Sylwester's 'Everlasting theory'

http://www.claymath.org/millennium/Yang-Mills_Theory/

We can read as follows: “Yang-Mills EXISTENCE AND Mass Gap: Prove that for any compact simple gauge group G, quantum Yang-Mills theory of R^4 exists and has a mass gap delta>0.”

In the original paper cited by you written by Witten and Jaffe we can read as follows (page 6): “Yang-Mills EXISTENCE AND Mass Gap. EXISTENCE includes establishing axiomatic properties at least as strong as those cited in [45, 35]”.

Can you see that there are two problems?
1.
The EXISTENCE of the Yang-Mills i.e. you as well must prove that the QCD confines at low energy!
2.
…AND Mass Gap.
Thanks for proving my point again. You think 'Yang-Mills' is 'prove that QCD confines at low energy'? 'Yang Mills' is the name for a particular general class of gauge theories, named after a Professor Yang and a Professor Mills. Yang Mills theories cover a huge range of gauge theories, some of which have confinement and some of which do not. For example, a trivial non-interacting gauge theory can fall into the Yang Mills category but it doesn't confine. The question of which gauge theories exhibit confinement is of great interest to mathematical physicists.

Since you like using wiki why didn't you look up their Yang-Mills theory page? You'd then have seen it is defined as an SU(N) gauge theory. Of course you don't know what that means but even to someone as clueless as you it should be obvious that isn't synonymous with a confining theory. Electroweak theory is an SU(2) Yang-Mills theory, yet it doesn't show confinement. QCD is an example of an SU(3) gauge theory. It isn't the only possible SU(3) gauge theory, it's a particular one.

The question of how to define and construct properly a Yang Mills gauge theory from a set of axioms is an open problem, which is what the document referred to. Once you then have defined axiomatically a Yang Mills gauge theory you can explore a particular example of such a theory, namely QCD, and then try to show whether it confines or not from the axioms. Witten and Jaffe give examples of how one might approach the problem, using things like the large N expansion 't Hooft popularised and which forms the core of the gravity/gauge duality.

Thanks for showing that despite all your assertions and proclamations you never fail to put your foot in it. You know you don't know this stuff, you know you have never studied it, you know you cannot do a single calculation within any of these quantum field theories so why do you persist in trying to pretend you understand them in any way, shape or form? At best all you do is run to Wikipedia and try to grasp the layperson explanations there. You manage to screw that up too.

You wrote something about my IQ. Now all can see that your IQ is much, much lower, the IQ of brucep as well.
Actually I didn't say anything about your IQ in a negative way. I commented that Witten has more published papers than you have IQ points. Witten actually has hundreds of published papers, with an H index above 100 (so he has at least 100 papers each with at least 100 citations, giving 10,000 citations!), so I could make such a statement to anyone. Of course the reason I said it was that I wished to suggest you have a small IQ, even if what I said didn't literately imply it. Given your lack of knowledge about such people as Witten I was confident you'd take it as a slight, which you indeed did. I do like how predictable you are.

AlphaNumeric, at first you did not write the link because the articles prove that you are not right. Just you were bluffing writing about the Millennium Prize Problem. The Mass Gap Problem is not sufficient.
You claimed the $1 million prize was for confinement. You were wrong, as the link demonstrates. I repeat : check ****ing mate.
 
You do not understand the problem and you proved that you still do not understand what you are reading, brucep as well.
On the main page of the Clay Mathematics Institute we can read as follows. The title is “Yang-Mills AND Mass Gap” and we can read “Progress in establishing the EXISTENCE of the Yang-Mills theory AND a mass gap….

On the main page is the link to the article titled “Report on the Status of the Yang-Mills Millennium Prize Problem”. See

http://www.claymath.org/millennium/Yang-Mills_Theory/

We can read as follows: “Yang-Mills EXISTENCE AND Mass Gap: Prove that for any compact simple gauge group G, quantum Yang-Mills theory of R^4 exists and has a mass gap delta>0.”

In the original paper cited by you written by Witten and Jaffe we can read as follows (page 6): “Yang-Mills EXISTENCE AND Mass Gap. EXISTENCE includes establishing axiomatic properties at least as strong as those cited in [45, 35]”.

Can you see that there are two problems?
1.
The EXISTENCE of the Yang-Mills i.e. you as well must prove that the QCD confines at low energy!
2.
…AND Mass Gap.

You wrote something about my IQ. Now all can see that your IQ is much, much lower, the IQ of brucep as well. AlphaNumeric, at first you did not write the link because the articles prove that you are not right. Just you were bluffing writing about the Millennium Prize Problem. The Mass Gap Problem is not sufficient.
Maybe your buddy 'Bugs Bunny' can show you how to derive the relativistic component of 'Venus' orbit?
 
Thanks for proving my point again. You think 'Yang-Mills' is 'prove that QCD confines at low energy'? 'Yang Mills' is the name for a particular general class of gauge theories, named after a Professor Yang and a Professor Mills. Yang Mills theories cover a huge range of gauge theories, some of which have confinement and some of which do not. For example, a trivial non-interacting gauge theory can fall into the Yang Mills category but it doesn't confine. The question of which gauge theories exhibit confinement is of great interest to mathematical physicists.

Since you like using wiki why didn't you look up their Yang-Mills theory page? You'd then have seen it is defined as an SU(N) gauge theory. Of course you don't know what that means but even to someone as clueless as you it should be obvious that isn't synonymous with a confining theory. Electroweak theory is an SU(2) Yang-Mills theory, yet it doesn't show confinement. QCD is an example of an SU(3) gauge theory. It isn't the only possible SU(3) gauge theory, it's a particular one.

The question of how to define and construct properly a Yang Mills gauge theory from a set of axioms is an open problem, which is what the document referred to. Once you then have defined axiomatically a Yang Mills gauge theory you can explore a particular example of such a theory, namely QCD, and then try to show whether it confines or not from the axioms. Witten and Jaffe give examples of how one might approach the problem, using things like the large N expansion 't Hooft popularised and which forms the core of the gravity/gauge duality.


AlphaNumeric, you indeed are very weak thinker. You write the nonsense or the obvious things all can find in Wikipedia. In your last post you almost rewrote the Wikipedia.

You do not understand that you at first write a statement I never wrote and next you prove that I am not right.

