Dear Sir,
We had gone through your excellent article. Here are a few of our comments.
You say: "The imaginary are abstract realities, but are illusions that can never be embodied in the phenomena because they do not conform to the laws of the phenomena in nature. Conversely, the real can be embodied in the phenomena."
But how is an imaginary concept is perceived? Even for an illusion to be perceived, we must have a prior cognition of the object thought to be perceived, which is real. A mirage is illusory. But the cognition of water that is imagined is not illusory. Without such prior cognition, no perception is possible. Thus, your statement appears to be self contradictory. Kindly elucidate. However, we agree that the imaginary phenomena do not conform to the laws of nature.
You say: "The time dimension is a one-dimensional continuum that can be illustrated using an endless line. The past, present and future of the ephemeral instance of existence may be represented along that line."
But then what is a dimension? It is the spread in a given direction associated with solids, which remain invariant under mutual transformation. We can rotate a solid so that its spread along any axes changes. But its shape remains unchanged, even though the values of the component along any axis go under mutual transformation. Since we cannot rotate the changes associated with time like we can rotate a solid, time cannot be a dimension like spatial dimensions. Though you are right about the direction of time, your example of a line is not enough. The line is a unidirectional straight line. Regarding duration transformation process, kindly read our essay.
You say: "The noumena and phenomena may further be categorized as fundamental passive essences and fundamental active occurrences." Though we understand your ideas, perhaps it could be better phrased to avoid misrepresentation. Further, this contradicts your earlier statement and proves our point. If noumena do, not conform to the laws of the phenomena in nature, they cannot be "essences" because "occurrences" are only perceptions arising out of these "essences". You say: "... substances in space are fundamental passive essences". Since "substances in space" actively participate in all transformations, this appears self-contradictory. Probably what you mean by these two divisions is indestructible matter and energy that induces the transformations in matter.
You say: "A duration transformation always corresponds to a motion transformation", which may be misleading. Though we generally agree with your views on space-time transformation, it need not be true always. A particle may remain in the same position (absence of relative motion) during a fixed duration. Talking about absolute motion is meaningless for physical processes. However, we got your meaning as "passage along the time dimension" to imply physical transformation in time, which is a continual process, independent of other factors. Other factors modify it differently, which causes time dilation. While it is the internal transformation, motion transformation is the transformation of the body as a whole from one position to another position.
We do not agree with Einstein's mathematics and we are surprised that though many people have pointed it out, it is still being not only considered, but also frequently quoted. We have our own reservations regarding it. Here we reproduce our comments on Einstein's 1905 paper "On the Electrodynamics of Moving Bodies", which introduced STR.
EINSTEIN'S FORMULATIONS: SPECIAL THEORY OF RELATIVITY.
The theory of relativity refutes any special privilege for a universal frame of reference. Yet, it provides the same status to time, by introducing the concept of "proper time" and making all time measurement relative to it; thus contradicting its own theory. The measurement system advocated by Einstein is also faulty. We are quoting the English translation of the original article of Einstein "On the Electrodynamics of Moving Bodies" published on 30-06-1905 in the German-language paper (published as Zur Elektrodynamik bewegter Körper, in Annalen der Physik. 17:891, 1905) which appeared in the book "The Principle of Relativity", published in 1923 by Methuen and Company, Ltd. of London. Side by side we will comment on the article. In Einstein's original paper, the symbols ( , H, Z) for the co-ordinates of the moving system k were introduced without explicitly defining them. In the 1923 English translation, (X, Y, Z) were used, creating an ambiguity between X co-ordinates in the fixed system K and the parallel axis in moving system k. Here and in subsequent references we use when referring to the axis of system k along which the system is translating with respect to K.
Einstein: §1. Definition of Simultaneity: "Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the "stationary system".
If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.
If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time".
Our comments: The values of the motion of a material point's co-ordinates can be described as functions of the time, only if the motion is uniform and follows a fixed trajectory, i.e., uniformly repetitive. In other cases, this description will not hold, as motion is related to (initial) position and forces acting on the body, both of which are time invariant. Thus, this description holds only in limited cases and is not universally true. The reference to Euclidean geometry and Cartesian co-ordinates proves our point.
Einstein: "Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by "time". We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say; "That train arrives here at 7 o'clock", I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events".
Our comments: While the systems of co-ordinates and the electromagnetic processes are governed by fixed rules, thus are immune from any arbitrary change in their exhibited results, the clocks stand at a different footing. It is not time proper, but is a measuring device, that ticks at reasonably similar intervals. However, this "ticking" is not a natural event, but an induced event dependent on the energy supplied by an artificial source; i.e., winding or by batteries. We have often experienced that the watch mat tick slowly or fast due to mechanical defects. Thus, equating the ticks of a clock with time or - "the pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events" - as Einstein puts it, is erroneous and can be misleading.
