They All
Laughed
They all laughed at
Christopher Columbus
When he said the world was round
They all laughed when Edison recorded sound
They all laughed at Wilbur and his brother
When they said that man could fly
They told Marconi
Wireless was a phony
I have sent this to physicists, but just so it is publicly dated.
I have since corrected the relativistic mass formula on a hyperbolic surface
The formulae for momentum, force, and energy are those established
by Isaac Newton.
Momentum is mass times velocity, m
*∂x/∂t.=mv.
Force is the change in,
differential of, momentum, m*∂2x/∂t2 =m ∂v/∂t =ma.
Energy is the integral of the change
in momentum, ∫ m ∂2x/∂t2 ∂t.= ∫ m*v*∂v.
If m is a function of v,
then this can be solved by integration by parts, and it is, ½*m*v2- ∫ m*∂v.
Classical, Newtonian, physics assumes that mass is a
constant at every velocity including zero, m0, such that:
Momentum = m0
∂x/∂t=m0 * v
Force= m0 *∂2x/∂t2
=m0 * a
Energy = m0 ∫v ∂v = ½ * m0 * v2
Newton’s Law of Gravity is
because if a system of two masses experience a change in momentum, then that change
is assumed to be due to a force ( gravity).
F=G* (m01 * m02)/d122
, G=6.67×10-11
where d12 is the
distance between mass 1 and mass 2, and m0x is the rest mass
for mass x.
Einstein’s General Theory of Relativity assumes that mass
is NOT a constant but is instead a function of velocity, and that the frame of reference
is important. If the frame of reference is flat Euclidean space, then the Lorentz
Transform applies, and this becomes:
Momentum = m0
*(1/√(1-(v/c)2))*v
Force= m0
*(1/√(1-(v/c)2)*v dv = m0 *(1/√(1-(v/c)2))*a
Energy = ∫m0
*(1/√(1-(v/c)2)v dv = m0 *(1/√(1-(v/c)2)) c2
If this is solved by integration
by parts, then you get Einstein’s triangle of energy, mc2= ½mv2+m0c2
A problem with this interpretation is that it allows v>c
where the mass becomes imaginary, and has a paradox at v=c, where the energy
has to, simultaneously, be both infinite and zero.
In a flat space, there is no reason for a system of two or
more masses to seek a lower energy system and any change in momentum of these
objects would still appear to be accompanied by a force (gravity).
F=G*(m01
(1/√(1-(v1/c)2)))*m02 (1/√(1-(v2/c)2))))/d122
,G=6.67×10-11
where d12 is the distance between mass 1
and mass 2, and m0x is the rest mass of mass x.
If space is not flat, but is hyperbolic, then the
equations might instead be
Momentum = m0 *
(1/(ln(2*cosh(√(1-(v/c)2))))*v
Force= m0 * (1/(ln(2*cosh(√(1-(v/c)2))))v
∂v = m1/(ln(2*cosh(√(1-(v/c)2)))0 * ()*a
Energy = ∫m0 *(1/(ln(2*cosh(√(1-(v1/c)2)))) *v
∂v = m0* (1/(ln(2*cosh(√(1-(v/c)2))))* c2
This solution does not create a paradox at v=c ,
and it is undefined, not imaginary, when v>c.
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. But while in curved, hyperbolic, space, this 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
G*m01*(1/(ln(2*cosh(√(1-(v1/c)2))))*m02*(1/(ln(2*cosh(√(1-(v2/c)2))))/exp(-d12),G=6.67×10-11
where d12 is the
distance between mass 1 and mass 2, and m0x is the rest mass of mass
x.
If velocity is less than 10% of the speed of light, then
there is less than a 1% difference between assuming that mass is constant or that
the mass varies with velocity. In this case classical, Newtonian, physics is
used because it is simpler. It is not until the velocity is greater than 82.2% of the speed of
light that there is an appreciable difference between the Euclidean, flat, and the
hyperbolic functions of relativistic mass.
As shown by Mabkhout,
assuming that the universe is hyperbolic can explain many apparent paradoxes
between the age and the size of the observable universe. If the universe is
hyperbolic, but it is viewed from a flat frame of reference, perspective, it
would appear to undergo inflation at its beginning. If the universe is
hyperbolic, then there is no need to resort to dark energy or dark matter to explain
its continued expansion. If the universe is hyperbolic, then the Planck Energy is
consistent with the Planck Length. If the universe is hyperbolic, then the paradox
of rotating galaxies can be resolved. If the universe is hyperbolic, then
gravity is an apparent force, not an intrinsic force, and no effort should be taken to include
gravity as a force in the standard model. If the universe is hyperbolic, then
the apparent discrepancy in the Hubble Constant might be merely be the computing
of that constant in a flat frame of reference while measuring it in hyperbolic frame
of reference, i.e. it is no different that the seeming paradox that a Great Circle
Distance on the Earth is not the hypotenuse of the triangle formed by the two
points at each end of that Great Circle.
If hyperbolic geometry is used to compute statistics, then
every moment, not merely odd moments, about the mean, are zero. The Standard
Deviation is then a measurement of Error, not of Variance. Even a system
without mean error, or any individual errors, will still have a Variance.
Just as on the surface of the Earth, Euclidean geometry is
used unless the distance between two points is large compared to the radius of
the earth, ( i.e. the Earth is flat locally but spherical globally), so too the universe can be assumed
to be Euclidean, flat, unless the distances and speeds involved are enormous (i.e. the universe is flat locally, but hyperbolic universally.)
