Rybczyk

01-21-2008, 11:17 AM

Two New Fundamental Discoveries

I appear to have made two new fundamental discoveries involving acceleration composition. To understand what I’m talking about it is necessary to first understand just exactly what is acceleration composition? So, I will explain it in as simple terms as possible.

Assume, as with velocity composition, there is a stationary frame to which there is another inertial frame that is moving at uniform speed v1 relative to it. Assume further that there is a second inertial frame that is moving in that same direction at that same speed now designated V2 relative to the first inertial frame during the same stationary frame time interval. Thus v1 = V2 throughout the discussion and can be anything from 0 to c.

Now, assume that an object accelerates at a constant rate of acceleration to reach speed v1 relative to the stationary frame during some chosen stationary frame time interval. Thus, during that time interval, this object transitions from the stationary frame to the inertial frame v1 initially given.

Next, assume that, during that same stationary frame time interval, using the corresponding time in inertial frame v1, a second object accelerates at a constant rate to achieve that same speed v1, (now labeled V2) relative to inertial frame v1.

If we take the total stationary frame distance traveled by the two accelerating objects and determine what speed v a third object would have to reach relative to the stationary frame during the same stationary frame time interval while accelerating at a constant rate to travel that same distance, as seen in the stationary frame, we have found the instantaneous speed from acceleration that equals the composition speeds of the other two objects. As stated previously on this forum, this acceleration composition speed will have the same value as the velocity composition speed given in Einstein’s velocity composition formula, discounting the fact that Einstein’s formula varies a maximum of about 2.5 %. More specifically, both results will start out the same, then vary slightly only to come together again at exactly v1 = V2 = 0.5c and then vary slightly and come together again at v1 = V2 = c.

The first discovery involves the fact that the total distance traveled by the two accelerating objects equals the distance traveled by uniform motion at that same speed v1 during that same time interval. This is a purely Newtonian result although it occurs in a rather strange way in the acceleration composition example that uses relativistic acceleration formulas. That is, whereas the two objects travel the same stationary frame distance at the beginning, the first object travels a progressively greater stationary frame distance as the achieved speeds are increase than the second object until finally at speed c it travels the entire distance and the second object travels none even though it reaches the same speed as the first object. At every instant, however, the two distances add up to exactly the distance traveled by uniform motion at speed v1 during the same time interval.

The behavior just described is not that surprising because it is the same behavior exhibited by Einstein’s velocity composition formula. It is this behavior that I continue to claim violates the second postulate of special relativity. In short, it goes like this: Whatever resources are used by the first object in the stationary frame are subsequently denied the second object in the v1 inertial frame. Whereas this behavior seems normal in acceleration composition, it seems wrong in uniform motion velocity composition.

The second discovery is far more exciting. Under the conditions stated, the total distance traveled equals the uniform motion distance that would be traveled during the time interval using speed, v1 (a purely Newtonian result) whereas the corresponding acceleration composition speed is less than the combined speeds v1 and V2, or more specifically, a purely relativistic curve never exceeding speed c regardless of the values of v1 and V2, even if both are given values in excess of speed c.

There appears to be many other fundamental discoveries involved here, but I’m still trying to sort it all out and have not drawn any final conclusions at this time.

Joseph

I appear to have made two new fundamental discoveries involving acceleration composition. To understand what I’m talking about it is necessary to first understand just exactly what is acceleration composition? So, I will explain it in as simple terms as possible.

Assume, as with velocity composition, there is a stationary frame to which there is another inertial frame that is moving at uniform speed v1 relative to it. Assume further that there is a second inertial frame that is moving in that same direction at that same speed now designated V2 relative to the first inertial frame during the same stationary frame time interval. Thus v1 = V2 throughout the discussion and can be anything from 0 to c.

Now, assume that an object accelerates at a constant rate of acceleration to reach speed v1 relative to the stationary frame during some chosen stationary frame time interval. Thus, during that time interval, this object transitions from the stationary frame to the inertial frame v1 initially given.

Next, assume that, during that same stationary frame time interval, using the corresponding time in inertial frame v1, a second object accelerates at a constant rate to achieve that same speed v1, (now labeled V2) relative to inertial frame v1.

If we take the total stationary frame distance traveled by the two accelerating objects and determine what speed v a third object would have to reach relative to the stationary frame during the same stationary frame time interval while accelerating at a constant rate to travel that same distance, as seen in the stationary frame, we have found the instantaneous speed from acceleration that equals the composition speeds of the other two objects. As stated previously on this forum, this acceleration composition speed will have the same value as the velocity composition speed given in Einstein’s velocity composition formula, discounting the fact that Einstein’s formula varies a maximum of about 2.5 %. More specifically, both results will start out the same, then vary slightly only to come together again at exactly v1 = V2 = 0.5c and then vary slightly and come together again at v1 = V2 = c.

The first discovery involves the fact that the total distance traveled by the two accelerating objects equals the distance traveled by uniform motion at that same speed v1 during that same time interval. This is a purely Newtonian result although it occurs in a rather strange way in the acceleration composition example that uses relativistic acceleration formulas. That is, whereas the two objects travel the same stationary frame distance at the beginning, the first object travels a progressively greater stationary frame distance as the achieved speeds are increase than the second object until finally at speed c it travels the entire distance and the second object travels none even though it reaches the same speed as the first object. At every instant, however, the two distances add up to exactly the distance traveled by uniform motion at speed v1 during the same time interval.

The behavior just described is not that surprising because it is the same behavior exhibited by Einstein’s velocity composition formula. It is this behavior that I continue to claim violates the second postulate of special relativity. In short, it goes like this: Whatever resources are used by the first object in the stationary frame are subsequently denied the second object in the v1 inertial frame. Whereas this behavior seems normal in acceleration composition, it seems wrong in uniform motion velocity composition.

The second discovery is far more exciting. Under the conditions stated, the total distance traveled equals the uniform motion distance that would be traveled during the time interval using speed, v1 (a purely Newtonian result) whereas the corresponding acceleration composition speed is less than the combined speeds v1 and V2, or more specifically, a purely relativistic curve never exceeding speed c regardless of the values of v1 and V2, even if both are given values in excess of speed c.

There appears to be many other fundamental discoveries involved here, but I’m still trying to sort it all out and have not drawn any final conclusions at this time.

Joseph