Mass was Re: Questions (Space)

Tim S <Tim@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:

Jonathan L Cunningham wrote:

No, the thing I'm talking about is usually called "mass"

(I've reformatted the following)

That depends who's doing the calling.

Yes.

Among physicists who work on these
things, "mass" means what you're calling "rest mass".

Perhaps. IME, communities tend not to homegeneity, and such
generalisations are dangerous. But it might be true in this
case.

And the next question: what about physicists who don't work
on "these things"? I won't ask what "these things" are.

What do the NASA scientists responsible for designing space
communications technology say? Some of them might not even
be physicists. They might even be engineers!

But arguing about terminology is very close to the most pointless
kind of argument I can imagine.

Except in one context: the historical one.

Which brings us back to some On-topic noodling. (I've changed
subject line as David Palmer requested.)

First, a lesson in egg-sucking, gran:

Mass was invented by Newton, AIUI. Before then we had "weight"
as a measure of an amount of substance. (Weights and measures.)

According to Newton's Second Law (not 3rd, that's not a typo,
even though the 3rd Law gets all the Oscars), the rate at which
you can accelerate things (I'm paraphrasing) is proportional to
the force applied (I think "force" was another of Newton's
inventions. Not sure about that.)

The thing about laws which say "X is proportional to Y" is
that they can be expressed in the form "X = K*Y". I.e. as
a linear equation with a constant in it (here K). The constant
in Newton's equation depends on the thing being accelerated.

This constant (for any Thing) is its "mass". More precisely
it's its "inertial mass".

This same Newton also came up with a "Law of Gravity" which
comes out as a formula a bit like F = GMm/d^2. Here, the force
(which we can work out from his 2nd law and knowing an object's
mass) is proportional to three things: M, m and 1/d^2. And
the constant of proportionality is given as G.

The "d" is the distance between two objects (I'm simplifying to
save several thousand words). We think we understand "distance".

And the M and m appear to be properties of the two objects. It's not
surprising that the force depends on both objects. It is (slightly)
surprising that they appear to be independent. However, it's not
difficult to make it appear "obvious".

SFnal question: could there be a "law of gravity" where
F = G*g(M,m)/d^2
where g(M,m) is not proportional to M*m ? I leave that as an
exercise for the reader :-)

Anyway, this "law of gravity" gives rise to a second notion of
mass: the "gravitational mass".

As it happens, the ratio of inertial mass to gravitational mass seems
to be constant for all matter. There is absolutely *no* reason why
that needs to be true in a Newtonian universe. There have even been
experiments to see if it is different for different elements.

SFnal point: In a Newtonian universe, a scientist could invent or
discover a material with positive inertial mass, but negative
gravitational mass. This would allow for "anti-gravity" without
running into weird paradoxes associated with "negative mass" in
an Einsteinian universe.

Anyway, and then along comes Einstein. According to General Relativity,
inertia and gravity are the same thing, and inertial mass necessarily
equals graviational mass. (But they still do experiments. Discovering
that the inertial/graviational mass of a proton differed from that of
an electron would disprove General Relativity, I think.)

The snag comes with Newton's 2nd law. *It is no longer the case that
the acceleration of a body is proportional to the force applied.*

This is particularly noticeable for photons etc. If you apply a force
in the direction of motion, it doesn't accelerate. It just gets heavier
(more energetic, if you prefer).

However, if you take something like an electron going at 99% of the
speed of light, and apply a force, you can still accelerate it; just
not as much as you can when it's stationary. If you fudge Newton's
original equation, you can change it to X = K(v)*Y, where X is no
longer proportional to Y with K a constant of proportionality,
instead we make K a function of velocity, i.e. say that the mass is
a function of velocity.

Which is where we came in. If (as I doubt) all physicists *do* mean
"rest mass" when talking about the mass of a lump of coal, then they'll
want to reject the notion of not-rest mass altogether. Instead, they'll
formulate Newton's 2nd law in a different form: they won't say "force is
proportional to mass times acceleration" they'll say "force is
proportional to rate of change of momentum".

The original intuition of "weight" as "amount of stuff" has come a long
way.

Now you can go away and design a universe with different laws of
physics: the sfnal insight is that your universe doesn't need objects
to have "mass". Mass is just an abstraction: a constant of
proportionality which has outlived its usefulness.

Jonathan

--
"I think too much - therefore I am mad!"
Agatha Clay playing Lucrezia Mongfish.
.

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