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Collector
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### Re: "Unified Revolution" new book by Espen Haug

\begin{eqnarray}
\frac{\sqrt{2\pi}}{e^{im\phi}}\frac{i^2 m^2 e^{i m \phi}}{\sqrt{2 \pi }}-m^2=0 \\
-m^2+m^2=0
\end{eqnarray}

\begin{eqnarray}
\frac{\sqrt{2\pi}}{e^{i\sqrt{B}\phi}}\frac{i^2 B e^{i \sqrt{B} \phi}}{\sqrt{2 \pi }}-B=0 \\
-B+B=0
\end{eqnarray}

"see what happens." yes 0 = Zero as expected!!     and? (my $E=G0^2$ still = zero!)

katastrofa
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### Re: "Unified Revolution" new book by Espen Haug

Serr?

$\Phi(\varphi) = \frac{1}{\sqrt{2\pi}} e^{im\varphi}$

$\frac{1}{\Phi}\frac{d^2 \Phi }{d \varphi^2}+B = 0$
$\frac{d^2 \Phi }{d \varphi^2} = -m^2 \frac{1}{\sqrt{2\pi}} e^{im\varphi}= -m^2\Phi$
Substituting this to ODE, you get $-m^2 \frac{1}{\Phi} \Phi+B = 0$ and thus $B=m^2$

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

https://www.math24.net/second-order-lin ... fficients/

Put ODE in less masokistic form

$\frac{d^2 \Phi }{d \varphi^2}+B\Phi = 0$

Then find constant c1 and c2 (boundaries ..)
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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http://www.datasim.nl

katastrofa
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### Re: "Unified Revolution" new book by Espen Haug

Kind of, but we discuss the application of this solution to the Schrodinger equation, and the resulting assumptions.

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

Kind of, but we discuss the application of this solution to the Schrodinger equation, and the resulting assumptions.
QM  is kinda based on this standard ODE stuff, nothing shocking AFAIR (50 years since ..).
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

katastrofa
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### Re: "Unified Revolution" new book by Espen Haug

I'd say modelling Hamiltonians as differential operators is rooted in the idea of modelling the underlying physics of observed energy spectra and phenomena as wave-like.

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

The whole idea of Hamiltonian systems is founded on the conservation of energy along the characteristics. And you want to find the local minimum of the Hamitonian $H(x,y)$.
A necessary and sufficient condition for a system to be Hamiltonian is that its orthogonal system be a gradient system. Then the latter can be solved to find minima.

https://people.math.osu.edu/costin.9/821/Classnotes.pdf

// One of the coolest things I learned undergrad Theoretical Mechanics was solving swinging pendulums etc, using Lagrange's and Hamilton's equations.etc.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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http://www.datasim.nl

katastrofa
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### Re: "Unified Revolution" new book by Espen Haug

That's only when all is "stable", unperturbed, adiabatically slow, etc. - boring. Take simple friction, or any interaction which makes the Hamiltonian time-dependent. You may arrive at fractional derivatives when attempting to solve such a problem. It's probably my schizophrenia, but it reminded me of the difference between the Levy flight and the boring Brownian motion. Only the latter has a defined scale, like the closed Hamiltonian system in which the energy is conserved. The Levy flight doesn't have the scaling invariance property, like the open Hamiltonian systems don't preserve their properties. It only shows how our knowledge of the natural world is chained by fundamental principles of mathematics.
I blame it on Euler. Newton and even Leibniz were natural philosophers who used and developed mathematics as a tool, but Euler raised it to the rank of science. We started to believe in its phantasmagorias instead of learning to experiencing the real world. I think the next step after mathematics was silence. But now it's too late - the world is crying louder and louder.
Yet another stream of half-asleep consciousness. I will delete it tomorrow.

