The Earth Falls Up
Gravity is often used as an example of a natural law that everyone could agree on at least in terms of what gravity does. If we release a quarter from our hand, everyone would agree that it would accelerate to the floor. This idea, or rather belief, in falling objects is one of the few metaphysical principles that has been allowed to remain within the standard model of physics.
A metaphysical principle is an idea that has such universal appeal that even physicists do not feel the need to subject it to any kind of experimental verification. This is particularly true when it comes to quarters falling to the floor because every physicist knows that such an event would be impossible to measure. If they were to place an accelerometer on the quarter as it was released, it would show no downward acceleration at all. In fact, air resistance would cause it to show a slight upward acceleration. If they were to place another accelerometer on the floor beneath the falling coin, it would show that it was the floor that was accelerating upward toward the quarter. In fact, with their entire array of sophisticated measuring instruments, no experimental physicists have ever been able to show that falling objects undergo any changes in motion toward the ground. Faced with this dilemma they quickly embrace the metaphysical Principle of the Equivalence of Gravity and Inertia, or the Equivalence Principle. This allows them to discard the results of their measuring instruments in favor of what everyone knows to be true. When a coin falls, it moves downward to a stationary floor. Some physicists will even tell you that the Equivalence Principle has been proved by experiment to many decimal places, but in each case their proof is in the form of a null result. This is because Equivalence is a purely negative principle that states that no instrument is capable of directly measuring the change in a bodys motion produced by gravity. The logic here seem to be that if our instruments show a falling coin to be absolutely motionless then we have proved the Equivalence Principle absolutely. Why not just discard all of this metaphysical mumbo jumbo and at least allow ourselves to consider the possibility that our instruments are right when they show us that the coin remains virtually stationary, and the earth falls up.
Equivalence is not a first principle of physics, as is often stated, but merely an ad hoc metaphysical concept designed to allow one to imagine that gravity has magical non-local powers of infinite reach. The appeal to believe in such a miraculous form of gravity is very strong. Virtually everyone, and especially physicists, accept Equivalence as an article of faith even though it has never been positively verified by either experimental or observational physics. All of the many experiments and observations show that the equivalence of gravity and inertia simply does not exist. Gravity and inertia can absolutely not be equal simply because they are exactly the same thing. There is only inertia and gravitation does not exist! Unlike the omnipresent and infinite effects of the mythical gravitational field, the inertial effects of each body of matter in the universe extend only to the outer extremities of the bodys physical structure. For one body to exert inertial forces on another body, they must be in physical contact with one another. A falling body perceives no inertial forces until it is struck by the ground. All measurements show that Chicken Little was wrong. The sky is not falling down, it is the earth that is falling up!
In our intuition, we all watch the sun pass overhead each day but in our intellect we know that this isnt true, because it is the surface of the earth that moves sideways (east) past a stationary sun. Likewise, we all see, as well as measure, the earth leaping up to collide with falling objects but insist that this isnt true either because just as our perceptions insist that the earth doesnt move sideways, they also demand that the earth doesnt move upwards. Any skydiver will tell you of those free fall fantasies of motionless floating while the earth rushes towards them. These perceptions then vanish like interrupted dreams once the jumper lands on the ground. This is because belief or even faith in an unmoving earth goes far deeper than just the conscious level of our minds. It is easy for our intellects to understand that the sun does not pass overhead every day but somewhere at the very foundation of our sub-conscious is a place where the earth doesnt move! Even though some of our most sensitive instruments show us that the earth falls up, that stubborn little place in our psyches wont allow our conscious minds to entertain any such thoughts, except as metaphors to help understand the Equivalence principle.
The Equivalence Principle, which by its very definition has no measurable effects, was developed not to account for any physical measurements but rather to satisfy the physicists deep psychological need for the permanence of mass, space and time. To say, as Einstein did, that space and time possess a non-intuitive curvature is just ambiguous enough to prevent the emotional regions of consciousness from rebelling at the idea that the actual values of mass, space and time are constantly changing in a complimentary way. The mind is comfortable in its inability to visualize a four dimensional curved space, but is very uncomfortable with the spectacle of the earths surface constantly moving away from its center. With the earths surface constantly moving upward at a velocity of 11,179 m/sec, it takes 19 minutes for the surface of the earth to quadruple in area and for the linear dimensions of its atoms and yardsticks to double. This process changes the definition of time from equal intervals of duration to intervals of constantly increasing duration. As the linear dimensions of matter doubles, the rate at which we measure the passage of time slows to one half.
