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Classical Fields and Newton's 2nd Postulate of Motion 
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#19
Feb713, 03:33 PM

P: 69

For those who design langrangians to see what the action spits out, it may be an interesting exercise. This is just a thought experiment that changes axiomatic definitions and postulates, to see how/if things change. 


#20
Feb713, 03:37 PM

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You should think about how you would measure your third mass. 


#21
Feb713, 04:24 PM

P: 69

I wouldn't interpret there being 3 masses, just 2. Let [itex]m_I[/itex] and [itex]q_I[/itex] stand for the intrinsic properties of matter, mass and charge, for an isolated test particle. They are part of the scalar function [itex]f(q_I,m_I)[/itex] that expands/contracts the acceleration in Newton's 2nd Postulate of Motion. [itex]m_{grav}[/itex], on the other hand, is defined by Newton's Postulate of Gravity, and [itex]q_{Coulomb}[/itex] is defined by Coulomb's Electrostatic Postulate. The series expansion of [itex]f(q_I,m_I)[/itex] gives, to first order, a term [itex]m_I[/itex] which is currently called the "inertial mass", where [itex]m_{inertial}\equiv m_I[/itex]. This is my fault, for being so vague w/ my words. I appreciate your input. Thanks. 


#22
Feb713, 05:44 PM

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P: 5,059

So, if you take m to be gravitational source mass, and f(m,q) to be <= m(grav), then GR already incorporates your idea, in a way. If you want to make f(m,q) >= m(grav), then it appears to me your concept is inherently counter factual, given the strength of evidence for GR. 


#23
Feb713, 06:09 PM

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P: 17,275

You are positing a third mass, "intrinsic mass", which is related to inertial mass, m, by [itex]m=f(q_I,m_I)[/itex]. Do you see that now? I don't know how I can be more clear. You can measure the gravitational mass using a balance scale. You can then measure the inertial mass by dropping the object and measuring the acceleration. I cannot think of a way to measure the intrinsic mass. 


#24
Feb713, 06:33 PM

P: 69

I placed my thread in this forum to get expert GR opinions; I appreciate your input. GR was not my specialty. I will ponder your recent comments. Thanks again. 


#25
Feb813, 09:46 AM

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P: 17,275

You are welcome. I would strongly encourage you to think about how to measure your "intrinsic mass". Unless you can come up with some independent way to measure it then all you have is [itex]m=f(q_I,m_I)[/itex] which is kind of one equation in two unknowns (f and [itex]m_I[/itex]). You simply won't have enough information to do it.



#26
Feb813, 11:10 AM

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P: 8,605

As DaleSpam said, there is inertial mass u, gravitational charge m, and electrical charge q. I don't believe there is any mathematical necessity in classical physics for u to be proportional to m or q. In Newtonian mechanics, the equivalence principle is put in by hand u=m. In GR the equivalence principle is also put in by hand using minimal coupling. In quantum mechanics, there is apparently Weinberg's low energy theorem for relativistic spin 2 particles in which the equivalence principle is derived.
So for each particle the force laws should go something like: Gm_{1}m_{2}/r^{2} + Gm_{1}m_{3}/r^{2} + ... + Kq_{1}q_{2}/r^{2} + Kq_{1}q_{3}/r^{2} + ... = u_{1}a_{1} I haven't thought it through, but I wonder if DaleSpams's concern about the number of equations for arbitrary u_{i} for each particle can be answered with enough particles and particle configurations? 


#27
Feb913, 07:03 AM

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#28
Feb913, 11:18 AM

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