norm of square energy

[AntonioLao]

The mathematical concept of norm is a measure which describes some sense of the length or size of the corresponding mathematical entity, for examples: the absolute value of a real number, the modulus of a complex number, the vector magnitude, the matrix norm, and the quaternion norm. The absolute value of a real number denoted by |��| where �� is the given real number, is �� if ��≥0 and –�� if ��<0. Thus |��| is positive definite except when ��=0. For any two real numbers �� and ��: |����|=|��||��|, |��+��|≤|��|+|��|, |��-��|≥||��|-|��||, and ��>0,|��|≤�� if and only if –��<��<��. The modulus of a complex number ��=��+���� denoted by |��| and is simply equal to the non-negative square root of ��²+��². The square of the vector magnitude is given by the matrix product of the transpose vector and the vector itself: |��|²=��†�� where �� is defined as the column vector. The matrix norm is defined for a square matrix �� with real or complex elements as a non-negative number with the properties that |��|>0 if ��≠0 and |��|=0 if ��=0, |����|=��|��| for any positive scalar ��, |��+��|≤|��|+|��|, and |����|≤|��||��|. The norm of a quaternion denoted by |��| is the scalar defined by the square root of the sum of squares of the corresponding numerical coefficients, for example the quaternion given by ��=2-2��+2��-2��, |��|²=2²+(-2)²+2²+(-2)²=16 → |��|=4.

For the squares of energy of the quantum vacuum fluctuations of zero-point energies, the square norm is given as the quadratic form of infinite order. For the 8th order, ��( 8 )=(��₁-��₂+��₃-��₄+��₅-��₆+��₇-��₈)²= ��₁² cos��₁₁+��₂² cos��₂₂+��₃² cos��₃₃+��₄² cos��₄₄+��₅² cos��₅₅+��₆² cos��₆₆+��₇² cos��₇₇+��₈² cos��₈₈-2 ��₁��₂cos��₁₂+2 ��₁��₃cos��₁₃-2 ��₁��₄cos��₁₄+2 ��₁��₅cos��₁₅-2 ��₁��₆cos��₁₆+2 ��₁��₇cos��₁₇-2 ��₁��₈cos��₁₈-2 ��₂��₃cos��₂₃+2 ��₂��₄cos��₂₄-2 ��₂��₅cos��₂₅+2 ��₂��₆cos��₂₆-2 ��₂��₇cos��₂₇+2 ��₂��₈cos��₂₈-2 ��₃��₄cos��₃₄+2 ��₃��₅cos��₃₅-2 ��₃��₆cos��₃₆+2 ��₃��₇cos��₃₇-2 ��₃��₈cos��₃₈-2 ��₄��₅cos��₄₅+2 ��₄��₆cos��₄₆-2��₄��₇cos��₄₇+2 ��₄��₈cos��₄₈-2 ��₅��₆cos��₅₆+2 ��₅��₇cos��₅₇-2 ��₅��₈cos��₅₈-2 ��₆��₇cos��₆₇+2 ��₆��₈cos��₆₈-2 ��₇��₈cos��₇₈. It can noted that for singular symmetric Hadamard coefficient matrices and if all ��’s have equal magnitudes then even order (even)=0, while ��(odd)>0 if there are more plus signs and ��(odd)<0 if there are more minus signs. Plus signs indicate excess useful energy. Minus signs indicate excess useless energy. On the other hand, changing the direction cosines can either increase or decrease useful energies and for every 3D Cartesian triple cos²��₁₁+ cos²��₂₂+ cos²��₃₃=1. Furthermore, rationalization of distinct products such that ��₁��₂=��₁-��₂ allows additional increase or decrease of useful energy. Extension into non-symmetric nonsingular coefficient matrices becomes known as the eigenvalue problem and solution of quantum mechanics.

[Lloyd Gillespie]

Energy of What, Antonio...? What, is the question...?

Neither vacuum nor energy are entities__they are measurements of fundamental entities in motion... What fundamental substance state are you using to derive vacuum and energies...?

No maths are entities either__they are merely abstract tools of measurement...

Until I see an absolute fundamental entity, as the ground state__to do the math about__I see only castles in the non-state sky...

[AntonioLao]

Energy of What

I'm sorry to keep repeating myself, I am talking about energy of the quantum vacuum. I can make you a deal to go one on one on this discussion. You can pay for my time, transportation, and lodging to get to where you are for a few days of serious conference or you can pay for my time plus the rent for a conference room for you to come here to Plano, Texas. Then we can clear up all the confusion.

[Lloyd Gillespie]

I'm sorry to keep repeating myself, I am talking about energy of the quantum vacuum.

Sorry, but that has no meaning to me, Antonio... All energy in the quantum vacuum is spent as Va, Vr and Vu, unless we, or it, collide more of it with lasers/motions of real particle/wave photons, etc., then in certain cases of frequencies, colors and particle collisions of, etc., we may get more out than we put in, but only by releasing what's curled up there already in the particles, electrons, protons, quarks, squarks or whatever__similar to all the radio actives. That's all I'm talking about, as you always seem to be talking about everything but the necessary ingredients of fundamental substances/entities in motion, to produce the real measurable energies of__gas don't explode without motion, neither do particles, yet only particles do__energy doesn't...! When a H-bomb explodes, that's its particles separating from their highly entangled spin states, into linear states, as I'm sure you're well aware__but it's always a fundamental entity/substance that's in, and going through a changed state motion__to produce the energy/blast__No...?

