+++ Propping Up Humbug. D. and S. Birks 3/19/2008

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Clemence McGee
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1 +++ Propping Up Humbug D. and S. Birks 3/19/2008 ABSTRACT: This article presents a mathematical, philosophical, semantical (and slightly humorous) look at relativity.

2 Propping Up Humbug Consider the following words quoted from Relativity: The Special and General Theory : I stand at the window of a railway carriage which is traveling uniformly, and drop a stone on the embankment I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices the stone falls to earth in a parabolic curve Do the positions traversed by the stone lie in reality on a straight line or on a parabola? The answer is self evident The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of coordinates rigidly attached to the ground it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (path), but only a trajectory relative to a particular body of reference. I ask the reader to examine this theory thoughtfully. Look to Figure 1: Consider a stone dropped from a railway carriage traveling uniformly in a direction from B to C. For the same stone to traverse a straight line (from A to B) for one observer, and a parabolic curve (from A to C) for the other observer (as a straight line A Fig. 1 and a parabolic curve describe different distances), relativity s two-trajectory theory L L 1 = ct would have the same falling stone traversing two different distances. B vt C Look at relativity s two-trajectory theory as a right triangle relationship shown in Figure 1: where AB (the distance for a stone to fall to the ground in a straight line) is defined as length L; the hypotenuse, AC, is defined as a length equal to the velocity the stone falls to the ground (in a parabolic curve) multiplied by the time interval, or L 1 = ct; and BC (the distance the railway 2

3 carriage moves as the stone falls to the ground) is defined as the velocity of the train multiplied by the time interval, or vt. This right triangle could be described with a Pythagorean equation: (L) 2 + (vt) 2 = (ct) 2 This equation could be developed: (L) 2 = (ct) 2 (vt) 2 L = t (c 2 v 2 ) 1/2 L = t [c (1 v 2 /c 2 ) 1/2 ] Then, with the length of the hypotenuse previously designated as L 1 = ct, the velocity the stone falls to the ground could be defined: c = L 1 /t Next, substituting L 1 /t for the c preceding the radical in the equation L = t [c (1 v 2 /c 2 ) 1/2 ], to produce L = t [L 1 /t (1 v 2 /c 2 ) 1/2 ] L = L 1 (1 v 2 /c 2 ) 1/2 would show the distance the stone falls to the ground in a straight line, L, to be shorter than the distance the stone falls to the ground in a parabolic curve, L 1, by a factor of (1 v 2 /c 2 ) 1/2. This means, for relativity s two-trajectory theory to be true, as the velocity of the train, v, approached the velocity of the falling stone, c, the length L would have to contract to the point that in the event the velocity of the train were to equal the velocity of the falling stone (so the ratio of v 2 /c 2 is one-to-one) as in L = L 1 (1 1 2 /1 2 ) 1/2 = 0 the distance the stone would fall to the ground in a straight line, L, would contract to zero! 3

4 Naturally, if relativity s two-trajectory theory shows length to contract, to be consistent, time would have to contract as well. That is, if the length for the stone to fall to the ground in a straight line, L, is assigned its own time interval, t 1 ; and thus defined as L = ct 1 returning to the equation, L = t [c (1 v 2 /c 2 ) 1/2 ], and replacing length L by its equivalent ct 1, in the manner of ct 1 = t [c (1 v 2 /c 2 ) 1/2 ] t 1 = t (1 v 2 /c 2 ) 1/2 shows the time interval for the stone to fall to the ground in a straight line, t 1, to be shorter than the time interval for the stone to fall in a parabolic curve, t, by a factor of (1 v 2 /c 2 ) 1/2 ; and thus (in concert with length L), in relativity s two-trajectory theory, when the velocity of the train approaches the velocity of the falling stone, the time interval for the stone to fall to the ground in a straight line, t 1, is shown to diminish to zero! Clearly, as this is not true length and time do not diminish to zero when the velocity of a train approaches the velocity of a falling stone the reader will recognize the error: The mathematics are false in that the same relative velocity of the falling stone, c, has been assigned for both observers. To explain why this error is occurring, I would ask the reader to return to the original concept of a passenger on the train and a pedestrian on the footpath observing a stone dropped from the moving train. Make a simple comparison: 4

