PRASHASTAPAADA OF ANCIENT INDIA REFUTED RELATIVITY. IT IS NOT A CUT & PASTE JOB.
By Basudeba Mishra
Sometime ego, I had posted a paper on the above subject and a friend shared it for wider evaluation. Some of the respondents have further asked some scientists to comment on it. He commented: First of all Relativity involved what Ken Hughes correctly points out – the issue of time and the finiteness of the speed of light. So that is where the above “philosophical” analysis collapses. The author ASSUMES that all measurements are done in one all-encompassing temporal frame. But we know today that is NOT the case. An equivalence relation on Minkowski spacetime can be defined for events and Set Theory as we know it – applies without contradiction only on Minkowskian Spacetime. The analysis above is very typical of pre Relativity ideas of one single cosmic time. But in Relativity where there is RELATIVE MOTION between the 2 frames, then their temporal coordinates are related by a Lorentz transformation. If there is NO relative motion then they are in the SAME frame of reference. Differs only by a translation. So the best way to deal with sets of events – is to define the set on Minkowskian spacetime and NOT Galilean spacetime. I responded as follows:
“Relativity involved the issue of time and the finiteness of the speed of light” – this is Special Relativity and not General Relativity. Darshana in India is used synonymously with Science. For example, Nyaya Darshana is our research methodology. Vaisheshika deals with particle physics. Ignorance of these aspects does not change their content. Thus, it does not collapse “the above ‘philosophical’ analysis”, as it is different from the Western philosophical approach.
Einstein did not define what time is except that it is the same as the tick of the clock. Then he tries to mislead as follows: 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.
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:
- If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
- 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.
The concept of relativity is valid only between two objects. Introduction of a third object brings in the concept of privileged frame of reference and all equations of relativity fall. In the above description, the clock at A is treated as a privileged frame of reference for proving synchronization of the clocks at B and C. Yet, he claims it is relative!
“But in Relativity where there is RELATIVE MOTION between the 2 frames, then their temporal coordinates are related by a Lorentz transformation”. Lorentz transformation are coordinate transformations between two coordinate frames that move at constant velocity relative to each other. The experimental basis of the Lorentz transform is the Michelson-Morley experiment. Michelson-Morley used light rays in their famous experiment. Light is a transverse wave and by definition, all transverse waves are background invariant. Hence, the null result of M&M experiment does not prove anything. The Lorentz transformation is based on this null foundation. Thus, it is only apparent and not real. A man standing on the platform sees the train along with the passengers contracting in length as they also see the man on the platform contracting in length. But really there is no such contraction. It is as apparent as the water in the mirage. What the observer observes is only apparent – there is no physical contraction. Yet, it has been treated here as if it is real! And instead of applying your mind independently, you are calling it real!
In fact, Einstein starts with misleading notions: Two possibilities of measurement of a moving rod suggested by Einstein in his 1905 paper on Special Theory of Relativity were:
(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, or
(b) By means of stationary clocks set up in the stationary system and synchronizing with a clock in the moving frame, 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 the length of the rod.
The method described at (b) is misleading. We can do this only by setting up a measuring device to record the emissions from both ends of the rod at the designated time, (which is the same as taking a photograph of the moving rod) and then measure the distance between the two points on the recording device in any unit. But the picture will not give a correct reading because:
• 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 recording device and the picture we get will be distorted due to different Doppler shift. Thus, there is only one way of measuring the length of the rod as in (a).
The fallacy in the above description is that if one treats as if all three were at rest, one cannot measure velocity or momentum, as the object will have zero relative velocity. Einstein missed this point when in the same paper, he said: 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. But is this the velocity of k as measured from k, or is it the velocity as measured from K? K and k each have their own clocks and measuring rods, which are not treated as equivalent by Einstein. Therefore, according to his theory, they will measure the velocity of k differently. Einstein does not assign the velocity specifically to either system. Everyone missed it and got misled. His spinning disk example in GR also falls for the same reason.
All objects fall in similar ways under the influence of gravity. Hence locally, it is said, the difference between an accelerated frame and an un-accelerated frame cannot be known. But these must be related to be compared as equivalent or not? In the example of a person in an elevator falling down a shaft, it is assumed that during any sufficiently small amount of time or over a sufficiently small space, the person can make no distinction between being in the falling elevator and being stationary in completely empty space, where there is no gravity. This is a wrong description – distinction of what? Unless we relate the elevator to the outside space, we cannot relate motion of the elevator to it. The moment we relate to the structures beyond the elevator, we can know the relative motion of the elevator. Inside a spaceship in deep space, objects behave like Brownian motion (unaccelerated) or like the asteroids in the asteroid belt (accelerated). Usually, they are relatively stationary within the medium unless some other force acts upon them. If the person can see the outside objects, then he can know the relative motions by comparing objects at different distances. If he cannot see the outside objects, then he will consider only his position with reference to the spaceship – stationary or floating within a frame. There is no equivalence because there is no other frame for comparison. Relativity theory needs revision.
A same logic applies to the ray of light that appears curved to the occupants of the spaceship. The light can be related to the spaceship only if we consider the bigger frame of reference containing the source of light and the spaceship. If we consider outside space as a separate frame of reference unrelated to the spaceship, the ray emitted by it cannot be considered inside it. If the passenger could observe the scene outside, he will notice this difference and know that the spaceship is moving. Otherwise, the consideration will be restricted to the rays emanating from within, which will move straight. In either case, the description is faulty. Thus, the foundation of GR – the EP – is wrong description of reality. Hence all mathematical derivatives built upon such wrong description are wrong. There is no inertial mass increase.
Einstein has used equations x2+y2+z2- (ct)2 = 0 and ξ2 + η2 + ζ2 – (cτ)2 = 0 to describe the evolution of the same light pulse that the observers see. But x2+y2- (ct)2 = 0 describes a circle with ct as the radius! Hence z and ζ have to be zero. It can’t be a sphere! Since (x. y. z) is a point on the circumference, moving in z direction will be tangential. It describes a cylinder and not a sphere! The geometer’s descriptions of π-sphere and the topologist’s descriptions of n-dimensional sphere are mathematically and physically void.
Einstein can describe two concentric spheres with the points (x,y,z) and (ξ, η, ζ ) on their respective circumferences. Since the second person is moving away from the origin, the second equation relates to sighting from his here-now (new origin). 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 case he takes a new measurement from his origin, according to Einstein, the reading from two frames will be different. In other words, he will either measure it independently as different or measure the same radius as the other, implying: either:
x2+y2+z2- c2t2 ≠ x’2+y’2+z’2-c2 τ 2, t ≠ τ.
Or c2t2 = c2 τ2 or t = τ.
This creates contradictions, which invalidates his mathematics.
Minkowski spacetime is just a name with manipulated “mathematics”. He was trying to solve a practical problem – how to treat the curvature of hot metal plates – when he coined these words. When heated, a metal plate curves. But everything does not curve when heated. Some get burnt also. And the universe is not a hot metal sheet. There only one analog space and one analog time. We use digitized segments of these two analog entities that coexist. If you do not agree, please precisely and scientifically define what space is, what is time, what is spacetime, and how is Minkowski spacetime different from the common spacetime? How can there be so many space-times? Are you suggesting we should not believe our experience, but think that we are living in a filmy matrix? Also if you disagree with their mathematics, please define what mathematics is. I had posted a paper challenging the foundations of tensors. While most of those who responded appreciated it, no one challenged it. You are welcome for a debate on the validity of tensors.