"The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events" only means that the arrival of the train is at a specific interval from a specific epoch. Without such epoch, the simultaneous events cannot imply time. For example, if the cawing of a crow and falling of a ripe date palm are simultaneous events, they do not imply time. It is true that "all our judgments in which time plays a part are always judgments of simultaneous events" because the interval between those events are compared with the interval between other repetitive events, which are treated as the unit. The reason for that has nothing to do with individual observers, but to the fact that comparison is a conscious action, which can only be performed by conscious agents. The justification given by Einstein can be highly misleading has been discussed below.
Einstein: "It might appear possible to overcome all the difficulties attending the definition of "time" by substituting "the position of the small hand of my watch" for "time". And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch.
We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and coordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought".
Our comments: In our book "Vaidic Theory of Numbers", we have explained that the views of Einstein are not correct and leave much scope for erroneous interpretation. We have also shown that this aspect was discussed in ancient times in the chapter on motion of a book and was rejected as unscientific. We have also shown that if we follow the logic of Einstein, then we will land in a problem like the Russell's paradox of set theory. In one there cannot be many, implying, there cannot be a set of one element or a set of one element is superfluous. There cannot be many without one meaning there cannot be many elements, if there is no set - they would be individual members unrelated to each other as is a necessary condition of a set. Thus, in the ultimate analysis, a collection of objects is either a set with its elements or individual objects, which are not the elements of a set.
Let us examine set theory and consider the property p(x): x x, which means the defining property p(x) of any element x is such that it does not belong to x. Nothing appears unusual about such a property. Many sets have this property. A library [p(x)] is a collection of books. But a book is not a library (x x). Now, suppose this property defines the set R = {x : x x}. It must be possible to determine if RR or RR. However if RR, then the defining properties of R implies that RR, which contradicts the supposition that RR. Similarly, the supposition RR confers on R the right to be an element of R, again leading to a contradiction. The only possible conclusion is that, the property "x x" cannot define a set. This idea is also known as the Axiom of Separation in Zermelo-Frankel set theory, which postulates that; "Objects can only be composed of other objects" or "Objects shall not contain themselves".
In order to avoid this paradox, it has to be ensured that a set is not a member of itself. It is convenient to choose a "largest" set in any given context called the universal set and confine the study to the elements of such universal set only. This set may vary in different contexts, but in a given set up, the universal set should be so specified that no occasion arises ever to digress from it. Otherwise, there is every danger of colliding with paradoxes such as the Russell paradox, which says that "S is the set of all sets which do not have themselves as a member. Is S a member of itself?" Or as it is put in the everyday language: "A man of Serville is shaved by the Barber of Serville if and only if the man does not shave himself?" Such is the problem in Special theory of Relativity.
Thus, "when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch", we must refer to a common reference point for time measurement, which means that we have to apply "clock corrections" to individual clocks with reference to a common clock at the time of measurement which will make the readings of all clocks over the same interval identical. (Einstein has also done it, when he defines synchronization in the para below). This implies that to accurately measure time by some clocks, we must depend upon a preferred clock, whose time has to be fixed with reference to the earlier set of clocks whose time is to be accurately measured. Alternatively, we will land with a set of unrelated events like the cawing of a crow and falling of a ripe date palm simultaneously. A stationery clock and a clock in a moving frame do not experience similar forces acting on them. If the forces acting on them affect the material of the clock, the readings of the clocks cannot be treated as time measurement. Because, in that case, we will land with different time units not related to a repetitive natural event - in other words, they are like individual elements not the members of a set. Hence, the readings cannot be compared to see whether they match or differ. The readings of such clocks can be compared only after applying clock correction to the moving clock. This clock correction has nothing to do with time dilation, but only to the mechanical malfunction of the clock.
There is nothing like empty space. Space, and the universe, is not empty, but full of the Cosmic Background Microwave Radiation from the Big-Bang - as it is generally referred to. In addition to this, space would also seem to be full of a lot of other wavelengths of electromagnetic radiation from low radio frequency to gamma rays. This can be shown by the fact that we are able to observe this radiation across the gaps between galaxies and even across the "voids" that have been identified. Since the universe is regarded as being homogeneous in all directions, it follows that any point in space will have radiation passing through it from every direction, bearing in mind Olber's paradox about infinite quantities etc. The "rips" in space-time that Feynman and others have written about are not currently a scientifically defined phenomenon. They are just a hypothetical concept - something that has not been observed or known to exist. Thus, "light signals, given out by every event to be timed, and reaching him through empty space" would be affected by these radiations and get distorted.