Temporal Velocity and the Non-linear Passage of Time
The first question that we must ask, once we allow ourselves to consider the principle of absolute motion and the gravitational expansion of matter, is how fast does matter expand? To determine this value, we must first establish a relationship between space, time, and gravity by measuring the period of a pendulum at sea level with a length of one meter and find it to be approximately two seconds. (P=2L/g = 2.006 sec). We then use this value to determine the upward acceleration of the Earth (g = 42L/P2) to be 9.807 m/s2 and the radius of the Earth (R) to be 6,371,316m. With these two values, we can determine how long it would take for the radius of the Earth to double in size by calculating how long it would take the Earths surface to fall upward a distance of one radius. (1T = 2R/g = 1,139.9 sec = 19 minutes). After making this calculation and then waiting 19 minutes for the dimensions of the Earth and our pendulum to double, we realize that this value can no longer be valid because now the meter bar in Paris is now twice as long as it was when we started. This means that the rate of time must also have slowed because our one-meter pendulum still has a period of 2 seconds. Also, the acceleration of gravity (g = 42L/P2 = 1/2) must also have slowed its rate to one-half.
As matter expands, the absolute rate of time slows at a proportionate rate. The rate of 19 minutes is in minutes that are absolute to the point in time at the beginning of the doubling. To determine the interval in terms of minutes that are absolute to the end of the doubling, we calculate the time it would take for the Earths surface to move a distance of one radius at its sea level escape velocity of 11,179 m/s. (EV = 2Rg) (2T = R/EV = 570 sec = 9.5 minutes). These minutes are twice as long as the minutes at the beginning of the doubling so if we double this value it is again 19 minutes. It also takes 19 minutes to accelerate to 11,179 m/s at an acceleration of 9.807m/s2 (1T = EV/g). To determine the duration of the doubling in the non-linear units of gravitational time as measured by a clock, we use the square root of the product of these two rates (3T = 1t 2t = 806.1 sec = 13.4 minutes). It also takes 13.4 minutes to travel one radius at the sea level orbital velocity of 7,905 m/s (OV = Rg) (3T = R/OV) and to accelerate to orbital velocity at 9.807 m/s2 (3T = OV/g). While they have value, these calculations only supply part of the dynamics of gravitational motion because they are arbitrary segments of a continuous process.
Doubling the Earth
To an outside observer watching the Earth expand, the doubling would seem to take longer because if he watched and measured the amount of clock time that it takes for a body, with no air resistance, beginning at rest one radius above the Earths surface to fall to sea level, he would observe that it takes over a half hour to reach the Earths surface. To obtain this value, we subtract the escape velocity at 2 radii (2REV = 1REV/ 2 = 7,905 m/sec) from the sea level escape velocity (11,179 - 7,905 = 3,274 m/sec). The radius divided by this velocity gives us a time of fall of R/3,274 = 1,946 sec = 32.4 minutes. This value is also equal to (19 + 13.4 = 32.4). The escape velocity at one radius above sea level is (EV = g2R = 7,905 m/sec) and at this velocity it takes 13.4 minutes to travel one radius. At the beginning of the doubling, a point (2R) in the Earths inertial void, one radius above its surface, would be moving upward at 7,905 m/sec. At the end of the doubling the Earths surface reaches that point in space and will have accelerated from rest to 7,905 m/sec (V = gT) at the moment that it reaches the point 2R. This value is clock time and is 2.42 times greater than the 13.4 minutes of clock time it takes for the Earths radius to double because the at rest position at which the body began its fall has an absolute velocity away from the Earth equal to the escape velocity at that point. The extra time is required for the faster sea level escape velocity (1REV) to catch up with the two-radius escape velocity (2REV).
Therefore, the question, How fast does matter expand?, has four correct answers depending on how you wish to define the meaning of time and whether you believe space to have two, three or four dimensions. The linear dimensions of matter double every 9.5 minutes, 13.4 minutes, 19 minutes, or 32.4 minutes depending on how a minute is defined, how a meter is defined and how rest is defined. The 9.5-minute value and the 19-minute value are absolute units of inertial time in which consecutive intervals have the same intrinsic duration and cannot be measured by a clock. The 13.4-minute value and the 32.4-minute value are non-linear units of gravitational time as measured by a clock, in which each consecutive interval has a longer duration. It follows from this that if we are to quantify the gravitational phenomenon in terms of clock time, we must characterize it not as a force, acceleration or attraction but as a velocity. The most logical quantity to identify as the quantum of gravity (Go) is the escape velocity of the hydrogen atom at the Bohr radius. It is equal to 9.2116013 x 10-14 m/sec (Go = 2aog). The acceleration of gravity (g) at the Bohr radius is 8.0175 x 10-17 m/sec2 (g = Go2/2ao). The constant for gravity is not a force but the velocity at this radius. This is the escape velocity at the Bohr radius (ao =5.29177249 x 10-11 m) which is the size of the mechanical bond between the proton and electron at the ground state of hydrogen. Thus, within the atoms of the Earth, the protons and electrons constantly grow larger at a velocity of 9.2116013 x 10-14 m/sec and the combination of these individual velocities creates the Earths sea level escape velocity of 11,179 m/sec (EV = 2gR). Actually, the proper term for this is surface velocity rather than escape velocity. While surface velocity and escape velocity have exactly the same values for points at or above the earths surface, for points inside the earth, the surface velocity decreases to zero at its center, whereas escape velocity continues to increase to a maximum at the center.