Please permit me a few more comments on this "fictitious forces" phase of
the Apparent Weight thread. I need to complete the current spiral round the
topic. I was going to put lots of quotations from people, but it seems
simpler without.
The topic interests me because I'm still trying to develop a pedagogically
viable and reasonably sound interface between Newtonian gravitation and GR,
since I have to explain the basic principles of GR (without mathematics) at
some point in the course I teach (even if this seems foolish).
Remember that students have done lots of mechanics and drawn many diagrams
with a force vector labelled "mg". Now what am I going to tell them? I could
start with a story about a physics class in a box in deep space being towed
by the Starship Enterprise, with an acceleration of 9.8 m/s^2 ("relative to
what" did I hear someone say? - and we have a little reminder about inertial
frames and accelerations being absolute, not realative) The physics class is
timing a pendulum and measuring "g", and so on. Then consider the box parked
on the surface of the earth, and once again the same box, this time falling
freely near the surface of the earth, or anywhere for that matter. Which is
the odd one out....?
- what we were calling "the acceleration due to gravity" is not really
acceleration. You get an inertial frame when "being accelerated by gravity".
- the effect that we were calling "the force of gravity" is (almost) exactly
like what the deep space physics class observes
- could we somehow find a way to make sense of the situation by saying that
sitting still on the surface of the earth we were in fact accelerating? (How
to make this mean something at this stage without resorting to using "in
space-time" as a mere mystifier?)
Whichever way we go at this point, a lot of difficulties do seem to stem
from the fact that we set most of our physics problems in a non-inertial
frame. (No doubt because we live in one).
Another question:
This business of fictitious forces having no 3rd Law counterpart keeps
cropping up. Of course, in my seat in the accelerating 747 I feel myself
being pressed back into the seat, and the seat pressing back on me, but I
guess the case in question is the force which is accelerating the escaped
drinks trolley down the aisle to the back of the plane. OK, there seems to
be no 3rd law counterpart for this force. So back to me seated in front of
my computer - I knock my coffee mug off the table and it falls to the floor.
In class (not the GR class) I would say that the Earth is pulling the
falling mug with force mg, and the mug is pulling the Earth back with
exactly the same force. Does this mean that mg is not fictitious after all?
Comments appreciated. Mark.
Mark Sylvester
United World College of the Adriatic
34013 Duino TS
Italy.
msylvest@spin.it
tel: +39 49 3739 255