At 03:31 pm 20-10-04 -0400, you wrote:
>Frank writes:
>>Both Ing.Saviour and I have quite independently recognised that
>>mass has the dimension of T/L (see http://www.blazelabs.com/)
>>and it is evident that materons have "hidden mass".
>
>Add me to the list too. In '91 I was studying the
>CGS system of measure and whilst contemplating the fact
>that a unit of magnetic charge was defined solely by the
>force, it occurred to me that the same trick can be
>played with defining mass. I'm looking at my old notes,
>and I have the unit of mass being something like.
>
>m = L^3 T^-2 G
>
>I wonder if this is because I couched things in terms
>of the CGS system, whereas saviour and yourself are
>using SI?
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.
In fact my derivation led to mass being T/L whereas
his gave T^3/L^3 - but that difference is merely
cosmetic.
The important thing is to recognised that mass is
the manifestation of a closed path inverse velocity.
of some kind. Whether this velocity is in one two
or three nested dimensions is of secondary importance.
In short, I'm saying it's d(n)T/dL(n)
Saviour's saying it's
{d(n)T/dL(n)}.{d(n+1)T/dL(n+1)}.{d(n+2)T/dL(n+2)}
Consider this.
Q. What is the dimension of velocity?
A. [L]/[T]
Q. But what is the dimension of speed?
A. [L]/[T]
So clearly, we can go unambiguously from property
to dimensions but not from dimensions to property.
If we are asked, "What property is [L]/[T],
and I say speed and you say velocity, we are
both right.
Let's take another example
Consider the fraction 3.3.3/4.4.4
Let the property of divisibility by 3 be T
and the property of divisibility by 4 be L
Supposing I view the fraction at the global level as 27/64
then I will say that the dimensions are [T]/[L] and I will
be correct because 27 has the property of divisibility by
three and 64 has the property of divisibility by 4.
Supposing Ing. views the fraction at the local level as
(3/4).(3/4).(3/4)
He will say that the dimensions are [T]/[L].[T]/[L].[T]/[L]
Since all the threes have the property of divisibility
by three and all the fours have the property of
divisibility by four, he will also be right.
The essential point is -
Mass is the same elephant viewed from different angles.
Once upon a time a great man wrote a great book.
The man was the late Professor J.L.Synge a
mathematician at Trinity College Dublin.
The book (Science and Nonsense) was based on his
acute insights into the nature of scientific
research made public in a series of Statutory
Lectures in the college's School of Theoretical
Physics.
Synge showed that definitions of the qualitative
concepts of physics are inevitably circular. This
idea is most readily illustrated by considering
the definition of words using a dictionary.
Ultimately the definitions must be circular since
words can only be defined in terms of other words.
If the vicious circles of definition are large
there is a natural but unfortunate tendency to
loose sight of the fact that a chain of definitions
must close upon itself. In terms of the dictionary
this danger can be avoided by setting up small
vicious circles of definitions such as,
To exist is to occur.
To occur is to exist.
Emulating Synge we can show mass has the dimensions
of an inverse velocity by a minimalist argument.
We can simply take the conservation of momentum and
write it in the PV = a constant format as
MV = a constant where M is mass, V is velocity
Since the choice of units is arbitrary we can put
MV = 1
And further more we can choose to look at mass in
a way that will make 1 dimensionless.
Whence from simple dimensional analysis
[M] = [T].[L]^-1
And since we know that we can use up mass to
give us velocity, what could be simpler. 8-)
And if the cognitive dissonance is too intense let's
look at it another way.
Turn on a monospace font.
Consider in the FIGURE 1 a body with the properties,
Mass M, Velocity V, direction L (i.e. from the Left)
which is heading towards a black box where a conservation
of momentum is going to take place.
Consider also a second body with the properties,
Mass M, Velocity V, direction R (i.e. from the Right)
which is also heading towards a black box where a conservation
of momentum is going to take place.
--------------------------------------------------------
Identity
-----------
| |
----- V=4 | Black | V=2 ---------
|M=2| ============>> | Box | <<====== | M=4 |
----- Lefty | | Righty ---------
-----------
FIGURE 1
--------------------------------------------------------
--------------------------------------------------------
-----------
| |
V=4 ----- | Black | --------- V=2
<<============ |M=2| | Box | | M=4 | ======>>
Righty ----- | | --------- Lefty
-----------
FIGURE 2
--------------------------------------------------------
Normally we think of the mass property as defining the
identity of the body just as Keith defines the identity of
your body.
But suppose we choose the direction as defining the identity
of the body. To help you psychologically to do this I will
tell you a true story.
When I was at school my friend John Barry had a cycle race
on the main road outside the school with another classmate
Peter Chamberlain. Peter fell under a lorry and lost his
right arm. After that everyone called him Lefty.
Cruel but very descriptive.
So in FIG.1 we see master Lefty entering the Black Box
with a mass of 2 and a velocity of 4. In FIG.2 master
Lefty exits the Box with velocity of 4 and a mass of 2.
Likewise with master Righty, who lost his arm in the
U.S. where they drive on the wrong side of the road <g>
Conservation of momentum. Q.E.D.
In "The Strange Story of the Quantum", Hoffmann
describes something a bit like this.
==========================================
"When Wheeler first has his idea he saw
in a flash a stupendous cosmic pattern:
a single electron shuttling back and forth,
back and forth, back and forth on the loom
of time to weave a rich tapestry containing
perhaps all the electrons and positrons in
the world."
==========================================
Now you might think that direction is a rather abstract
property to be taken as Identity.
But why should you think that, Keith.
After all, once upon a time your mass was only half
what it is now - but you are still the same Keith.
And if you live long enough you will be only able to
run half as fast as you once did, but you will still
be the same Keith.
------------------------------------------------
I took a longer, less mentally traumatic route to
show that mass had the dimensions of [T].[L]^-1
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.
As for experiments, I haven't a clue.
There are three orders of angels and there are
three divisions of Scientific Civil servants.
Just like the army in fact.
There are those who think about what to do.
There are those who think about how to do it.
There are those who do it.
I was in the First Division. <G>
Cheers
Grimer