Einstein: If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighborhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an "A time" and a "B time". We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time" tA from A towards B, let it at the "B time" tB be reflected at B in the direction of A, and arrive again at A at the "A time" t'A.
In accordance with definition the two clocks synchronize if: tB - tA = t'A - tB.
Our comments: Light leaving A and reaching B are two different events with some interval. Similarly, Light leaving B and reaching A are two different events. Since the distance between points A and B and the velocity of light is assumed to be constant, then all that the equation tB - tA = t'A - tB means is that the need for "clock correction" between the clocks located at A and B and otherwise synchronized, is zero. It does not define the "A time" t'A or the "B time" t'B or a common "time" for both other than its synchronization with a common reference frame, as has been explained by Einstein below (clock at A with reference to clocks at B and C). The constant speed of light only means that it measures equal distance in equal time. Using this or a fraction of this as the unit, the fixed distance between A and B can be measured by way of length comparison. But this will not be time measurement, as A and B are not time variant events, but time invariant positions.
The definition of simultaneity of Einstein is contradicted by the phenomenon of quantum entanglement. In the universe as we experience it, we can directly affect only objects we can touch either directly or indirectly. If A affects B without being right next to it - then the effect in question must be indirect - the effect in question must be something that gets transmitted by means of a discrete chain of events in which each event brings about the next one directly, in a manner that smoothly spans the distance from A to B. All seeming violations to this intuition - such as flipping a switch that turns on the lights (this happens through wires) or listening to a radio broadcast (radio waves propagate through the air) - are found to be wrong on deeper analysis. This intuition of experiencing through only touch (directly or indirectly) is termed as "locality".
Prior to the advent of quantum mechanics scholars believed that in principle a complete description of the physical world could be had by describing each of the universe's smallest and most elementary physical constituents one by one. The universe could be expressed as the sum of its constituents'. The concept of superposition of states in quantum mechanics postulated that real, measurable, physical features of collections of particles can, in a perfectly concrete way, exceed or elude or have nothing to do with the sum of the features of the individual particles. One can arrange a pair of particles so that they are precisely two feet apart and yet neither particle on its own has a definite position. Furthermore, the Copenhagen interpretation insists that it is not that we do not know the facts about the individual particles' exact locations; it is that there simply aren't any such facts. To ask after the position of a single particle would be as meaningless as, say, asking after the marital status of the number five. The problem is not epistemological (about what we know) but ontological (about what is). Physicists say that particles related in this fashion are quantum mechanically entangled with one another. The entangled property need not be location: Two particles might spin in opposite ways, yet with neither one definitely spinning clockwise. Or exactly one of the particles might be excited, but neither is definitely the excited one. Entanglement may connect particles irrespective of where they are, what they are and what forces they may exert on one another - in principle, they could perfectly well be an electron and a neutron on opposite sides of the galaxy. This phenomenon called non-locality - the possibility of physically affecting something without touching it or touching any series of entities reaching from here to there creates the notion of "action at a distance". This introduces the concept of "absolute simultaneity".
What is uncanny about the way that quantum-mechanical particles can non-locally influence one another is that it does not depend on the particles' spatial arrangements or their intrinsic physical characteristics - as all the relativistic influences do - but only on whether or not the particles in question are quantum mechanically entangled with one another. The kind of non-locality one encounters in quantum mechanics seems to call for an absolute simultaneity, which would pose a very real and ominous threat to special relativity.
Einstein and his colleagues Boris Podolsky and Nathan Rosen took it for granted that the apparent non-locality of quantum mechanics must be apparent only. They assumed that it must be some kind of mathematical anomaly or notational infelicity or that it must be a disposable artifact of the algorithm. Surely one could cook up quantum mechanics' predictions for experiments without needing any non-local steps. And in their paper they presented an argument to the effect that if (as everybody supposed) no genuine physical non-locality exists in the world and if the experimental predictions of quantum mechanics are correct, then quantum mechanics must leave aspects of the world out of its account. There must be parts of the world's story that it fails to mention.
However, the compatibility of non-locality and special relativity was a much more subtle question than the traditional platitudes based on instantaneous messages would have us believe. Contrary to popular belief, Special relativity is perfectly compatible with an enormous variety of hypothetical mechanisms for faster-than-light transmission of mass and energy and information and causal influence. The theory of a hypothetical species of particle - tachyons - for which it is physically impossible ever to travel slower than light - is an internally consistent and fully relativistic theory as can be easily explained.
