I’m Sorry
You tell me,
mistakes
Are part of being young
But that don't right
The wrong that's been done
I'm sorry
(So sorry) So sorry
Please accept my apology
Mistakes are obviously part of being old too!
In a previous blog post I regretted not being able to
show my work that the Lortenz Transform which is traditionaly expressed as √(1-(v/c)2
should be expressed as 1/(1-ln(½)*ln(1-(v/c)2)).
My work obviously had a mistake and while this appears to be a useful approximation, ...it
is wrong.
On a flat
surface the hypotenuse/radius of a triangle is r=√(a2+b2). I had said that on a
hyperbolic surface this is r=1/(1+ln(.5)*ln(a2+b2)), which I arrived as a solution and it
seems to work, but I did not save my work. The correct solution, which I did save this time, on a
hyperbolic surface is
r=ln(cosh(a2+b2)*cosh(n*π) ± sinh(a2+b2)*sinh(n*π)). This makes the solution to the Lorentz Transform,
which can be solved from Einstein's Triangle of Energy as ln(cosh(1-v2/c2)±sinh(1-v2/c2)),
where cosh(1-v2/c2) is the constant term, location, and sinh(1-v2/c2) is the variance, uncertainty. Logarithms are not defined for negative numbers, i.e. when the uncertainty
is greater than the constant term, so the Lorentz Transfrom is properly in the range
between 1 and ln(cosh(1-v2/c2)+sinh(1-v2/c2)). At a speed of zero, the location dominates and the uncertainty is almost zero. The uncertainty increases and the location decreases as the
speed of the particle approaches the speed of light.
This means that the formulas originally given in https://dbeagan.blogspot.com/2023/04/on-beyond-einstein.html should instead be :
“If space is not flat, but is hyperbolic
then the equations might instead be
Momentum = m0* ln(cosh(1-v2/c2)±sinh(1-v2/c2))*v
Force= m0* ln(cosh(1-v2/c2)±sinh(1-v2/c2))*v ∂v
= m0* ln(cosh(1-v2/c2)±sinh(1-v2/c2)) *a
Energy = ∫ m0* ln(cosh(1-v2/c2)±sinh(1-v2/c2))*v ∂v=
= m0* ln(cosh(1-v2/c2)±sinh(1-v2/c2))*c2
This solution does not create a paradox at v=c ,
and it is undefined, not imaginary, when v>c. The rest mass,
The Second Law of Thermodynamics requires that
the energy of a system of objects will seek the state of lowest energy and any
reduction in the energy of the system will be equal to an increase in the
entropy of the system. In curved, hyperbolic, space, two masses will each seek
to lower their energy and approach a common center along a geodesic. This
change in energy will be accompanied by a change in momentum. This change in momentum could be viewed in flat space as an
apparent force, like centrifugal force, and NOT an intrinsic force. The
apparent force of gravity is these masses seeking to lower their energy,
maximize their entropy, and this is
where d12 is the distance between
mass 1 and mass 2, m0x is the rest mass of mass x,
vx is the velocity of mass x, and c
is the speed of light and k is the average distance. "
This does mean
that:
In a curved universe, gravity should be an
apparent force and should NOT be combined with the three intrinsic (electromagnetic,
weak nuclear, and strong nuclear) forces in a Unified Field Theory.
In a hyperbolic universe, there is a discontinuity at the Big Bang and our universe may be only one sheet in a asymmetrical two-sheeted hyperboloid.
In a hyperbolic universe,
there is only one absolute, and that absolute is both random AND deterministic.
If there is one absolute,
then there is also only one choice: choosing that absolute, or not choosing
that absolute, aka absolute zero.
In a hyperbolic universe,
regressions and statistics using least squares should be redone; the formula
for what is called the standard deviation is in fact the formula for error; and
the Bessel adjustment, n/(n-1), is not necessary.
In a hyperbolic universe,
when there is no error, every moment about the mean should be 0, not just those
odd movements where the moment is currently expressed as multiples of i and even
movements which are multiples of i2 , which are currenly expressed as a real
number is - 1.
The universe has a variance of .822, and thus its standard deviation can never be 0.
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