Generalized Probable Causation Maxwell's Equations

[Osher]

I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').

Consider the expression:

1) P(AB) - P(A'B') = P(AB) - P(A U B)' = P(AB) - [1 - P(A U B)] = P(AB) - 1 + P(A U B) = P(A) + P(B) - P(AB) + P(AB) - 1 = P(A) = P(A) + P(B) - 1

Since P(B) = 1/2 maximizes logistic probable effect P(B)(1 - P(B)), we set P(B) = 1/2 in (1) to get:

2) P(AB) - P(A'B') = P(A) - 1/2 = g - 1/2 (since g = P(A))

One is tempted to set g = constant, but here is a remarkable "trick", namely, set g = P(A-->B) because P(A-->B) usually is the Probable Causation analog of d/dt or Dt or even Dtt (2nd time derivative or partial derivative operator), and we know that Maxwell's equations involve Dt(E) and Dt(B*) where E is the electric field and B* is the magnetic field.

A slight complication occurs because Faraday-Maxwell's equations have form:

3) curl(E) = -Dt(B*)
4) curl(B*) = (1/c^2)Dt(E)

So we extend P(A-->B) to include curl(E) or curl(B*) via:

5) P(A-->B) = curl +/- Dt applied respectively to E, B*, etc.

Replacing g in (2) by P(A-->B) of (5) yields an additive analog of Maxwell's equations with:

6) P(AB) - P(A'B') = P(A-->B) - 1/2, with P(A-->B) given by (5).

Note the remarkable fact that P(A-->B) = P(A) = g here, which is precisely very strong causation as I defined it several weeks ago here.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:
> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

Typo: in (1), immediately to the left of the last = sign on the right, the expression P(A) should be dropped (= P(A) = is a typo).

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

We have now determined each component of EM, namely EM1 = P(AB) and EM2 = P(A'B'), from the other and from g = P(A-->B) which is gravitation! Thus, Maxwell's "Classical" equations (other than the source or first 2 equations) are generalized to gravitation and indirectly to strong and weak interactions from yesterday's and the previous days' posts here.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

If we used the generalized Maxwell equations here to ask questions about the original Maxwell equations, then the original equations seem to be inapplicable under the following conditions:

1) Probable Causation and hence gravitation g is not very strong in the sense of g = P(A-->B) = P(A), or else Probable Causation is maximal in the sense of P(A-->B) = 1 or very near 1.

2) Effect B or P(B) is not maximal logistic in the sense of maximal P(B)(1 - P(B)).

Thus, GR seems likely to be inapplicable in cases (1) and (2). (1) likely includes Black Holes for the case of P(A-->B) = 1 or very near 1.

Osher Doctorow

2)

[Osher]

On Friday, April 18, 2014 11:29:09 AM UTC-4, Osher wrote:
> On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:
>

Readers who want to follow research developments in Probable Causation 4-interaction-unification should especially study gravitomagnetic papers in arxiv. An especially interesting one arguably is:

1) "Gravitomagnetic effects in conformal gravity," Jackson Levi Said et al., U. Malta in Malta and U. Oxford in U.K., arxiv:1401.2898v1 [gr-qc] 10 jan 2014.

Of course, the machinery of Probable Causation has not yet been used in such papers, but unification with Probable Causation is arguably only a matter of time and lack of bureaucratic research control.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

The "monopole problem" can be intuited from looking at Maxwell's first two equations with regard to divergences, which indicate that magnetic poles do not exist (0 source-sink terms) whereas electric point charges do exist (nonzero divergence as density).

But the Probable Causation picture discussed here may give a different interpretation, namely that of the two components of Electromagnetism, one is bounded and one is unbounded. The bounded component P(AB) is arguably VISIBLE, while the unbounded component P(A'B') is arguably INVISIBLE. This is precisely what distinguishes visible light (with vacuum speed c) from invisible velocities/speeds like superluminality in the picture that I discussed here earlier.

Returning to Special Relativity, recall what happens when we transform the beta-factor or inverse-beta-factor or gamma factor 1/sqrt(1 - v^2/c^2) to Probable Causation. In general the rule for transformation is:

1) y/x --> 1 + y - x

and therefore:

2) v^2/c^2 --> 1 + v^2 - c^2

3) 1 - v2/c^2 --> 1 - [1 + v^2 - c^2) = c^2 - v^2

This is literally the reverse of the square root argument above (1) and if we consider the Probable Causation definition P(v^2 --> c^2) = 1 + c^2 - v^2, it is the velocity which is the Cause and the light speed which is the Effect, which makes sense either if light speed is not really constant in all scenarios in vacuum or if the range of v forms phases with respect to critical boundary c, that is, superluminal above c, ordinary below c or equal to c.

The square root is not of critical importance to the above arguments.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 12:11:31 PM UTC-4, Osher wrote:
> On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:
>

Of course, enough searching of the internet will reveal the monopole solution version of Maxwell's equations (not using Probable Causation, however), in which 0is replaced by rho_M (the density or energy density of monopoles).

