Re: Fraudulent Laws

[Hugh Logan <hlogan@ix.netcom.com>]

Merlin wrote:
>

> Mr. Logan, thank you for your reference. It would seem that a great amount
> of effort has be put into insuring conservation in a closed system.
> Obviously, though, in an open system energy will always be lost, mostly to
> the universe, "universal loss". Would you agree that this fact would apply
> not only to energy and velocity of light, but as well to many other
> conservable "Laws"?

If by a "closed system" you mean an isolated system (isolated from any
interaction that could change the quantity to be conserved), and by an
"open system" one that is not isolated in this sense, then I would 
agree that the "conserved" quantity would be exchanged with its
surroundings, the universe. For example, a system of particles isolated
from any external forces, would obey conservation of momentum, but in 
an open system, the particles could transfer momentum to particles
outside the system by virtue of the impulse produced by the force.
Similarly for angular momentum conservation, except that torque rather
than impulse changes angular momentum. I am assuming Newtonian physics,
and I think this can be extended to the flat spaces of special
relativity. And this would include the locally flat space of, say a
freely falling space capsule, in the curved spacetime of general
relativity.

I think one would have difficulty transferring all the conservation laws
of classical physics and special relativity to general relativity. In GR
one looks for constants of the motion for a particle in curved
spacetime. These constants depend on the nature of the spacetime as
given by the metric for the spacetime in question. For the case of a
spherically symmetric, non-rotating mass distribution, one uses the
static Schwarzschild metric. It turns out that quantites corresponding
to energy and angular momentum are conserved. (They reduce to the
familiar definitions for flat space at great distances from the
spherical mass distribution). As far as I know, there is no such
constant of the motion corresponding to momentum. It seems that there is
no globally meaningful definition of momentum in Schwarzschild space
(such that it would be constant and reduce to the expression for flat
space at great distances from the spherical mass).

As mentioned in my last posting, the situation regarding conservation is
more complicated in a space described by a non-static metric such as the 
Robertson-Walker metric. The energy of the universe is not conserved.

There are different cases of the Robertson-Walker metric corresponding
to a constant k. If k is positive, the universe is "closed" with a
finite volume. If k<0 or k=0, it is "open" with infinite volume. But I
don't think this is the same as the use of "open" and "closed" that you
were referring to. As I see it, in the application to cosmology, if the
universe is the system, then there are no surroundings -- whether the
universe is finite or infinite.  


> As well, I'm easy to admit that I'm new and poorly
> educated compared to most. However, I've read alot and seems these >issues,

Likewise, although retired, I am only a beginner at general relativity
and cosmology. I hope others more knowledgable will correct my errors.

Hugh Logan