This is given in “Vector Analysis Problem Solver” chapter 16, the chapter on volume integrals. I use example 16.3 of VAPS to justify the correct expression for the intensity of black body radiation from the Planck distribution. This is Eq. (16) and has two terms missed entirely by the old theory. I worked out the integration mathematics with close logic by directly adapting the mathematics of volume integrals. Unless there is an error in this close logic the usual expression for the Stefan Boltzmann law is completely wrong. Rayleigh gave no justification in 1900 for his neglect of higher order infinitesimals, Jeans simply made a proportionality correction in 1905.

## Archive for December, 2014

### 290(5): Mathematical Background of Higher Order Infinitesimal Integrals

Wednesday, December 31st, 2014### Happy New Year to Horst Eckardt and Family

Wednesday, December 31st, 2014Good to hear of the visit. This village of Craig Cefn Parc was started as a drift mining village, and I gave some steam coal to Steve Bannister to take back to Utah to present to the examination board alongside his Thesis on the first industrial revolution. Robert Cheshire found some coal mining artifacts near Hendy Drift Mine. It was an entirely Welsh speaking village with a vigorous and famous culture – the hymn singing and so on. My grandfather the Head Deacon (Prof Ddiacon) composed hymns in this same room. he was also the Capel Meister and choir leader, brass band leader and so on. For a living he was a coal miner (Autobiography Volume One above my coat of arms on www.aias.us). This house is to be preserved under the Newlands Family Trust as you know. This famous and indigenous culture unique to Wales has been completely destroyed in Craig Cefn Parc by closures of industry by remote non existent government, so I would say that things here can only get better, and I have posted many proposals on this blog. The older people loath what is happening. I founded the Newlands Family Trust to try to reverse the disastrous decline in values, language, sense of community and culture. I would say that investment is needed to counter the sharp rise in lawlessness and anti social conduct and to reinvigorate the culture, to protect the chapels and to make all the schools in Mawr teach in the Welsh language to all children from age about three onwards. Thi swoudl be simple to implement by any real government. I have created my own industry in this house, so if everyone did this, there would be no problem of unemployment and idle abusive wasters becoming vandals. The late Head Deacon, Cen Williams, greatly enjoyed listening to you playing the great Bach D Minor work on the organ of Elim, even though some stops didn’t work. One of the aims of the Trust would be to buy back his house (the one next door), put it back in to its pristine condition and to try to heavily protect the Mans, the Head Deacon’s house and the chapels. Maybe we can team up with the Llangiwg Community. It is not a good idea to throw our own culture in Wales into skips. They would not do that with the works of J. S. Bach, or Beethoven in Vienna. Some of the Bavarian churches like Vierzenheiligen are masterpeices of art, and they would not be thrown into skips or be lived in as houses – a ghastly desecration that should be outlawed.

In a message dated 30/12/2014 18:47:40 GMT Standard Time, writes:

I visited my mother near to Göttingen over Christmas, the village is even smaller than yours. Some peopled complained about too few investments into rural infrastructure by the community, may be similar as at your site.

I will try to find a mathematician as soon as I am back to work at 7th Jan.Horst

Am 30.12.2014 um 18:39 schrieb EMyrone:

Welcome back, I trust you had a nice Christmas. I think that both methods can be tried, the (d omega)^n to dx and the multiple integral method, where (d omega) squared = d omega d omega and (d omega) cubed = d omega d omega d omega. This is analogous to dV = dxdydz . If you know an unbiased mathematician by all means invite him to look at the mathematics.

To: EMyrone

Sent: 30/12/2014 16:30:35 GMT Standard Time

Subj: Re: 290(4): The Correct Derivation of the Stefan Boltzmann LawI am back now from my holiday.

I went through the notes for paper 290 today. Nearly unbelievable that the Stefan Boltzmann law contains terms that have been overlooked so far. I am not sure how powers of the differential integration interval d omega have to be treated. One argument would be that differential calculus is linear in the infinitesimal limit (see definition of the derivative), therefore higher orders of d omega can be neglected.

