g = c*s / r^2
As I've been sitting here and getting a bit hung up on the F=G(M+m)/r^2-Kepler-Centripetal-angular momentum stuff, I've decided to just get right to the meat of my theory that gravity is not an applied external force.
This is my theory (and put on your Relativity thinking caps and hold them down tightly!):
If bodies in free-fall in gravitational field are in a state of inertial rest, then gravity is not an applied external force. And, if gravity is not an external force then what the heck is it?
Electromagnetic radiation (light) that has been released as pure energy expands as a light sphere in all accessible directions. Sometimes the photon-wave is reflected, other times it's absorbed by matter and becomes a part of that matter.
Light expands at a constant speed (c) of 299,792,458 m/s in a vacuum.
When light is absorbed by matter it does not expand at c anymore. It's previous latent energy now contributes to the structure and mass of whatever particle absorbed it; it becomes matter.
Electromagnet energy and matter have already been theoretically united as matter-energy by E=mc^2 (much as space and time have been united as space-time).
But unifying gravity with the other elements and forces of physics has been a tough go. But, I have an idea.
If motion is relative, then the speed of light is, too. Now, I hear you say "c is a constant." Yes, in any frame of reference, c is a constant. And so is mass, time, and all of the fundamental principles of classical mechanics.
But light (energy) that has been absorbed and is now a part of a particle (matter), has entered a very different frame of reference for itself. It now has mass, it's staying reasonably still...it can be pushed around.
So, what happened to it's unstoppable urge to expand at the speed of light?
My answer: It never lost it.
Just as a photon-wave can't do anything but expand at c, so can't a particle of matter. The difference is the frame of reference. Rather than the energy expanding through space at c, the particle is *ahem* expanding through space at c.
Gravity obeys an inverse-square law. If one planet is twice as far away from the sun as another, then the gravitational effect of the sun on that planet is 1/4 of that planet that's twice as close. If it's 3 times further away then the effect is 1/9. 4 times? 1/16, etc.
This is due to the simple Euclidian law of geometry; that the surface of a sphere grows as the square of the radius.
Let's assume a standard sphere where we call the radius 1 and the surface area 1. If the radius of another sphere is 2, then the surface area of that sphere is 4. If the radius = 3, then surface area = 9, etc.
If the force g = 1 at a radius r = 1, then the same progression applies.
Imagine a sphere at any given radius from a mass (body) as a shell.
The force of gravity at any given spherical shell at a given radius from the center of the source mass is the same as it is at any other shell at any given radius from that body,.but it's effect is dispersed -- by an inverse square law -- as the shells become larger at greater distances.
(Expanding light spheres do the same thing. Let's say there are two stars of equal mass and brightness, but one is twice as far away as the other. The star that is twice as far away is four times as dim as the one that is twice as close.)
That matter is "expanding through space at c" -- causing the effect we call gravity -- is perfectly sensical if we can just picture in our minds a light sphere expanding through space at c; then picture the light sphere frozen; then (since that can't happen, can it?) the relative velocity of that "frozen" sphere through space.
Or, let me try it this way: Imagine that we have a really expensive camera that can zoom back to follow the light sphere as it expands, so it's always the same size on the screen. The sphere will look to be at rest (like a particle mass), while the space around it would seem to be getting sucked in.
Here's the cool part: If we were to pan back fast enough to keep the expanding light sphere at a constant size in the center of our screen, we would have to retreat at the speed of light. This would mean that the sphere would always be frozen in time as far as we could tell. The nearest matter around it that's being "sucked in" would seem to just sit there; time has stopped. But there would be new stars buzzing by us at the speed of light, seemingly rushing at c to get to that light sphere; and it would appear to us to be progressing as some kind of crazy backward inverse law.
As you get closer to a mass it's gravity effect increases according to the inverse-square law. I decided, one day, to assume that a particle's radius was determined by (or, in proportion to) it's mass and gravity effect. I further assumed that, at it's "surface radius," it's g-force would produce an acceleration of c*s. Then I wondered; what size would a particle of 1 Earth-mass be when it's surface g was equal to c*s?