I wrote exactly as follows.
“Yang-Mills EXISTENCE AND Mass Gap. EXISTENCE includes establishing axiomatic properties at least as strong as those cited in [45, 35]”.
Now you claim that you wrote it as the first! Incredible.
Next I wrote following sentence.
“You must prove the EXISTENCE of the Yang-Mills i.e. you as well must prove that the QCD confines at low energy!”
All can see that “axiomatic properties at least as strong as those cited in [45, 35]” does not mean the SAME as “to prove that the QCD confines at low energy”. BUT I WROTE IT! What it means? It means that I know that each theory applying the Yang-Mills Theory must prove that this theory ACTS CORRECTLY in whole spectrum of energy. Do you understand this obvious statement? We discussed the asymptotic freedom, confinement and mass gap in the QCD which applies the Yang-Mills Theory and in my Everlasting Theory. My theory shows that there are the gluon fields as it is in the Yang-Mills Theory. We know that in the Yang-Mills Theory appears the gluon propagator. In this paper

J. Phys. G: Nucl. Part. Phys. 38 (2011) 045003 (17pp),

O Oliveira and P Bicudo find that “the infrared data (low energy) can be associated with a massive propagator up to momenta ~ 500 MeV, with a CONSTANT GLUON MASS of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis.”
On the other hand, there are the two states of the core of baryons in my theory. The masses of the states are 727.4 MeV and 724.8 MeV and they are the entangled (torus) and confined (the ball in the centre) ZERO-energy gluons. My theory shows how should look the Yang-Mills theory in the non-perturbative regime. I proved that my theory is obligatory for whole spectrum of energies and confines at low energies AS WELL. There appear the mass gaps as well. For example, the mass distance of the two states of the core of baryons leads indirectly to the mass of the sham Higgs boson (125 GeV) just due to the MY confinement. It means that I proved that the SPECIFIC and very simple model presented in the Everlasting Theory proves EXISTENCE of the Yang-Mills and mass gap.

So once more: Each theory which applies Yang-Mills Theory (i.e. QCD, my theory and so on) must prove that the theory acts correctly in whole spectrum of energy so must confine at low energy as well. My theory shows how should look the Yang-Mills in the non-perturbative regime.

AlphaNumeric, can you stop to write the obvious for all things which for you are the EUREKA? I would not to violate the Forum rules but your IQ is indeed very low. Do you know that the gauge theories which do not confine at low energies you can throw on the scientific scrap-heap immediately? They are the pure mathematics not realized by the nature.
 
Maybe your buddy 'Bugs Bunny' can show you how to derive the relativistic component of 'Venus' orbit?

Brucep, incredible, you started to think!

At first I should explain on base of my Everlasting Theory why Lifshitz and Landau claimed that sometimes same laws of physics do not look the same in all reference frames. The Principle of General Covariance applied in the General Theory of Relativity is correct only partially. For strong interactions relativistic masses of sources and carriers of strong interactions do not transform the same. The strong interactions behave as if there were simultaneously two different reference frames. Within the Everlasting Theory I proved that we must introduce the term “dominating gravitational gradient”. For the strong interactions the GR is correct when all reference frames have the same speed or are in the rest in the dominating gravitational field. To unify the Quantum Physics with the General Theory of Relativity we need more fundamental theory than these two theories i.e. we need the arithmetic Everlasting Theory.

The GR is very simple when reference system is properly chosen. See, for example, Chapter titled “Foundations of General Theory of Relativity” in which I calculated the curving of light in gravitational field of the Sun. The theoretical result obtained within my theory is the same as in the GR, i.e. 1.75 seconds of arc (page 115, formula 263), because in both derivations appears the gravitational radius of the Sun.

And now the answer to your question
My theory shows that for the strong fields of baryons is obligatory the Titius-Bode law for the strong interactions which is some analog to the Titius-Bode formula for planets. The Titius-Bode formula looks as follows R = A + dB, where for the strong interactions is A/B = 1.3898 (pages 16-18) whereas for gravitational black holes I obtained A/B = 1.394 (pages 68 and 69). The states d = 0 and 1 are placed below the Schwarzschild surface for the strong interactions (the core of baryons is the BLACK HOLE IN RESPECT OF THE STRONG INTERACTIONS) and for the gravitational interactions of the gravitational black holes. The orbits of Mercury and Venus are the analogs to the d = 0 and 1 states. Under the Schwarzschild surface, there is common the entanglement between the Einstein spacetime component. Such entangled (not confined) field arose during the evolution of the solar system and spreads out from the orbit of Mercury to distance two times greater than the radius of the orbit of Mercury i.e. the orbit of Venus is inside this field. This entangled field arose due to the radiation masses.
We can see that there was a resonance between the relativistic phenomena described within the GR and the phenomena described within my theory FOR THE FIRST PLANET, i.e. MERCURY i.e. for d = 0. It is the reason why within the GR and my theory we obtain practically the same result for perihelion precession of Mercury (575 = 532 + 43 and 573 arc seconds whereas the observational result is 574.10±0.65 arc seconds per century).
Why within my theory we obtain correct result for Venus (204 arc seconds per century) whereas we still cannot do it within the GR? And my answer is as follows. The entangled field dominates for Venus in such way that we can neglect the relativistic correction.

So once more
Mercury – the resonance of the two different phenomena.
Venus – the entangled field dominates.
Other planets – the GR is obligatory.

Within the GR for the small relativistic correction, we obtain:
angle = 3(pi)rrmmcc/(2JJ) where r is the gravitational radius of the Sun r = 2GM/(cc) whereas the J is the angular momentum of a planet.
 