[AntonioLao]

you always seem to be talking about everything but the necessary ingredients of fundamental substances

I'm merely talking about the direction cosines of the infinitely dimensional vector space-time charges. On the other hand, if you try to understand everything with a bird's eye view then you begin to lose sight of the important details at the microscopic infinitesimal region of the space-time continuum.

[Lloyd Gillespie]

I'm merely talking about the direction cosines of the infinitely dimensional vector space-time charges. On the other hand, if you try to understand everything with a bird's eye view then you begin to lose sight of the important details at the microscopic infinitesimal region of the space-time continuum.

Antonio, to me, the most microscopic possible infinitesimal region of the space and time continuum is still real photons, or some other possible boson, which is inter-acting to produce what scientists call energy, which is really just a finer grained substance of fundamental matter... I do not accept that the most fundamental level of the continuum can ever be separated below the absolute fundamental level of a triadic FS of matter/motion/energy__This is the base unit, as any separation of any one of these three, from the fundamental triad destroys all functioning of the continuum... All continuum field actions function within this fundamental triad, yet exist as extremely small infinitesimals of particles, with eternally inter-locking fields, that are capable of the intra-trading of fields and particles, at this most fundamental of levels... It's all theory, but it's better than what the std. models are working with__as far as I'm concerned... To me, it's a non-viscous fluidic FS, that black-holes and stars, or possible big-bangs, cook into the heavier level atomic elements, then planets, moons, rocks and galaxies, etc., upon all the trillions of explosions and re-formations__re-condensations or whatever...

We're coming at this problem from two entirely different fields of view...

[AntonioLao]

most microscopic possible infinitesimal region of the space and time continuum is still real photons

But you are seeing from a vantage point that is one step backward and therefore farther from agreeing with what is shown in a Feynman diagram. Later, I can give a mathematical proof that Stefan-Boltzmann law of blackbody radiation holds the same general covariance as the space-time quantization of squares of energy.

[Lloyd Gillespie]

But you are seeing from a vantage point that is one step backward and therefore farther from agreeing with what is shown in a Feynman diagram. Later, I can give a mathematical proof that Stefan-Boltzmann law of blackbody radiation holds the same general covariance as the space-time quantization of squares of energy.

And I intend to stay backward, way away from any 'squares of energy' non-entities__if you choose to not clearly define the fundamentals of what you speak...

"There's no ghosts in the machine__just a lotta quantum motion of FS..."

The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per unit surface area of a black body in unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth power of the black body's thermodynamic temperature T (also called absolute temperature):
A more general case is of a grey body, the one that doesn't absorb or emit the full amount of radiative flux. Instead, it radiates a portion of it, characterized by its emissivity, ε:
The irradiance j* has dimensions of energy flux (energy per time per area), and the SI units of measure are joules per second per square metre, or equivalently, watts per square metre. The SI unit for absolute temperature T is the kelvin. ε is the emissivity of the grey body; if it is a perfect blackbody, ε = 1. Still in more general (and realistic) case, the emissivity depends on the wavelength, ε = ε(λ).
To find the total absolute power of energy radiated for an object we have to take into account the surface area, A(in m2):
The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan's constant, is non-fundamental in the sense that it derives from other known constants of nature. The value of the constant is
where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. Thus at 100 K the energy flux density is 5.67 W/m2, at 1000 K 56,700 W/m2, etc.
The law was deduced by Jožef Stefan (1835-1893) in 1879 on the basis of experimental measurements made by John Tyndall and was derived from theoretical considerations, using thermodynamics, by Ludwig Boltzmann (1844-1906) in 1884. Boltzmann treated a certain ideal heat engine with the light as a working matter instead of the gas. The law is valid only for ideal black objects, the perfect radiators, called black bodies. Stefan published this law in the article Über die Beziehung zwischen der Wärmestrahlung und der Temperatur (On the relationship between thermal radiation and temperature) in the Bulletins from the sessions of the Vienna Academy of Sciences.

In physics, a black body is an idealized object that absorbs all electromagnetic radiation that falls on it. No electromagnetic radiation passes through it and none is reflected. Because no light (visible electromagnetic radiation) is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black-body radiation.[nb 1]
At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By the time an object is white, it is emitting substantial ultraviolet radiation.
The term "black body" was introduced by Gustav Kirchhoff in 1860.
Black-body emission gives insight into the thermal equilibrium state of a continuous field. In classical physics, each different Fourier mode in thermal equilibrium should have the same energy. This approach led to the paradox known as the ultraviolet catastrophe, that there would be an infinite amount of energy in any continuous field. Black bodies could test the properties of thermal equilibrium because they emit radiation which is distributed thermally. Studying the laws of the black body historically led to quantum mechanics.

[labelwench]

Hoy!

This discussion is way over my head, yet in following it, things are starting to tug on the peripheries of my mind.

Amazing what thoughts begin to emerge when various pairings of minds begin a fruitful dialogue, though they may not be coming at the topic from similar experience or identical frameworks.

This is only getting better, gentlemen, here and on other threads.

Lots of excellent material to contemplate, even at a less comprehending level, as per myself, and likely some others viewing this forum.

[AntonioLao]

The Stefan–Boltzmann law

I'm not trying to understand this law but what I'm trying to show is its general covariance with square of energy using the math of quadratic forms as precursors to the method of eigenvalue problems of quantum mechanics.