At 07:50 am 13-09-04 -0700, you wrote:
<snip>
>And the larger implication is cosmological.
>We have always assumed that our galaxy is
>held together by an inverse square law, but
>if not... what if it were just a pure inverse
>distance relationship, past a certain dimensional
>interface?
I thought this recent bit of correspondence with a
colleague on the inverse square law of gravitation
might contribute to the topic of an inverse distance law.
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Clayton wrote:
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Frank,
1) You mentioned in your email today about the
inverse square law of gravitation as the
difference between two inverse laws. I remember
you saying this [many years ago] but I am sorry
to say I have lost the details. My apologies
for this. Please could you send them to me again?
Or, if it is posted on the web, then I can refer
directly to it if the opportunity arises.
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Grimer wrote: ...
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1/x - 1/(x+dL) = [(x+dL)-x]/[(x).(x+dL)]
Where dL is a small constant amount compared with
any value of x
= dL/[(x).(x+dL)]
Now dL is small compared with x so in the limit we
can write,
= dL/x^2
Here's a point I hadn't seen before. The fact that
one is x and the other is x+dL suggests that different
shells of the bodies are involved. The repulsive force
could be the external radiation that is reflected from
one shell surface and so pushes bodies apart whereas the
attractive force would arise from absorbtion and
consequent shadowing.
Mmm.....this is beginning to sound interesting. It could
account for the enormous strain in the atom. The apple
core is the nucleus, the outer flesh is the electron shells.
I've often wondered why the atom has the structure it has.
After all, you must admit it's terribly weird and no one
dreamt of it before it was discovered.
So what it means is the x and the (x+dL) are not just
mathematical devices. They are actually telling us something.
A bit like the power curves were telling us to look at
concrete as already being under strain.
Interestingly enough we can get a 4th power law from the
difference of two inverse square laws by the same technique.
1/x^2 - 1/(x^2+dA) = [(x^2+dA-x^2]/[(x^2).(x^2+dA)]
= dA/[(x^2).(x^2+dA)]
Now dA is small compared with x^2 so in the limit we can write
= dA/x^4
Which is Stefan's law and can be seen as the difference between
magnetic attraction at one level say and electric repulsion at
the other - or the other way round - I'm not too sure which but
it will all come out in the wash as my mother used to say. 8-)
Hang on a minute you might say, "Stefan's law is proportional to
the 4th power, not the inverse power."
No problemo. One doesn't work with temperature but its inverse
I did suggest a good name for the inverse in one of my earlier
posts but I can't find it. I shall have to copy all those posts
to a file so that I can search.
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Also, off topic, but interesting, was the following,
Clayton wrote:
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2) Reading the Vortex correspondence and your description
about the two approaches to crossing a ravine reminded me
of a book I read recently about the pyramids of Egypt.
Unusually, it was written by an engineer. He describes how
the stone blocks must have been moved, not by dragging on
sledges, but by attaching wooden curved pieces to each of
the four long faces, thus making each block into one great
cylinder, so that they could be simply rolled along by a few
men, even though they may weigh a couple of tons.
Interestingly, such wooden curved pieces have been found
and are in the Cairo museum for all to see. Yet the popular
view remains that the blocks were dragged on sledges and
the curved pieces are seen as being used for some other,
minor, purpose.
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Cheers
Grimer
