Over the past few weeks I’ve been thinking about gravity and the various laws that Newton proposed. One of the main questions I have pertains to the equation for F (force) which is F=ma and the so-called law of universal gravitation which is:
F1 = F2 = G⋅m1 x m2 / r(squared)
And this is put into normal language as:
The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them
meaning, if the mass increases then the product increases. For example, as a mass accelerates the value of F will increase. This can be seen in the extreme example of a mass that approaches the speed of light; as it approaches, it’s mass approaches an infinite value. The difficulty with this concept (as it is only a concept without any empirical evidence) is Newton’s 3nd law which states that “for every force there is an equal and opposite force”.
If you take the 2nd law and apply it to any accelerating mass, you increase the total amount of force which also an increase in energy (e=mc2).
Now if you take the law of universal gravitation (as shown above), and apply the 2nd law to m2, the total force between the two objects will increase. you can ignore the increase of r(radius) since the increase in radius is insignificant relative to the size of m1. In other words, an object like a rocket could not possibly launch if gravity acts according to the prevailing theory since the acceleration adds to the objects total energy (as shown above). By increasing energy you increase the force between m1 and m2 with a “…a force that is proportional to the product of the two masses” and with equal force (as per the 2nd law). Therefore for every pound of thrust an equal amount of force is brought to bear between the rocket and the earth.
This would also apply to anything accelerating away from the center of the earth (ie. rapidly raising my hand above my head). In other words, gravity should be acting like a brake against the accelerating body. To “break free” (think of an inverted pendulum flywheel) of the gravitational force, an object would have to accelerate with a force greater than m1 * acceleration. Therefore, if we take two equal masses (m3 = m4) and accelerate one of them (m4) it would require the second mass (m4) to accelerate at a greater value than m3 * acceleration. Essentially, it is an application of e=mc2. This a far better explanation as to why the mass of an object increases as it approaches the speed of light – the mass itself is not increasing but the affect of gravity increases proportionally to the accelerated mass therefore the effective mass increases.
The great irony here is that this makes gravity all but impossible since any object on the surface of a globe (ie. Earth) would be held fast against the surface. Anything pushing against gravity would encounter massive (no pun intended) resistance (like blood flow, plant growth, etc) to the point where no life could form. Nor could objects be buoyant. An object floating on the ocean surface is essentially accelerating away from the center of the earth (until it finds equilibrium at the ocean surface). The gravity of the Earth is far greater then the total outward thrust of the buoyant object (ie. air inflated beach ball). In a nutshell, buoyancy would be completely overwhelmed by gravity. As well, the lift experience by commercial airplanes would also be insufficient to overcome gravity.
However, no matter how reasonable this line of thinking is, many gravity apologists will simply drag out their favorite solution:
Einstein – The grand-daddy of excuses
If we push aside Newton for the moment a look at what Einstein proposed, we are actually in a less favorable possible (if you believe in gravity). Firstly, Space-Time needs to bend or be distorted to create this magical affect. Looking at the area around an object (like a planet), we see it is spherical. The so-called gravity “well” needs to encompass the entire planet not just a portion underneath. I talked about this in a previous post. The point being, the distortion of space time is not like this:
It needs to be an gravity sphere. So what about the distortion around objects on the earths surface? Is this not what causes gravity? Does space-time wrap around a cube or a oddly shaped stone?
The explanation is somewhat specious:
Bodies with spatial extent
If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. In the limit, as the component point masses become “infinitely small”, this entails integrating the force (in vector form, see below) over the extents of the two bodies.
In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object’s mass were concentrated at a point at its centre. (This is not generally true for non-spherically-symmetrical bodies.)
Right. This explanation effectively reduces all objects to single point masses and runs gravitational vectors between two bodies. It’s really a rather grotesque idea. Then the gravity within a body is nullified since all the internal objects of a “single mass” are counted as one:
The portion of the mass that is located at radii r < r0 causes the same force at r0 as if all of the mass enclosed within a sphere of radius r0 was concentrated at the center of the mass distribution (as noted above).
The portion of the mass that is located at radii r > r0 exerts no net gravitational force at the distance r0 from the center. That is, the individual gravitational forces exerted by the elements of the sphere out there, on the point at r0, cancel each other out.
As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.
So now we have a hollow uniform body and only the surface itself has gravity. So if all the gravitational forces are cancelled out as per the explanation above, then all the gravitational forces most somehow come from the surface. How is that even possible? Geometrically, the math flattens out the sphere by pushing everything to the surface so the concept of a larger mass having greater density and therefore greater gravity is expunged and we are left with flat plane – in essence.
So does the math coincide with reality? If the math says all the gravity is on the surface, then is it really on the surface? I mean really only on the surface. If yes, then how could a surface, no matter how big, generate a sufficiently potent gravity field as to warp space-time?