Special Relativity sans Lorentz Transformation (OR) Perceptional Relativity

: This paper shows that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a simple and straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in paradoxical Lorentz Transformation. This paper also proves that Lorentz Transformation has failed in its attempt to do the impossible task of establishin g t' ≠ t to explain the constancy of the speed of light in all inertial frames without contradicting the interchangeability of frames demanded by the First Postulate of the Special Theory of Relativity. This paper also points out the misconceptions regarding the claimed experimental verifications of Lorentz Transformation's predictions in the Hafele – Keating experiment and μ meson experiment . This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.


Section 1: Introduction
Everyone's world is his or her perception. Any absolute reality beyond the perceptional realities of the observers seems to be beyond the cognitive limits of human capabilities.
But, fortunately for all human beings, though their perceived 'facts' may differ, the laws of Nature connecting one's perceived 'facts' are the same. A stone's trajectory dropped by a passenger in a moving train is a straight line for him, whereas it is a parabola for an observer standing on the platform. Both observers would agree that the same laws of Physics govern the physical realities perceived by them. The First Postulate of Special Relativity succinctly states this fact as follows; "The laws of nature have the same mathematical form in all inertial reference frames" [1]. Though the laws are the same, the scenarios of the same reality observed in different inertial frames need not be the same as has been exemplified by the stone's trajectory being a straight line in the train frame and a parabola in the platform frame. This paper is a relook of Special Relativity in the Light of Perceptional Relativity, which means that the same reality is perceived differently by the observers stationed in different inertial frames. There is no absolute perception of that reality. The rest of this paper consists of the following five parts, namely- The following two premises constitute the whole gamut of Physics.

The Laws of Physics have been discovered and derived from an observer's
perspective while that observer rests in an inertial frame of reference.

Space is at rest relative to the observer's Frame of reference, and all other
inertial frames are moving in that Space.
The second premise ensures the certainty of measurements of the distances in Space travelled by the moving objects, which is not guaranteed when Space also is moving relative to the observer.
Space is static in his Frame for any observer, and the other frames move in that Space.
Just like there is a common perception of the stationary observers in every Frame that their Frame alone is at rest while all other frames are moving, those observers share another common perception that Space is at rest in their Frame. Since an observer observes that the objects attached to his Frame are at rest and Space is static, he assumes that Space is also linked to his reference frame. This perception implies that any Point in Space can be claimed to be attached to his Frame of reference by any observer regardless of his motion relative to other observers.
Let an observer stationed in an inertial frame, say S, places a minuscule material marker p at a spatial point to identify that point. An observer stationed in another inertial frame, say S', which moves at a speed v m/s relative to the frame S, also places a minuscule material marker q at another spatial point to identify that point. Let the distance between the markers p and q be v meters at one instant of time. After 1 second, the two markers would collide. That spatial point of the happening of the event of collision would be the point p from the perspective of the observers of the frame S; it would be the point q from the perspective of the observers of the frame S'.  There is an infinite number of inertial frames of referenceeach Frame moving with a non-zero velocity relative to any other frame. When a spherical electromagnetic wave propagates with a speed c from a Space point in all directions, it spreads in each of the infinite inertial frames of reference. But, for an observer in any one of those frames, his perceived facts are the following: beyond his perception and hence of no concern to him.
Suppose the velocity of a moving material particle (i.e., a particle having mass) relative to a frame of reference is known. In that case, to calculate the particle's velocity relative to  (2) While their Frame has been remaining at rest occupying the same part of the Space, the Slab of the other frame S' has moved in the Space towards the right through a distance vt and occupied a different part of the Space.    Any Light Detector can detect Light originating from a light source that is at rest in the same Frame in which it is also at rest. It follows that no static observer in an inertial frame detects Light that has originated from a Light Source that is not at rest relative to his Frame. To make this fact amply clear, we may adopt the following statement as the

Third Postulate of the Special Theory of Relativity (STR) in place of Lorentz
Transformation.
"The detection of light by an inertial reference frame is an event that is exclusive to that frame." The above statement implies that the Speed of Light relative to any inertial reference frame cannot be measured by any observer who is not stationary in that Frame. The

Constancy of the Speed of Light measured in all frames of references is due to each
observer's perceptions that Space is at rest relative to his Frame of Reference, and the light source and the light Detector are static in his Frame of reference.
Space is the medium for the transmission of electromagnetic waves. The speed of the propagation of electromagnetic waves relative to Space is c, a constant. Since Space is at rest in any inertial frame of reference, the speed of the transmission of electromagnetic waves relative to any inertial frame of reference is also c. Thus, we have derived a precise explanation for the Speed of Light's constancy measured in all frames of references without 'torturing' the observers' measuring rods and clocks.
PART -II

