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[Phys-l] inertial +- gravitational mass



Hugh Haskell raised some interesting points:
https://carnot.physics.buffalo.edu/archives/2006/11_2006/msg00295.html

Here's how I think about such matters:

1) We don't /know/ that gravitational mass is equivalent to inertial mass. [1]
As a point of physics, metaphysics, and logic, this is absolutely true.
This is not news, but it is not trivial, either.

a) It is not news, because as Popper and others have pointed out, it is
never possible for science to establish the "truth" of such propositions.
We don't /know/ F=ma. [2]
We don't /know/ F=GmM/r^2 [3]
We can disprove such propositions, but never prove them. The highest
praise we can give such a proposition is to say it is "good enough for
all practical purposes, so far as we know".

FWIW there are fewer practical difficulties with [1] than with [2] or [3].

b) This is not trivial, and we need to be reminded of it now and again,
because if everyone were to /assume/ the truth of such propositions,
nobody would ever check them, and that would be bad. A check with a
non-null result can be very exciting
http://physics.nist.gov/GenInt/Parity/parity.html
So far all inertial/gravitational checks have yielded null results,
but that's no reason to stop checking. In my judgement it is not
worth devoting huge resources to such checks, but /some/ resources
once in while seems reasonable.

2) The question arises whether the inertial/gravitational distinction
should be emphasized in intro physics courses.

I say no. There isn't enough time in the day for everybody to question
everything. IMHO it would make /more/ sense to do away with [2] and [3]
than to do away with [1] in an introductory class. That is, it would
make more sense to do away with F=ma and use fully-relativistic dynamics,
and do away with F=GmM/r^2 and use general relativity instead ... while
leaving questions about the equivalence principle for another day.

To say the same thing in slightly different words:

-- As professional physicists, we should keep an open mind about
the equivalence principle. Indeed the more elegant the principle, the
more often we should remind ourselves that it is never proven, just
undisproven.

-- In real life we have to make approximations. I see nothing wrong
with saying that "for the purposes of this course, and many other
purposes besides, it is safe to approximate gravitational mass as
being equal to inertial mass".


3) We now discuss terminology. The available terminology is horribly
unhelpful whenever we try to discuss the uncertainty principle.

For example, several people have suggested that we measure gravity in
Nt/kg instead of m/s^2 ... but that is problematic to say the least,
because the SI newton is /defined/ to be the SI kg multiplied by the SI
m/s^2. Therefore this is officially a distinction without a difference.

It might be an amusing exercise to rederive all of classical physics
*without* using the equivalence principle. In my judgement this
would be a grad-school exercise (possibly an admission-to-candidacy
exam question) -- but not a high-shool exercise, or even a college
level intro-physics exercise.

For starters, you would need two kilograms: kg_i (inertial) and
kg_g (gravitational). I wonder whether the prototype kilogram at
Sèvres would suffice to define one or the other or both.

You would then need to argue about the definition of force. Either
you would have two newtons: Nt_i (used to measure the forces in a
centrifuge) and Nt_g (used to measure weight) -- or you could have
only one Nt ... and a big fight about how to define it.

And on and on ..........

Do you really want to dive into this in an introductory class???


4) On 11/20/2006 10:24 AM, Bob LaMontagne wrote:

.... it makes no sense to the student when an object is lying on a
table.

I agree it can be confusing. But lots of things are initially confusing.
That's why they pay the teacher to show up each day and explain things.

The object-on-a-table is the most minor of problems, and can be solved by
explaining that the equation of motion has two terms on the RHS:

a_total = a_gravitational + a_table [4]

where in equilibrium a_total is zero because the two terms on the RHS
cancel each other. Accelerations are vectors, and we can add them
just like any other vectors.

Defining it as gravitational force per unit mass (or as the field)
seems far less confusing.

As discussed above, that is a distinction without a difference, without
any observable difference anyway, so far as anybody knows. As a related
point: what units are you going to use to measure "force per unit mass"???

This approach seems vastly more complicated than equation [4]. You
presumably could work out all the complications, but that would be a
grad-school exercise, not at all appropriate for an introductory class.