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From: eric gisse on 30 Oct 2009 07:22
Jarek Duda wrote:

> Yes it's called Hamiltonian ... in quantum mechanics. In classical
> field theories it's usually ignored.
> The interesting thing about it is that for Lorentz invariant theories,
> this energy density doesn't emphasize any direction - time for
> evolution is chosen arbitrary!

So?

Scalars don't emphasize direction, by virtue of being scalar.

> Now the transformation into Lagrangian makes kind of Wick's rotation
> of this coordinate.

No.

A Wick rotation is something else.

> It looks that our flowing time is practically only the result of
> entropy gradient...

Are you a crazy person?

From: Jarek Duda on 30 Oct 2009 07:32
.... entropy gradient which is statistically created orthogonally to
directions in which the only always attracting force works: the
gravity - it gives physics tendency to sporadic collapses - entropy
minimals.
From: Jarek Duda on 30 Oct 2009 07:49
> Scalars don't emphasize direction, by virtue of being scalar.
But Lagrangian density for scalar field emphasize (time) direction,
while its energy density doesn't do it.

> > Now the transformation into Lagrangian makes kind of Wick's rotation
> > of this coordinate.
> No.
> A Wick rotation is something else.
Wick rotation makes e.g that the square of time derivative is negated,
what is imagined that time dimensions would be multiplied by imaginary
unit.
It was a magic trick for me, but now I see that it's just a result of
energy -> Lagrangian transformation for selected time dimension -
along which we make evolution.

> > It looks that our flowing time is practically only the result of
> > entropy gradient...
> Are you a crazy person?
I'm only saying what math is saying.
You believe that energy density is physical, don't You?
And in Lorentz invariant theories it cannot choose any time dimension!
Because there is no one emphasized - it has full symmetry.
So it has to be chosen accordingly to thermodynamics - fourdimensional
entropy gradient.
To connect it with the choice of time from general relativity -
statistically this entropy gradient should be created orthogonally to
directions in which the only always attracting force works: the
gravity - it gives physics tendency to sporadic collapses - entropy
minimals.
From: Jarek Duda on 30 Oct 2009 07:50
> Scalars don't emphasize direction, by virtue of being scalar.
But Lagrangian density for scalar field emphasize (time) direction,
while its energy density doesn't do it.

> > Now the transformation into Lagrangian makes kind of Wick's rotation
> > of this coordinate.
> No.
> A Wick rotation is something else.
Wick rotation makes e.g that the square of time derivative is negated,
what is imagined that time dimensions would be multiplied by imaginary
unit.
It was a magic trick for me, but now I see that it's just a result of
energy -> Lagrangian transformation for selected time dimension -
along which we make evolution.

> > It looks that our flowing time is practically only the result of
> > entropy gradient...
> Are you a crazy person?
I'm only saying what math is saying.
You believe that energy density is physical, don't You?
And in Lorentz invariant theories it cannot choose any time dimension!
Because there is no one emphasized - it has full symmetry.
So it has to be chosen accordingly to thermodynamics - fourdimensional
entropy gradient.
To connect it with the choice of local time from general relativity -
statistically this entropy gradient should be created orthogonally to
directions in which the only always attracting force works: the
gravity - it gives physics tendency to sporadic collapses - entropy
minimals.
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