Re: Newton's inverse-square force law from Einstein's equation
- From: "JMA" <jmDOTa@xxxxxxx>
- Date: Thu, 5 Jan 2006 19:27:48 -0000
"John Baez" <baez@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> escreveu na mensagem
news:dpidu7$79v$1@xxxxxxxxxxxxxxx
> Happy New Year!
>
> Ted Bunn has just used my simple formulation of Einstein's equation
> to derive Newton's inverse-square force law from general relativity
> without using tensor calculus. Check it out!
>
> Einstein's equation in more or less plain English:
>
> http://math.ucr.edu/home/baez/einstein/node3.html
Congratulations.
Indeed it is explained in plain English, but it is just philosophy.
You have assumed that:
««The flow of -momentum in the -direction is
just the energy density, often denoted .»»
Since time is changing, or flowing, then your conclusion becomes
quit obvious:
"Density is changing and therefore there was a Big-Bang and
the Universe is expanding".
You have assumed the conclusions to get the conclusions.
If the speed of light depends on the distance travelled the
expansion of the Universe is explained and your assumption
that density changes over time is not required.
> Deriving the inverse-square force law:
>
> http://math.ucr.edu/home/baez/einstein/node6a.html
In the above link it is shown that your assumption that density
changes over time is wrong, since planets don't shrink.
Actually you only have seen half of the problem.
The full problem, or the reality, is that every mass in the
Universe rotates like a rigid body.
All that we see in the Universe rotates and rotation is
not included in your description.
You must analyse the following problem:
"A small ball of freely falling test particles initially at rest with
respect to each other, and rotating as a whole (that is a rigid
body like a planet is)."
Given that particles are initially at rest with respect to each other,
it is a solid body at least initially.
Hence you get a gyroscope.
So Euler's equation of motion do apply.
The problem becomes the transformation between an inertial
frame of reference and a rotating frame of reference.
Since there is no solution for the said transformation, nor there
is a solution for Euler's equation of motion, all that you have said
is just philosophy, not the reality.
Gyroscopes show that gravity and uniform motion are equivalent.
Gyroscopes also show the equivalence principle.
Gravity = circular motion
Circular motion = gravity
Gravity could not be due to density change, but due to circular
motion, once you analyse the full picture.
The full picture shows that every body in the Universe rotates.
So far no non-rotating body was found in the Universe.
Rotation must not be forgotten.
Happy New Year!
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