At 03:00 pm 22-10-04 -0400, you wrote:
>Hey,
>
>>I doubt it. My approach was totally different to
>>Ing.Saviour's and in my case the system, SI or CGS,
>>or Imperial for that matter, is totally irrelevant.
>
>But it does matter, in how you divide and compose
>the derived units. As you say, this stuff can be
>cut up in any number of ways. Some more meaningful
>than others. I generally adhere to the notion that !more! dimensions
>are more enlightening than less,
It's a point of view 8-)
>yet the
>'91 version of me (allusion to your earlier post)
>seemed enamored enough of the LT system to write
>several pages of notes...
>
>>In fact my derivation led to mass being T/L whereas
>>his gave T^3/L^3 - but that difference is merely
>>cosmetic.
>>I took a longer, less mentally traumatic route to
>>show that mass had the dimensions of [T].[L]^-1
>
>I look forward to seeing it. I seem to remember somewhere
>else running into the notion of momentum being
>more fundamental than mass.
Well, since mass is [T]/[L] and velocity is [L]/[T] it
follows as night follows day that,
[T].[L]
Momentum = -------
[L].[T]
Mmm....Now THAT is interesting - very! 8-)
It follows that momentum is a pure number.
What's more, since the unit values of L and T are arbitrary
it follow that we can choose unit values of T and L so that
dimensionless Momentum = 1
The number 1 more fundamental than mass?
Yes. I think I'll buy that. ;-)
And if you can dredge up from the depths of your memory
just where you ran into:
"the notion of momentum being more fundamental than mass."
I'm sure Ing.Saviour and I would be most appreciative.
>>Ing.Saviour has part of the maths on his website.
>>When I've OCR'd it I'll put the whole Note on my
>>web site for you to read.
>
>I seem not to have the link anymore... What is it?
The URL for Ing.Saviour's website is:
http://www.blazelabs.com/
The page which contains a quotation from Synge I gave in N103/87
and part of the maths derivation is:
http://www.blazelabs.com/f-u-massnature.asp
>Here's my derivation based on the CGS style of a fundamental
>definition using the force law. As you may know, the basic
>quantities of magnetic and electric charge are derived units
>based on the inverse square force laws ( Coulombs law ).
>
>-----------------------------------------------------------
>LT System : Units for the derived quantity of mass
>-----------------------------------------------------------
>Newton's law has the gravitational attraction
>between two masses as
>
>(1) F = GM^2L^-2
>
>with G being a constant having dimensions
>
>(2) G = M^-1L^3T^-2
>
>so that relation (1) can be satisfied.
>
>The old CGS system used Coulombs laws to
>define the basic quantities of magnetic and electric
>charge. This stands distinct from the SI system
>which uses a velocity ( C ) to tie magnetic
>and electric systems together. We'll use
>the force law approach below, saving the
>SI approach for a separate paper.
>
>What we want to do is find a new dimension for mass M
>so that instead of (2) we can satisfy (1) with
>
>(3) G = 1
>
>We'll call the new thing M prime, to distinguish it
>from the old symbol for mass. It can be shown that
>
>(4) M' = L^3T-2
>
>will satisfy the new relationship from (1)
>
>(5) F = M'^2L^-2
>
>as so.
>
>(6a) M'LT^-2 = M'^2L^-2
>(6b) ML^3T-2 = M'^2
>(6c) L^3T-2 = M'
>
>--------------------------------------------------------
>
>Comments or criticism gladly accepted.
Well apart from the Synge quotation regarding the virtue of
small vicious circles, I would only add the quotation the
Ing.Saviour saw fit to put on his excellent website.
===================================================
..... Thought is difficult and painful. The
difficulties and pain are due to confusion.
From time to time, with enormous intellectual
effect, someone creates a little order - a
small spot of light in the dark sea of confusion.
At first we are all dazzled by the light because
we are used to living in the darkness. But when
we regain our senses and examine the light we
find it comes from a farthing candle - the candle
of common sense. To change the metaphor, the sages
chase their own tails through the ages. A little
child says 'Gentlemen, you are chasing your own
tails.' The sages gradually lose their angular
momentum, and, glancing over their shoulders, see
what they are pursuing. But most of them cannot
believe what they see, and the tail chasing does
not die out until a generation has passed.....
===================================================
Cheers
Grimer
