Re: How can I tell if F is a string or if it is a number?
- From: tchow@xxxxxxxxxxxxx
- Date: 11 Apr 2008 20:09:31 GMT
In article <48fa12ff-8344-411e-80d5-5d1e235aaabb@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pioneer1 <1pioneer1@xxxxxxxxx> wrote:
On Apr 9, 10:55 am, tc...@xxxxxxxxxxxxx wrote:
If "F" were just an abbreviation for
"m*a" then that would be just a purely logical fact and would not tell us
anything about what physical laws happen to hold in our universe.
Why logical? I would say that an abbreviation is notation, it is a
time saving device.
"Notational" is fine; maybe even better than my word "logical." I meant to
contrast it with "empirical."
If F is an abbreviation it would tell a lot about what physical laws happen
to hold in our universe. It would tell us that those laws do not involve force.
No. If F were an abbreviation for "m*a" then that's all it would be: an
abbreviation. I could just as well use "G" or "H" as an abbreviation for
"m*a". All I would be doing is playing with notation. I would be saying
nothing about force, because force does not show up anywhere. I have m,
I have a, and I have an abbreviation for "m*a". Who said anything about
force? Force does not enter the picture at all in this setup.
Only if you use "F" to represent force can you claim that assertions about F
are assertions about force. If "F" is merely a notational abbreviation for
concepts not involving force, then talking about "F" tells you nothing about
force.
Anyway, this is all moot, because "F" is not, in fact, merely an abbreviation
for "m*a." But maybe this discussion will help you see *why* F is not merely
a notational abbreviation. F = ma is supposed to be a law of nature, and for
it to be a law of nature, it must assert something more than "F is an
abbreviation for m*a" since the latter tells us nothing about nature.
But, I now think I understand the problem. F=ma is actually two
expressions:
F_occult = m_occult a
F_contact = m_weight a
F_contact is the force used in the science of mechanics and it is the
force of weights and pulleys. Newton overlayed his occult force
F_occult on this contact force and utterly confused the issue. I am
talking about F_occult. This is the force used in Newtonian
theoretical astronomical derivations but F_occult always cancels out
of the formulas used to calculate orbits. So F_contact may be an
empirical force but F_occult is not. It has never be observed. It
always cancels out of the orbital formulas. That's why I am
questioning the assumption that force is a "physical quantity."
Your metaphysical assertions here are a little odd, but I will not criticize
them here; instead I will try to rephrase your argument more coherently.
What I believe you are trying to say is this. Newton's second law F = ma
and Newton's law of gravitation F = Gmm'/r^2 are commonly taken to be two
statements. But in fact, there is a third, hidden statement here that is
rarely made explicit: namely, that the "F" in Newton's second law is the
same as the "F" in Newton's law of gravitation. So we should really write
three equations:
F_contact = ma
F_occult = Gmm'/r^2
F_contact = F_occult
Again, I'm not trying to defend your argument, but trying to help you
articulate it more clearly.
If so, do you think it is relevant that if F can be replaced for ma
it's an abbreviation? Thanks for the help.
No, F is not an abbreviation for "m*a". However, according to Newton's
second law, the value of F is the same as the value of m*a. So if you
are doing calculations where all that matters are the *values* of the
quantities you are manipulating (and not what they "mean"), then you can
substitute one for the other, even though one is not merely an abbreviation
for the other.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.
- Follow-Ups:
- Re: How can I tell if F is a string or if it is a number?
- From: Pioneer1
- Re: How can I tell if F is a string or if it is a number?
- References:
- How can I tell if F is a string or if it is a number?
- From: Pioneer1
- Re: How can I tell if F is a string or if it is a number?
- From: Pioneer1
- Re: How can I tell if F is a string or if it is a number?
- From: tchow
- Re: How can I tell if F is a string or if it is a number?
- From: Pioneer1
- How can I tell if F is a string or if it is a number?
- Prev by Date: Re: How can I tell if F is a string or if it is a number?
- Next by Date: BPL = L ?
- Previous by thread: Re: How can I tell if F is a string or if it is a number?
- Next by thread: Re: How can I tell if F is a string or if it is a number?
- Index(es):
Relevant Pages
|
