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

January 11th, 2019, 2:22 pm

Joing two posts:

I always thought that the symbol was called nabla and the various vector calculus products were dependent on what you did with it e.g. div, grad or curl. My Electromag lecturer called it nabla.

However also my electromag teacher used m and n as a subscript. He had a serif writing and hence the n and m were almost impossible to tell apart.
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 12:08 pm

And in code debugging one can overlook 'Commmand' for 'Command'. (C++ does not have spelling checkers).
Shortly afterwards I decided to buy spectacles.
 
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Collector
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 12:36 pm

rooted in my new relativistic energy momentum relation (that is correct, gives same values as old, but rooted in Compton instead of de Broglie) I go forward and try to make a wave equation...dose this makes more sense (than my last idiot attempt)?

\begin{equation}
- \hbar \frac{\partial \Psi }{\partial t}=-\hbar \nabla \cdot(\Psi \textbf{c})
\end{equation}
where \(\textbf{c}=(c_x, c_y, c_z)\) would be the light velocity field. Dividing both sides by  \(\hbar\), we can rewrite this as

\begin{equation}
-  \frac{\partial \Psi}{\partial t}=- \nabla\cdot(\Psi \textbf{c})
\end{equation}

The light velocity field satisfy

\begin{equation}
\nabla \cdot  \textbf{c}=0
\end{equation}
that is the light velocity field is a solenoidal which means we can re-write our wave equation as 

\begin{equation}
 \frac{\partial \Psi }{\partial t}-\textbf{c}\cdot \nabla \Psi = 0
\end{equation}
and yes same structural form as the Advection equation, thanks for tips C. 

 On the ``expanded" form we have

\begin{equation}
  \frac{\partial \Psi }{\partial t}- c_x\frac{\partial \Psi }{\partial x}- c_y\frac{\partial \Psi }{\partial y}- c_z\frac{\partial \Psi }{\partial z}=0
\end{equation}

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time?? or nothing there, errors, grave errors? light is special so have to be careful when cooking with it,  uncooking also risky, especially when new to the art...hemmm....  :roll:
Last edited by Collector on January 12th, 2019, 12:58 pm, edited 7 times in total.
 
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katastrofa
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 12:53 pm

@Cuchulainn I use Doxygen and there are many spell checker plug-ins available. BTW, yesterday I was praised by a guy from a big cybersecurity firm for my code documentation. It turns out that my absolute minimum written in a hurry is the most detailed documentation he's ever seen! I'd prefer to be praised for my C++ code, but still... :-D
(Apologies for the off-topic. That's the last one.)
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 1:09 pm

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time??

It's a 3d first-order hyperbolicPDE. Is 3+1 = 4 so scary?
 
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Collector
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 1:14 pm

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time??

It's a 3d first-order hyperbolicPDE. Is 3+1 = 4 so scary?
4 is a nice number, far better than 10, 11 and 26
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 1:45 pm

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time??

It's a 3d first-order hyperbolicPDE. Is 3+1 = 4 so scary?
4 is a nice number, far better than 10, 11 and 26
The numbers are blinding you. 
No such thing as a magic number.
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 1:51 pm

rooted in my new relativistic energy momentum relation (that is correct, gives same values as old, but rooted in Compton instead of de Broglie) I go forward and try to make a wave equation...dose this makes more sense (than my last idiot attempt)?

\begin{equation}
- \hbar \frac{\partial \Psi }{\partial t}=-\hbar \nabla \cdot(\Psi \textbf{c})
\end{equation}
where \(\textbf{c}=(c_x, c_y, c_z)\) would be the light velocity field. Dividing both sides by  \(\hbar\), we can rewrite this as

\begin{equation}
-  \frac{\partial \Psi}{\partial t}=- \nabla\cdot(\Psi \textbf{c})
\end{equation}

The light velocity field satisfy

\begin{equation}
\nabla \cdot  \textbf{c}=0
\end{equation}
that is the light velocity field is a solenoidal which means we can re-write our wave equation as 

\begin{equation}
 \frac{\partial \Psi }{\partial t}-\textbf{c}\cdot \nabla \Psi = 0
\end{equation}
and yes same structural form as the Advection equation, thanks for tips C. 

 On the ``expanded" form we have

\begin{equation}
  \frac{\partial \Psi }{\partial t}- c_x\frac{\partial \Psi }{\partial x}- c_y\frac{\partial \Psi }{\partial y}- c_z\frac{\partial \Psi }{\partial z}=0
\end{equation}

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time?? or nothing there, errors, grave errors? light is special so have to be careful when cooking with it,  uncooking also risky, especially when new to the art...hemmm....  :roll:
Looks like a transport equation

http://www.mathematik.uni-dortmund.de/~ ... nsport.pdf
 
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katastrofa
Posts: 7657
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 5:03 pm

rooted in my new relativistic energy momentum relation (that is correct, gives same values as old, but rooted in Compton instead of de Broglie) I go forward and try to make a wave equation...dose this makes more sense (than my last idiot attempt)?

