MISSING THE WOODS FOR THE TREES
Does the structure and availability of existing mathematics shape the formulation of physical theories? Yes! Examples:
Dimension is the perception of differentiation between internal structural space and external relational space of an object. Since we observe through electromagnetic radiation, where the electric field and the magnetic field move perpendicular to each other and both move perpendicular to the direction of motion, we have three mutually perpendicular dimensions representing length, breadth, height that are invariant under mutual transformation. There are no extra large or compact or n’th dimension. The surface of a cube is not 2D, as it has no independent existence. There is no independent straight line in 1D. It is a mark on a three dimensional paper or space. The surface of a sphere is not 1D, but 3D.
Directions (axes) and sequential arrangement (coordinates) of an object are used with reference to an origin in relation to other objects. With only one object, direction is meaningless. Direction is used to:
- Measure distance between two objects from origin by assigning + or – signs from origin along various axes.
- Indicate shortest distance between two objects on a curved surface like a geodesic.
- Reflect the behavior of fundamental forces of Nature; i.e., strong interactions move towards center, part of weak interactions limits movement away from center, e.m. interaction move out from center to lower concentration, beta-decay separates a part from the center, gravitational interaction relates interaction between bodies. But often, dimension is exchanged for direction in phase space portrait and its quantum Avatar, Hilbert space. This leads to the undecidable propositions.
If we divide 20 by 5, then we take out bunches of 5 from the lot of 20. When the lot becomes empty or the remainder is zero or below 5 (divisor) so that it cannot be considered a bunch and taken away further, the number of bunches of 5 are counted. That gives the result of division as 4. In case of division by zero, we are supposed to take out bunches of zero, which is impossible as it is not at here-now of the operator. At no stage the lot becomes zero or less than zero. Thus, the operation is not complete and result of division cannot be known, just like while dividing 20 by 5, we cannot start counting the result after taking away two bunches. Conclusion: division by zero is mathematically void; hence it leaves the number unchanged. Since zero does not exist at here-now, it does not affect addition or subtraction. During multiplication by zero, one non-linear component of the quantity is extended to zero, i.e., moves away from here-now to a superposition of states. Thus, the result becomes zero for the total component, as we cannot have a Schrödinger’s undead cat in real life. In division by zero, the non-existent part is sought to be reduced from the quantity (which is an operation akin to collapse reversal in quantum mechanics), leaving the quantity unchanged. Division by zero leaves the number unchanged.
Two possibilities of measurement of a moving rod suggested by Einstein in his 1905 paper4 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 paper4, 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.
On the definition of synchronization Einstein says: 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!
Russell’s paradox raises an interesting question: If S is the set of all sets which do not have themselves as a member, is S a member of itself? The general principle is that: there cannot be a set without individual elements. Collection of different objects unrelated to each other would be individual members as it does not satisfy the condition of a set. Thus a collection of objects is either a set with its elements, or individual objects that are not the elements of a set.
Example: p(x): x Ï x, is the defining property p(x) of any element x such that it does not belong to x. Many sets have this property. A library p(x) is a collection of books. But a book is not a library x Ï x. Suppose this property defines the set R ={x : x Ï x}. It must be possible to determine if RÎR or RÏR. However if RÎR; then the defining properties of R implies RÏR, which contradicts the supposition that: RÎR. Similarly, the supposition RÏR 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 Ï x cannot define a set. 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’s paradox. In the case of EP, we do blunder!
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.
LOOKING AHEAD
Recent discovery of galactic blue-shift (Lowell Observatory Bulletin No. 58 Vol. II No. 8) and arXiv: 1402.6319 v1 [astro-ph.GA], galactic merger (Astronomy Newsletter – 18th July, 2014) and the absence of red-shift in galactic or lesser scales should prove dark energy a myth. Energy is perceived through its interactions. If it is not interacting, it cannot be energy. Fluids are also smooth and persistent. Interpretation of M & M experiment is faulty, as light is a transverse wave, which is background invariant. Like the solar system, the universe is spinning around a galactic center. Dark energy is the universal background structure.
Abundance of ‘Hot Jupiters’ among alien planets and protons in cosmic rays shows macro-micro relation. Separately we have shown that the internal structures of Jupiter and proton are similar.
Bare mass or bare charge is fiction. The equation e = mc2 is mathematically invalid as LHS is time invariant and RHS time variant (per second). It should be written as (m) e → (mc)2 which balances it to show the rate at which energy acts on mass. Energy cannot be confined in packets, but only by mass. Confined mass-energy is fermion (hence half integer spin) and unconfined mass-energy is boson (zero spin). Fluid (intermediate) behavior is integer spin.
Result of Time dilation experiment with atomic clocks was faked. This can be verified from the original data kept at US Naval Archives. The delayed signal of GPS is due to refraction when the signal re-enters the denser atmosphere of Earth. Time dilation is relative time evolution of elements in entropy, where thermodynamic process sustains life and total disorder is annihilation of form.
There is a need to ponder over these issues, introspect and rewrite physics.
REFERENCES
1. Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in Communications in Pure and Applied Mathematics, vol. 13, No. I2. Abh. Math. Sem., Univ. Hamburg, 157 (1922), or Gesammelte Werke (Berlin: Springer, 1935), p. 188.3. “Is Reality Digital or Analogue” published by the FQXi Community on Dec. 29, 2010,4. “On the Electrodynamics of Moving Bodies” by Einstein.