The inverse square law

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />From Newton's equation the force of gravity is generally proportional to (m1 x m2) / r^2<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Yes, but gravitational force is an unobservable abstraction. In all astrophysical problems, we actually observe acceleration, not force. We verify this formula:
<center>a = GM/r^2</center>
It describes the acceleration (a) of any target mass (m) in the field of a source mass (M) at distance (r), and is clearly an inverse square effect. As Galileo showed, the gravitational acceleration of any mass is indepemdent of its own mass.

Then the formula for abstract force (F) is F = m a. That can be combined with the previous formula, if you wish; but it should be clear that there is nothing "inverse r" about the way the mass of the target body enters the formula.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">a curved space theory is multiplicative on top and bottom since the field attenuates as 1/r (the curvature relative to some standard of length significantly greater than the radius of curvature).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

There is no "curved space" theory in existence. See p. 32 of MTW. GR calls for "curved spacetime". But "spacetime" is essentially proper time, with no spacial component. See metaresearch.org/cosmology/gravity/spacetime.asp .

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What does MM have to say about the relationship of mathematical logic and physical logic?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

They can be made consistent when one gets the math right and the physics straight, and carefully adheres to the principles of physics. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">As Galileo showed, the gravitational acceleration of any mass is independent of its own mass.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
For small bodies this is true. However, if you drop Jupiter on the Earth it will accelerate a good deal more quickly than a bowling ball ;o)

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Yes, but gravitational force is an unobservable abstraction. In all astrophysical problems, we actually observe acceleration, not force.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I would say that the extent of compression of a spring would amount to the observation of force sans acceleration. Though we don't have any spring scale on the astronomical level, those at our level should be assumed to scale up.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There is no "curved space" theory in existence.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
In existence ... yes ... mine at least. In the literature ... unfortunately, I agree.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: As Galileo showed, the gravitational acceleration of any mass is independent of its own mass.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">For small bodies this is true. However, if you drop Jupiter on the Earth it will accelerate a good deal more quickly than a bowling ball ;o)<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The gravitational acceleration of any target body remains independent of a target body's own mass (m) for target bodies of any mass because the formula describes only the acceleration of the target body: GM/r^2, which is proportional only to the source mass (M).

A separate formula for the acceleration of the source mass is factored by the target body mass: Gm/r^2. The two independent acceleration formulas combined yield the total relative acceleration between any two bodies, which is equal to the sum of their individual, separate accelerations.

For studying whether the force law is inverse linear or inverse square, it is reasonable to adopt target body masses in the huge range wherein their back-acceleration on the source mass is utterly negligible and unobservable. We then plainly see the source mass field drops off with the square of distance, as does any phenomenon that spreads in two dimensions while propagating through a third, such as light intensity.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: gravitational force is an unobservable abstraction. In all astrophysical problems, we actually observe acceleration, not force.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I would say that the extent of compression of a spring would amount to the observation of force sans acceleration. Though we don't have any spring scale on the astronomical level, those at our level should be assumed to scale up.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Force is real enough and can be observed and measured for types of force other than gravity. My remark about force being unobservable was qualified to gravitational force in astrophysical problems, where we can observe only acceleration and must infer force.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: There is no "curved space" theory in existence.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">In existence ... yes ... mine at least. In the literature ... unfortunately, I agree.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">As MTW comment on p. 32, Riemann spent his entire life in an unsuccessful search for a curved space theory.

In general, the primary reasons for failure of such theories are:
(a) Only a single curvature can be attached to a single point in space at a single instant of time. Yet bodies of different speeds passing through that point all curve by different amounts. And a taut rope passing through it is Euclidean straight.
(b) A stationary body cannot be induced to commence motion by space curvature alone. An external force must act.
(c) Changes of momentum require a source for the new momentum which must itself possess that momentum (i.e., must move) before it can deliver it to a target body. Curved space postulates new momentum <i>ex nihilo</i>, which is a miracle, forbidden in physics.

How does your theory deal with these allegedly fatal objections that stopped all attempts by the minds that preceded you?

(I trust you realize that shooting down your own theory is a <i>good</i> thing. The only way any of us can make real progress in understanding is by falsifying most of the great ideas that occur to us, so as to hone the possibilities for describing nature down to a few solid ones that work. Our worst enemy in achieving that goal is the tendency to fool ourselves.) -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />From Newton's equation the force of gravity is generally proportional to

(m1 x m2) / r^2

Therefore, algebraically speaking ...
(m1/r) x (m2/r) would indicate that the attenuation of the gravitational field must proceed as 1/r.

If you give it as
m1/(r^2) x m2/(r^2)
we get
(m1 x m2) / r^4

It seems that to use a 1/r^2 attenuation, we must apply it to two masses additively giving ...
m1/r^2 + m2/r^2 = (m1+ m2)/r^2

but, clearly, the masses must be multiplicative when we examine the details of any theory whatsoever. So, for any radiative flux at 1/r^2, the top part of the equation must be multiplicative while the bottom must be additive ... this is in contradiction to mathematical logic.

But, a curved space theory is multiplicative on top and bottom since the field attenuates as 1/r (the curvature relative to some standard of length significantly greater than the radius of curvature).

What does MM have to say about the relationship of mathematical logic and physical logic?

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It's weird how two unrelated individuals can generate practically
identical ideas.