Thus, the mere existence of a non-locality in quantum mechanics does not mean that quantum mechanics and special relativity are not incompatible. However, the particular variety of action at a distance that we encounter in quantum mechanics is an entirely different animal from the kind exemplified by Feinberg's tachyons or Maudlin's other examples.
We accept entanglement as a fact and have discussed its different aspects in detail in later pages. For the present it would suffice to point out that entanglement results from two particles that have resulted from the decay of a single particle. The original particle was required to satisfy various conservation laws and the daughter particles must also satisfy the same laws. When a property of a particle like spin is measured, quantum mechanics tells us that the measurement process selected one of a number of possible states the particle occupies. However, all those states are connected to the states of the other particle by the conservation laws. Hence, when the measurement process has picked one of the states occupied by one of the particles, the state of the other particle is automatically established by the conservation law operating when the two particles were generated. While we do not contribute to the concept of "absolute simultaneity", the fact that entanglement can produce action at a distance violating the restriction of limiting velocity of light proves that the views of Einstein may not hold fully.
In fact, in later years, Einstein changed his views on the constancy of the velocity of light. In fact he declared that: "In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuum, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position". If the velocity of light is not constant, then it cannot be used as a measuring unit. For how do we define c? It is the velocity of light in vacuum? How do we measure it? It is well known that the velocity of light changes depending upon the density of the medium. It is also known that there is no true vacuum. Empty space is really not empty. Since it is accepted that the mass and energy are convertible, one cannot deny the density of the space. Then c is reduced to the velocity of light in a medium of a particular density. The question then rises is how can we say that c is a constant in a medium of a particular density and changes in other dense mediums? If it changes in mediums of different density, it is obvious that it should slow down near a massive star, as there is no isolated object in the universe and the environment of the massive star is affected by its density. Thus, the entire issue boils down to mass-energy interaction.
Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:
1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.
Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of "simultaneous", or "synchronous", and of "time". The "time" of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.
Our comments: Einstein sets out in the introductory part of his paper: "...the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate...". The "Principle of Relativity" is restricted to comparison of the motion of one frame of reference relative to another. Introduction of a third frame of reference collapses the equations as it no longer remains relativistic. The clock at B has been taken as a privileged frame of reference for comparison of other frames of reference. If privileged frames of reference are acceptable for time measurement, then the same should be applicable for space measurement also, which invalidates the rest of the paper.
Simultaneity refers to occurrence of more than one action sequences, e.g.; events, which measure equal units in two similar action sequence measuring devices, e.g.; clocks, starting from a common reference point, e.g.; an epoch. It is the opposite of successive events. Synchronisation refers to the readings of more than one clock (or interval between event from an epoch), which do not require "clock correction", i.e.; when such readings are compared with a common or identical repetitive action sequence or action sequence measuring devices, their readings match. It is not the opposite of successive events, but can also be simultaneous - for example, two clocks synchronised with each other will give similar readings simultaneously. If one of the clocks give 24 hour reading while the other gives 12 hour reading, then half of the time they will give readings that are synchronized and simultaneous, while half of the time they will not be so. Yet, the results can be made to synchronize by deducting 12 hours from any reading beyond it in the clock giving 24 hours reading. Here the clocks will be synchronized through out, but give simultaneous readings alternatively in succession or otherwise.
In the definition of simultaneity given by Einstein, the two clocks situated at two distant points in the same frame of reference (whether the frame of reference is inertial or not is not relevant as both the clocks and points P and P' are fixed in the frame) are said to be synchronous, if their readings of the identical events in both clocks match. This only refers to the accuracy of mechanical functioning of the clocks and uniformity of the time unit used in both the clocks. This definition is nothing but telling the obvious in a complicated and confusing manner. Since the two clocks are synchronised, they should record equal time in both the frames of reference over equal interval.
Einstein: In agreement with experience we further assume the quantity
2AB / (t'A - tA) = c.
to be a universal constant - the velocity of light in empty space.
It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it "the time of the stationary system".
