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Lorentz Invariance
From
a Physicist of the Virginia University:
"I
glanced at the page. It seemed interesting, but I see no mention of AD
allowing Maxwell's equations to remain invariant. Did I miss this??"
From
the moment AD discards two frames in relative motion, the concept of "invariance"
becomes meaningless. AD doesn't use the Lorentz equations. AD replaces
the Lorentz equations by Carezani's equations. Equations (1) and (2) are
replaced by equations (3) and (4).
On
the other hand, the question about "invariance" here is also a purely
semantic question, regarding the following:
Maxwell's
equations at rest, in a system in motion with relative velocity to another
system, is the same as saying that the phenomenon described by Maxwell's
equations is in motion with respect to the observer.
In
AD, the phenomenon and observer form a physical system. We speak constantly
about the Lorentz transformation, but in practice there is no transformation:
The phenomenon is described by the phenomenon itself and the observer.
In AD, the time t' in equation (4) is reversible, that is to say:
t' = t / (1-B^2)^1/2
Here's
an example using Maxwell's equations:
Taking
the classical Maxwell's equation in the form:
1/c E/dt = curl H (a) div E = 0 (b)
Writing
the equation in general form and working it out we have
1 dEx d v
1 d v
1
-- ------ = ---- (Hz - --- Ey) --- - ---- (Hy
+ --- Ez) ---
c dt dy'
c Z dz'
c Z
Where
Z = (1 - B^2)^1/2
It
is deduced that an observer in motion, as well as observing an electric
field E, will also observe a magnetic field H. The equations are "invariant,"
but a different phenomenon appears when the observer, or the phenomenon,
is in motion. Are the equations "invariant"?
The
same application of AD when the "Maxwell Equation" (phenomenon described
by ME) are in motion with respect to an observer, gives the following
equation:
1 dEx d v
d v
-- ------ = ---- (Hz - --- Ey) Z - --- (Hy + --- Ez) Z
c dt dy'
c dz' c
These
two equations are conceptually equal with the exception that in the SR
equation, the coefficient Z divides the equation and in AD, the coefficient
multiplies the equation!
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