Re: Frequency based gravity


Sue... wrote:
Golden Boar wrote:
Sue... wrote:
Golden Boar wrote:
Energy, momentum, and mass are all proportional to frequency as shown
below.

E = f * h/c^0
p = f * h/c^1
m = f * h/c^2

For massive particles, f = gamma * f_C

where

gamma is the Lorentz factor
f_C is the Compton frequency

The above equations can be given by

E_n = f.h / c^n

So,
E_0 is energy
E_1 is momentum
E_2 is mass
E_3 is coefficient of damping? (maybe).

Because the above quantities are all proportional to frequency, it is
reasonable to assume to that gravity acts upon frequencies.

Newton's G can be given by:

G = 2 * pi * l_P^2 * c^3 / h = l_P^2 * c^3 / hbar

and the gravitational force is then

F_g = G * m_1 * m_2 / r^2

We can then get a new equation for gravity based on frequency as
follows:

G_f = 2 * pi * l_P^2 * h / c = (2 * pi * l_P)^2 * hbar / c

F_g = G_f * f_1 * f_2 / r^2

where

G_f = frequency based gravitational constant
G = mass based gravitational constant (Newton's)
l_P is the Planck length
h is Planck's constant
hbar is Planck's constant over 2 pi
c is the speed of light in vacuum
F_g is the gravitational force
f_1 is the frequency of body 1
f_2 is the frequency of body 2
m_1 is the mass of body 1
m_2 is the mass of body 2
r is the distance between the bodies

The value of the frequency based gravitational constant is about 3.6 *
10^-111 kg m^3.

You might find some spice for your musings in the use of a
Fourier transform in this simulation:
http://www.research.ibm.com/grape/grape_ewald.htm

Happy hunting,

Sue...

Thanks for the link but unfortunatley I do not understand the Fourier
transform at the moment, though I will try to learn about it. Could you
give me an overview of what that webpage is saying?

<< The Ewald sum is possibly the most common method
for evaluating long-range interactions in simulations.>>
http://cmt.dur.ac.uk/sjc/thesis_dlc/node61.html

<< The sinusoidal basis functions are eigenfunctions of
differentiation,
which means that this representation transforms linear differential
equations with constant coefficients into ordinary algebraic ones.
(For example, in a linear time-invariant physical system, frequency
is a conserved quantity, so the behavior at each frequency can
be solved independently.) >>
http://en.wikipedia.org/wiki/Fourier_transform

<< A Fourier transform is an operation which converts functions
from time to frequency domains. >>
[click for animations}
http://www.cis.rit.edu/htbooks/nmr/chap-5/chap-5.htm

<< Dimensional analysis shows that the terms in the field
equations involving more than two spacetime derivatives
would have to be accompanied by constant factors proportional
to positive powers of some length. If this length was anything
like the lengths encountered in elementary-particle physics,
or even atomic physics, then the effects of these higher
derivative terms would be quite negligible at the much larger
scales at which all observations of gravitation are made.
There is just one modification of Einstein's equations that
could have observable effects: the introduction of a term
involving no spacetime derivatives at all-that is, a cosmological
constant. But Einstein did not exclude terms with higher
derivatives for this or for any other practical reason, but for an
aesthetic reason: They were not needed, so why include
them? And it was just this aesthetic judgment that led him
to regret that he had ever introduced the cosmological
constant. -- Steven Weinberg >>
http://www.aip.org/pt/vol-58/iss-11/p31.html

Sue...

Thanks for the links.

.

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