Re: CAUSATION IN PHYSICS

[John Denker <jsd@MONMOUTH.COM>]

At 12:27 AM 10/16/00 -0700, Tucker Hiatt wrote:

> "Mathematics describes all possible universes.  Physics describes THIS
> universe."

I agree.

> Mathematically speaking, "a = F/m" and "F = ma" are equivalent.

True.

>   Physically speaking, they are not.

False.

> in this universe, acceleration is PHYSICALLY DETERMINED by force and mass.

OK -- but it is equally true that force is PHYSICALLY DETERMINED by the
mass and acceleration.  In particular:

At 04:12 PM 10/15/00 -0400, John Denker wrote:
> Suppose we have a wheel spinning on an axle at some rate $omega$.  Everything
> would be in balance, except that we have attached to the wheel a mass $m$ at
> a distance $r$ from the center.  Calculate the force.

It would be natural to calculate $F$ in terms of $ma$ in this case.  It
would be bizarre to calculate $a$ in terms of $F/m$ in this case.

At 12:27 AM 10/16/00 -0700, Tucker Hiatt wrote:
> In discussing simple waves, lots of physics books tell us the following:
>
> wave speed = wavelength x frequency.
>
> Then, when we ask our students, "What happens to a slinky wave's speed when
> the wave's frequency is doubled?", they dutifully report that the wave's
> speed doubles!  They're living in the "wrong universe."
>
> This is why we might want to emphasize causation in wave production and
> propagation, and why it's causally-correct ("CC", as opposed to "PC"!) to
> write:
>
> wavelength = wave speed x period.

This has nothing to do with causality.  It is a classic mix-up having to do
with OTBE (Other Things Being Equal).  The question above suffers from
being underspecified.  It asks what happens if the frequency is doubled,
Other Things Being Equal, but doesn't explicitly say what Other Things are
Being held Equal.  It is easy to contrive cases where the answer labelled
"wrong" above is in fact the right answer.  For example: suppose I have a
standing wave of sound in a particular mode in a chamber of gas.  I heat up
the gas until that mode's frequency is doubled.  The wavespeed has doubled.

Now for slinkies, it is usually taken for granted that the wavespeed
doesn't change (even though this is not strictly true).  For my sound
chamber, it is usually taken for granted that the chamber-size doesn't
change with temperature (even this is unlikely to be strictly true).  BUT
THIS SIDE-INFORMATION HAS NOTHING TO DO WITH THE WAY WE WRITE THE EQUATIONS
THAT RELATE SPEED, WAVELENGTH, AND FREQUENCY.  IT HAS NOTHING TO DO WITH
CAUSATION.  It has to do with OTBE.

"OTBE" questions come up whenever there are multiple variables floating
around.  They are conspicuous in thermodynamics, where the difference
between "specific heat at constant pressure" and "specific heat at constant
volume" is obviously a difference in OTBE.

When in doubt, calculate a small change and use the rules of calculus:
      d(wavespeed) =  d(wavelength) *  frequency
                     +  wavelength * d(frequency)

or perhaps more elegantly:
      d(wavespeed)/wavespeed =   d(wavelength)/wavelength
                               + d(frequency)/frequency

and if you have side-information that one of the terms on the RHS vanishes,
well that's delightful.  HOWEVER, IT IS NOT THE GENERAL CASE, AND IT HAS
NOTHING TO DO WITH THE MEANING OF THE EQUATION
        wave speed = wavelength * frequency
AND IT HAS NOTHING TO DO WITH CAUSATION.



> By the same token, a = F/m describes the causal link between force and
> acceleration

false.

> while F = ma does not.

false

> Acceleration is PHYSICALLY DETERMINED by acceleration and mass;

true as written, but the implication that force is not physically
determined by mass and acceleration is false.