Re: special relativity: accelerated frames

[Chuck Britton <britton@NCSSM.EDU>]

Having just wrapped up a VERY brief intro to SR for HS students, I
appreciate this thread.
I DID have one bright student who asked about circular motion. I have
stopped emphasizing the necessity of of the word INERTIAL in relating
postulate one for just this reason stated by John.  Things DO get
more complicated with non-inertial frames but shouldn't require a
whole new paradigm of thinking.

I DO have a serious question for these accelerating reference frame
problems however.

If I choose my car to be my RF, and notice that the highway, trees
etc are going past me at a reasonable constant speed of 20 m/s and I
suddenly mash down on the middle pedal of my car.

I notice that the stuff piled on the back seat of my car 'rushes
forward' onto the floor, (presumably, somehow pulled forward by the
outside world) but the things outside my car seem to be indifferent
to my having stopped the world from moving.

In John's example of CONSTANT acceleration, I can easily imagine some
shift of direction of the local g field 'making things work'. Just
CHANGING the acceleration (jerk) is detected by the riders et al.

(I ALSO have to wonder how my little Saturn is able give the highway
such a tremendous amount of KE and have the brakes absorb it - but
Leigh would just say that I am reifying energy and should stop DOING
that!!  :-)



At 1:55 AM -0400 5/3/01, John S. Denker,  you wrote about Re: special
relativity: accelerated frames:

> Let me coin a scale of complexity or sophistication:
>   Level 1 := Newtonian mechanics
>   Level 2 := Special relativity, as it is usually presented.
>   Level 3 := General relativity
>
> Then I would say that accelerated reference frames are at level 2.1 or some
> such -- more sophisticated than the usual introductory SR discussion, but
> certainly not requiring the heavy-duty machinery of GR.
>
> I remember being bothered by this for a day or so, back when I was a
> student.  At first, nobody offered an explanation of why SR should work for
> accelerated reference frames.  The discussion consisted of asking "why the
> heck shouldn't it work" and deciding that there's no reason why it shouldn't.
>
> Later, the outline of an explanation emerged:  The trick is to arrange for
> a succession of ___instantaneously comoving___ unaccelerated observers.  We
> know SR works for each observer separately.  We then arrange to have enough
> observers at the right places at the right velocities, so that they can
> observe the action.  Afterwards, we collect all their observations and
> integrate them.
>
> [By the correspondence principle, everything (including a modest
> acceleration) will look Newtonian to the instantaneously comoving
> observers, so life is easy for them.]

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Chuck Britton                                   Education is what is left when
britton@ncssm.edu                               you have forgotten everything
North Carolina School of Science & Math         you learned in school.
(919) 286-3366  x224                            Albert Einstein,        1936