a brief survey of the equations of physics

[tony_fleming]

A BRIEF SURVEY OF THE VARIOUS FIELD EQUATIONS SINCE 1864

The terminology of quantum field theory (QFT) is somewhat misleading; the 'field' referred to by QFT is NOT a field, not a measureable E- or H-field at any rate, rather it is defined as a theoretical 'field'. When compared to SFT, a true 'field' theory, it is necessary to examine exactly what a field is and isn't, especially in the real world of measurements. It is thus instructive to briefly survey the main systems of equations used by physicists since the discovery of Maxwell's equations. The four equations were formulated by Maxwell in 1873 and describe the macroscopic E- and H-fields, and their associated currents, that had been measured in careful experiments by Coulomb, Faraday, Ampere, Biot, Savart and others. Several forms of EM wave equations were formulated including decoupled forms where either the E- or H-field variables appeared in isolation; Maxwell's equations were specialized for various applications e.g. where quasistationary simplifications are ssumed or where radiation conditions cannot be simplified. Hertz's potentials introduced a mixed-field substitution that lead to a Lagrangian or energy density formulation suitable for solving via integrations over radiation surfaces where infinite regions needed to be considered. These are Hertz's famous vector and scalar potential wave equations.

Following theoretical and experimental demonstrations by Planck and Einstein of the existence of a quantum physics, there was a failure by physicists to discover a mathematics based on Maxwell's equations that applied to the electron's motion in the atom. In 1926 Schrödinger used energy conservation to obtain a quantum mechanial equation in a variable called the wave function that accurately described single-electron states such as the hydrogen atom. The wave function was a variable that depended on the Hamiltonian and the total energy of the atomic system and thus was compatible with the Hertzian potential formulation. The wave function was a coupled field variables depending on the sum of the square of both the E- and H-fields as can be seen by examining the energy density function of the electromagnetic field. In 1928 Dirac realised that the wave functions were not relativistic and sought to find corresponding equations to incorporate Einstein's relativity. Dirac's equations were described in terms of two 'fields', the Dirac fields, and could be described as 'field equations of motion'. The term "Dirac's two wave equations" is also used. But like Schrödinger's equation, mixing the underlying Maxwellian fields had lead to a mathematical smearing of the fields. Thus the problem was now only 'wave-like' rather than uncoupled fields and lead Heisenberg to his uncertainty principle.

But the underlying physically measureable fields had long been lost in the potential equations; any dipole or loop measurements would not be useful (nor possible). By the time the equations governing the weak and strong nuclear forces were found using modern versions of QFT, namely quantum electrodynamics (QED) and quantum chromodynamics (QCD) the physical fields were a long-forgotten reality. So the question remains: do the E- and H-fields of Maxwell's equations where the fields are determined between point-charges exist within the nanoscopic domain of the atom? At present it has been demonstrated by SFT for the hydrogen atom that these E- and H-field forms are no longer applicable for the sub-atomic charges. What is the proof? The analytic equations obatined from EMSFT for the hydrogen atom are validated by the known spectroscopy.

[tony_fleming]

A BRIEF SURVEY OF THE VARIOUS FIELD EQUATIONS SINCE 1864

....So the question remains: do the E- and H-fields of Maxwell's equations where the fields are determined between point-charges exist within the nanoscopic domain of the atom? At present it has been demonstrated by SFT for the hydrogen atom that these E- and H-field forms are no longer applicable for the sub-atomic charges. What is the proof? The analytic equations obatined from EMSFT for the hydrogen atom are validated by the known spectroscopy.

We require to determine the fields between centres of motion as per self-field theory where it is no now longer sufficient to merely wave about a loop or a dipole. What's more we need a very tiny loop or dipole that somehow don't interfer with the photon-exchange process of the atom, so we can't measure them directly but must use theory that can be validated by other means apart from measuring the field directly!!

you can view a further discussion of the maths of QFT and SFT at
http://www.unifiedphysics.com/mathematics.htm

[tony_fleming]

We require to determine the fields between centres of motion as per self-field theory where it is no now longer sufficient to merely wave about a loop or a dipole. What's more we need a very tiny loop or dipole that somehow don't interfer with the photon-exchange process of the atom, so we can't measure them directly but must use theory that can be validated by other means apart from measuring the field directly!!

you can view a further discussion of the maths of QFT and SFT at
http://www.unifiedphysics.com/mathematics.htm

-----
But the underlying physically measureable fields had long been lost in the potential equations. By the time the equations governing the weak and strong nuclear forces were found using modern versions of QFT, namely quantum electrodynamics (QED) and quantum chromodynamics (QCD) the physical fields were a long-forgotten reality. But in any case why cannot these potentials give us a correct picture of the E- and H-fields at atomic levels? After all we have Hertz's potential equations that give us a correspondence between potentials and fields?