I wrote exactly as follows.
“Yang-Mills EXISTENCE AND Mass Gap. EXISTENCE includes establishing axiomatic properties at least as strong as those cited in [45, 35]”.
Now you claim that you wrote it as the first! Incredible.
Next I wrote following sentence.
“You must prove the EXISTENCE of the Yang-Mills i.e. you as well must prove that the QCD confines at low energy!”
All can see that “axiomatic properties at least as strong as those cited in [45, 35]” does not mean the SAME as “to prove that the QCD confines at low energy”. BUT I WROTE IT! What it means? It means that I know that each theory applying the Yang-Mills Theory must prove that this theory ACTS CORRECTLY in whole spectrum of energy. Do you understand this obvious statement? We discussed the asymptotic freedom, confinement and mass gap in the QCD which applies the Yang-Mills Theory and in my Everlasting Theory. My theory shows that there are the gluon fields as it is in the Yang-Mills Theory. We know that in the Yang-Mills Theory appears the gluon propagator. In this paper

J. Phys. G: Nucl. Part. Phys. 38 (2011) 045003 (17pp),

O Oliveira and P Bicudo find that “the infrared data (low energy) can be associated with a massive propagator up to momenta ~ 500 MeV, with a CONSTANT GLUON MASS of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis.”
On the other hand, there are the two states of the core of baryons in my theory. The masses of the states are 727.4 MeV and 724.8 MeV and they are the entangled (torus) and confined (the ball in the centre) ZERO-energy gluons. My theory shows how should look the Yang-Mills theory in the non-perturbative regime. I proved that my theory is obligatory for whole spectrum of energies and confines at low energies AS WELL. There appear the mass gaps as well. For example, the mass distance of the two states of the core of baryons leads indirectly to the mass of the sham Higgs boson (125 GeV) just due to the MY confinement. It means that I proved that the SPECIFIC and very simple model presented in the Everlasting Theory proves EXISTENCE of the Yang-Mills and mass gap.
And you once again screw it up. The 'existence' part of the Millenium prize is not about what physically QCD does but rather whether there actually exists a gauge theory with an SU(N) gauge group which satisfies the axioms given in references 35 and 45. You're misunderstanding it, thinking that the 'existence' refers to the physicality of QCD. It doesn't.

No one knows whether or not it is actually possible to construct a Yang Mills gauge theory from the axioms given in the references. No one has ever done it, instead we all just start at the definition of a Yang Mills gauge theory and assume they follow from the field theoretic axioms. For someone to win the prize they must show that it's possible to construct the Yang Mills theory, ie a gauge theory with a compact SU(N) gauge symmetry, from the stated axioms and then show it possesses a mass gap. This has nothing to do with how nucleons really behave in the real world, it has nothing to do with showing QCD is an accurate description of the real world, it has nothing to do with showing QCD does what is claimed at all energy levels. It is about showing you can construct a general compact SU(N) gauge theory from a particular set of axioms and then go on to show it must possess a mass gap. Once that is done you win $1million and then you can go on to try to work out what are the conditions for confinement in such Yang Mills theories.

You interpreted the statement "You must prove the EXISTENCE of the Yang-Mills" to be equivalent to " you as well must prove that the QCD confines at low energy" but that isn't the case. Existence in this regard is an abstract mathematical construction, do the field theoretic axioms allow for the step by step construction of Yang Mills theory? Whether a particular SU(3) case, which we call QCD, accurately models nucleon behaviours across all energy scales is an entirely separate matter. Most Yang Mills theories are not physically valid but that is irrelevant to the prize. Whether or not a theory confines is irrelevant to the prize, particularly the existence part. It's well known there exist non-confining Yang Mills theories, the electroweak force is an example of that. Showing QCD confines wouldn't win the prize. Neither would showing it doesn't. Showing QCD is an accurate model of nucleon physics across all energy scales wouldn't win the prize. Neither would disproving it. Proving not all Yang Mills theories confine wouldn't win the prize. Neither would proving they all do (which is impossible since they don't all confine).

I've explained this to you several times now and I've given you the original definition of the problem. It is clear that you are mistaken about the prize being about showing confinement, particularly confinement in QCD. It's there in black and white, the original authors clearly state that considering confinement is something for after the prize is won. If the prize required showing confinement why would they say that confinement is still an open question after someone has won the prize? Come on, even you should grasp what that means.

Do you know that the gauge theories which do not confine at low energies you can throw on the scientific scrap-heap immediately? They are the pure mathematics not realized by the nature.
You again show how little you know and how little you learn because I've actually given explicit examples of physically accurate models which don't confine, namely the electroweak force. It's an SU(2) gauge theory, so falls under the remit of Yang Mills theory, but it doesn't confine at low energy. In fact at low energy it reduces to quantum electrodynamics (thanks to symmetry breaking). QED is the most accurately tested physical model in human history. It does not exhibit confinement at low energy. You say that this would mean it should be 'throw[n] on the scientific scrap-heap immediately, they are the pure mathematics not realised by the nature". Electromagnetism doesn't confine a low energy, a fact readily seen by anyone because we're able to ionise atoms and molecules. If electromagnetism confined at low energy it would be impossible to form ions as ions are non-confined electromagnetic charges. If QED confined we'd not exist because molecules couldn't form ions, essential for chemical processes, particularly in biological systems. Modern technology is centred around electronics, which rely on the ability to isolate electromagnetic charges and control them, ie the flow of electrons in circuits. Should I be surprised that the most well understood and most accurately tested physical model in history is which you don't realise is a counter example to your assertions? Probably not, you make it abundantly clear you know nothing of mainstream science.

By the way, QED in 2+1 dimensions is confining and even has a massive photon. Should we discard that into the scientific scrap heap too? Plenty of people might say yes, given space-time is 3+1 dimensional and photons are massless and electromagnetism doesn't confine but in fact it's finding applications in condensed matter physics and the modelling of graphene. Amazing what a bit of open minded intellectual exploration can do, you should try it some time. Unfortunately you seem incapable of it.
 
AlphaNumeric, my theory (this arithmetic theory is more fundamental than the GR and Quantum Physics) shows that nobody will be able to prove the Yang-Mills existence without describing CONFINEMENT AS A PHENOMENON, not as a part of the QCD. Today only I understand the Yang-Mills-confinement-mass-gaps-asymptotic-freedom relations.

The confinement, mass-gaps and asymptotic freedom described within my theory are the FOUNDATIONS of the Yang-Mills acting CORRECTLY.

So, AlphaNumeric, …..but RATHER whether….. as you wrote.
 
AlphaNumeric, my theory (it arithmetic theory is more fundamental than the GR and Quantum Physics) shows that nobody will able to prove the Yang-Mills existence without describing CONFINEMENT AS A PHENOMENON, not as a part of the QCD. Today only I understand the Yang-Mills-confinement-mass-gaps-asymptotic-freedom relations.

The confinement, mass-gaps and asymptotic freedom described within my theory are the FOUNDATIONS of the Yang-Mills acting CORRECTLY.

