Re: the metric tensor 1

Lesson two

Movement in the precense of matter.

the traslation from now to soon in the presence of matter needs a formula in
the diagonal metric tensor to represent the change from now to soon,

if now is 15,000 km from earth's centre, and soon is 14,991 from the earths
centre then a potential energy change takes place of Gm/15000-Gm/14991 G is
the universal constant of gravity (mearurable) and mass is the mass+energy
within the point.

So the metric means that as we do the translation the space shape factor
changes
Now the shape factor of space is = Gm/r as far as I understand it.

so far away the factor is 0

The light here is of freqency f and wavelegth L=cf

at a disdance r the shape factor is Gm/r so the energy of light will be
higher.The energy of light is hf in flat space but as it goes closer to a
mass+energy it is of higher energy, Gm/r the light gains potential energy
(Gm/big to GM/less big)=hf to hf + small bit

so Gm/r2-Gm/r1=hf1-hf2 to put that into the diffential form for integration
is not needed if we use the metric tenso. the shape has changed from
(Gm/r2)/h to (Gm/r1/h) to get the length we have to use the wavelegth this
is fL=c so L=c/f

So the length of space has changed from c/(Gm/r1/h) to c/(Gm/r2/h). So space
can be mapped in shape according to the location relative to massive objects
or areas of energy, includes light energy.

to make it simple the tensor is a series of sums so the column vector
x1...x4 is for sums
x1 x a number >y2 now if y2 is r2 from a massive object and x1 is r1 from a
massive object then the shape factor is included. x1 is a point the ordinate
of the massive object is x0 and also y0 this is the same point, then the
translation is from a shape of c/Gm/(x1-x0)/h to c/Gm/(y1-y0)/h.

end of lesson two

"PureGold" <PureGold@xxxxxxxxxx> wrote in message
news:xV9ei.99651$hj5.23202@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
I made a mistake when I changed the co-ordinates from linear to exponential
to look inside a black hole. You see the scale is similar to the Kelvin
scale. By using a linear scale we can see 0 but it cannot be reached. We
should really be using a log scale so 0 is - infinity so cannot be reached.



The theory of the black hole is wrong in the same way.



To understand it you need the theory of metric spaces and the Einstein's
concept of sitting at the foot of a cliff. Now light is falling down
towards you and it gains energy as it falls but since it cannot go any
faster (or slower) it increases in frequency, so shortening the
wavelength. This wavelength can be thought of as the shape factor of space
at that point and the frequency as the local shape factor of time.



Going up the same thing applies.



So space is smaller as you go towards a massive object (like your left
index finger). Now as a small object goes near a big object the space gets
changed in length, (it is not real, it is 4-perspective), so like a beam
of light passes through a change in refractive index it is bend towards
the region of space is shorter. It is as if light moves more slowly.



Boring is it not.



Now to do the sums, you need a tensor (this is a matrix) now a position in
space-time is a 4 vector. This is a column of 4 numbers.



1

3

5

2



Now to get from one place to another you need a matrix.



The matrix operation x takes you from the column vector (now) to the
column vector (soon).



The matrix is a square 4 x 4 that is the result of taking each element of
now to each element of soon.



The simple diagonal matrix,



1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1



is the identity matrix that means you stay put.



The diagonal matrix:



2 0 0 0

0 4 0 0

0 0 2 0

0 0 0 3



gives you the translation event now to soon. Which generally means you
have moved and the velocity in the 3- subspace and is given by the 3
subspace numbers divided by the time subspace.



Here the 4-space is flat.



With curved space there are off diagonal numbers that mix the 4 dimensions
thus making space linear but curved. (linear algebra).



End of lesson one.






.

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