[tony_fleming]

But why can't the potentials give us a correct picture of the E- and H-fields at atomic levels? After all we have Hertz's potential equations that give a correspondence between potentials and fields? The question is: do Maxellian E- and H-fields determined between point-charges exist within the nanoscopic domain of the atom? Recently it has been demonstrated by EMSFT for the hydrogen atom that these E- and H-field forms are not applicable to sub-atomic charges. Why? The analytic solutions obtained from EMSFT for the hydrogen atom are validated by the known spectroscopy where we determine the atomic fields between centres of motion and not between charge points. This issue is at the crux of why classical vector and scalar potentials cannot obtain the correct solution; the macroscopic fields of Coulomb and Biot-Savart do not hold at atomic dimensions; the fields caused by the motions of the photons inside the atom are not correctly formulated point-charge to point-charge. The classical potentials cannot give us the correct answer, because the classical field theory as we have long known is wrong. The potential solution was in a sense chasing its tail; the classical fields and potentials are incorrect over atomic dimensions as Heisenberg had correctly determined. Reality wasn't in error; but classical field theory and hence also quantum field theory is. Coulomb's, and Biot's and Savart's famous E- and H-field forms apply to macroscopic phenomena not to atomic systems. The photons inside atoms in fact stream between electrons and nucleons. These photonic streams are not ubiquitous nor continuous, they are discrete and therefore discontinuous. They behave more like Dirac delta functions, an interesting fact in terms of their role in solving Maxwell's equations for the self fields (further discussion coming on numerical methods FEM vs FDM).

[AntonioLao]

if the zero-point energy is given by [math]\frac{1}{2}\hbar\omega_c[/math] then the lowest value for [math]\omega_c[/math] is unity giving the value of frequency as [math]\frac{1}{2\pi}[/math]. But would it be better for a theory where the frequency is unity? And the angular frequency is [math]2\pi[/math]?

[tony_fleming]

"ORIGIN OF ZERO-POINT ENERGY

The basis of zero-point energy is the Heisenberg uncertainty principle, one of the fundamental laws of quantum physics. According to this principle, the more precisely one measures the position of a moving particle, such as an electron, the less exact the best possible measurement of momentum (mass times velocity) will be, and vice versa. The least possible uncertainty of position times momentum is specified by Planck's constant, h. A parallel uncertainty exists between measurements involving time and energy. This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter.

A useful calculational tool in physics is the ideal harmonic oscillator: a hypothetical mass on a perfect spring moving back and forth. The Heisenberg uncertainty principle dictates that such an ideal harmonic oscillator -- one small enough to be subject to quantum laws -- can never come entirely to rest, since that would be a state of exactly zero energy, which is forbidden. In this case the average minimum energy is one-half h times the frequency, hf/2. "


quoted from http://www.calphysics.org/zpe.html

according to self-field theory, heisenberg's uncertainty equation or principle is a term that gives the mathematical accuracy associated with quantum field theory, not a limit on reality itself.

what is seen as the 'ocean' of energy in the vacuum of deep space is probably associated with the 'streams' of photonic particles of varying energy states criss-crossing deep space as a result of all the dynamic motions and balances that has been going on between all matter within the unverse since the big-bang.


due to statistical mechanics, we can average this radiation into fourier frequencies, so how you normalize its mean with respect to frequency doesn't matter; what matters is that a mean energy or frequency will exist.

[AntonioLao]

what wave phenomena have their frequencies exactly equal to unity? Since frequency is defined as cycle per unit period of time then frequency unity is just one cycle per period.

[math]f=\frac{1}{T}[/math]

if the the period of the universe is 1 then its wave function frequency is also 1.
In other words: Do 1-cycle-per-period waves exist?

[tony_fleming]

what wave phenomena have their frequencies exactly equal to unity? Since frequency is defined as cycle per unit period of time then frequency unity is just one cycle per period.

[math]f=\frac{1}{T}[/math]

if the the period of the universe is 1 then its wave function frequency is also 1.
In other words: Do 1-cycle-per-period waves exist?

does the universe oscillate at 'one' hertz per second??

well, if we put it in terms of the self-field theory version of Planck's 'constant'

h_bar=q^2/(8*pi*eps_0*v_0)
where v_0=omega_0*r_0

(from the EMSFT application to hydrogen atom)

then we can use the best estimate for r_0 as 10^10 light years

so this means we should know omega_0; let me think about it more.

[tony_fleming]

what wave phenomena have their frequencies exactly equal to unity? Since frequency is defined as cycle per unit period of time then frequency unity is just one cycle per period.

[math]f=\frac{1}{T}[/math]

if the the period of the universe is 1 then its wave function frequency is also 1.
In other words: Do 1-cycle-per-period waves exist?

i presume what we're talking about is the fundamental mode of the universe

[AntonioLao]

i presume what we're talking about is the fundamental mode of the universe

Does it make any sense to talk about this fundamental mode? Quantum mechanically speaking, the universe is a superposition of all the linear combinations of quantum states (fermions and bosons). So if the period T is the age of the universe approaching infinity then the inverse of the period as frequency aproaches 1 instead of zero.