So, AlphaNumeric, …..but RATHER whether….. as you wrote.
You'll be just as clueless tomorrow as you were today and the day before. Troll.
 
AlphaNumeric, my theory (this arithmetic theory is more fundamental than the GR and Quantum Physics) shows that nobody will be able to prove the Yang-Mills existence without describing CONFINEMENT AS A PHENOMENON, not as a part of the QCD. Today only I understand the Yang-Mills-confinement-mass-gaps-asymptotic-freedom relations.
What a complete and utter body swerve. You've gone from arguing whether or not the prize is awarded for proving confinement to now just saying that your work shows they are equivalent. You were telling me I didn't understand QCD or confinement because I had supposedly misunderstood what the prize was for. Now you've been proven wrong and so you're changing from making assertions about the prize to making assertions about what your work says about the things the prize pertains to.

You obviously know you've been shown to be wrong, you wouldn't be trying to change the discussion away from the prize itself. Clear and obvious dishonesty on your part. If you aren't being dishonest then please answer this direct question. Do you accept that the Clay Institute prize for the Yang Mills existence and mass gap is not about confinement?

The confinement, mass-gaps and asymptotic freedom described within my theory are the FOUNDATIONS of the Yang-Mills acting CORRECTLY.
Given you didn't even understand what Yang Mills theory was (and you still don't) and you didn't understand what the 'existence' part of the prize was do you really think anyone is going to believe that your work leads to the axiomatic construction of Yang Mills theory, as is implied by your claim it is the foundation of the theory?

This is just like when you claimed your work explained M theory. You don't understand M theory or even quantum field theory (of which M theory is a generalisation) so claiming your work explains it is ridiculous. You must realise such approaches by you are blatantly laughable. You kept talking about 'effective M theory' when you didn't even know the correct meaning of 'effective', you took it to mean it's layperson meaning rather than its physicist meaning, yet again showing you don't know any quantum field theory.

You might be used to lying and making up nonsense about mainstream physics, as most people on most forums cannot distinguish between actual physics and nonsense, but that doesn't fly here, just like it didn't fly when you spam emailed 1600 physicists with your work. This constant barrage of lies and baseless assertions you make is getting you nowhere. When are you going to learn to convince actual scientists you need to be honest. Lying to physicists about their own work will only make them ignore you.

So, AlphaNumeric, …..but RATHER whether….. as you wrote.
I suppose you'd eventually just become incoherent, it was only a matter of time.
 
Brucep, incredible, you started to think!

At first I should explain on base of my Everlasting Theory why Lifshitz and Landau claimed that sometimes same laws of physics do not look the same in all reference frames. The Principle of General Covariance applied in the General Theory of Relativity is correct only partially. For strong interactions relativistic masses of sources and carriers of strong interactions do not transform the same. The strong interactions behave as if there were simultaneously two different reference frames. Within the Everlasting Theory I proved that we must introduce the term “dominating gravitational gradient”. For the strong interactions the GR is correct when all reference frames have the same speed or are in the rest in the dominating gravitational field. To unify the Quantum Physics with the General Theory of Relativity we need more fundamental theory than these two theories i.e. we need the arithmetic Everlasting Theory.

The GR is very simple when reference system is properly chosen. See, for example, Chapter titled “Foundations of General Theory of Relativity” in which I calculated the curving of light in gravitational field of the Sun. The theoretical result obtained within my theory is the same as in the GR, i.e. 1.75 seconds of arc (page 115, formula 263), because in both derivations appears the gravitational radius of the Sun.

And now the answer to your question
My theory shows that for the strong fields of baryons is obligatory the Titius-Bode law for the strong interactions which is some analog to the Titius-Bode formula for planets. The Titius-Bode formula looks as follows R = A + dB, where for the strong interactions is A/B = 1.3898 (pages 16-18) whereas for gravitational black holes I obtained A/B = 1.394 (pages 68 and 69). The states d = 0 and 1 are placed below the Schwarzschild surface for the strong interactions (the core of baryons is the BLACK HOLE IN RESPECT OF THE STRONG INTERACTIONS) and for the gravitational interactions of the gravitational black holes. The orbits of Mercury and Venus are the analogs to the d = 0 and 1 states. Under the Schwarzschild surface, there is common the entanglement between the Einstein spacetime component. Such entangled (not confined) field arose during the evolution of the solar system and spreads out from the orbit of Mercury to distance two times greater than the radius of the orbit of Mercury i.e. the orbit of Venus is inside this field. This entangled field arose due to the radiation masses.
We can see that there was a resonance between the relativistic phenomena described within the GR and the phenomena described within my theory FOR THE FIRST PLANET, i.e. MERCURY i.e. for d = 0. It is the reason why within the GR and my theory we obtain practically the same result for perihelion precession of Mercury (575 = 532 + 43 and 573 arc seconds whereas the observational result is 574.10±0.65 arc seconds per century).
Why within my theory we obtain correct result for Venus (204 arc seconds per century) whereas we still cannot do it within the GR? And my answer is as follows. The entangled field dominates for Venus in such way that we can neglect the relativistic correction.

So once more
Mercury – the resonance of the two different phenomena.
Venus – the entangled field dominates.
Other planets – the GR is obligatory.

Within the GR for the small relativistic correction, we obtain:
angle = 3(pi)rrmmcc/(2JJ) where r is the gravitational radius of the Sun r = 2GM/(cc) whereas the J is the angular momentum of a planet.
You said: "The entangled field dominates for Venus in such way that we can neglect the relativistic correction."
That's not a derivation it's just you spewing nonsense. This is the derivation from GR

You can derive the natural precession rate of Einstein orbits. All Einstein orbits naturally precess.

Start with the Schwarzschild metric [geometric units] setting theta at 0.

dTau^2 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2(dphi)^2

Substituting constants of geodesic motion E/m and L/m for dt and dphi

dt = [(E/m)/(1-2M/r)]dTau

dphi = [(L/m)/r^2]dTau

The solution relates squared values for radial motion (dr/dTau)^2, energy per unit mass (E/m)^2, and the effective potential per unit mass
(V/m)^2 = (1-2M/r)(1+[(L/m)^2/r^2]).

