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Re: [Phys-l] Equations (causal relationship)

Ken Caviness wrote:

The particle stays lined up with the top stage. The (zero) acceleration
of the top stage is the vector sum of the relative accelerations of the
various stages, each with respect to the stage/table below them. The
"components" of the acceleration of the top stage (i.e., the individual
relative accelerations of each stage with respect to the stage/table
below it) are physically meaningful, thus there is some meaning to these
"components" of the acceleration of the particle itself.

Is this a correct restatement of the argument?

Sounds good to me.

It's clear that the experiment can be generalized to N springs and N
stages,

Indeed to N springs and M stages, without any requirement that M=N.
This should put to rest any thought that the situation needs to be
symmetric.

to springs and stages operating in 3 dimensions, even to nonzero
particle acceleration (at least as an approximation for a short period
of time, until the particle moves and the springs are no longer parallel
to the axes of the stages). Yes, a very nice thought experiment!

:-)


The laws of physics say we can add force vectors to find the net
force.

The laws of physics say we can add acceleration vectors to find the
net acceleration.


Under special relativity, only the first is actually correct, the second
is an approximation of strictly limited validity.

What's wrong with the second? Why should I not define acceleration as
delta(u)/delta(tau), in the limit of really small deltas? In
that limit u=v and tau=t, so the classical notions should apply just
find in a frame comoving with the particle. This trick of using a
sequence of instantaneously comoving frames is one of the standard
schemes for deriving GR from SR. I think if it didn't work, somebody
would have noticed by now.


Perhaps this
distinction seems not very important to you, but much of the elaboration
of your argument has been based on an assumed *equivalence* of the two
techniques: vector addition of forces, vector addition of
accelerations.

OK, but I don't see it as an assumption ... or perhaps we can call
it the standard physicist's assumption that the laws of physics are
a reasonable description of the situation.