Our comments: The conclusion arrived out of the above description is highly misleading. Any object moving with repetitively uniform speed over a fixed distance and bouncing back (such as a pendulum or echo) satisfies the above condition. This does not make the velocity of such an object any thing special or a "universal constant". Though Einstein was referring to light only and no other motion has the same velocity, it does not invalidate the above principle. It may be noted that he is referring to "In agreement with experience" and experience also tells that a pendulum or an echo also behave like-wise. Though the pendulum does not move with uniform speed, the time taken in swinging from one end to the other and back remains constant satisfying the condition: 2AB / (t'A - tA) = c. The same is true for echo also. In the example given by Einstein, the light pulse does the same: move from A to B and back to A at a fixed time. Einstein has also used the light pulse to travel like the pendulum or an echo. Further, there is nothing like "empty space". The velocity of light varies in different media with different density. There is no justification for choosing the velocity of light only in empty space. In fact it goes against the principles of general relativity. If gravity determines the curvature of space (?), the density of different regions of space is affected by gravity. This will change the velocity of light in different regions of space. Hence, according to this view, the velocity of light cannot be a universal constant. In fact, as has been shown earlier, Einstein himself has changed his view later.
Einstein: §2. On the Relativity of Lengths and Times
The following reflexions are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows:--
1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
2. Any ray of light moves in the "stationary" system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body. Hence:
Velocity = light path / time travel,
where time interval is to be taken in the sense of the definition in §1.
Our comments: The first of the postulates is highly confusing. Changes of states of physical systems are governed by the internal and external energy content of the system and other particles or fields interacting with it. It has no relation with the one or the other of two systems of co-ordinates in uniform translatory motion. Possibly he was referring to the changes in one frame as observed from the other frame - like planetary motion in the helio-centric system and the geo-centric system, which, when calculated properly, match with each other. If that is the correct interpretation of his first postulate, then, this is true only in a system, where the bodies are in uniform translatory motion with reference to each other. (The planets go round the Sun in circular orbits, but due to the movement of the Sun, their orbits appear elliptical). In a non-uniformly moving system, the distance to be traveled will depend on the direction of the light pulse and the system. Depending upon whether the light pulse and the system are moving in the same or the opposite or any other direction, the distance between them will vary. Since light travels at a fixed speed in any medium and its velocity differ in different media, the readings will also vary accordingly. For the same reason, the deduction in his second postulate: Velocity = light path / time travel; is not correct. In fact it proves the time dilation described by us earlier. For example, the equation can be written as:
time travel = light path / Velocity.
Since velocity of light in different medium varies, the time travel for the same light path will be different in different media. It is accepted that the light slows down in the vicinity of a massive star. Thus, there will be time dilation for the same light path in different media or different regions of space as compared to the time travel in the so-called empty space.
Einstein: Let there be given a stationary rigid rod; and let its length be l as measured by a measuring-rod which is also stationary. We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod. We now inquire as to the length of the moving rod, and imagine its length to be ascertained by the following two operations:-
(a) The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest.
(b) By means of stationary clocks set up in the stationary system and synchronizing in accordance with §1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated "the length of the rod".
In accordance with the principle of relativity the length to be discovered by the operation (a) - we will call it the length of the rod in the moving system - must be equal to the length l of the stationary rod.
The length to be discovered by the operation (b) we will call "the length of the (moving) rod in the stationary system". This we shall determine on the basis of our two principles, and we shall find that it differs from l.
Our comments: The method described at (b) is impossible to measure by the principles described by Einstein himself. Elsewhere he has described two frames: one fixed and one moving along it. First the length of the moving rod is measured in the stationary system against the backdrop of the fixed frame and then the length is measured at a different epoch in a similar way in units of velocity of light. We can do this only in two ways, out of which one is the same as (a). Alternatively, we take a photograph of the rod against the backdrop of the fixed frame and then measure its length in units of velocity of light or any other unit. But the picture will not give a correct reading due to two reasons:
• If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.
• If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the camera and the picture we get will be distorted due to the Doppler shift of different points of the rod. Thus, there is only one way of measuring the length of the rod as in (a).
Here we are reminded of an anecdote related to Sir Arthur Eddington. Once he directed two of his students to measure the wave-length of light precisely. Both students returned with different results - one resembling the accepted value and the other different. Upon enquiry, the student replied that he had also come up with the same result as the other, but since everything including the Earth and the scale on it is moving, he applied length contraction to the scale treating Betelgeuse as a reference point. This changed the result. Eddington told him to follow the operation as at (a) above and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of light is infinite. To a surprised Eddington they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of light.
Some scientists try to overcome this difficulty by pointing out that length contraction occurs only in the direction of travel. If we hold the rod in a transverse direction to the direction of travel, then there will be no length contraction for the rod. But we fail to understand how the length can be measured by holding it in a transverse direction to the direction of travel. If the light path is also transverse to the direction of motion, then the terms c+v and c-v vanish from the equation making the entire theory redundant. If the observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod while moving with it, he will not find any difference what-so-ever. Thus, the views of Einstein are contrary to observation.