Collector
Posts: 4862
Joined: August 21st, 2001, 12:37 pm

### Re: "Unified Revolution" new book by Espen Haug

That's only when all is "stable", unperturbed, adiabatically slow, etc. - boring. Take simple friction, or any interaction which makes the Hamiltonian time-dependent. You may arrive at fractional derivatives when attempting to solve such a problem. It's probably my schizophrenia, but it reminded me of the difference between the Levy flight and the boring Brownian motion. Only the latter has a defined scale, like the closed Hamiltonian system in which the energy is conserved. The Levy flight doesn't have the scaling invariance property, like the open Hamiltonian systems don't preserve their properties. It only shows how our knowledge of the natural world is chained by fundamental principles of mathematics.
I blame it on Euler. Newton and even Leibniz were natural philosophers who used and developed mathematics as a tool, but Euler raised it to the rank of science. We started to believe in its phantasmagorias instead of learning to experiencing the real world. I think the next step after mathematics was silence. But now it's too late - the world is crying louder and louder.
Yet another stream of half-asleep consciousness. I will delete it tomorrow.
"Newton and even Leibniz were natural philosophers who used and developed mathematics as a tool,"

the way to do it!

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

That's only when all is "stable", unperturbed, adiabatically slow, etc. - boring. Take simple friction, or any interaction which makes the Hamiltonian time-dependent. You may arrive at fractional derivatives when attempting to solve such a problem. It's probably my schizophrenia, but it reminded me of the difference between the Levy flight and the boring Brownian motion. Only the latter has a defined scale, like the closed Hamiltonian system in which the energy is conserved. The Levy flight doesn't have the scaling invariance property, like the open Hamiltonian systems don't preserve their properties. It only shows how our knowledge of the natural world is chained by fundamental principles of mathematics.
I blame it on Euler. Newton and even Leibniz were natural philosophers who used and developed mathematics as a tool, but Euler raised it to the rank of science. We started to believe in its phantasmagorias instead of learning to experiencing the real world. I think the next step after mathematics was silence. But now it's too late - the world is crying louder and louder.
Yet another stream of half-asleep consciousness. I will delete it tomorrow.
Don't you think you should rephrase that?

"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

katastrofa
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### Re: "Unified Revolution" new book by Espen Haug

Traitors!

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

Traitors!
They were only doing their job!
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

Collector
Posts: 4862
Joined: August 21st, 2001, 12:37 pm

### Re: "Unified Revolution" new book by Espen Haug

Traitors!
They were only doing their job!
correct, Newton and even Leibniz where pointing out what had to be pointed out!

Cuchulainn
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### Re: "Unified Revolution" new book by Espen Haug

Traitors!
What do you think of Pat Boone? He was the great White hope of the sixties.

Get rid of the saxaphones.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

Collector
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Joined: August 21st, 2001, 12:37 pm

### Re: "Unified Revolution" new book by Espen Haug

After staring at the same formula for some years now F=GMm/R^2 it is now clear to me that the  assumption among researchers that Newton gravity is instantaneous and therefore imply infinite speed of gravity assumption in Newton is heavily flawed. They are looking at G and M without knowing what G and M truly represent and then have made conclusions.

It is a bit similar to look at a car made from wood (for Example a Morgan 3-wheeler), and claim it not can move because it is a tree! Give me a break!

Proof That Newton Gravity Moves at the Speed of Light and Not Instantaneous (Infinite Speed) as Thought!

Both the Newtonian gravity force law and the Newtonian field equation contains the speed of gravity equal to the speed of light, not by assumptions, but by calibration. It is concealed inside G and M.

I can now extract both the Planck length and c from gravity observations with no knowledge of G, c or h. And can predict all gravity phenomena from these two constants (+ naturally variables dependent on mass size etc.). This is what part of string theory hoped to do, but had little success with, except making the math complicated.

We get reductions of constants, from G, c and h, to c and Planck length, and much more simple logic and intuition. What on earth do G represent? Has anyone observed anything that is meters cubed, divided by kg and second squared recently? Newton never invented nor used G, he was not mad!