5 In a one-trajectory theory for the falling stone, there would be one distance of travel, one time interval, and two relative velocities (that is, with the train traveling uniformly, there would be one velocity of the falling stone relative to the person on the train and a different velocity relative to the pedestrian on the footpath). In contrast, when relativity theorizes two different trajectories for the same falling stone (thus, a different distance and time interval of the falling stone for each of the two observers) this allows for only one velocity of the falling stone relative to both observers! Think about it: If relativity theorized two different distances, two different time intervals, and two different velocities, relativity would have two different falling stones. In order to be the same falling stone for both observers, there must be a common factor; and if distance and time are theorized to be different, the only factor remaining for both observers to have in common is relative velocity! So herein lies the mathematical error in relativity s two-trajectory theory: 1. With the positions traversed (that is, the distances, L and L 1, and the time intervals, t 1 and t) for the same falling stone theorized to be different, unequal, for the two observers, L/t 1 L 1 /t 2. and the only factor left for both observers to have in common is relative velocity, c, 3. relativity is theorizing two unequal distance over time intervals being equal to the same relative velocity, c: L/t 1 = c = L 1 /t Meaning, either relativity has gone full circle to have demonstrated its two theorized unequal trajectories, being equal to the same relative velocity, c, are in fact equal, and thus in reality there is only one trajectory of the falling stone for both observers; 5

6 Or, with each observer in their own inertial system (one on the moving train and the other on the footpath), and the velocity of the falling stone shown to be equal for both observers, relativity is theorizing the velocity of the falling stone to have the same value for both observers independent of their motion or the motion of the train! In other words, with the velocity of the falling stone, c, as a constant the same for both observers, relativity s twotrajectory theory would have the measurement of length (i.e., space) and the passage of time shown to adjust and conform to the velocity of the falling stone! The reader will understand the implication: With its two-trajectory theory relativity has formulated a counterfeit reality. Moreover, considering relativity s postulate that there is no such thing as an independently existing trajectory (path), but only a trajectory relative to a particular body of reference is by no means restrictive (to the falling stone), but is stated to apply to the set of all trajectories; accordingly, relativity would have each and every trajectory observed by the passenger on the train and the pedestrian on the footpath (whether that of a falling stone, light reflected off a mirror, a bird flying overhead, or even a tortoise crossing the road ) theorized to have two trajectories, and thus one relative velocity for both observers. Consequently, triangulating the hypothesized different trajectories for the two observers (in a manner similar to the illustration in Figure 1) would produce these same equations for length contraction and time dilation for every trajectory imaginable: L = L 1 (1 v 2 /c 2 ) 1/2 t 1 = t (1 v 2 /c 2 ) 1/2 Thus, relativity would postulate an infinite number of counterfeit realities in conflict with each other where the relative velocity of each and every trajectory, c, would be cast as a common constant connecting all inertial systems (a universal speed limit that nothing could exceed); and the universe in general would act as a contortionist, with space, time, mass, etc., contracting, expanding, warping, distorting in relation to the velocity of each and every trajectory! 6

7 Ergo, relativity disproves itself. In its two-trajectory theory (for the falling stone, reflected light, a bird flying overhead, a tortoise crossing the road, etc.) relativity is simply theorizing more than one distance and time of travel for what is in reality only one distance and time of travel. Thus, relativity lays the foundation for a false mathematical structure, where space and time are shown to be relative and the relative velocity of every trajectory becomes and absolute. In closing, the Special and General Theory of Relativity demonstrate the basic philosophical flaw in the doctrine of relativism in general. Theorizing the universe to be relative requires something absolute to be relative to: However, if everything is theorized to be relative nothing can be absolute: Therefore, in abrogation of its own philosophy, relativism must create a pseudo absolute. So, in theorizing the characteristics of the universe as relative that the criteria of measurement of distance and time are different and vary with individuals and their environments according to their relative velocity relativity establishes each and every relative velocity as a false absolute; something not only physically and mathematically impossible, but semantically is a contravention: How can relative velocity, which is by its very definition relative, be theorized to be absolute? In turn, to theorize distance and time to be relative, and relative velocity (the mathematical expression of distance over time) to be absolute is a contradiction. Any way you analyze it, physically, mathematically, philosophically, semantically, the theory of relativity is a non sequitur simply propping up humbug. By its own hypothesis concerning trajectories, the theory of relativity is shown to be untenable. The theory, along with the falling stone, goes out the window! 7

Notes - Special Relativity

Notes - Special Relativity 1.) The problem that needs to be solved. - Special relativity is an interesting branch of physics. It often deals with looking at how the laws of physics pan out with regards