Re: Nova / Einstein's 100th anniversary show
- From: "Koobee Wublee" <kublai@xxxxxxx>
- Date: Sat, 1 Oct 2005 23:16:23 -0700
<warded8@xxxxxxx> wrote in message
news:1127967111.208263.122110@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> Just read about this cool new two-hour edition of NOVA, called
> "Einstein's Big Idea." It's supposed to be airing for the 100th
> anniversary of the e=mc2 equation and really comprehensive. There are
> vivid re-enactments of Einstein and his wife, and it even goes into
> detail about the scientists that have preceded him, like Faraday and
> even those that followed him - like Lise Meitner, who ultimately came
> up with the nuclear fusion theory. The producer is David Bodanis, who
> also wrote that book "e=mc2."
>
> http://www.pbs.org/wgbh/nova/einstein/
The equation, E = m c^2, is an absolute simple and elegant form of
mathematical expression that equates observed energy and the observed mass.
Before the creative interpretations to GR ever become more rampant in style
and frequency, energy actually means the observed mass, and the observed
mass actually means the observed energy. It is dependent on where and
perhaps when an observation is performed. After these creative
interpretations of GR became ever more ubiquitous and were deeply rooted
into the academics, the meaning of this equation has been downgraded into
just an description of the energy associated with the rest mass. To
describe the observed energy, the creative interpreters of GR chose to
promote, E^2 = m^2 c^4 + p^2 c^2.
Why? Because they became disoriented when trying to write down, E = m c^2,
describing an object with this mass traped in the curvature of spacetime.
Why disoriented? Because of failure to follow through the powerful
Noether's Theorem which states that whenever the derivative of the density
function, that describes an event represents the absolute minimal effort,
with respect to one of the state variables becomes null, there is a
conserved quantity.
In GR with Schwarzschild solution to the Grossmann/Einstein/Hilbert field
equations, there are two state variables that result in conditions according
to Noether's Theorem. One is the conservation of angular momentum where it
does not take a genius to figure it out becase the state variable involved
is none other than the longitudinal coordinate in polar coordinate system.
However, the other eludes these creative interpreters of GR, although it is
just there just for anyone to identify as a conserved parameter in
accordance with Noether's Theorem. This state variable should be time
itself whether it is the proper (or local) time or the observed (or the
stuff on the right hand side of the spacetime equation with Schwarzschild
metric) time. However, it is mistakenly identified as the proper spacetime
where it is an inner product of the proper time and the proper space. Since
time is only meaninful where there is a change of an event going on, space
plays no role in the purpose of minimal action as described by Fermat and
Lagrange long time ago. Although by minimizing these way-too-many field
equations with respect to spacetime gives the same and (should be) proper
answer as minimizing time (either the proper time or the observed time),
there is a crucial mis-conclusion that GR in general does not manifests a
conservation of [observed] energy.
If properly done in accordance to the Langragian method by minimizing the
time, one gets a Lagrangian, altough dependent on the derivative of the
proper spacetime with respect to time (either proper or observed), that is
independent of the proper time itself. That means the Euler-Lagrange
equation associated with the partial derivative of the state variable of
proper spacetime becomes always zero in every general case. This means the
law of the conservation of energy is a fundamental phenomenon applying to
everything observable. This, of course, includes the system with binary
stars. Only with the skills of magicians specializing in manipulations of
mathematics, it is shown how GR predicts the orbital frequency of some
binary system without the conservation of energy. Although the energy must
also be conserved in such a system, the angular momentum does not because it
does not satisfy Noether Theorem where the state variable is the longitude.
The current established observed rotational rate of some binary system might
have something to do with the lack of the conservation of angular momentum
but certainly not because of lack of conseration of energy. A proper
interpretation of GR does not allow gravitons.
For some one intrested in following up with the equation, E = m c^2, below
is what is derived from the Mikowski (flat) spacetime equation.
E = m c^2 / sqrt(1 - B^2)
Where
** m = rest mass
** B c = observed speed
** m / sqrt(1 - B^2) = observed mass
One can apply the same to the spactime equation corrected with Schwarzschild
metric to arrive at the following.
E = m c^2 sqrt(1 - 2 U) / sqrt(1 - B^2)
Where (at lattitude = 0, equitorial plane)
** U = G M / c^2 / r
** B^2 c^2 = (dr/dt)^2 / (1 - 2 U)^2 + r^2 (dH/dt)^2 / (1 - 2 U)
** m sqrt(1 - 2 U) / sqrt(1 - B^2) = observed mass
The equation above can be simplified to
E - m c^2 = m B^2 c^2 / 2 - m U c^2
Where
** 1 >> B
** 1 >> U,
With the conservation of energy where the change in the kinetic energy must
be the same as the change in potential energy, our solar system is super
stable. To explain Newtonian interpretation to gravity, we start with what
we have learned in junior high schools that
** m B^2 c^2 / 2 = kinetic energy
** - m U c^2 = potential energy
Yes, I re-iterate the beauty and simplicity of the equaton, E = m c^2, if m
= observed mass. We ought to toss away the equation, E^2 = m^2 c^4 + p^2
c^2, where it does not properly addresses an observed mass trapped in the
curvature of spacetime.
.
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