(dr/dTau)^2 = +/- (E/m)^2 - (1-2M/r)(1+[(L/m)^2/r^2])

Taking some license for the weak field and multiplying through by 1/2 after multiplying out the squared effective potential

1/2(dr/dTau)^2 = 1/2(E/m)^2 - [1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3]

setting (V/m)^2 = U/m

U/m = 1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3

1st derivative

d(U/m)/dr = M/r^2 - (L/m)^2/r^3 + 3M(L/m)^2/r^4

2nd derivative d'2(U/m)/dr'2 = rate of radial oscillation = w^2_r

w^2_r = M(r-6M)/r^3(r-3M)

Without writing down details the rate of angular velocity becomes

w^2_phi ~ (dphi/dTau)^2 = M/r^2(r-3M)

Both are really close in the weak field. We could approximate a large value for r and we would have Newton's result M/r^3 for both radial rate of oscillation and rate of angular velocity but we would end up with the wrong answer that GR orbits and Newton orbits are the same.

So

w^2_phi - w^2_r = 6M^2/r^3(r-3M)

This is the difference so we can find a factor * M/r^3 which closely approximates
6M^2/r^3(r-3M)

That factor is 6M/r

(6M/r)(M/r^3) = 6M^2/r^4

The last step is further license for the weak field taking the root of the factor and doing the approximation

(6M/r)^1/2 ~ 1/2(6M/r) = 3M/r

So a very close approximation for the rate of orbital precession, in the weak field [our solar system] is 3M/r. You can plug in numbers and get an answer that matches observation.

3M_Sun = 4431m
r_mean Mercury = 5.8x10^10 meters
415.1539069 times Mercury orbits the Sun in 100 Earth years
360 degrees per year
3600 arcseconds per degree
etc...

You said GR is only partially correct. Prove it beyond assertions. So far I have 0 respect for you or your theory since you can't use the theory to make any theoretical predictions beyond the unphysical nonsense that matter can exceed the invariant local coordinate speed of light. Which are probably more baseless assertions rather than theoretical predictions. AN said this has been going on for 48 years. You against the entire scientific community for 48 years. That's what crackpots do. For 48 years. Actually read some of your nonsense

"The strong interactions behave as if there were simultaneously two different reference frames." No wonder you're so confused.
I broke down and read your entire post. What a load of unadulterated hogwash. Landau and Lifshitz would think you're a nonsense machine.
 
AlphaNumeric, you rejected my explanation. OK.

You rejected the explanation in Wikipedia: “Proof that QCD confines at low energy is a mathematical problem of great relevance, and an award has been proposed by the Clay Mathematics Institute for whoever is ALSO able to show that the Yang–Mills theory has a mass gap and its existence.” and “It has already been well proven—at least at the level of rigor of theoretical physics BUT NOT THAT OF MATHEMATICAL PHYSICS—that the quantum Yang–Mills theory for a non-abelian Lie group exhibits a property known as confinement.” OK.

Can you stop the idiotic discussion?
 
You said: "The entangled field dominates for Venus in such way that we can neglect the relativistic correction."
That's not a derivation it's just you spewing nonsense. This is the derivation from GR

You said GR is only partially correct. Prove it beyond assertions. So far I have 0 respect for you or your theory since you can't use the theory to make any theoretical predictions beyond the unphysical nonsense that matter can exceed the invariant local coordinate speed of light.

"The strong interactions behave as if there were simultaneously two different reference frames." No wonder you're so confused.
I broke down and read your entire post. What a load of unadulterated hogwash. Landau and Lifshitz would think you're a nonsense machine.

Since 1964 we cannot define the all parameters in the SM.
For decades we cannot unify Gravity and Quantum Physics.
But such people as you do not understand that it is due to the tremendous number of incorrect interpretations and wrong assumptions in these two flag mainstream theories. Are you able to assume that the tens unsolved basic problems for decades in physics and cosmology follow from the fact that the initial conditions in these two theories ARE INCOMPLETE so there appear the nonsense as well. We must find theory more fundamental than the cited theories to eliminate the incorrect interpretations as the gravitational waves, time loops, the parallel worlds and so on. We must find theory which leads to the GR and QP. Then unification of these theories will be possible. I claim that the more fundamental theory is the Everlasting Theory. It is obvious that the GR and QP are the incomplete theories because for r –> 0 both theories lead to singularities and infinities. My theory is free of singularities and infinities.

Scientists have their incomplete and partially wrong theoretical particle physics and theoretical cosmology and it will be for ever unless they will accept the Everlasting Theory.

We never will unify the GR and QP if we will accept that the formula for relativistic mass acts correctly always and that for the carriers of the strong interactions this formula is more important than the Uncertainty Principle. My theory leads to the asymptotic freedom which is free of ADDITIONAL PARAMETERS and consistent with experimental data. I predicted that in the high-energy regime there is the asymptote alpha_strong = 0.1139 and the future experiments will show that I am right. If the result 0.1139 is correct then my assumption that the GR is incomplete (i.e. that my formula for the relativistic mass of the carriers of strong interactions differs from the Einstein formula) will be correct as well.

Now about the perihelion precession of Venus i.e. 204 arc seconds per century:
Only for Venus we obtain theoretical result tremendously inconsistent with observational data. It suggests that the gravity is incomplete. The small additional sunward acceleration of the Pioneer proves it as well. Of course, there are many theories which try to explain the acceleration but I described the acceleration and the perihelion precession of Venus within the same model. It is obvious that gravity is the incomplete theory because there appear the infinite mass densities. The nature does not act in such stupid way. My theory shows that the masses of black holes (in respect of the gravitational, weak and strong interactions) ARE QUANTIZED. This means that such black holes must emit energy which they absorb and it is possible via the spacetimes. More massive black holes consist of the quantized-mass black holes.
BTW, the calculations leading to the perihelion precession of Mercury and Venus you can find on page 111 whereas the formula in my post is the small relativistic correction obtained within the GR. I wrote it in my post. Can you see the sentence: “Within the GR for the small relativistic correction, we obtain:”?

The Einstein spacetime components (i.e. the binary-systems/weak-dipoles of neutrinos) always are moving with the speed c. The Einstein spacetime components are the non-relativistic objects i.e. their mass does not depend on their speed. The neutrinos from the weak decays outside the strong fields are moving with the speed c as well. Only neutrinos from the weak decays inside the baryons can be superluminal (not numerous on Earth). It is because the neutrinos are TODAY the classical and non-relativistic particles. I explained it in many previous posts.

