Re: MOND's similarity to Le Sage's Model
- From: Aetherist <TheAetherist@xxxxxxxx>
- Date: Tue, 26 Sep 2006 18:46:28 GMT
On 26 Sep 2006 00:31:53 -0700, "George Dishman" <george@xxxxxxxxxxxxxxxxx> wrote:
On Mon, 25 Sep 2006 20:41:28 +0100, "George Dishman"
<geo...@xxxxxxxxxxxxxxxxx> wrote:
"Aetherist" <TheAether...@xxxxxxxx> wrote in message
news:jgkdh25q1lpcma72t9lafsc04lfhrpsqn5@xxxxxxxxxx
In (MO)dified (N)ewtonian (D)ynamics it is proposed that the flat
galactic rotation profiles observed is due to a modification to
Newton's force equation such that,
F = ma
is modified to be,
F = kma
Where,
k = µ(x)
and µ and x are arbitrarily determined constants.
<snip my explanation>
You have a fundamental misunderstanding of my comments
which I cannot help you with...
Paul, you have a fundamental misunderstanding
of MOND if you believe what you wrote. µ(x) is
a function which is intended to make F=ma
non-linear.
Clearly MOND is 'intended' to modify F = ma. That modification
is also clearly specified as F = ma µ(x). Just as clearly,
x is defined as |a|/a_o where a_o is an 'arbitrary' constant
picked to match observations. Of course |a|/a_o is a dimensionless
ratio (scalar). Further, JUST AS CLEARLY MOND defines this as,
µ(x) << 1 becomes x
and
µ(x) >> 1 become unity...
Let's quote the Reference shall we,
"The exact form of µ is unspecified, ...
only its behavior when the argument x is small
or large."
Given that µ is also dimensionless, we have a vaguely defined
'function' µ(x) such that when x << 1 µ(x) = x and when x >> 1,
unity . Now what continuous mathematical form behaves in such
a manner? Given this form, by its very definition, µ(x) MUST!
be non-linear for all x's > 0 & < infinity... Further, is it
a discontinuous function???
It is _not_ a constant, arbitrary or otherwise.
That's funny, quote...
"The term a_o is a proposed new constant,
...
Milgrom proved in his original paper, the form of µ
does not change most of the consequences of the
theory, such as the flattening of the rotation
curve. ..."
The exists a strong correlation of a characteristic inverse of
a property to the property itself, such as the standard radiation
transport equation,
-ht
¢' = ¢ e
Where t is the thickness of a shield and h the 'linear attenuation
coefficient' which has dimensional units of inverse length. If
one wanted to know how much of the radiation's momentum was lost
in transiting t it is simply,
-ht
dp = p(1 - e )
Nothing stops me from writing this as,
dp = p f(ht)
And further defining f(ht) as,
-ht
f(ht) = 1 - e
Certainly, when ht << 1 we get,
f(ht) = ht
and when ht >> 1 we get,
f(ht) = 1 (unity)
So George, what IS the difference in the mathematical
characteristics of f(ht) and µ(x)?
It is NOT clear to me how anyone can misunderstand these obvious
mathematical facts...
Paul Stowe
.
- References:
- MOND's similarity to Le Sage's Model
- From: George Dishman
- MOND's similarity to Le Sage's Model
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