Einstein: Current kinematics tacitly assumes that the lengths determined by these two operations are precisely equal, or in other words, that a moving rigid body at the epoch t may in geometrical respects be perfectly represented by the same body at rest in a definite position.
We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the "time of the stationary system" at the places where they happen to be. These clocks are therefore "synchronous in the stationary system".
We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in §1 for the synchronization of two clocks. Let a ray of light depart from A at the time tA, let it be reflected at B at the time tB, and reach A again at the time t'A. Taking into consideration the principle of the constancy of the velocity of light we find that:
tB - tA = γAB / (c - v) and t'A - tB = γAB / (c + v)
where γAB denotes the length of the moving rod - measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.
So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.
Our comment: We have already shown that this conclusion is not correct. Since one frame is moving in the same direction as that of the light pulse, the distance covered by light to reach the other end of the rod AB will be increased by an amount proportionate to v. In the return trip, light has to cover less distance due to the same reason, as the distance traveled by light BA has been decreased by an equal amount. Applying the formula:
time travel = light path / Velocity
we find that the distance traveled by light in the onward journey AB is more than that in the return journey. Thus, in view of the fact that velocity of light is constant in a medium, it is no wonder that the time taken in both journeys do not match. This will happen to all clocks synchronized with each other irrespective of whether it is placed in the rest frame or the moving frame. However, since the rod is moving away from A, the clock at A can measure the time only when light reaches it covering a further distance. Hence, he will measure a longer time, as he is measuring light path over a long distance. This does not affect the concept of simultaneity in any way.
Einstein: § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former.
Einstein: Let us in "stationary" space take two systems of co-ordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and issuing from a point. Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel. Let each system be provided with a rigid measuring-rod and a number of clocks, and let the two measuring-rods, and likewise all the clocks of the two systems, be in all respects alike.
Now to the origin of one of the two systems (k) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks. To any time of the stationary system K there then will correspond a definite position of the axes of the moving system, and from reasons of symmetry we are entitled to assume that the motion of k may be such that the axes of the moving system are at the time t (this "t" always denotes a time of the stationary system) parallel to the axes of the stationary system.
We now imagine space to be measured from the stationary system K by means of the stationary measuring-rod, and also from the moving system k by means of the measuring-rod moving with it; and that we thus obtain the co-ordinates x, y, z, and ξ, η, ζ. respectively. Further, let the time t of the stationary system be determined for all points thereof at which there are clocks by means of light signals in the manner indicated in §1; similarly let the time τ of the moving system be determined for all points of the moving system at which there are clocks at rest relatively to that system by applying the method, given in §1, of light signals between the points at which the latter clocks are located.
To any system of values x, y, z, t, which completely defines the place and time of an event in the stationary system, there belongs a system of values ξ, η, ζ. τ, determining that event relatively to the system k, and our task is now to find the system of equations connecting these quantities.
In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.
If we place x'=x-vt, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time. We first define τ as a function of x', y, z, and t. To do this we have to express in equations that τ is nothing else than the summary of the data of clocks at rest in system k, which have been synchronized according to the rule given in §1.
From the origin of system k let a ray be emitted at the time τ0 along the X-axis to x', and at the time τ1 be reflected thence to the origin of the co-ordinates, arriving there at the time τ2; we then must have ½ (τ0+ τ2) = τ1, or, by inserting the arguments of the function τ and applying the principle of the constancy of the velocity of light in the stationary system:
Hence, if x' be chosen infinitesimally small,
It is to be noted that instead of the origin of the co-ordinates we might have chosen any other point for the point of origin of the ray, and the equation just obtained is therefore valid for all values of x', y, z.
An analogous consideration - applied to the axes of Y and Z - it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √(c2 - v2) gives us:
∂ τ / ∂ y = 0, and ∂ τ / ∂ z = 0,
Since τ is a linear function, it follows from these equations that
τ = α [{t - v / (c2 - v2) } x']
where α is a function φ(v) at present unknown, and where for brevity it is assumed that at the origin of k, τ = 0, when t=0.
Our comment: Although Einstein creates a time function (or "funktion" as he calls it) as noted in his original manuscript, he incorrectly treats it as an equation in the remainder of his derivation as follows. According to his original manuscript (Einstein has used V for velocity of light):
" Aus diesen Gleichungen folgt, da τ eine lineare Funktion ist:
wobei α eine vorlaufig unbekannte Funktion g (υ) ist und der
Kürze halber angenommen ist, dαβ im Anfangspunkte von k
für τ = 0 t = 0 sei."
