  ## Heisenberg's Uncertainty Principle Heisenberg’s Uncertainty Principle is one of the fundamental concepts of Quantum Physics, and is the basis for the initial realization of fundamental uncertainties in the ability of an experimenter to measure more than one quantum variable at a time. Attempting to measure an elementary particle’s position to the highest degree of accuracy, for example,  leads to an increasing uncertainty in being able to measure the particle’s momentum to an equally high degree of accuracy.  Heisenberg’s Principle is typically written mathematically in either of two forms:

DE  Dt  ³  h / 4 p            Dx  Dp  ³  h / 4 p

In essence, the uncertainty in the energy (DE) times the uncertainty in the time (Dt)  -- or alternatively, the uncertainty in the position (Dx) multiplied times the uncertainty in the momentum (Dp) -- is greater or equal to a constant (h/4p).  The constant, h, is called  Planck’s Constant (where h/4p = 0.527 x 10-34 Joule-second).  The implication is that in extremely small time elements (such as might be encountered in Connective Physics,  The Fifth Element, Zero-Point Energy, Hyperdimensional Physics, and the Casimir Effect -- among other subjects), the uncertainty in the value of the energy of a particle is significant.  A legitimate question might be: Why does this energy uncertainty exist?

This question becomes extremely relevant when according to Barone : “in classically chaotic systems, irreducible uncertainties required by the Heisenberg principle are amplified exponentially to the macroscopic level in short times.”  On the one hand, “at the macroscopic level the minimum uncertainties in initial conditions required by the uncertainty principle usually do not lead to significant effects on the numerical values of dynamical variables in time intervals of interest.”  But in “much shorter time intervals” this is not necessarily the case. This apparently stems from the fact that solutions of Newton’s differential equations are exponentially sensitive to variations in initial conditions.

Barone, et al  also pointed out in the chaotic behavior of the solutions of nonlinear differential equations, some systems may be “deterministic” (i.e. have a solution uniquely determined by the differential equations and initial conditions), but still “unpredictable”.  According to Barone: “The chaotic solutions of nonlinear differential equations are extremely sensitive to the numerical values of the initial conditions.” “Any set of differential equations represents a model of a system which incorporates some insights into the phenomena being studied and at the very least ignores numerous perturbations.  The ignored small physical perturbations which might be modeled, for example, by additional ‘forces’ in the differential equations may totally change the behavior of the system in time intervals of interest.  In this situation the behavior of the system is ‘unpredictable’ in the sense that it is not practical to include all perturbations which have a significant effect on the behavior of the system.” [emphasis added]  This not only brings the uncertainty principle into the realm of classical mechanics, but also suggests the “additional ‘forces’” of which and the associated inertial forces might well qualify.

In the case of an electron orbiting close to a charged sphere in a uniform magnetic field, “the classical dynamics of this system is known to yield chaotic orbits for some ranges of parameters.”  Also, “in order for Newtonian dynamics to accurately predict chaotic electron orbits in this system for times longer than about 10 micro-seconds the initial conditions would have to be specified to an accuracy inconsistent with Heisenberg’s uncertainty principle.” 

This is extremely important in that it should be feasible to observe on a macroscale results which depend upon the microscale of Planckian physics.  In other words, those activities at the atomic, nuclear and potentially smaller scale levels may manifest in readily observable variables such as pressure, temperature and macro displacements.  At the same time, the macroscopic time element is critical and needs to be quite small -- a reality which may be readily observed in cases of extreme acceleration or deceleration (the essence of Connective Physics, The Fifth Element, and potentially Hyperdimensional Physics).

Furthermore, traditional interpretations of the v tend to emphasize the inability to measure the energy at a precise time. Raymer , for example, states that “Heisenberg’s original argument for the uncertainty principle involved the perturbation to a particle’s state by a measurement of one variable, which affects one’s ability to predict the outcome of a subsequent measurement of the conjugate variable.”  Note that this is not some form of “measurement error”, but due instead, supposedly, to the physical variables intrinsic to a particle’s state.

In effect, the Uncertainty Principle is not about measurements at all, but instead about actual fluctuations within an elementary particle as to its energy or momentum.

For example, at a precise time, t, the energy of an electron is not determinable to a precision greater than h/4p, because the energy of the electron physically varies by this amount within a Planck like time parameter.  In effect, the electron’s energy fluctuates within narrow bounds, and what is supposed as the electron’s energy is, in fact, an average value over the very narrow time parameter.

This fluctuating electron energy might suggest a violation of the conservation of energy, but not if the electron is exchanging energy at the Planck level with other electrons or particles.  In effect, we might argue that the Heisenberg Uncertainty Principle provides evidence to support Mach’s Principle with respect to the interconnectedness of all masses (including electrons).  Specifically, the “unfortunately unspecified” interaction of an electron with the rest of the universe, as specified by Mach’s Principle, is contained within the Heisenberg Uncertainty Principle as a continuously fluctuating exchange of energy or momentum.  For if there is a continuous fluctuation of energy between particles as the quantum level, then by Einstein’s famous Energy equals mass times the velocity of light squared, this would include mass as well, and indirectly define inertia.

If on the other hand, Mass is an illusion, then mass does not exist and inertia becomes a property of energy fluctuations at the quantum level.  Puthoff’s contention that electric charges are connected, and that Mass is merely a convenient tag we apply to certain parts of energetic electric charges, simply implies that it is the energy which connects the parts of the universe.  And in all likelihood, the Superconductivity of the electrons.

In either case, the theory of (et al) is likely based on a Machian interconnectedness of inertia, whereby energy and/or momentum is exchanged between different particles under Planck time frames and within the constraints and capabilities of the Heisenberg Uncertainty Principle.

A particularly important postscript to the above is that the fuzziness of the uncertainty -- in the form of the greater than or equal to aspect of the equation -- may no longer be quite so fuzzy.  (As in Fuzzy Wuzzy was a bear.  Fuzzy Wuzzy had no hair.  Fuzzy Wuzzy wasn’t so fussy, was he?)

Samuel  has reported on research by Michael Hall and Marcel Reginatto  in which the latter have developed an expression for the uncertainty in the measurements, but one which is “an equation rather than an inequality, which is ‘a far stronger relation’.”  This new work thus implies an Exact Uncertainty -- such that an inequality is replaced with what sounds like a contradiction in terms.  O’ Vey!  Such is the state of physics!

Forward to:

___________________________

References:

 Barone, S.R., Kunhardt, E.E., Bentson, J., and Syljuasen, A., 1993, “Newtonian Chaos + Heisenberg Uncertainty = macroscopic indeterminacy”, American Journal of Physics, Vol 61, No. 5, May.

 Raymer, M.G., 1994, “Uncertainty Principle for Joint Measurement of Noncommuting Variables,” American Journal of Physics, Vol. 62, No. 11, November.

  Samuel, E., “Exact Uncertainty brought to quantum world,” New Scientist -- available at < http://www.newscientist.com/news/news.jsp?id=ns99992209>.

  Hall, M.J.W. and Reginatto, M., “Schroedinger equation from an exact uncertainty principle,” Journal of Physics A, Vol 35, April 12, 2002, pages 3289-3303.

## The Library of ialexandriah 