ENTANGLEMENT IN THE VEDAS (संयोगः) – 2
– Basudeba Mishra
Some scientists have drawn attention towards Bell’s inequalities to counter EPR’s postulation of the hidden variables. Bell showed that if two observers randomly and independently choose between measuring one or another property of their particles, like position or velocity, the average results cannot be explained in any theory where both position and velocity were pre-existing local properties. This raises the question: what is so special about “measurement”?
Also there are some confusing but related issues. Wigner devised a thought experiment, in which his friend measures some quantum properties – say position – in a tightly sealed laboratory by using polarized photons. For the observer from outside, the friend becomes entangled with the particle and is infected with the uncertainty like the Schrödinger’s famous cat. Since it is absurd, he believed that, on observation by an intelligent observer, the “superposition” has “collapsed”. This conclusion was based on the role of one of two paths each photon may take in the setup, depending on the “polarization” of the photon. The “path” “measures” the polarization. (Wigner wrote “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. My paper on “REASONABLE EFFECTIVENESS OF MATHEMATICS” can be seen at http://fqxi.org/community/forum/topic/2325).
Others built upon it with two hypothetical scientists Alice and Bob with their friends Charlie and Debbie, measuring a pair of entangled particles in two laboratories. Yet others like de Broglie-Bohm postulated “action at a distance” – actions can have instantaneous effects elsewhere in the universe – which conflicts with relativity. Some postulated “backwards causality” or “super-determinism”. I will not discuss these fantasies for the reason given below. Those interested may read it from texts or the internet.
We may send a light pulse to some body, but after interacting with the body, the SAME light pulse will NOT come back to us. Part or whole of it may be absorbed by the body or deflected by other effects. Information is the result of measurement of the “received impulse” (emitted by a body) and not the “initial impulse” bounced from a body. What we measure through observation is the emission by the body received by us and not the state of the body that emits it (अनवर्णे इमे भूमी – Taittiriyaranyakam – Prathama Prashna). Thus, the speed of light is not relevant here. At one moment we can look at a distant star and the next moment another in the opposite direction thousands of light years away. We can know their position instantaneously. They are not entangled (इयं चाऽसौ च रोदसी – ibid). The same principle applies to polarized photons also. No information is transferred between polarized photons. There is no proof. As already explained, superposition is only our inability to know the present state accurately.
Often it is said that Schrödinger also came across the uncertainty principle from his wave mechanics. He represented the momentum p by a differential operator – iħ d/dx, which does not commute with the position operator x. Schrödinger based his proposition on the wave-function ψ, which gives the probability |ψ|^2 of finding a particle at a particular point. Since the position of the electron cannot be determined with certainty (which is true), the probability refers to the location within an interval of space of length δx (which is misleading). This implies that only those values of ψ have to be chosen which become non-zero within the range of δx and cancel each other out to become zero outside it. These are done through Fourier analysis. Thus, the narrower the space δx is, the more stringent is the cancel requirements outside it. As a consequence, a greater number of different waves will have to be added together to achieve this. In other words, the width of the band of wavelengths thus required will be inversely proportional to δx.
It is known from de Brogli’s formulation relating to matter waves that the wavelength and the momentum of the particle are related by the equation: p = h/λ. Thus, a broader band of wavelength means a wider range of momentum values. In other words, as δx decreases (location is better specified), the uncertainty δp increases (the momentum is further spread out). Thus, δx. δp ≥ h. It can be seen that in the event of x being precisely known, i.e., δx = 0, which implies a fixed position, δp = 0 and vice versa. This is because, particles have fixed dimensions and momentum requires displacement from their position to a position outside it. Since only those values of ψ have to be chosen which become non-zero within the range of δx and cancel each other out to become zero outside it, when δx is narrowed down to 0, which means that it has a fixed position, then outside its position δp = 0 also and vice versa.
This also implies that within the space occupied by the particle, δp ≠ 0, which means, all particles have internal “momentum”, which arises due to its internal structure. We will prove that all particles, however small they might be, have an internal structure till they decompose to a state where particles and fields become indistinguishable and the concept of position and momentum vanishes. This also means that when the particle has a fixed position, it does not have a momentum in the same frame of reference. But this does not mean that the object is at rest. It may be in motion with reference to other frames of reference, which cannot be ascertained without referring to those frames of reference. Similarly, if the object has a known momentum, it does not have a fixed position in the same frame of reference. But it may be at rest with reference to some other frame of reference.
The description of measurement in these examples misses some vital factors. Measurement is a process of comparison between similars. We measure length with a rod – by comparing its length (unit) with that of the object (according to Einstein, the length is what we measure by a measuring rod). We measure volume by comparing it with containers of unit volume. We measure velocity by comparing the distance traveled in unit time (irrespective of mass).
If the particle has momentum (mass times velocity), its velocity can be measured by comparing it (and not bouncing light off it, as Einstein and others suggest) with the velocity of a photon, whose velocity per second can be treated as the unit. But this measurement, which is time variant and different from the measurement process of the spread components of the respective coordinates representing dimensions, will not give us position, which is a fixed co-ordinate in the specific frame of reference and time invariant. To that extent, there is no “uncertainty”, as, while measuring momentum we do not measure position and vice-versa. In other words, the so-called “uncertainty” is not in the process or the result of measurement, but it is a description of exclusive information (since time invariant fixed co-ordinates of position and time variant mobile co-ordinates of momentum are mutually exclusive). Thus, the so-called “uncertainty” is a logical conclusion wrongly described. Logical because other factors beyond our control may affect the outcome.
Thus, the so-called “uncertainty” is a logical conclusion wrongly described. Logical because other factors beyond our control may affect the outcome.
The problem with the Schrödinger equation is that no one is clear about what exactly the wave-function represents. The confusion was compounded when Poincare came up with the equation: e = mc^2. Einstein also arrived at the same equations five years later through a different route. In spite of the evident contradictory properties of mass and energy, they were thought to be interchangeable. It is like telling the cost of 1 kg of apple is $1. Hence 1 kg of apple = $1. All the equation shows is that the rate of mass and energy interaction (distribution of mass by energy over an area) is related as e/m = c^2 or m/e = 1/c^2. This is not the same as e = mc^2 because c also represents energy of the photon, which is a part of electromagnetic wave and velocity is time variant. The energy does not go up with time.
The value of the parameter c is defined in the above equation from the fundamental concept requiring an absolute constant K, which is a constant of proportionality between mass and energy. Thus, we can say: e = Km. It has been observed experimentally that the value of K is equal to the square of what is interpreted to be the velocity of light. Whatever c stands for, we can define it as: c = √K. If mass and energy are convertible, then total mass can be converted into energy and vice versa. In such a case, total energy should have been in one side of the equation to make it convertible with mass in proportion with K. Substituting c^2 for K, we can write e/c^2 = m or e = mc^2. But the equation e/c^2 = m or e = mc^2 is meaningless, as there is nothing like bare mass or bare charge. Thus, the equation must have some other meaning. It can only be the constant rate at which unit mass is displaced by unit energy or unit energy is confined by unit mass, i.e., e/m = K or m/e = 1/K.
Thus, the equation must have some other meaning. It can only be the constant rate at which unit mass is displaced by unit energy or unit energy is confined by unit mass, i.e., e/m = K or m/e = 1/K.
(to be continued).