The problem occurs because Einstein wrote the function as well as the equation informally. The differences between the formal and informal equation can be exemplified as follows: While the informal equation is
,
The formal equation would be
Functions must be invoked before they are used. They can be explicitly or implicitly invoked. In computer science, functions are typically explicitly invoked due to the specific way in which instructions are communicated to the computer. This is a fundamental difference between the human brain and the computer and the reason why computers can never become "alive". In other disciplines, which are basically functions of the brain, the functions are more often implicitly invoked and treated as equations. Generally, this does not result in a problem unless the arguments invoked have complex numbers. In order to illustrate the problem, the function must be explicitly invoked. By presenting the derivation in this manner, it will be easy to show that Einstein actually uses two time equations; one as the stand alone equation and the other that is used to produce the x-axis transformation equation. The time function:
By invoking the function explicitly, Steven Bryant has shown that Einstein implicitly invoked the function twice, once to produce the stand-alone time equation and once as used to create the X-axis transformation equation. Einstein implicitly performed the function invocation by replacing t with x'/(V-v) in creating the X-axis transformation. However, he does not use the same complex argument when producing the stand-alone time equation. The result is an invalid system of equations that is discovered and validated using the "if a=bc then b=a/c" math rule. For details, please refer to the website www.relativitychallenge.com. Earlier, we had shown that replacing t with x'/(c-v) or x'/(c+v) is erroneous.
Further, Einstein says that, "instead of the origin of the co-ordinates we might have chosen any other point for the point of origin of the ray, and the equation just obtained is therefore valid for all values of x', y, z." This statement is not correct, as the equation for a circle with its center at the origin is different from that of another, whose center is not at the origin. The same applies to a sphere.
Einstein: With the help of this result we easily determine the quantities ξ, η, ζ. by expressing in equations that light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system. For a ray of light emitted at the time τ = 0 in the direction of the increasing ξ,
ξ = c τ or ξ = α c [t - {v /(c2 - v2)} x']
But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v, so that: x'/(c-v) = t.
If we insert this value of t in the equation for ξ, we obtain:
ξ = α {c2 / (c2 - v2)}x'.
In an analogous manner we find, by considering rays moving along the two other axes, that:
η = c τ = αc [t - { v / (c2 - v2)}x']. When: y / √(c2 - v2) = t, x' = 0.
Thus: η = α {c / √ (c2 - v2)}y and ζ = α {c / √ (c2 - v2)}z.
Substituting for x' its value, we obtain:
where,
and φ is an as yet unknown function of v. If no assumption whatever be made as to the initial position of the moving system and as to the zero point of τ, an additive constant is to be placed on the right side of each of these equations.
Our comments: As per the mathematical rule: "if a = bc, then b = a/c". However, the above formulation of Einstein fails the test of this rule. By following Einstein's computation, we find that:
Now, we find further that generally: ξ / c ≠ τ,
This represents a mathematical error that must be corrected. This mistake invalidates the remainder of Einstein's derivations of Special Theory of Relativity.
Einstein: We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity.
At the time t = τ = 0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted there from, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then
x2+y2+z2=c2t2.
Transforming this equation with the aid of our equations of transformation we obtain after a simple calculation: ξ2 + η2 + ζ2 = c2 τ2
The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible.
Our comments: Einstein has allowed the time variable "t" to behave as an independent variable in the final equations. In each derivation, the time variable "t" begins (in some manner) as a dependent variable. For example, he has used equations x2+y2+z2-c2t2 = 0 and ξ2 + η2 + ζ2 - c2 τ2 = 0 to describe two spheres that the observers see of the evolution of the same light pulse. Apart from the fact that the above equation of the sphere is mathematically wrong (it describes a sphere with the center at origin, whose z-axis is zero, i.e., not a sphere, but a circle), it also shows how the same treats time differently. Since general equation of sphere is supposed to be x2+y2+z2+Dx+Ey+Fz+G = 0, both the equations can at best describe two spheres with origin at (0,0,0) and the points (x,y,z) and (ξ, η, ζ ) on the circumference of the respective spheres. Since the second person is moving away from the origin, the second equation is not applicable in his case. Assuming he sees the same sphere, he should know its origin (because he has already seen it, otherwise he will not know that it is the same light pulse. In the later case there is no way to correlate both pulses) and its present location. In other words, he will measure the same radius as the other person, implying: c2t2 = c2 τ2 or t = τ.
Again, if x2+y2+z2-c2t2 = x'2+y'2+z'2-c2 τ 2, t ≠ τ.
This creates a contradiction, which invalidates his mathematics.
Einstein: In the equations of transformation which have been developed there enters an unknown function φ of v, which we will now determine.
