pounded this
out over a summer. It was a real education, because every one of us came
to realize that we didn't really understand special relativity all that
well, and creating the spacetime diagrams to match the approach in a
typical textbook gave us all a new appreciation for the power of the
spacetime approach in terms of understanding.
Over 4 semesters now of having done it this way and ironing out most of
the kinks, we all feel that it has paid off for students as well. After
3 lectures and 3 studios with worksheets, which include very little in
the way of quantitative work, it's rather amazing how conversant
students are in the topic, and how well they actually "get it," instead
of endless confusion about hunting for equations to plug and chug. We do
our best to emphasize proper times and lengths, the relativity of
simultaneity, paths through spacetime (e.g. odometers), and shy away
from time dilation and length contraction when possible (not typically
possible, because we still assign homeworks from the textbook).
During the 4th lecture and studio, we do Lorentz transform and interval
calculations to put some quantitative grit into the spacetime diagrams,
at which point the students generally have fewer issues because they
have such a good grounding in how to picture what is happening. We save
relativistic kinematics (energy, momentum) for the last module, and
leave it at these 5 lessons. Scores on our relativity midterm tend to be
about 10-15% higher than our other midterms, and I don't think it's
because we go easy on them. Even the poorest students can typically draw
a correct diagram with axes for multiple observers, worldlines, lines of
simultaneity, and distinguish between when events are seen and occur,
which is rather amazing since the poorest students also typically don't
fare well with straightforward energy or momentum conservation
questions. Students generally reflect positively on the relativity
experience, and many wish we could go back to it ("it's simpler!") when
we move on to torque and angular momentum, which seem to be the most
difficult topics for intro students in the first semester.
It's a lot of work to create the materials, but I would recommend it as
a general teaching approach to this particular topic. Side benefits
include easier discussions about about classical inertial and
non-inertial reference frames, reference frames in general and relative
motion, and a springboard to talking just a little during the semester
about general relativity.
Stefan Jeglinski
On 5/20/16 10:35 AM, John Denker wrote:
I'm not saying that's wrong physics. It is known that
you can formulate all of relativity (special and general)
in terms of clocks that can't be trusted, rulers that
can't be trusted, et cetera.
I'm just asking, why would you want to?
I say again, it can be done
http://www.feynmanlectures.caltech.edu/II_42.html
It would be perverse, but not impossible.
In ordinary three-dimensional space, you could define the
notion of arc-length along a path in terms of odometers
that can't be trusted ... but why would you want to? It's
so much easier to say that the odometers are correct, and
the path-length is just plain different from path to path.
Also note that temperature affects various clocks differently,
so anything that affects all clocks (and all odometers) the
same must be considered a "coincidence" of the kind that is
off-scale implausible ... especially given that a simpler
explanation is readily available.
There was a period in the history of physics when the
state-of-the-art approach to relativity was built around
velocity-dependent rulers, velocity-dependent clocks,
various mutually-inconsistent notions of velocity-dependent
mass, et cetera. HOWEVER that period ended more than 100
years ago.
This is one of those things that is easier to explain to
the students than to the faculty. The students are not
heavily invested in the archaic (pre-1908) way of doing
things, and are happy to adopt the modern viewpoint,
including the idea that clocks are like odometers in
spacetime.
In contrast, those who are heavily invested in the old
way of doing things will have to do a lot of unlearning.
Indeed, Einstein initially did not appreciate or even
understand what Minkowski had done. Eventually, though,
he figured it out and used it for all of his later work.
Without spacetime, he never would have figured out GR.
I reckon the idea of spacetime is like the idea of horseless
carriages. Such things have been around for a while now.
We ought to incorporate them into our thinking and our
teaching.
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