Archive for August, 2011

Aug 14 2011

Topology of the Vacuum

Whether we are looking at nuclear fission or the results of scattering experiments, the way spin-parity assignments are often kept in order in nature would be similar to the cause of a de Broglie wavelength.  Rotational states ratchet through the gravitational flux, with potential wells rising and falling in one of the most fundamental of quantum phenomenons that exist.

During and shortly after high flux, high velocity hadron collisions at Fermilab or the CERN LHC nevertheless, some of the scattering resonances seen may be due to a blitz through the gravitational field, not organized very well in a manner, for example, such as an electric field.  The static we typically see in Goldhaber plots generated from hadron colliding experiments may in part be due to a cascade of momentum generated through the gravitational field.

Another evidence of the gravitational field is the Bohm-Aharonov effect.  As Ryder puts it, “the Bohm-Aharonov effect owes its existence to the non-trivial topology of the vacuum, and the fact that electrodynamics is a gauge theory.  In fact, it has recently been realized that the vacuum, in gauge theories, has a rich mathematical structure, with associated physical consequences,” ([1], pg 101).

Astronomically, and for the sake of history, it is somewhat reminiscent of the luminiferous aether.

Another concept related here is that “the configuration space of the vacuum is not simply connected.” ([1], pg 102)  When we speak of ‘one loop’ consequences, we can liken it to the Cauchy integral, which Greiner calls “The surprising statement of the integral formula (4.16), namely, that it is sufficient to know a function along a closed path to determine any function value in the interior,” ([2], pg 109).  For those more willing to trust the mathematicians for pure math, the Cauchy integral formula is presented in Brown and Churchill:

f(z) = (1/2πi) ∫ (1/(s-z)) f(s) ds                     ([3], pgs 166 and 429)

With “the gauge invariance of electrodynamics” ([1], pg 97), the perfect balance of charge that exists in the near universe, – possibly the entire universe, and the quantum steps of the Coulomb force by phonon transmission, the Bohm-Aharonov effect does indeed show us that there are physical consequences to the vacuum that are non-trivial, relating to the gravitational field in which the Bohm-Aharonov test and other tests are set up and run.

As a final thought, it is probable that planar electromagnetic waves would not turn into spherical electromagnetic waves were it not for traveling through a gravitational field.


[1] Ryder, Lewis H., Quantum Field Theory, Second Edition, Cambridge University Press, 1996

[2] Greiner, Walter, Classical Electrodynamics, First German edition, Klassische Elektrodynamik, 1991 Verlag Harri Deutsch. 1998 Springer-Verlag New York, Inc.

[3] Brown, James Ward and Churchill, Ruel V., Complex Variables and Applications, Eighth Edition, McGraw-Hill Higher Education, 2009

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