Non-Linear Electrodynamics Gedanken Experiment for Modified Zero Point Energy and Planck’s “Constant”, h Bar, in the Beginning of Cosmological Expansion, So h(Today) = h(Initial). Also How to Link Gravity, Quantum Mechanics, and E and M through Initial Entropy Production  in the Early Universe

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, given zero-point energy calculation with an unexpected “length’ added to the ‘width’ of a graviton wave just prior to specifying the creation of ‘gravitons’, while using Karen Freeze’s criteria as to the breakup of primordial black holes to give radiation era contributions to GW generation. The GW generation will be when there is sufficient early universe density so as to break apart Relic Black holes of the order of Planck mass (10^15 grams) which isabout when the mass of relic black holes is created, 10^-27 or so seconds after expansion starts. Need to state a key result will be in the initial potential V calculated, in terms of other input variables

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XII.—Quantum Mechanics of Fields. II. Statistics of Pure Fields

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences ◽

10.1017/s0080454100006464 ◽

1944 ◽

Vol 62 (1) ◽

pp. 92-102

Author(s):

Max Born ◽

H. W. Peng

Keyword(s):

Quantum Mechanics ◽

Wave Vector ◽

Fourier Coefficients ◽

Zero Point ◽

Zero Point Energy ◽

Point Energy ◽

Radiation Oscillator ◽

Usual Quantum ◽

Usual Theory ◽

Theory Of Fields

The quantum mechanics of fields recently developed by us leads to a modification of statistical mechanics of elementary particles which seems to overcome some of the difficulties (divergence of integrals) occurring in the usual quantum theory of fields. The main difference between the new theory and the usual one is as follows.In the usual theory the wave-vector k is introduced classically and, so to speak, kinematically by the Fourier analysis of the field. The Fourier coefficients of the field components are then treated according to quantum mechanics as non-commuting quantities; those belonging to the wave-vector k describe the corresponding “model” mechanical system, namely the kth radiation oscillator. But the statement that the Fourier coefficients belonging to a certain k all vanish, which statement classically is significant, is now meaningless because there is a lowest state with zero-point energy for each radiation oscillator. The field is thus made to be equivalent to the assembly of radiation oscillators of all possible wave-vectors which, being necessarily infinite in number, contribute an infinite zero-point energy for the pure field and lead to other divergent integrals for the interaction between different fields.

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Zero Point Energy

Van Nostrand's Scientific Encyclopedia ◽

10.1002/0471743984.vse7649 ◽

2005 ◽

Keyword(s):

Zero Point ◽

Zero Point Energy ◽

Point Energy

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Zero-point energy of linear triatomic molecules

Journal of the Chemical Society Faraday Transactions 2 Molecular and Chemical Physics ◽

10.1039/f29747000871 ◽

1974 ◽

Vol 70 ◽

pp. 871 ◽

Cited By ~ 2

Author(s):

Jan Bron

Keyword(s):

Zero Point ◽

Zero Point Energy ◽

Point Energy ◽

Triatomic Molecules

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An investigation into the existence of zero-point energy in the Rock-Salt Lattice by an X-Ray Diffraction Method

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1928.0055 ◽

1928 ◽

Vol 118 (779) ◽

pp. 334-350 ◽

Cited By ~ 41

Keyword(s):

Rock Salt ◽

Diffraction Method ◽

Zero Point ◽

Temperature Factor ◽

X Rays ◽

Zero Point Energy ◽

Chlorine Atoms ◽

Point Energy ◽

X Ray ◽

State Of Rest

In the present paper we shall attempt to collate the results of four separate lines of research which, taken together, appear to provide some interesting checks between theory and experiment. The investigations to be considered are (1) the discussion by Waller* and by Wentzel,† on the basis of the quantum (wave) mechanics, of the scattering of radiation by an atom ; (2) the calculation by Hartree of the Schrödinger distribution of charge in the atoms of chlorine and sodium ; (3) the measurements of James and Miss Firth‡ of the scattering power of the sodium and chlorine atoms in the rock-salt crystal for X-rays at a series of temperatures extending as low as the temperature of liquid air ; and (4) the theoretical discussion of the temperature factor of X-ray reflexion by Debye§ and by Waller.∥ Application of the laws of scattering to the distribution of charge calculated for the sodium and chlorine atoms, enables us to calculate the coherent atomic scattering for X-radiation, as a function of the angle of scattering and of the wave-length, for these atoms in a state of rest, assuming that the frequency of the X-radiation is higher than, and not too near the frequency of the K - absorption edge for the atom.¶ From the observed scattering power at the temperature of liquid air, and from the measured value of the temperature factor, we can, by applying the theory of the temperature effect, calculate the scattering power at the absolute zero, or rather for the atom reduced to a state of rest. The extrapolation to a state of rest will differ according to whether we assume the existence or absence of zero point energy in the crystal lattice. Hence we may hope, in the first place to test the agreement between the observed scattering power and that calculated from the atomic model, and in the second place to see whether the experimental results indicate the presence of zero-point energy or no.

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