Another approach would be to make a variable substitution to obtain a linear termd omega^n –> dx

Then omega and E have to be transformed to functions of x to abtain an integrand like

omega(x) E(x) dx.

This is the standard way of handling this to my opinion. To be honest, I am not very convinced that powers of d omega can be handled as n-fold integrals. But I do not know a comparable case in physics. Perhaps a mathematician could help here.

Horst

Am 30.12.2014 um 11:08 schrieb EMyrone:

This is given in Eq. (2), which must be evaluated numerically. However, it is easily shown by hand in the high temperature or low frequency limit (5) that the obsolete derivation is completely wrong. Therefore the law could not have been tested experimentally with great precision. Incorrect mathematics cannot be tested experimentally with great precision. The error made by Lord Rayleigh and Sir James Jeans was to assume that the higher order infinitesimals (d omega) squared and (d omega) cubed can be neglected in the calculation of (omega + d omega)) cubed – omega cubed. As shown in this note they cannot be neglected at all because one is double integrated and the second is triple integrated.

### Daily Report 29/12/14

Wednesday, December 31st, 2014There were 5,429 files downloaded from 472 reading sessions, many due to the Rense Radio broadcast of 29/12/14 Pacific time, 30/12/14 GMT. Main spiders baidu, MSN, google and yahoo. Auto1 494, Auto2 139, F3(Sp) 213, UFT88 131, Book of Scientometrics 155, Englynion 96, CEFE 52, Engineering Model 65, Llais 48, Evans Equations 70 (numerous Spanish), Autobiography Sonnets 32 to date in December 2014. Calgary Dream Centre for the Disadvantaged, Canada Definitive proofs, introduction equation flowcharts, Autobiography volume one; William S. Richardson School of Law University of Hawaii general; Indian Institute for Mathematical Sciences UFT214; United States National Archives general; Chicago Public Library AIAS Staff. Intense interest all sectors, updated usage file attached for December 2014.

## Usage Statistics for aias.us aias.us

** Summary Period: December 2014 – URL
Generated 30-Dec-2014 11:47 EST
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### Discussion of Note 290(4)

Tuesday, December 30th, 2014Welcome back, I trust you had a nice Christmas. I think that both methods can be tried, the (d omega)^n to dx and the multiple integral method, where (d omega) squared = d omega d omega and (d omega) cubed = d omega d omega d omega. This is analogous to dV = dxdydz . If you know an unbiased mathematician by all means invite him to look at the mathematics.

To: EMyrone@aol.com

Sent: 30/12/2014 16:30:35 GMT Standard Time

Subj: Re: 290(4): The Correct Derivation of the Stefan Boltzmann LawI am back now from my holiday.

I went through the notes for paper 290 today. Nearly unbelievable that the Stefan Boltzmann law contains terms that have been overlooked so far. I am not sure how powers of the differential integration interval d omega have to be treated. One argument would be that differential calculus is linear in the infinitesimal limit (see definition of the derivative), therefore higher orders of d omega can be neglected.

Another approach would be to make a variable substitution to obtain a linear termd omega^n –> dx

Then omega and E have to be transformed to functions of x to abtain an integrand like

omega(x) E(x) dx.

This is the standard way of handling this to my opinion. To be honest, I am not very convinced that powers of d omega can be handled as n-fold integrals. But I do not know a comparable case in physics. Perhaps a mathematician could help here.

Horst

Am 30.12.2014 um 11:08 schrieb EMyrone:

This is given in Eq. (2), which must be evaluated numerically. However, it is easily shown by hand in the high temperature or low frequency limit (5) that the obsolete derivation is completely wrong. Therefore the law could not have been tested experimentally with great precision. Incorrect mathematics cannot be tested experimentally with great precision. The error made by Lord Rayleigh and Sir James Jeans was to assume that the higher order infinitesimals (d omega) squared and (d omega) cubed can be neglected in the calculation of (omega + d omega)) cubed – omega cubed. As shown in this note they cannot be neglected at all because one is double integrated and the second is triple integrated.