First; here are some basic facts:
c*s = 299,792,458 m/s^2
g = 9.78 m/s^2
c*s/g = 30,653,625.56
1 / (c*s/g) = 0.000000032
surface area of a sphere = 4*pi*r^2
radius of Earth = 6,378,000 meters
surface area of Earth = 511,185,500,700 meters^2
So, let's take the actual measurements for the Earth's surface:
r = 6,378,000 meters
g = 9,78 m/s^2
surface area is 511,185,500,700 meters^2
and reduced them to the point where g=c*s:
r = 1,151.976424 meters
g = c*s
surface area is 16,676,184.03 meters^2
As expected:
If you divide the surface area of the Earth by the reduced surface area you get:
30,653,625.54
Dividing the radius of the Earth by the reduced radius:
5,536.571641 (the sq.rt. of 30,653,625.54)
and dividing actual sea-level g by c*s:
0.000000032
There are several ways of playing with the numbers, but there's a kicker.
Looking through the results, here's how gravity finally gets to be in an equation with c:
r^2 = c*s / g
c*s = g*r^2
g = c*s / r^2
(c*s is how I write the speed of light as an acceleration; it means 186,000 m/s^2.)
These equations are only for supra-atomic bodies like the Earth, and G(m) for other bodies would have to be factered in to get a concrete answer; and it may not tranlate to subatomic particles. Also, relativistic time dialations might skew the effects (i.e. the reduction represents a "Black Hole").
It's a hypothesis in progress that may lead to nowhere else, but I'll crunch some numbers (for electrons and protons) and see what happens.
I woul like to encourage you to continue exploring the mysteries of gravity. Your assertion (paraphrased): "A falling body is not accelerating; it is we, standing on the ground, that are undergoing an acceleration," may be much closer to the truth than most people suspect.
I would advise you, however, to be more careful in your treatment of physical quantities. For example, a Force MUST ALWAYS have the dimensions of a Force (i.e., MASS x LENGTH / TIME^2). A velocity squared must always have the dimensions LENGTH^2 / TIME ^2, and so on.
By ADDING the second mass in Newton's equation instead of multiplying it, you have made the end result an ACCELERATION, not a Force.
Similarly, "g = c^2" as you have written it, is meaningless because you have an acceleration on one side and a velocity squared on the other.
You MUST keep these things straight.
As an excersize to heighten your sensitivity to maintaining the dimensional integrity of your equations, you may want to simply contemplate the dimesions of Newton's constant: LENGTH^3 / TIME^2 x MASS.
I like to think of this as "Acceleration of Volume per Mass."
One more thing. Being ever on the lookout for ways to test your hypotheses experimentally (as I presume you are) I would urge you to contemplate the implications of your "falling" and "accelerating" assertions as they would apply to observers who are either falling within or firmly attached to the walls of a tunnel bored through the center of an evacuated, uniformly dense spherical mass.
Have fun.
Rick
Posted by: Rick Benish at February 27, 2005 04:59 PMHowdy, Rick.
Thank you so much for your comments at Blather Review!
Two things:
You wrote:
"By ADDING the second mass in Newton's equation instead of multiplying it, you have made the end result an ACCELERATION, not a Force."
Yes. I don't know why I left the "F" in the equation. It should read a=G(M+m)/r^2. I suppose I left it as F=G(M+m)/r^2 because I still tended to think of the cause of the "acceleration" of two bodies toward each other as a "force" even though a huge part of the thesis is that gravity is not a force at all. Silly me! I'm going to fix that.
"Similarly, "g = c^2" as you have written it, is meaningless because you have an acceleration on one side and a velocity squared on the other."
Hmm. I didn't write g=c^2, did I? The equation is g=c*s to write c as the extreme acceleration, i.e.:
g at sea level = 32 feet per second per second,
g = c*s = 186,000 miles per second per second.
"c*s" looks weird, but it's the only way I know how to write it.
Oddly, though, when I first posted all of this I actually DID mistakenly write "g=c^2". A fellow blogger, DFMoore, quickly corrected me in comments he wrote on his blog. Did you find my post via a link from DFMoore? Or, did I mistakenly leave a "g=c^2" uncorrected somewhere? Just curious.
The only idea I've had that mught test the hypothesis would be to observe the orbit of a distant planet like Neptune. Perhaps the difference that might be observed by replacing F=G(Mm)/r^2 with a=G(M+m)/r^2 could explain the unexplained eccentricity of Neptune's orbit that leads many in search of a large 10th planet. Unfortunately, I've yet to find any specific detailed data about the observed "eccentricity". (And if I ever did find it, my eyes would probably glaze over and I wouldn't know what the world I was looking at!)
Thanks again for your comments!!