The Genesis of the absurdity of Lorentz Transformation
We shall follow the convention that x and t denote the space and time intervals between two events respectively from the perspective of an inertial frame of reference, say S; and, x' and t' denote the space and time intervals between the same two events respectively from the perspective of another inertial frame of reference, say S' moving with a uniform velocity v relative to the frame S along the X-Axis.
Whatever way the Lorentz Transformation Equations are derived, the one and only situation covered during that derivation is: It is assumed that Lorentz Transformation Equations derived for the above situation are universally valid for all events. We shall prove in the following sections that this assumption is fundamentally wrong.
For a pair of events whose space and time distances are measured by the observers in the frames S and S', let us define two values p and q as follows: We shall derive Generalized Lorentz Transformation Equations involving p and q so that that in our derived Equations, if we substitute both p and q with c we shall get the usual Lorentz Transformation Equations.
Let us consider two events. Let the first event be taken as the Origin Event and assigned the coordinates (0,0) by both frames. Let the space difference and the time difference between the events be pt and t for the frame S respectively and qt' and t' for the frame S' respectively.
The following figure depicts the scenario of the second event E from the perspective of the frame S, Equations (1) and (2) represent the same reality from the perspectives of two referential frames. The First Postulate of the Special Theory of Relativity demands that both equations must be mathematically identical. Since the object is to explain the constancy of the speed of light in all inertial frames, the Transformation Equations should include the scenario when x = ct (or) -ct, x' = ct' (or) -ct' respectively. This requirement seems to demand t' ≠ t. But, Equations (1) and (2) are not identical if t' ≠ t. To make them identical, Lorentz Transformation includes a factor, say a, to the RHS of the two equations with a view to derive an expression for a so as to make the Equations (1) and (2) identical. This factor a is named ᵞ in many text books) is called Lorentz Factor.
With the inclusion of Lorentz Factor (a), the Equations (1) and (2) become When we rewrite the above Equations (3) and (4) in the following formats, The above Equations Using the two values p and q, which we have already defined, we can rewrite Equations (3) and (4) as follows: From Equations (3c) and (4c), The above Equation (5) gives the general expression for Lorentz Factor (a). follows: The above Equations may be written in the following format to make explicit the fact that the two Equations are identical: x' For the particular case p = q = ± c, The above is the pure form Lorentz Transformation Equation for Space Difference.
Obviously, the above Equations are identical, and also there is no intertwining of Space and Time.
Now we shall discuss a real case where p (or) q ≠ ± c, The following discussion would prove that Lorentz Transformation does NOT apply to any event of detection of Light at a spatial point that does not fall on the X-Axis, that is, the straight line through the common Origin along the direction of the relative velocity between the Frames.
The following Picture gives an 'assumed' scenario (from the perspective of a stationary observer in the Frame S) of an event of detection of Light at a spatial point in the X-Y Plane that does Not lie on the X-Axis.
Since x' = ct cos Ф, Equation (3) can be written as Substituting the value of x' given by the Equation (4e) in Equation (3e) This means, - We can get the same expression for a by taking p = c cos θ and q = c cos Ф in Equation (5), which we derived as a general case.
The above restriction for the value of θ means that Lorentz Transformation's ambit is confined to the events of detection of Light on the spatial points lying on the X-Axis in Pictures S and S'.

Therefore, Lorentz Transformation fails in respect of the events of detection of
Light at the spatial points NOT lying on the X-Axis, that is, the straight line through the common Origin along the direction of the relative velocity between the Frames.

We can derive the Generalized Lorentz Transformation Equation for Time
Difference as follows: If we substitute v for p and 0 for q, then the value of a would take the form 0/0 and thereby become an indeterminate. So, in order to define a in this circumstance, let us proceed as follows.
Therefore, a = ∞ The same value for a can be obtained in the following manner also.
If a = ∞ is absurd, then taking the value of a as equal to t √1 − 2 2 by applying the value related to transmission of light to the moving clock is also equally absurd. The genesis of absurdity is the very 'invention' of a as Lorentz Factor.
The above detailed discussion emphasizes that even if one assumes for argument's sake that there is a need for Lorentz Factor a (in fact, there is no such need), its value has to be individually calculated for every pair of events based on the values of p i.e., (x/t) and q i.e., (x'/t') and there is no universal value of a applicable to a given relative velocity, say v, as has been adopted in the Special Theory of Relativity.
The following expression for a, Lorentz Factor in the Special Theory of Relativity a = 1 / √1 − In some text books, Lorentz Transformation Equations have been derived from the identity x' 2 + y' 2 + z' 2c 2 t' 2 = x 2 + y 2 +z 2ct 2 Since y' = y, z' = z, the above identity is reduced to The Detection of a Light Signal at a spatial point in X-Y plane (not on X-axis) from the perspective of the Frame S' The expression for t' can have a linear form if and only if y' = 0 i.e., the point of detection of Light Signal falls on X-axis