### The Role of B(3) in the Corrected Stefan Boltzmann Law

Tuesday, December 30th, 2014The question is whether B(3) adds a third state of polarization, and whether it is an oscillator. The B(3) field adds a classical energy density:

(E / V) (B(3)) = B(3) dot B(3)* / mu0

so adds an intensity:

I = (c / muo) B(3) dot B(3)*

to the usual intensity:

I = epso (E(1) dot E(1)* + E(2) dot E(2)*) + (B(1) dot B(1)* + B(2) dot B(2)*) / muo

so B(3) also changes the proportionality constant in the Stefan Boltzmann law if it is incorporated in this way. However B(3) does not have a phase so is not an oscillator as defined by Rayleigh. The only contribution of Jeans was to adjust a proportionality constant.

### 290(4): The Correct Derivation of the Stefan Boltzmann Law

Tuesday, December 30th, 2014This is given in Eq. (2), which must be evaluated numerically. However, it is easily shown by hand in the high temperature or low frequency limit (5) that the obsolete derivation is completely wrong. Therefore the law could not have been tested experimentally with great precision. Incorrect mathematics cannot be tested experimentally with great precision. The error made by Lord Rayleigh and Sir James Jeans was to assume that the higher order infinitesimals (d omega) squared and (d omega) cubed can be neglected in the calculation of (omega + d omega)) cubed – omega cubed. As shown in this note they cannot be neglected at all because one is double integrated and the second is triple integrated.

### Daily Report 28/12/14

Tuesday, December 30th, 2014There were 1,611 files downloaded or hits from 367 distinct visits or reading sessions, main spiders from baidu, google, MSN and yandex. Auto1 467, Auto2 122, F3(Sp) 208, Book of Scientometrics 160, UFT88 125, Englynion 94, Engineering Model 57, CEFE 50, Llais 46, Autobiography Sonnets 32 to date in December 2014. Earth Sciences and Geography Keele University UFT140; St Clements Electrical Services Family History. Intense interest all sectors, updated usage file attached for December 2014.

## Usage Statistics for aias.us aias.us

** Summary Period: December 2014 – URL
Generated 29-Dec-2014 11:47 EST
**

### 290(3) : Refutation of the Rayleigh Jeans Desnity of States

Monday, December 29th, 2014This is a straightforward refutation of the Rayleigh Jeans density of states and therefore of the claim that the Stefan Boltzmann law is derived from the Planck distribution, a cornerstone of quantum theory. The correct density of states is the sum of terms (19) involving single, double and triple integrals. Probably these will have to be worked out with a numerical integrator but Maxima may be able to evaluate them. The source of this error is the arbitrary neglect of the second and third terms in Eq. (12), the second and third order infinitesimal terms. There is no reason to assume that the second and third terms in Eq. (19) are smaller than the first term, the usual term from the Rayleigh Jeans density of states. This looks like another very loud howler, so the whole theory disintegrates. This claim of mine in this note can now be checked by computer and by hand by co author Horst Eckardt when he returns from holidays. The other AIAS Fellows and Professors are requested to look over this note carefully to see if they can find any errors of concept or algebra. If AIAS is agreed on this note, then the claims of precise experimental verification of the Stefan Boltzmann law (10) cannot be true. This is an exact parallel to the collapse of the Einstein field equation. Claims to its precise experimental verification cannot be true – the Einstein theory is geometrically incorrect and collapses completely when tested experimentally in galaxies. This has been known for almost fifty years. So standard physics is in danger of being dismissed by the general public as a meaningless cover up. That would be a pity because there is a lot of good physics. The tiny minority of dogmatists that still rejects ECE does the subject much harm.

