Ken S. Tucker wrote:
Tom Roberts wrote in message ...
In short, to solve Poisson's equation one must
a) apply it in an inertial frame (it's not valid in a non-inertial
frame)
b) apply boundary conditions at spatial infinity.
These must be put in "by hand"; there is no avoiding it. At base this is
required in order to apply geometry to the problem (and without geometry
we have no way to analyze anything physical...).

Essentially Tom uses Mach's Principle here.

No. Mach's principle is rather vague, mostly because he made about a
dozen different statements that are similar, but are all lumped together
as "Mach's principle". But its essence is that all the matter in the
universe is inherently involved, AND NOTHING ELSE. My point above is
that boundary conditions are also involved.


The
boundary at spatial infinity is Mach's "distant star's",

No, it's quite different.


in a real universe.

Look back and note that my theoretical context was Newtonian mechanics.
It is well known that that cannot possibly apply to cosmological things
like spatial infinity.


There is a dichotomy in TR's arguement
above, Mach's principle was described by TR as "mysitcal"
but Tom's "b" renames that, a "boundary condition".

There is no mysticism about boundary conditions -- they are essential to
solving differential equations.


I think Mach's Principle is a boundary condition,
but IMHO, (agreeing with TR) is mystical.

Mach was not discussing boundary conditions at all, he was discussing
mass 'way out there.


[Ken S. Tucker inserts an irrelevant and erroneous diversion about
E&M]

You keep getting the basics wrong:
E x B = c

In your notation, both E and B are 3-vectors, so E x B is also a
3-vector, but c is not. This equation cannot possibly be correct.

In fact, E x B is known as the Poynting vector, and for a light ray is
proportional to its momentum. In particular, a more intense light ray
has a larger momentum and a larger Poynting vector; it cannot possibly
be constant as you suppose. And as a 3-vector, it also has a direction.


Tom Roberts

Tom Roberts wrote in message y.com...

Ken S. Tucker wrote:

Tom, I doubt the EM stuff you deleted would appeal
to you, it's quite advanced.

E x B = c
I should add is the DIRECTION of TRAVEL,
as the context suggested.

In your notation, both E and B are 3-vectors, so E x B is also a
3-vector, but c is not. This equation cannot possibly be correct.
In fact, E x B is known as the Poynting vector, and for a light ray is
proportional to its momentum. In particular, a more intense light ray
has a larger momentum and a larger Poynting vector; it cannot possibly
be constant as you suppose. And as a 3-vector, it also has a direction.

Right I should have specified c as a direction only of
the light-ray, without the magnitude. I did that because
it was the direction that was the principle argument.
Sorry for the confusion. (We at C-dyn, use short forms,
and I forget others don't).

Tom Roberts

Tom Roberts wrote:

Ken S. Tucker wrote:

Tom Roberts wrote in
message ...

In short, to solve Poisson's equation one
must a) apply it in an inertial frame (it's
not valid in a non-inertial frame) b) apply
boundary conditions at spatial infinity.
These must be put in "by hand"; there is no
avoiding it. At base this is required in
order to apply geometry to the problem (and
without geometry we have no way to analyze
anything physical...).


Essentially Tom uses Mach's Principle here.


No. Mach's principle is rather vague, mostly
because he made about a dozen different
statements that are similar, but are all lumped
together as "Mach's principle". But its essence
is that all the matter in the universe is
inherently involved, AND NOTHING ELSE. My point
above is that boundary conditions are also
involved.

Maybe not all the matter, as not all matter might be
in gravitational/inertial contact with us.
This translates also in some initial boundary condition.
[..]
Tom Roberts

Uwe Hayek.

--
To be controlled in our economic pursuits,
is to be controlled in everything -- F.A.Hayek.