For this purpose we introduce a third system of co-ordinates K', which relatively to the system k is in a state of parallel translatory motion parallel to the axis of Ξ, such that the origin of co-ordinates of system K', moves with velocity -v on the axis of Ξ. At the time t=0 let all three origins coincide, and when t = x = y = z = 0 let the time t' of the system K' be zero. We call the co-ordinates, measured in the system K', x', y', z', and by a twofold application of our equations of transformation we obtain:
Since the relations between x', y', z' and x, y, z do not contain the time t, the systems K and K'are at rest with respect to one another, and it is clear that the transformation from K to K'must be the identical transformation. Thus: φ(v) φ(- v) = 1.
We now inquire into the signification of φ(v). We give our attention to that part of the axis of Y of system k which lies between ξ = 0, η = 0, ζ = 0 and ξ = 0, η = l, ζ = 0 . This part of the axis of Y is a rod moving perpendicularly to its axis with velocity v relatively to system K. Its ends possess in K the co-ordinates:
The length of the rod measured in K is therefore l / φ(v); and this gives us the meaning of the function φ(v). From reasons of symmetry it is now evident that the length of a given rod moving perpendicularly to its axis, measured in the stationary system, must depend only on the velocity and not on the direction and the sense of the motion. The length of the moving rod measured in the stationary system does not change, therefore, if v and -v are interchanged. Hence follows that l / φ(v) = l / φ( - v), or φ(v) = φ( - v).
It follows from this relation and the one previously found that φ(v) = 1, so that the transformation equations which have been found become:
where,
Our comments: The above derivation is erroneous and invalid due to the reasons already discussed. There is no signification of φ(v), as it has been derived erroneously. However, as we have explained elsewhere, the perceived length contraction is apparent induced by the Doppler effect, and not real. By way of an example, we quote here from a report by Kaća Bradonjić, a physicist at Boston University in the US, whose job is to carry out research on general relativity. She has used the Doppler effect (the change in the pitch of a sound that occurs when its source and the listener are moving relative to each other) to show how the perceived emotional character of a chord changes as the listener moves. She has calculated exactly what velocities a listener would need to travel at to create specific variations of mood, in order that they can tailor their "listening experience" (arXiv:0807.2493). The perceived mood of a chord can be relative to a listener's frame of reference, even though the character of a chord does not change. In her paper, she considers the conventional Western "chromatic" musical scale, in which the frequencies of neighboring notes differ by a factor of 21/12 (an interval known as a semitone). Using the Doppler transformation for a stationary emitter and moving observer she shows that a listener must travel (1-2-1/12) times the speed of sound away from the source of a note in order to reduce the perceived pitch of that note by a semitone. Bradonjić then considered the velocities that a listener must travel at to transform specific three-note chords when the notes are emitted by three separate sources positioned away from the listener along orthogonal axes.
We can go on and on. But we rest here with the following words. Einstein, who borrowed the term "space-time" from his teacher Minkowski and Palagyi, has used different methods at different times to arrive at the same answer. This has been possible because he has not precisely and scientifically defined time (time is what we measure by a clock) and space (space is what we measure by a measuring rod). Gravity has infinite range and its strength follows the inverse square law. Thus, it affects all bodies, which varies according their masses and distance. The Special Theory of Relativity ignores this. He had to invent General theory of Relativity to cover up this mistake. Here also it was a work of plagiarism. The complete field equations of the general theory of relativity were first deducted by David Hilbert, which Einstein had to admit in 1916. Paul Gerber solved the problem of the perihelion of Mercury in 1898, though Einstein took credit for it. On 24-08-1920, Ernst Gehrcke gave a lecture on relativity in Berlin Philharmonic, where he told the public in front of Einstein that he had plagiarized the Lorentz's mathematical formalism of the Special Theory of Relativity, Palagyi's space-time concepts, Varicak's non-Euclidean geometry and the mathematical solution of the problem of the perihelion of Mercury arrived at by Gerber. Three days after on 27-08-1920, Einstein responded weakly in Berliner Tageblatt und Handels-Zeitung that Gerber's derivations were wrong. However, he was silent about the rest. For more details please visit the web site "Albert Einstein: The Incorrigible Plagiarist (ISBN 0971962987) at www.amazon.com. He deduced the same equations in different methods at different times as he was forced to change his views frequently due to its inconsistency or the charge of plagiarism. He proposed the Cosmological constant and then said it's the greatest blunder. The postulates and deductions of Einstein are mathematically incorrect. Yet, thanks to the cult of incomprehensibility and superstition, he is still described as the greatest scientist ever!
Regards,
Basudeba