### Some Ideas for the Second Rense Program Broadcast

Monday, December 29th, 2014It will be very interesting. My contact phone number is +44 1792 446088 , same as for the first interview. The main points might consist of a discussion of the discovery of the B(3) field at Cornell Theory Center in late 1991. This was a simple theory meant at first to explain magnetization by circularly polarized electromagnetic radiation – the inverse Faraday effect. In early 1993 Jean-Pierre Vigier pointed out that the idea of a longitudinal B(3) meant that the mass of the photon is not zero, the point of view of the Einstein / de Broglie School that developed at the Solvay Conference of 1927. The idea of photon mass led to the de Broglie wave particle dualism, and shortly later to the Schroedinger equation and Dirac equation in the golden age of physics. The idea of finite photon mass was suggested by Henri Poincare in 1905. At about the same time Albert Einstein suggested zero photon mass, an idea that led to the standard physics, now made obsolete by ECE theory. Einstein invited Vigier to become his assistant at Princeton, Vigier co aouthored four monographs with myself, the first four volumes of “The Enigmatic Photon”. In 2003 B(3) led to the Einstein Cartan Evans unified field theory of physics (ECE theory), which has become “The Post Einstein Paradigm Shift” in the words of the eminent editor, Alwyn van der Merwe. The ECE theory has produced two hundred and eighty nine scientific papers since March 2003, (UFT section of www.aias.us) and sets out to cover all aspects of physics, chemistry and engineering. The ECE theory gives a plausible explanation for new sources of energy such as low energy nuclear reactors, and energy from sapcetime, (www.upitec.org, www.et3m.net, www.atomicprecision.com) but has also made many other fundamental discoveries (www.aias.us). All 289 papers are read at all the best univeristies and similar institutes all over the world and are all in Google Scholar. About 160 of them have been translated into Spanish. I carried out a survey yesterday and posted it on this blog. There is no doubt the the old standard model is obsolete, many of it sideas have been refuted logically or experimentally: Big Bang, black holes, Higgs boson, the Heisenberg Uncertainty Principle, the Einstein field equation, the Maxwell Heaviside equations and much more. Some of the old physics still remains intact, notably the Schroedinger equation and a lot of classical physics. Therefore B(3) and photon mass changes the whole of physics. The attached feedback summaries give an idea of the vast readership of ECE theory.

n a message dated 29/12/2014 08:34:16 GMT Standard Time, sightings@mindspring.com writes:

Thank you, Myron.

Talk to you tomorrow night, 9 pm my time on the 29th….5 am your time on Dec 30.

Please send your contact phone number and

some specific talking points you’d like to cover.All good wishes…

Jeff

On Dec 28, 2014, at 9:56 PM, EMyrone wrote:

Jeff Rense,

California,

U. S. A.,Best Wishes to you too for a Happy New Year! I will be happy to do the interview tomorrow morning at 5.00 a.m. my time, on 30th Dec., my date,, 9 a.m. your time, 29th Dec. your date in California. I enjoyed the first program and thanks for inviting me.

In a message dated 28/12/2014 23:28:35 GMT Standard Time:

Hello Myron…

Best wishes for the Holiday Season to you.

I am expecting you tomorrow night, my Monday, 9-10, pm Pacific.

THERE IS AN OPTION… I can put you on my Wednesday, same time, which

would be your Thursday, New Years MORNING.Which would you rather do?

On Oct 2, 2014, at 1:34 AM, EMyrone wrote:

Background for Jeff Rense

I understand that I have been given permission by Jeff Rense and Michael Jackson to post this edited version of the radio interview on my blog on www.aisa.us and if asked I have agreed to an hour interview. Michael Jackson did well in presenting the ECE theory. Jeff Rense asked for a book I may have written on the topic. Before reading the books it is best to listen to some of the hundred broadcasts by Robert Cheshire of my essays on www.aias.us. These do not have any equations and have been heard intensely around the world for about four years. The books are all listed on the home page of www.aias.us. My autobiography volumes one and two are available above my coat of arms on www.aias.us and I am listed in thirty one editions of Marquis Who’s Who in America, World, Science and Engineering. I have produced over a thousand books, reviews and papers in my career, all in Google Scholar, many translated into Spanish by Alex Hill, and I am a Civil List Pensioner appointed by the Prime Minister on behalf of Queen Elizabeth, naturalized a U. S. dual Citizen at Cornell in 2000. The Civil List Pension is a token of personal gratitude of the British Head of State (currently Queen Elizabeth II) and the countries of Britain for distinguished service to science. It is something similar to Congressional Medal of Honor, an appointment and honour akin to the British Order of Merit and Companion of Honour. I agree that burning petroleum will lead to disaster. It is needed for petrochemicals and needs to be conserved. The Alex Hill company is producing spacetime energy devices and selling them routinely to Fortune Fifty Companies (www.et3m.net, www.upitec.org, www.atomicprecision.com, www.aias.us). The ECE theory has been read an estimated forty million times in about eleven years since inception in essentially all the best universities, institutes, government departments and large corporations in essentially all the countries of the world. We know this from very detailed feedback monitored daily over more than a decade. There are two hundred and seventy two scientific papers on the subject (UFT Section of www.aias.us). Low energy nuclear reactors are already available (LENR). The Einstein theory has actually been heavily criticised by many scholars for a hundred years. As Michael Jackson points out, one of the basic properties of all geometry, torsion, was unknown in the Einstein era (1905 – 1915), and in consequence his famous field equation is meaningless. ECE sets out to improve the Einstein theory, in its era of course it became famous, but it is deeply flawed. It collapses completely in whirlpool galaxies. This is well known to scholars. The general public does not understand the flaws in the Einstein theory. The entire ECE theory is based on the equally well known and completely accepted geometry of the great mathematician, Elie Cartan. There are currently two schools of thought, ECE and the obsolete standard physics. ECE has inferred a new source of energy from spacetime, and this energy is being used all the time as mentioned already. The unification of physics is achieved straightforwardly with Cartan geometry, and also the unification of quantum mechanics and general relativity. The B(3) and ECE theories have been nominated several times for a Nobel Prize, Wolf Prize, Milner Prize and Priestley Medal. The standard model has been influential in the award of funding, jobs and prizes but in Britain its funding has been cut by a half in the past decade becaue it is known to be riddled with errors and is widely regarded as non Baconian. Obviously it is not going to award prizes to the rival ECE theory, but many nominations come in form the ECE School. I am deeply honoured by these nominations, and I am grateful for them. Many parts of standard physics cannot be tested experimentally, because it has far too many adjustable parameters. String theory has recently fallen apart (its predictions disproved at CERN) and dark matter has been refuted experimentally. Hawking has admitted that black holes do not exist. Big Bang has been refuted many times over. So that leaves ECE as the only plausible theory of physics. You would never know this from the media. I resigned in protest from UNCC and that was twenty years ago. I was appointed Civil List Pensioner by Crown and Parliament ten years after UNCC, whch was subjected to intense international criticism. This is all posted on www.aias.us. I was naturalized a U. S. Dual Citizen five years after UNCC. Wikipedia is controlled by the rival standard physics, and it is no friend of ECE physics. Marquis on the other hand is rigorously imaprtial. It is generally regarded as the leading reference vehicle, founded by Mr. Marquis in Chicago in 1899.

Myron Evans

(Dr. M .W. Evans, Armiger (Membre of the Gentry or UNtitled Nobility in Britain), Civil List Pensioner, D. Sc., Ph. D., B. Sc. (Wales)

AIAS President

www.aias.us<2014Sep30RenseECETheory.mp3>

=

=

### 290(2): Intensity and Number Density of Photons, Monochromatic Theory

Monday, December 29th, 2014This note develops the Evans Morris effects in terms of beam intensity (watts per square metre) and number density of photons (number of photons in a given volume of radiation). The intensity theory:

I = I1 + I2

is the most complete theory because it uses a Planck distribution over many photons for the incident, refracted and reflected beams as in Note 290(1). In Note 290(1) there should be a factor (6 pi squared) in the denominators of Eqs. (6) and (8) of that note. The intensity theory leads to Eq. (15) of this note, which must be solved as in Note 290(1) with the momentum theory. If it is assumed that the number of photons per unit volume of the incident beam is equal to the sum of the number density of photons in the refracted and reflected beams, then Eq. (14) of this not results. This could also be solved with the momentum conservation equation of Note 270(1). This note also explains why the Compton theory is applicable at gamma ray frequencies without Planck averaging and density of states theory. The reason is that the volume of radiation at gamma ray frequencies is comparable to the classical volume of the electron. At visible and microwave frequencies the volume of radiation is many orders of magnitude bigger than that of the classical electron.