Gravity

I had an idea about gravity that turned out to be complete crap after struggling with the math for awhile. I'd written a couple pages about it, but they were lost in a fire when I tripped on the cord and the computer shut off. No sense repeating the theory or explaining how the math schooled my ass. But I'll try to retell the parts I want to keep.

[Well I'll mention the theory in a nutshell, for the sake of... I don't know what. The theory was that gravity wasn't due to some force acting from afar, but rather due to the difference of the apparent "force" of gravity across some fundamental constant distance. This idea basically describes gravitational gradients, which by the way is what causes tides. So rather than being pulled by something an astronomical unit away, we are pulled (or pushed) by some difference say between one side of a neutron and the other. My hope was that calculations based on existing measurements would produce an alternate formula for gravity, with a new constant analogous to G but which would have to be much much greater (to produce the same forces that the existing formula calculates for r², but for the much much smaller delta r²). If the resulting constant was similar in value to the other fundamental force constants, that might suggest some exciting new hidden relationship. Unfortunately, the math shows that while gravity is inversely proportional to the square of the distance from a mass, the gradient is roughly inversely proportional to the cube. Fairly simple geometry can show why. In other words the calculations differ depending on which r you choose, so no such constant can be found. Or, the "fundamental constant distance" would need to grow proportionally to r. A good candidate for an idea that needs to be abandoned when shown to be wrong.]

The force of gravity exerted by a mass at a distance of r, is inversely proportional to r². The magnitude of the force is the same at all the points on a sphere with radius r centered on the mass. Interestingly, the area of a circle with a radius of r is also inversely proportional to r². This suggests that the force of gravity can be "spread evenly" across that sphere, making the "total force" on the sphere the same for any different value of r. As when blowing up a balloon, its radius increases and the latex is spread thinner, but the total amount of latex remains the same. If you imagine a gravity wave propagating like an expanding bubble ;) from the mass, it is similar to sound (pressure) waves, whose energy across some fixed area also is inversely proportional to r². This is because the total energy of a single pressure wavefront remains the same, but gets spread evenly over the total area of the wave's expanding sphere. As a side note, I think this requires the wave to move at a constant speed (c for gravity waves; the speed of sound for pressure waves)... otherwise, a slowing bubble expansion might allow energy to build up, or allow the wave to be compressed laterally and compensate with an increase in amplitude.

So, gravity gets weaker as you move farther from a gravitation body, as its force gets spread across a larger area. I'd drawn a bunch of triangles to show the ratios involving a slice of a sphere around a gravitational body, and another body (a spaceship, say) that is affected by it. I realized that the force would be the same for any r, if the spaceship grew in size relative to r... in 2 dimensions that is. Then, the spaceship at r would cover the same area relative to a sphere of radius r, as the different-sized spaceship at r₁ would cover relative to a sphere of radius r₁. And so it would experience the same gravitational force at the different distances. A conical "slice" of gravity shares the same total gravitational force across the (curved) base of the cone, for any cone height. This is a consequence of simple ratios.

The idea occurred to me to try to visualize a spaceship that expands as it moves away from a mass, in a way that keeps the apparent size of the spaceship the same, by warping space so that lines that radiate away from the mass become parallel. In such a view, a "normal" spaceship would appear to decrease in size as it moved away from the mass. At this point I felt that now-familiar feeling that things were getting too abstract to be conceivable. Another idea came to mind of modifying gravity by somehow warping its field this way possibly through some sort of gravity lens (a lens that warps gravity, not the more familiar lens that warps light using gravity).

An interesting idea that comes out of this is that a spaceship decreasing in size as it moves away from a gravitational mass, is exactly what appears to happen to the object when viewed from the gravitational mass. The apparent area that an object takes up relative to my entire field of view, is once again inversely proportional to r². This suggests a theory that the gravitational force on an object is related to how that object is "seen" by the mass. Interestingly, all of these ideas may be converging on some Theory of Everything that centers around the effects of observation as the core mechanism for describing physical interaction. Things affect me relative to how much I am aware of them.

Note that I'm not talking about simple visual observation. You can't hide from the sun's gravity by ducking behind a planet. The mass can "see" through matter, and can "see" the various layers or depth of matter (so a long rocket with the same visual area as a short rocket will not experience an equal force), and it can "see" the density of the matter.

As an example, consider the Sun and the Moon. From Earth, they appear to be roughly the same size. The Sun is about 400 times as far away as the Moon is, and also has a radius about 400 times the Moon's (anything that appears the same size should have the same proportion). However, it is about 0.42 times as dense. So, compensating for density, the Sun has approximately 400*0.42 = 167 times the gravitational "depth" as the Moon. Since they occupy roughly the same area in the sky on Earth, we would expect the Sun's gravitational pull to be roughly 167 times the Moon's, which it is (The actual factor is about 178).

Final Thought

I've been working on some things that make you go hmmm involving defining time in terms of distance (of which the apparent speed of light propagation is a side-effect) and may one day relate it back to this gravity stuff. One idea to explore is this: perhaps the increase in mass experienced in objects traveling at relativistic speeds, is some consequence of length stretching, which makes the object appear "larger", as far as gravity is concerned. It may even involve removing mass from one time (where it appears smaller) and moving it to a time where it appears larger, or being relative to the "rate of time", but either way obeying some "conservation of mass over time" law.