Brucep, too many people think the same as you are so there is stagnancy in theoretical physics and theoretical cosmology. It lasts decades and it will last forever unless someone (i.e. I) will beat at the empty pates.
 
……beyond the unphysical nonsense that matter can exceed the invariant local coordinate speed of light.

It is obvious that the GR is not valid for distances shorter than the Planck length i.e. less than about 10^-35 m. On the other hand, the Everlasting Theory shows that the ground state of the Einstein spacetime consists of the non-rotating-spin binary systems of neutrinos. The neutrinos consist of objects which size is much smaller than the Planck length i.e. about 10^-45 m. This means that the internal structure of the neutrinos is BEYOND the GR but the structure of the neutrinos as A WHOLE leads to the gravitational constant G outside the neutrinos. The c and G applied in the GR does not concern the internal structure of the Einstein spacetime components. On base of the GR, you can say nothing about the internal structure of the neutrinos. The internal structure of neutrinos causes that sometimes they can be superluminal as, for example, the neutrinos from the supernova SN 1987A. Such is MY INTERPRETATION of the time distance between the neutrino- and photon-front.

So once more: the GR is not valid inside neutrinos. It is because the G is not characteristic for the components the neutrinos consist of.

All can see that the spacetime is the scene for gravity and quantum effects. This leads to conclusion that we can unify the GR and QP ONLY via the internal structure and behaviour of the spacetime. To do it we need theory beyond the Planck length as well and the Everlasting Theory is such theory.

Such theory is very simple. There are the 4 phase transitions of the fundamental spacetime described within the same formula. The first transition leads to the internal structure of the neutrinos, the second leads to the second spacetime i.e. the Einstein spacetime whereas the third to the core of baryons i.e. to the quantized black holes in respect of the strong and weak interactions. Outside the core of baryons is obligatory the Titius-Bode law for the strong interactions. The fourth phase transitions leads to the new cosmology. Such is the foundations of my theory. The c is the natural speed of the Einstein spacetime components, which carry the photons and gluons, in the fundamental spacetime. The known particles, besides neutrinos, consist of the Einstein spacetime components i.e. the binary systems of neutrinos. Particles cannot exceed speed of their components. It is the reason why the known particles, besides neutrinos, cannot exceed the speed of light. My theory shows that the binary systems of neutrinos are the stable objects due to the entanglement. But in my previous posts I explained that in regions composed of CONFINED Einstein spacetime components pressure between neutrinos is negative. This leads to conclusion that neutrinos from weak decays in regions composed of confined Einstein spacetime components can slightly exceed the speed c. When energy of colliding nucleons increases then inside them there is more and more regions composed of the confined Einstein spacetime components. It leads to conclusion that very big number of superluminal neutrinos should be emitted during the supernova explosions.

Recapitulation
The c depends on the inertial mass density of the fundamental/Newtonian spacetime. Lower density means higher speed of light. The pressure inside the fundamental spacetime is tremendous 10^180 Pa. This causes that the fundamental spacetime is exactly flat so the c is constant. The density changes only for distances smaller than about 10^-32 m. Moreover, we need regions composed of confined Einstein spacetime components sufficiently large the weak decays of the particles could take place.

So once more: To explain possible existence of the superluminal neutrinos we need confinement described within the Everlasting Theory, atom-like structure of baryons and sufficiently high energy of colliding nucleons/other-baryons.
 
AlphaNumeric, you rejected my explanation. OK.

You rejected the explanation in Wikipedia: “Proof that QCD confines at low energy is a mathematical problem of great relevance, and an award has been proposed by the Clay Mathematics Institute for whoever is ALSO able to show that the Yang–Mills theory has a mass gap and its existence.” and “It has already been well proven—at least at the level of rigor of theoretical physics BUT NOT THAT OF MATHEMATICAL PHYSICS—that the quantum Yang–Mills theory for a non-abelian Lie group exhibits a property known as confinement.” OK.

Can you stop the idiotic discussion?
Except that your claim, that the prize involves confinement, was wrong. This 'idiotic discussion' is because you didn't (and don't) understand the prize or anything to do with Yang Mills theory. All of your posts in the last few pages have shown that.

Do you admit the prize is not for confinement? It's a simple question.
 
You're hanging on to 'a personal theory' which has been empirically falsified.

It is not true. Where are the needed scientific arguments?
Brucep, you are a lazy man. Among a few hundred results calculated within my theory there are many results which scientists cannot calculate within the mainstream theories. It is because the mainstream theories are INCOMPLETE. The incompleteness causes that there appear many wrong interpretations as well.
I calculated following physical quantities which cannot be calculate within the mainstream theories from properties of the spacetime or internal structure of particles:
Planck constant – formula 4
Speed of light – formula 10
Gravitational constant – formula 11
Mass of bare electron – formula 18 and due to the formula 69 I calculated the total mass of electron. Just we should multiply the result 18 by the result 69.
Electric charge of electron – formula 20
Mass of proton – formula 40
Mass of neutron – formula 41
Frequency of the radiation emitted by the hydrogen atom under a change of the mutual orientation of the electron and proton spin in the ground state – see formula 149. You know, you must calculate it from the internal structure of proton. Can you do it within the quark model? Of course you cannot whereas I did it within the Everlasting Theory.
Perihelion precession of Venus – formula 251b
Exact mass of the up and down sham quarks – page 92
And many others……

Can you see that the mainstream theories are incomplete? Can you see that the Everlasting Theory is the lacking part of the ultimate theory? You know, origin of the physical constants is the most important problem which is not solved within the today mainstream theories.
 
You cannot prove Yang-Mills existence without the confinement. Can you? Just try.
That is an assertion on your part. The prize is for existence of Yang Mills theory from a particular set of axioms and then showing a mass gap exists. There is no proof that proving confinement is necessary to show that. As Witten explained in the paper which defined the prize, it's fully expected that confinement will still be an open problem even after someone has won the Yang Mills millenium prize.

So you saying it cannot be done is utterly unjustified. The burden of proof is on you to justify that claim of yours. Saying "Go on, prove it without confinement!" is a shifting of the burden of proof. I never made any statement about whether I think it's possible to prove without confinement but rather that the prize is for existence and a mass gap, not confinement, as you claimed. If someone presents a proof of existence and the mass gap which doesn't prove confinement then they will still win the money. If they happen to also prove confinement then great.

