Monday, July 19, 2010

The N-Body Problem

Anonymous said...

Mass is supposed to be dimensionless. It has nothing to do with volume. The job of density is to relate mass and volume to one another. It is not the responsibility of mass to do so on it's own.

F=ma is structured as it is because, experimentally, the acceleration of an object is uniquely determined by only the force being applied to it and it's mass, independent of volume.
If I have two spheres of differing density but identical mass, and applied an identical force, F=ma tells us that they'll both experience identical accelerations, and this is exactly what we see in experiment.

Your equation factors in volume. So F=da tells us that if one instead has twice the density of the other, it will experience half the acceleration. So according to F=da, if the two spheres weighed exactly the same, but one was twice as dense, meaning half the size, it would accelerate at half the rate. Or put another way, F=da means I can squish an object, without changing it's weight, and it will accelerate more slowly under equal load. Is this the behavior you're predicting? Have you been able to verify it?
So a balloon filled with 1kg of helium and a balloon filled with 1kg of lead will have experience identical accelerations. That does not occur. 
Or do you have another definition of density other than d = m / v? For instance, you say: "Density is the vibration intensity within a volume in relation to the density of the surrounding medium." It's relative? So the density of an object changes when it's surrounding density changes?


I do have an idea of what the complex density equation would look like but I lack the resources needed to provide the necessary data to substantiate the equation. I have created a general equation of baryonic density in the paper 'Variables involved in Baryonic Density'
Anonymous said...
Regarding constants, there is no problem there. G or c are perfectly valid constructs, and don't point to any sort of illegitimacy of the theory.

If anything, they're simply the product of an unfortunate choice of units. We arbitrarily chose grams and seconds and miles and furlongs and hogsheads and bushels and meters, and those arbitrary decisions are reflected in the constants.

If our units aligned better with the universe, the silly constants would drop out of the equations.

For instance, everyone's favorite e = m c^2, under a particular choice of units for mass, would simply become e = m, which is really much more to the point, isn't it? Energy is mass is exactly what the equation says. c^2 was just a constant, and has no effect on the behavior of the equation.
Constants are like perfect solids. They don't exist in the universe. It is not possible to have a natural sphere. I explain this in many postings throughout the blog. 
And the law of gravity, under a particular choice of units for mass, would become F = m1 m2 / r^2, which states exactly the idea intended, that each mass increases the effect linearly, and the distance decreases it quadratically.

And you might argue that I'm just hiding the constant in the unit, and yes! I am! But there's nothing wrong with that. The unit itself was arbitrary to begin with. The constant just scales the equation to fit the units of the universe, but the structure of the equation--it's behavior over the domain--stays the same.

If the equation is fundamentally wrong, there could be no constant that would result in correct behavior. The constant can't make an invalid equation valid, it can only scale the resultant units.

Anonymous said...
Regarding multi-body... Gravity works just fine for N bodies. It's simply:

F-sub-i = G * m-sub-i * Sigma-sub-j [ ( m-sub-j / r-sub-ij ^ 2 ) * r-hat-sub-ij ]

where i and j range over 1..N, and r-hat-sub-ij is the normal vector pointing from i to j (I sincerely apologize for the phonetic syntax... not sure if your blog supports math markup). Or in other words, the force on each body is the superposition of the law of gravitation applied to each other body. There is no trickery here, and interestingly, to solve for a body, all I have to do is sum the mass/distance-scaled vectors to each body, then apply my mass.

This is the best solution to the N-Body Problem I have seen. 

The hat is an iterative process. It is a mathematical way of describing the mean after all the summations are completed iteratively. I agree that there is no trickery here. You would have one solution to a many iteration problem. This will help me in describing multiple bosons interacting in one ruleset. Thank you for that. 

But that is not the real problem with gravity. Gravity does not allow for the interactions of magnetism, electricity, temperature or density. Each of these forces does affect the motion of an object. Each of these forces are (in this model) associated with a specific boson. This model does not need, and works well without; gravity or the higgs boson. In my opinion the higgs is an attempt to protect gravity by validating mass. Gravity describes a force that has not been found. Gravity is also 1 dimensional, it cannot be dimensionless. It is a scalar, it has a number. 

We have found the planets are ordered by density.

Thanks for reading my work. 
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