Re: E = 3/4 mc² or E = mc²? The forgotten Hassenohrl 1905 work.

On 12/01/2024 04:19 AM, Richard Hachel wrote:

Le 01/12/2024 à 01:28, hertz778@gmail.com (rhertz) a écrit :
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Now, E = 3/4 mc² or E = mc²?

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E=mc².sqrt(1+Vr²/c²)
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If Vr~0 then E=mc².
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If a mass is at rest in a system, it has no real speed in this system.
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Nor any observable speed since Vo=Vr/sqrt(1+Vr²/c²)
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Its only displacement is in time, and only the energy of displacement in
time is counted.
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E=mc² is the energy of a particle by its passage in time.
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If, in addition, the particle moves in space, it also takes on an energy
of movement (not to be confused with kinetic energy).
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This energy is E=mVr².
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It is extremely simple.
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Since this does not add longitudinally since the axis of time and the
axis of movement are perpendicular, we must call upon Pythagoras.
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E=sqrt[(mc²)²+(mVr²)²]
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E=mc².sqrt(1+Vr²/c²) and, if Vr=Vo/sqrt(1-Vo²/c²)
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So :
E=mc²/sqrt(1-Vo²/c²)
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It's that simple.
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R.H.

When linear and rotational are different,
then the rotational just makes for both
space-contraction-rotational and mass-energy equivalency,
while space-contraction-linear just hauls along,
it's kind of like light speed:
"in deep space in a vacuum",
that mass-energy equivalency with light's speed being infinite,
that v -> c => 1/(v-c) = +-infinity,
simply is not in accords with "apparent super-luminal motion",
as is evident plainly in the sky-survey.
c = infinity is _not_ a natural unit. Furthermore,
it doesn't necessarily "reflect", usual derivations
that have the perfectly, linearly equal-and-opposite,
of usual linear and one-dimensional and symmetric
and one-dimensional accounts, since that entire
one-dimensionality, is contrived, in real space.
Then, this 4/3 bit about the self-energy of the electron,
is plainly arrived at, about continuum mechanics, of
which particle mechanics is a conceit, a concession,
to that physics is just lacking some necessary mathematics.
The zero meters per second is infinity seconds per meter.
About "making the corner", with regards to ideas like
the Dirac delta, the radial basis function, and otherwise
kernels as they are about the origin, whose area equals one,
and the whole endeavor after deMoivre of Eulerian/Gaussian,
and the quadrature, makes not only for the yenri, has that
there are many, many assumptions in the stack of derivations,
that the "three regularities" of "increment, dispersion,
_and dimension_", of a continuum analysis, has that the
entire notion of path travel, makes for a greater dimensional
analysis, here with regards to mathematical notions like
the "dimensional, dimensionless, dimensioned resonator/alternator"
with regards to a "walk integral".
Now, that's a bit under-defined, but so is mechanics, and
so is the mathematics about mechanics, so, it fits underneath,
and makes for "around". There is quite a bit involved in
this sort of "original analysis", making a real kind of,
so-to-say, "coordinate-free", that though is sort of having
set aside as un-used, all what follows deMoivre.
So, deMoivre is great, it's like l'Hospitale (an approximation)
and Rodriguez formula (an approximation) when not
"reducible to the first-order", or neglecting the
infinitude of remaining terms.
So, a usual "severe abstraction of a mechanical reduction",
where "whatever Lagrange says, his theory of potentials
always wins", has that mechanics has that any change at
all in velocity and thus arbitrarily displacement about
arbitrarily an origin or frame, has that the walk integral's
origin is where it's at.
Mechanics: and all above it, is underdefined, right beneath.
So, infinity seconds per meter, may be zero meters per second,
then that c = infinity is _not_ a natural unit.