So I'll ask my question again.... Do you admit the prize is not for confinement?
 
AlphaNumeric, the Everlasting Theory, which is the lacking part of the ultimate theory, shows that the confinement is the FOUNDATIONS NEEDED to prove the mass gap existence. No one will win the Yang-Mills millennium prize neglecting confinement. Peoples say wrong things because they do not understand the confinement and mass gap. In my previous posts I described the origin of these physical quantities. It is obvious that the confinement is the prelude to the mass gap.
 
Brucep, incredible, you started to think!

At first I should explain on base of my Everlasting Theory why Lifshitz and Landau claimed that sometimes same laws of physics do not look the same in all reference frames. The Principle of General Covariance applied in the General Theory of Relativity is correct only partially. For strong interactions relativistic masses of sources and carriers of strong interactions do not transform the same. The strong interactions behave as if there were simultaneously two different reference frames. Within the Everlasting Theory I proved that we must introduce the term “dominating gravitational gradient”. For the strong interactions the GR is correct when all reference frames have the same speed or are in the rest in the dominating gravitational field. To unify the Quantum Physics with the General Theory of Relativity we need more fundamental theory than these two theories i.e. we need the arithmetic Everlasting Theory.

The GR is very simple when reference system is properly chosen. See, for example, Chapter titled “Foundations of General Theory of Relativity” in which I calculated the curving of light in gravitational field of the Sun. The theoretical result obtained within my theory is the same as in the GR, i.e. 1.75 seconds of arc (page 115, formula 263), because in both derivations appears the gravitational radius of the Sun.

And now the answer to your question
My theory shows that for the strong fields of baryons is obligatory the Titius-Bode law for the strong interactions which is some analog to the Titius-Bode formula for planets. The Titius-Bode formula looks as follows R = A + dB, where for the strong interactions is A/B = 1.3898 (pages 16-18) whereas for gravitational black holes I obtained A/B = 1.394 (pages 68 and 69). The states d = 0 and 1 are placed below the Schwarzschild surface for the strong interactions (the core of baryons is the BLACK HOLE IN RESPECT OF THE STRONG INTERACTIONS) and for the gravitational interactions of the gravitational black holes. The orbits of Mercury and Venus are the analogs to the d = 0 and 1 states. Under the Schwarzschild surface, there is common the entanglement between the Einstein spacetime component. Such entangled (not confined) field arose during the evolution of the solar system and spreads out from the orbit of Mercury to distance two times greater than the radius of the orbit of Mercury i.e. the orbit of Venus is inside this field. This entangled field arose due to the radiation masses.
We can see that there was a resonance between the relativistic phenomena described within the GR and the phenomena described within my theory FOR THE FIRST PLANET, i.e. MERCURY i.e. for d = 0. It is the reason why within the GR and my theory we obtain practically the same result for perihelion precession of Mercury (575 = 532 + 43 and 573 arc seconds whereas the observational result is 574.10±0.65 arc seconds per century).
Why within my theory we obtain correct result for Venus (204 arc seconds per century) whereas we still cannot do it within the GR? And my answer is as follows. The entangled field dominates for Venus in such way that we can neglect the relativistic correction.

So once more
Mercury – the resonance of the two different phenomena.
Venus – the entangled field dominates.
Other planets – the GR is obligatory.

Within the GR for the small relativistic correction, we obtain:
angle = 3(pi)rrmmcc/(2JJ) where r is the gravitational radius of the Sun r = 2GM/(cc) whereas the J is the angular momentum of a planet.

Since you make this ignorant claim I thought I'd post this for you. Hopefully it helps you to understand what the real science is. It's called relativity theory.

"At first I should explain on base of my Everlasting Theory why Lifshitz and Landau claimed that sometimes same laws of physics do not look the same in all reference frames. The Principle of General Covariance applied in the General Theory of Relativity is correct only partially. For strong interactions relativistic masses of sources and carriers of strong interactions do not transform the same. The strong interactions behave as if there were simultaneously two different reference frames."

This is Chapter 2, Curving, from Taylor and Wheeler's text Exploring Black Holes. I'm going to ask you to look at several Figures.
http://www.eftaylor.com/pub/chapter2.pdf

Figure 2 on page 2-5 The significance: Over each path through curved spacetime a local segment of the path very closely approximates the flat spacetime of Special Relativity. Subsequently the effects of gravity can generally be ignored when making local empirical measurements [accounting for local miniscule gravitational effects won't change empirical measurements in a meaningful way]. One experiment where local gravitational effects must be accounted for is the GPS. Another experiment is the Gravity Probe B. The length of the path segment, where the effects of gravity can generally be ignored, is much larger in the weak field than a path segment in the strong field. For our solar system it's approximately 1 AU. Around the black hole it's very small. It's the reason why gravitational effects are ignored in the laboratory frame of the LHC. It means that we can generally use the simpler mathematics of SR for analyzing the local spacetime [physics].

Figure 6 and 7 on page 2-26 the dreaded embedding diagrams. They're actually very useful if you know what they signify and not just tossed out there for folks to wonder what they mean. We're going to use Figure 6 to understand where measurements are made for our comparative analogy between the local measurements and remote bookkeeper measurements of the same event in spacetime. The event is measuring the velocity of a stone falling towards the black hole. The remote velocity measurement is going to be dr/dt_bkkpr and the local velocity measurement is dr_shell/dt_shell. The local measurement is made in the proper frame of the falling stone as it crosses r_shell and the bkkpr measurement is made from remote coordinates far away.
2 formulas derived from GR

dr/dt_bkkpr = (1-2M/r)(2M/r)^1/2 [measurement made from the remote bkkpr coordinates]

dr_shell/dt_shell = (2M/r)^1/2 [local proper frame measurement made at r_shell as the stone passes over]

It's very easy to make the calculations by setting r_shell = nM. Example r=2M is the distance from the center of the black hole to the coordinate singularity at the event horizon. So r=4M is twice the distance and r=200M is 100 times the distance, etc.. So for making our comparisons in the weak and strong fields we can pick any r=nM that we choose. Large r=nM for the weak field and small r=nM for the strong field. We just substitute our choice for r=nM for r in the formulas.