I will also take this opportunity to encourage readers to keep following arxiv developments in exobiology and "habitable planet" studies (or habitable stellar systems), including:

1) "Earth-like habitats in planetary systems," J. Fritz et al, Museum fur Naturkunde berlin Germany, Observatoire de la cote d'azur France, Deutsches Zentrum fur Luft und raumfahrt Germany, CEED U. Oslo Norway, arxiv:1404.4460.pdf [astro-ph.EP]v1 17 Apr 2014.

Note that researchers in observatories and natural history museums join academic or private astrophysicists in this type of non-imitative study, an example of my argument that both teaching and research needs to be free of conflict of interest involving either Big Government control or Big Corporation control. True, these Big sources tend not to be interested in far-from-Earth research because they cannot use them for immediate gratification and immediate power-craziness, but that suggests that conflict of interest is a far deeper problem ethically in science and mathematics than researchers and teachers have realized. Human beings arguably tend to be backwards when they can be dominated by a few other people (not just by trolls on the internet!).

Osher Doctorow

[Osher]

On Friday, April 18, 2014 12:21:15 PM UTC-4, Osher wrote:
> On Friday, April 18, 2014 12:11:31 PM UTC-4, Osher wrote:
>

I would add to the statement of the scientific method:

1) Absence of conflict of interest such as occurs when a few powerful groups like big government or big corporations control research funds.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

From P(AB) - P(A'B') = g - 1/2 = P(A-->B) - 1/2, we can solve for various quantities. For example, it turns out that:

1) P(A-->B) = (1/2) + EM1 - EM2

Although it looks as though EM2 is increasing as P(A-->B) decreases and as though EM1 is increasing as P(A-->B) increases, P(A-->B) has a quite different interpretation because in general P(A-->B) = 1 + y - x requires 0 < = y < = x < = 1. It therefore has EM2 > = EM1 in (1) except for a rescaling term of 1/2 contained in EM1 - EM2, and P(A-->B) is maximum at 1 iff y = x, although P(A-->B) can be very strong causation at P(A-->B) = P(A) or very near P(A) when P(A-->B) = P(A) = g as in (1).

Let us rewrite (1) by returning the fact to the symbols that g = P(A-->B), obtaining:

2) g + EM2 = 1/2 + EM1

But g = 1 - s, so we obtain:

3) 1 - s + EM2 = 1/2 + EM1

and so finally:

4) s = 1/2 + EM2 - EM1

which has reversed EM2 and EM1 compared to (1). In this form, we see that the Strong Interaction increases with EM2 as expected and decreases with EM1.

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

It will be useful for readers to know the workings of engines and motors, for example internal combustion engines:

1) "Internal combustion engine," Wikipedia (online).
2) "Otto cycle," Wikipedia (online).

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

See also:

1) "Rocket Engine," Wikipedia (online)
2) "Spacecraft propulsion," Wikipedia (online)
3) "Jet engine," Wikipedia (online)
3) "Turbine," Wikipedia (online).

Osher Doctorow

[Osher]

On Friday, April 18, 2014 10:28:09 AM UTC-4, Osher wrote:

> I have been discussing here yesterday the relationships between the bounded and unbounded components of EM (Electromagnetism), EM1 = P(AB) and EM2 = P(A'B').
>
>

The rather remarkable variations of the two EM components with s, g, w (strong, gravitation, weak interactions respectively) and with Probable Causation P(A-->B) can be somewhat paralleled in the arXiv literature by a number of papers on Asymptotic Freedom in QCD and Confinement in QCD, including:

1) "The importance of asymptotic freedom for the pseudocritical temperature in magnetized quark matter," R.L.S. Farias et al, U. Federal de Sao Joao Del Rei and de Santa Maria and de Snta Catarina Brazil, arXiv:1404.3931 v1 [hep-ph] 15 Apr 2014.

In that paper, discrepancies in predictions between lattice and non-lattice results are resolved by considering that the important Nambu-Jona-Lasinio (NJL) model of effective chiral quarks has a coupling constant G that decreases with the magnetic field B and with temperature. NJL lacks asymptotic freedom even though it is very important in QCD, and for explanation of NJL see:

2) "Nambu-Jona-Lasinio model," Wikipedia (online).

NJL is a low-energy approximation of QCD which parallels the construction in BCS theory of superconductivity of interacting Cooper pairs, except that in NJL it constructs from interacting Dirac fermions with chiral symmetry, an effective theory of nucleons and mesons. Its fermionic Lagrangian density is invariant under U(2)_f x SU(Nc) globally and when m = 0 under chiral SU(2)_L x SU(2)_R.

Osher Doctorow

[Newtonian J Applemeister]

OH MY GOD GIVE IT A FUCKING REST YOU INSANE BALLS-SUCKING MEGA-TARD.

[benj]

So which of those engines are EM1 and which EM2?