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

[John Denker <jsd@av8n.com>]

Ken Caviness wrote:

> 1.  Why do you have one spring attached to a stage, the other two
> attached to posts attached to the table?  

I needed to attach the particle to the stack-of-stages somehow.
I treat this attachment as one of the springs, and account for
the associated force as one of the forces.

> That appears to be an
> essential asymmetry in your setup. 

Life can be so asymmetric sometimes.

>  I had understood that all forces
> were measured with respect to the lab frame, therefore we want all
> springs attached to fixed posts in the lab frame. 

The force is the force.  You do not need a reference frame in order
to measure the force (non-relativistically speaking).  All observers
in all frames agree what the force is.  So what I have done may
look ugly to some eyes, but it doesn't cause any problems with the
physics.

> 2.  .... The particle is subjected to _multiple_ forces.  We can
> measure them.  The particle experiences _one_ acceleration, we can
> measure it. 

I still see that as a matter of opinion, having nothing to do with
the laws of physics.

The laws of physics say that only the net force matters.
The laws of physics say that only the net acceleration matters.

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.

Maybe you *want* to decompose the force into a set of forces, and
maybe you *don't* want to decompose the acceleration in the same
way ... but what you "want" isn't physics.

> ......... But notice
> here neither F nor m need be considered causative, we simply have a
> correlation between them.

That's the general case.  Why not just accept it as the general case,
and move on?

>  We can still add the forces as vectors in
> special relativity, but we can't add relative velocities with our
> non-relativistic formulas and although I haven't done it I would think
> that relative accelerations would be even worse.  Does this mean force
> is more "basic" in some way than acceleration? 

No.

Force is not much used in general relativity (or even special relativity).
There are even different schools of thought as to whether force should
be defined as d(p)/d(t) or d(p)/d(tau).  Most people don't care enough
to even have an opinion on the matter.

Instead, they just keep track of the momentum.  Any force problem can
trivially be transformed into a momentum problem.