Wednesday, February 22, 2017


The famous Gita dictum: कर्मण्येवाधिकारस्ते मा फलेषु कदाचन  explains uncertainty scientifically in a much better way. 

When Heisenberg proposed his conjecture in 1927, Earle Kennard independently derived a different formulation, which was later generalized by Howard Robertson as: σ(q)σ(p) ≥ h/4π. This inequality says that one cannot suppress quantum fluctuations of both position σ(q) and momentum σ(p) lower than a certain limit simultaneously. The fluctuation exists regardless of whether it is measured or not implying the existence of a universal field. The inequality does not say anything about what happens when a measurement is performed. Kennard’s formulation is therefore totally different from Heisenberg’s. However, because of the similarities in format and terminology of the two inequalities, most physicists have assumed that both formulations describe virtually the same phenomenon. Modern physicists actually use Kennard’s formulation in everyday research but mistakenly call it Heisenberg’s uncertainty principle. “Spontaneous” creation and annihilation of virtual particles in vacuum is possible only in Kennard’s formulation and not in Heisenberg’s formulation, as otherwise it would violate conservation laws. If it were violated experimentally, the whole of quantum mechanics would break down.
The uncertainty relation of Heisenberg was reformulated in terms of standard deviations, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable disturbance in measurement process had been ignored. A correct formulation of the error–disturbance uncertainty relation, taking the perturbation into account, was essential for a deeper understanding of the uncertainty principle. In 2003 Masanao Ozawa developed the following formulation of the error and disturbance as well as fluctuations by directly measuring errors and disturbances in the observation of spin components: ε(q)η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π.
Ozawa’s inequality suggests that suppression of fluctuations is not the only way to reduce error, but it can be achieved by allowing a system to have larger fluctuations. Nature Physics (2012) (doi:10.1038/nphys2194) describes a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of experimental parameters. Even when either the source of error or disturbance is held to nearly zero, the other remains finite. Our description of uncertainty follows this revised formulation.
While the particles and bodies are constantly changing their alignment within their confinement, these are not always externally apparent. Various circulatory systems work within our body that affects its internal dynamics polarizing it differently at different times which become apparent only during our interaction with other bodies. Similarly, the interactions of subatomic particles are not always apparent. The elementary particles have intrinsic spin and angular momentum which continually change their state internally. The time evolution of all systems takes place in a continuous chain of discreet steps. Each particle/body acts as one indivisible dimensional system. This is a universal phenomenon that creates the uncertainty because the internal dynamics of the fields that create the perturbations are not always known to us. We may quote an example.
Imagine an observer and a system to be observed. Between the two let us assume two interaction boundaries. When the dimensions of one medium end and that of another medium begin, the interface of the two media is called the boundary. Thus there will be one boundary at the interface between the observer and the field and another at the interface of the field and the system to be observed. In a simple diagram, the situation can be schematically represented as shown below:
Here O represents the observer and S the system to be observed. The vertical lines represent the interaction boundaries. The two boundaries may or may not be locally similar (have different local density gradients). The arrows represent the effect of O and S on the medium that leads to the information exchange that is cognized as observation.
All information requires an initial perturbation involving release of energy, as perception is possible only through interaction (exchange of force). Such release of energy is preceded by freewill or a choice of the observer to know about some aspect of the system through a known mechanism. The mechanism is deterministic – it functions in predictable ways (hence known). To measure the state of the system, the observer must cause at least one quantum of information (energy, momentum, spin, etc) to pass from him through the boundary to the system to bounce back for comparison. Alternatively, he can measure the perturbation created by the other body across the information boundary.
The quantum of information (seeking) or initial perturbation relayed through an impulse (effect of energy etc) after traveling through (and may be modified by) the partition and the field is absorbed by the system to be observed or measured (or it might be reflected back or both) and the system is thereby perturbed. The second perturbation (release or effect of energy) passes back through the boundaries to the observer (among others), which is translated after measurement at a specific instant as the quantum of information. The observation is the observer’s subjective response on receiving this information. The result of measurement will depend on the totality of the forces acting on the systems and not only on the perturbation created by the observer. The “other influences” affecting the outcome of the information exchange give rise to an inescapable uncertainty in observations.
The system being observed is subject to various potential (internal) and kinetic (external) forces which act in specified ways independent of observation. For example chemical reactions take place only after certain temperature threshold is reached. A body changes its state of motion only after an external force acts on it. Observation doesn’t affect these. We generally measure the outcome – not the process. The process is always deterministic. Otherwise there cannot be any theory. We “learn” the process by different means – observation, experiment, hypothesis, teaching, etc, and develop these into cognizable theory. Heisenberg was right that “everything observed is a selection from a plentitude of possibilities and a limitation on what is possible in the future”. But his logic and the mathematical format of the uncertainty principle: ε(q)η(p) ≥ h/4π are wrong.
The observer observes the state at the instant of second perturbation – neither the state before nor after it. This is because only this state, with or without modification by the field, is relayed back to him while the object continues to evolve in time. Observation records only this temporal state and freezes it as the result of observation (measurement). Its truly evolved state at any other time is not evident through such observation. With this, the forces acting on it also remain unknown – hence uncertain. Quantum theory takes these uncertainties into account. If ∑ represents the state of the system before and ∑ ± ∑ represents the state at the instant of perturbation, then the difference linking the transformations in both states (treating other effects as constant) is minimum, if ∑<<∑. If I is the impulse selected by the observer to send across the interaction boundary, then ∑ must be a function of I: i.e. ∑ = f (I). Thus, the observation is affected by the choices made by the observer also.
The inequality: ε(q)η(p) ≥ h/4π or as it is commonly written: δx. δp ≥ ħ permits simultaneous determination of position along x-axis and momentum along the y-axis; i.e., δx. δpy = 0. Hence the statement that position and momentum cannot be measured simultaneously is not universally valid. Further, position has fixed coordinates and the axes are fixed arbitrarily from the origin. Position along x-axis and momentum along y-axis can only be related with reference to a fixed origin (0, 0). If one has a non-zero value, the other has indeterminate (or relatively zero) value (if it has position say x = 5 and y = 7, then it implies that it has zero momentum with reference to the origin. Otherwise either x or y or both would not be constant, but will have extension). Multiplying both position (with its zero relative momentum) and momentum of the same particle (which is possible only at a different time t1 when the particle moves), the result will always be zero. Thus no mathematics is possible between position (fixed coordinates) and momentum (mobile coordinates) as they are mutually exclusive in space and time. They do not commute. Hence, δx.δpy = 0.
Uncertainty is not a law of Nature. We can’t create a molecule from any combination of atoms as it has to follow certain “special conditions”. The conditions may be different like the restrictions on the initial perturbation sending the signal out or the second perturbation leading to the reception of the signal back for comparison because the inputs may be different like c+v and c-v or there may be other inhibiting factors like a threshold limit for interaction. These “special conditions” and external influences that regulate and influence all actions and are unique by themselves, and not the process of measurement, create uncertainty. As the universe evolves in time, its density fluctuates from the mean density within a certain range. Thus, the degree of uncertainty also changes over time. We will discuss this later. The disturbances arising out of the process of measurement are operational (technological) in nature and not existential for the particles. Hence it does not affect the particle, but only its description with reference to observation by others.

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