Re: a few simple questions (from a layman)


lamoore0777@xxxxxxxxxxxxx wrote:
> Eric Gisse wrote:
>
> > We call it the equivalence principle.
> >
> > Although it has been greatly extended into ways that are harder to
> > explain, it basically means that under identical conditions, two
> > objects dropped will fall at the same rate. What I mean by identical
> > conditions is equal amounts of drag, or lack of. The famous style of
> > testing of the EP is called Eotvos, named after a Hungarian fellow.
>
> Thanks Eric,
>
> I visited the site you suggested and came away with this (in addition
> to much more): "The simplest way to state the equivalence principle is
> this: inertial mass and gravitational mass are the same thing. Then,
> gravitational force is proportional to inertial mass, and the
> proportionality is independent of the kind of matter. This implies the
> Universality of Free Fall(UFF): in a uniform gravitational field, all
> objects fall with the same acceleration, e.g. 9.8m/s2 near the surface
> of the earth".
>
> And if I may, impose on you once more, can you clarify a few terms
> mentioned above? Being I suppose a rhetorical question given I'm going
> to ask you whether or not you respond. lol. Seriously though, I much
> appreciate your understanding and your ability to communicate it in
> non-rocket-scientist type terms. So to speak. No easy feat.

Well that is going to change in a minute.

We have "inertial mass" being defined as the m_i in F = m_i * a.
[Newton's second law]

Then we have "gravitational mass" being defined as the m_g in F = m_g *
MG/r^2. [Newton's law of gravitation]

More or less. Newtonian mechanics is only an approximation to general
relativity, which more accurately describes the universe. However, it
is still useful in situations like this.

Here is how it becomes important.

We can predict how a falling object will act using these two laws as
follows:

[1] F = m_i*a

[2] F = m_g * MG/r^2.

If we assume the change in r is small, we can just approximate [2] by F
= m_g * g. It becomes more clear.

We equate them, because hey, force is force.

[3] m_i*a = m_g*g

IF m_i = m_g [equivalence principle], we have a = g. I haven't
explained a though. a is acceleration. In calculus, a = d^2x/dt^2.

[4] d^2x/dt^2 = g

The resulting equation is called a differential equation, and its'
solution is the formula you may remember from highschool physics: d =
1/2*at^2 + v_i*t + x_0. As you can see, the position [and velocity] of
the falling object is *not* influenced by its' mass as it is written.

However, if m_i =/= m_g the solution would be similar but different.
Gravitational and inertial mass would not be equal and they would not
cancel out. The differential equation would be this:

[5] d^2x/dt^2 = g * [m_g/m_i]

Then the solution would be d = [m_g/m_i] * (1/2*at^2 + v_i*t + x_0).
Freefall would be influenced by mass.

>
> Here's one of the things I'm trying to understand: Is inertial mass and
> gravitational mass considered to be the *same thing* owing to a
> universal predictability in regards to both? Hmmm. that was muddy. Let
> me go back to the opening words I read at the site and try it from
> there: I read: "Gravitational mass is the charge to which gravity
> couples. Inertial mass is a measure of how fast an object
> accelerates--given the same force, increasing the inertial mass implies
> decreasing acceleration".

Yea, they are considered to be the same thing. What is funny is that we
have no real reason to think they would be the same thing other than
four centuries of people trying to show that they aren't.

How you read it isn't quite correct. Yes, mass is essentially gravity's
charge. But no, increasing inertial mass does not decrease acceleration
when you are talking about gravity. Two objects of different mass
accelerate at the same rate. *THAT* is the equivalence principle.

>
> Let me ask this (#1.): is the term or phrase *inertial mass*
> meaningless in the absence of being a measurement of how fast an object
> is accelerating? And if the question is stupid, please, once again, I
> beg your indulgence. I'm trying to construct my own (simple yet
> accurate) understanding of physics, from square one. With the help of
> only human resources on the internet and the web sites those humans
> refer me to, for further consideration, contemplation and study. As you
> did. And I did.

If you can't measure something or otherwise use it, it is useless.

>
> #2. Does the phrase: "gravitational mass is the charge to which gravity
> couples" mean that all mass in the universe has a measurable
> *gravitational mass* independent of the gravitational field that mass
> exists in? or does the gravitational mass of an object change relative
> to the gravitational field it is found in? It seems to me the word
> *charge* is what I am most unclear about. And how it relates to mass
> and it's measurability relative to gravity. I know, I know, still muddy
> questions. I intend to get better, each day.

When we say mass, we mean gravitational or intertial mass unless
otherwise specified. Such as in Eotvos experiments seeking to find a
difference. We are yet to find a verified instance of them being
different. Though someone on this newsgroup may have found a way, it
isn't published. So I stick to "still equal, always".

The gravitational field is *created* by the gravitational mass. The
strength of the field, while modeled best by GR, is adequately modeled
for most purposes by Newton's law of gravitation.

There is a direct analogy between an electrostatic field and electric
charge, and a gravitational field and gravitational mass. You can call
mass "gravitational charge" if you want. Back in the late 19th century,
physicists were intrigued by the similarity between Newton's law of
gravitation and Coulomb's law of electrostatics that they thought
gravitation and electromagnetism were related in a more fundamental
way.

Over a century later and we still haven't found a way to unify them,
though.

>
> #3. In terms of how fast an object acclerates. i.e. it's inertial mass
> (or gravitational mass): does light itself escape these perimeters? I
> guess what I'm asking is whether or not light has mass? It seems to me
> light must not have mass, either gravitational nor inertial owing to
> the, well, universal speed of it, regardless of the gravitational field
> in which it finds itself. So to speak. In other words it seems to me
> light is not bound by the laws of gravity. Which necessarily requires I
> consider it to without mass. Or, continue to study. Lol.

This is where it starts to get hairy. This is also where Newtonian
gravitation goes to ***, and general relativity comes into play.

First, while we can't say for SURE that light is massless, we have no
theoretical justification for it to have mass nor do we have any
experimental evidence that says it does have any mass. If you keep
talking to Y. Porat, he will bring up that light must have mass. He
will be unable to justify it theoretically nor will he be able to
justify it experimentally.

Light doesn't appear to have mass, but it does have energy. In GR,
light affects matter through gravitation just as much as anything else.
Newtonian gravitation does not have this particular prediction.
Regardless of that, it is governed by gravity as much as anything else.
Read up on deflection of starlight by the sun, and gravitational
lensing.

>
> Thanks again Eric for your input. As you know a number of other
> considerate folks here offered their help in the development of my
> understanding. And, something having to do with the psycholgocial
> equivalence principle, demands I can only fall in one place at one
> time.

No problem. It is a change from the usual litany of idiots.

>
> Lar

[snip]

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