In my earlier posting I said I thought this is not a "simple
situation." Some have disagreed with that. Perhaps they would feel
more comfortable with my comments if I had said this is not an
"intuitive situation." I have equated simple with intuitive. Although
treating these as synonyms is something I often do, it is not always
correct (depending upon what the definitions are, and depending upon
how accustomed one is with the subject). E=mc^2 an extremely simple
equation, but it is not intuitive to many people. Relativity, quantum
physics, etc. have some pretty simple equations in them, but they are
not intuitive to many people. I suppose some people younger than I
have heard nothing but quantum since they were born, so maybe it's
intuitive to them. Anyway, I accept that that my usage of "simple" was
a poor choice on my part; and I acknowledge that switching the word to
"intuitive" will still strike some as incorrect.
I think Bob Sciamanda expressed well what I was trying to say by
pointing out some historical context and reminding us that relativistic
E&M flew in the face of common thought at the time Einstein introduced
it. This implies to me it was not intuitive to physicists at that
time. The fact we are having this discussion today tells me it is not
intuitive to physicists today.
When physicists observe the same system and come up with different
observations, how appropriate this feels depends on the situation and
the experience of the physicists. It never bothered me too much that
observers moving with respect to each other could measure a different
velocity for a third object. Relative velocities in inertial frames
seemed intuitive to me. It was a bit more troublesome in high-school
and college to begin dealing with non-inertial frames and trying to
understand that people in non-inertial frames would detect forces that
people in inertial frames would not detect. Although I am now
comfortable with this, my sophomore college students are not. Their
experience of driving around curves in cars tells them that objects
following a curved path have outward centrifugal forces on them. When
we analyze this motion from an inertial frame and decide there must be
an inward centripetal force on the rotating object, it blows away some
students so much that they literally do not believe it. The equations
are simple, but apparently not intuitive to everyone.
That some observers will observe an electric field only, while others
will observe both a magnetic field and an electric field is not
intuitive to everyone. Einstein showed us that this is okay, and he
showed us that by using the proper viewpoint and equations we can
predict what the other person will observe based upon what we observe.
I believe Jack Uretsky said it well and succinctly when he said:
<begin quote>
I imagine, in the inertial frame where the magnets are at rest, two
circular pole pieces with a uniform B-field between them. There is an
axis of cylindrical symmetry; the electron moves with speed v at a
fixed radius R from the symmetry axis. You know how t calculate the
speed v, knowing B, R, m and e.
In the rest frame of the electron (non-inertial) there is a centrifugal
force mv^2/R. This force is exactly balanced by an E-field that
resuls from the Lorentz transformation from the inertial frame to the
new frame. The electron therefore remains at rest in the new frame.
<end quote>
I don't want to put words in William Beaty's mouth (or thoughts in his
mind) but I would guess that his original problem was the failure to do
both of the things mentioned in Jack's 2nd paragraph quoted above: (1)
Treat the rest frame of the electron as non-inertial whereas the rest
frame of the magnet is inertial; (2) realize that a Lorentz
transformation of the magnetic field from the magnet's frame to the
electron's frame results in an E-field being manifest in the electron's
frame.
Regardless of whether some of us view this as simple, or intuitive (or
both), I infer it was not intuitive to Bill. I readily admit it was
not intuitive to me when I encountered this for the first time, and if
it seems intuitive to me now it is only because I have been through
this type of thing so often with class after class of modern physics
students. Unfortunately I also reluctantly admit that after my modern
physics course has ended, this is not intuitive to most of the
students.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817