I'll pick 2M/4M for the strong field and r=2M/20,000M for the weak field

Weak field

dr/dt_bkkpr = (1-2M/r)(2M/r)^1/2 = (1-2M/20,000M)(2M/20,000M)^1/2 = (.9999)(.01) = .00999c

And

dr_shell/dt_shell = (2M/r)^1/2 = (2M/20,000M)^1/2 = .01c

Remote and local measurements are very close.

Strong field

dr/dt_bkkpr = (1-2M/r)(2M/r)^1/2 = (1-2M/4M)(2M/4M)^1/2 = (.5)(.7071068) = .3535534c

dr_shell/dt_shell = (2M/r)^1/2 = (2M/4M)^1/2 = (.5)^1/2 = .7071068c

The remote measurement is 1/2 the local measurement.

The analogy becomes: the local measurement only accounts for spacetime curvature in the local proper frame where the stone velocity is measured at. The small area of the pumpkin. The remote measurement accounts for the entire spacetime curvature over the stones path. Over a long line on the pumpkin. That's why GR names the remote observer the Schwarzschild bookkeeper. Later in the chapter they discuss the model for bookkeeper measurements which are essentially global in nature.

Finally the end. Hope it works.

One final thing substitute rM=2 (2M for r at the event horizon) to get the greatest delta of all. Think about why the remote bookkeeper can no longer access information about the stone's future path inside the black hole. Switching to a proper frame metric where all the measurements are made by the stone rider allows GR to evaluate the spacetime inside the black hole.
 
It is not true. Where are the needed scientific arguments?
Brucep, you are a lazy man. Among a few hundred results calculated within my theory there are many results which scientists cannot calculate within the mainstream theories. It is because the mainstream theories are INCOMPLETE. The incompleteness causes that there appear many wrong interpretations as well.
I calculated following physical quantities which cannot be calculate within the mainstream theories from properties of the spacetime or internal structure of particles:
Planck constant – formula 4
Speed of light – formula 10
Gravitational constant – formula 11
Mass of bare electron – formula 18 and due to the formula 69 I calculated the total mass of electron. Just we should multiply the result 18 by the result 69.
Electric charge of electron – formula 20
Mass of proton – formula 40
Mass of neutron – formula 41
Frequency of the radiation emitted by the hydrogen atom under a change of the mutual orientation of the electron and proton spin in the ground state – see formula 149. You know, you must calculate it from the internal structure of proton. Can you do it within the quark model? Of course you cannot whereas I did it within the Everlasting Theory.
Perihelion precession of Venus – formula 251b
Exact mass of the up and down sham quarks – page 92
And many others……

Can you see that the mainstream theories are incomplete? Can you see that the Everlasting Theory is the lacking part of the ultimate theory? You know, origin of the physical constants is the most important problem which is not solved within the today mainstream theories.

No, you're the only one who thinks your arithmetic theory describes any natural phenomena. Provide evidence that some physicist uses Everlasting Theory in their research. After 48 years.
 
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It is obvious that the GR is not valid for distances shorter than the Planck length i.e. less than about 10^-35 m. On the other hand, the Everlasting Theory shows that the ground state of the Einstein spacetime consists of the non-rotating-spin binary systems of neutrinos. The neutrinos consist of objects which size is much smaller than the Planck length i.e. about 10^-45 m. This means that the internal structure of the neutrinos is BEYOND the GR but the structure of the neutrinos as A WHOLE leads to the gravitational constant G outside the neutrinos. The c and G applied in the GR does not concern the internal structure of the Einstein spacetime components. On base of the GR, you can say nothing about the internal structure of the neutrinos. The internal structure of neutrinos causes that sometimes they can be superluminal as, for example, the neutrinos from the supernova SN 1987A. Such is MY INTERPRETATION of the time distance between the neutrino- and photon-front.

So once more: the GR is not valid inside neutrinos. It is because the G is not characteristic for the components the neutrinos consist of.

All can see that the spacetime is the scene for gravity and quantum effects. This leads to conclusion that we can unify the GR and QP ONLY via the internal structure and behaviour of the spacetime. To do it we need theory beyond the Planck length as well and the Everlasting Theory is such theory.

Such theory is very simple. There are the 4 phase transitions of the fundamental spacetime described within the same formula. The first transition leads to the internal structure of the neutrinos, the second leads to the second spacetime i.e. the Einstein spacetime whereas the third to the core of baryons i.e. to the quantized black holes in respect of the strong and weak interactions. Outside the core of baryons is obligatory the Titius-Bode law for the strong interactions. The fourth phase transitions leads to the new cosmology. Such is the foundations of my theory. The c is the natural speed of the Einstein spacetime components, which carry the photons and gluons, in the fundamental spacetime. The known particles, besides neutrinos, consist of the Einstein spacetime components i.e. the binary systems of neutrinos. Particles cannot exceed speed of their components. It is the reason why the known particles, besides neutrinos, cannot exceed the speed of light. My theory shows that the binary systems of neutrinos are the stable objects due to the entanglement. But in my previous posts I explained that in regions composed of CONFINED Einstein spacetime components pressure between neutrinos is negative. This leads to conclusion that neutrinos from weak decays in regions composed of confined Einstein spacetime components can slightly exceed the speed c. When energy of colliding nucleons increases then inside them there is more and more regions composed of the confined Einstein spacetime components. It leads to conclusion that very big number of superluminal neutrinos should be emitted during the supernova explosions.

Recapitulation
The c depends on the inertial mass density of the fundamental/Newtonian spacetime. Lower density means higher speed of light. The pressure inside the fundamental spacetime is tremendous 10^180 Pa. This causes that the fundamental spacetime is exactly flat so the c is constant. The density changes only for distances smaller than about 10^-32 m. Moreover, we need regions composed of confined Einstein spacetime components sufficiently large the weak decays of the particles could take place.

So once more: To explain possible existence of the superluminal neutrinos we need confinement described within the Everlasting Theory, atom-like structure of baryons and sufficiently high energy of colliding nucleons/other-baryons.

You said: "The internal structure of neutrinos causes that sometimes they can be superluminal as, for example, the neutrinos from the supernova SN 1987A. Such is MY INTERPRETATION of the time distance between the neutrino- and photon-front."

Scientific illiterate. That's MY INTERPRETATION of you. Pull your head out of the sand.
 
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