Mutual Length Contraction.
When Jill is shorter than Jack, it means Jack is taller than Jill. But, according to Lorentz Transformation, when two rods of equal length L, say AB and A'B' are in motion with a uniform, linear, relative velocity, say v, for the observer S stationed on the rod AB, the moving rod A'B' would be found to be shorter than his rod by the factor a. Mystically, for the observer S' stationed on the rod A'B' also, the moving rod AB would be found to be shorter than his rod by the same factor a. Let us see how this seemingly impossible feat happens.
When the ends A and A' coincide, let the observers set the clocks to read 0. Let us use the notation (x,t) to define an event, where x gives the space coordinate, and t provides the Time with a coordinate. Let us take the coincidence of the ends A and A' as the Origin Event (0,0).  But now, the above measurement of the length of AB as L/a by S' would not be agreeable to S for the reason that S noted the ruler mark of the end A at the instant 0. and later the ruler mark of the end B at the instant vL/c 2 . The vicious cycle repeats.

Discussion
If every event happens at the same instant of time for all observers, then the physical realities observed by both observers would have been the same, and the mutual accusation of one rod is shorter than the other rod would not have arisen. Lorentz Transformation unrealistically predicts that whenever an event happens at a particular time for a frame, it has already happened in the past or will happen in the future for any other frame.
The end B' of the rod A'B' coinciding with the ruler marker L/a of the rod AB really happened because the observers on both frames did not deny the event's happening.
They disagree only on when that event occurred. According to the observer in frame S, it happened when the Time was 0. According to the observer in frame S', it happened when the Time was -vL/c 2, and at that instant, its end A' was not coinciding with the end A but was at a distance v 2 L/c 2 from it. This stand of S' is unassailable because it is axiomatic that all clocks of each frame are always synchronized, and it would be unrealistic to say that the clocks at its two ends were showing different times at the instant when the observer in another frame was observing them simultaneously.
The event of the end B' of the rod A'B' coinciding with the ruler marker L/a of the rod AB happening at time t = 0 is true for the observer in the Frame S. The same event happening vL/c 2 seconds earlier is true for the observer S'.
According to Lorentz Transformation, every event in the universe happens at different times for different inertial frames, which implies that the same event recurs infinite times.
When a specific event is represented by (X, T) in the frame S, for that frame, it had happened when the Time was T. For any other frame moving with a velocity v relative to it, the same event has occurred at the time t' given by the following expression.
Since the value of v is different for different frames, it varies between -∞ to + ∞. So, the event repeats infinite times -one instance for each inertial frame. The following Graph depicts Simultaneous Events observed in one frame being spread over an infinite time spectrum for another frame.   It may be seen that out of the above six pairs of events, the predictions of Lorentz Transformation were found to agree with the experimental results only in respect of two pairs of events. Hence, Lorentz Transformation cannot be said to have been experimentally confirmed.

The Mu-Meson Experiment
Let us consider the phenomenon of rapidly falling μ mesons first from a frame of reference attached to the earth and then from the perspective of a frame of reference attached to a frame of reference that moves with the mesons.
In the following figures, an event is defined as (x, t), where x and t denote the space and time coordinates, respectively. Since the time elapsed in μ mesons frame is h/av from the viewpoint of both earth frame and μ mesons frame, it has been concluded that the time dilation is a fact of experience.
But, in the perspective of μ mesons frame, the time elapsed in the earth frame is h/a 2 v, which is less than h/av, which is the time elapsed in μ mesons frame. It means that for an observer moving along moving μ mesons, the μ mesons stationary on the earth would be decaying at a slower rate. This reduction of the decay rate of μ mesons stationary on the earth from the perspective of an observer moving along with moving μ mesons has not been experimentally verified. When Time Dilation has been predicted as a mutual phenomenon between the two frames, one-sided verification of the phenomenon cannot be taken as the confirmation of that prediction.
Therefore, the reduction in fast-moving μ mesons' decay rate cannot be attributed to Time Dilation predicted by Lorentz Transformation. The real reason for such reduction has to be traced elsewhere. The possibility of attributing such delayed decay of radioactive substances to the Relativistic variation of Mass with Velocity may be examined.
As already said, the observed slowing down of clocks moving with a high-speed relative to the Earth in Hafele-Keating experiment may be due to the variation of the mass of the clock with its velocity.
It has been shown in many textbooks [5] on Special Theory of Relativity that from the above equation giving a variation of mass with velocity, the following famous mass- 2. The detection of Light by an inertial reference frame is an event that is exclusive to that Frame.