\begin{equation}
- \hbar \frac{\partial \Psi }{\partial t}=-\hbar \nabla \cdot(\Psi \textbf{c})
\end{equation}
where \(\textbf{c}=(c_x, c_y, c_z)\) would be the light velocity field. Dividing both sides by  \(\hbar\), we can rewrite this as

\begin{equation}
-  \frac{\partial \Psi}{\partial t}=- \nabla\cdot(\Psi \textbf{c})
\end{equation}

The light velocity field satisfy

\begin{equation}
\nabla \cdot  \textbf{c}=0
\end{equation}
that is the light velocity field is a solenoidal which means we can re-write our wave equation as 

\begin{equation}
 \frac{\partial \Psi }{\partial t}-\textbf{c}\cdot \nabla \Psi = 0
\end{equation}
and yes same structural form as the Advection equation, thanks for tips C. 

 On the ``expanded" form we have

\begin{equation}
  \frac{\partial \Psi }{\partial t}- c_x\frac{\partial \Psi }{\partial x}- c_y\frac{\partial \Psi }{\partial y}- c_z\frac{\partial \Psi }{\partial z}=0
\end{equation}

This last equation seems to makes some logical sense to me..   4 dimensional quantum space-time?? or nothing there, errors, grave errors? light is special so have to be careful when cooking with it,  uncooking also risky, especially when new to the art...hemmm....  :roll:
You're not an idiot, Cat-Collector. You are one of those people who have intuition and idea, but cannot express it in the standard language (either because they are not fluent in it or it cannot describe them). Einstein was like that when he was starting :-) (It's hard to explain anything to such people, because one needs to be careful not to trample on the differences between the status quo and what they see.)

Your equation
\begin{equation}
 \frac{\partial \Psi }{\partial t}-\textbf{c}\cdot \nabla \Psi = 0
\end{equation}
is an advection equation for a vector c, which is constant. This would mean that your wave's density is constant within your "wave parcel" - in analogy to a "fluid parcel" that you need to define to speak of the motion of continuum (motion of some continuous medium); fluid parcel is an infinitesimal amount of this medium. If fluid parcel's volume doesn't change as the medium flows, you formally say that the divergence of the flow velocity is zero (for you this means that [$]\nabla \cdot \textbf{c} = 0[$]). This indicates that the flowing medium is non-compressible (doesn't compress or expand as it flows).

The advection without the incompressibility condition is
\begin{equation}
 \frac{\partial \Psi }{\partial t}-\nabla \cdot (\textbf{c}\Psi) = 0
\end{equation}
but obviously if c is constant (you assume incompressibility), you can take it outside of the operator and you get your equation.
(If not obvious: [$]\nabla \cdot (\textbf{c}\Psi) = \nabla_x (c_x\Psi) + \nabla_y (c_y\Psi) + \nabla_z (c_z\Psi) = [$] [$]\Psi \nabla_x c_x + \Psi\nabla_y c_y + \Psi\nabla_z c_z + c_x \nabla_x \Psi + c_y \nabla_y \Psi + c_z \nabla_z\Psi = [$] [$]\Psi \nabla  \cdot\textbf{c} + c\cdot\nabla\Psi[$]. For incompressible flow the first term is zero because [$]\nabla \cdot \textbf{c} = 0[$].)
 
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Collector
Posts: 4186
Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 5:45 pm

Thanks :-  )  ("but cannot express it in the standard language", because people dont understand cat-language and need to have everything explained as waves)
Last edited by Collector on January 12th, 2019, 5:56 pm, edited 3 times in total.
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 5:47 pm

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

January 12th, 2019, 6:23 pm

Einstein was like that when he was starting

He skipped Lagrangian mechanics as an undergraduate?
 
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Collector
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Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 6:36 pm

Einstein was like that when he was starting

He skipped Lagrangian mechanics as an undergraduate?
he started before undergrad to think about these things?  people have different life cycles, some start at 12 (geniuses) and some start at 30+ ( cowboys like me, shooting sling shot equations from the wrist, if lucky hits a small target every now and then, mostly misses grossly)
 
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Cuchulainn
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Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 6:50 pm

Compared to Euler (inviscid) equations
https://en.wikipedia.org/wiki/Leonhard_Euler
 
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FaridMoussaoui
Posts: 370
Joined: June 20th, 2008, 10:05 am

Re: "Unified Revolution" new book by Espen Haug

January 12th, 2019, 7:11 pm

Einstein was like that when he was starting

He skipped Lagrangian mechanics as an undergraduate?
may be an answer to your question: Einstein's Studies at the Polytechnic Institute in Zurich (1896–1900)

Have a look at the document "Matrikel Albert Einstein", his grades vary from 4 to 6 (with an outilier of 1).
In Switzerland (still today), the grades are on a basis of 6.
Last edited by FaridMoussaoui on January 12th, 2019, 7:19 pm, edited 2 times in total.
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