Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
caution about primitive axiom terms borrowed from math #1198 New
Physics #1318 ATOM TOTALITY 5th ed
Posted:
Feb 4, 2013 1:07 AM
|
|
I need to spend some time on primitive axiom terms.
In mathematics these are terms that we agree upon to use, but which
have no further explanation, such as a point is without length width
or depth. Or a line has length only. Equality and equivalence are also
primitive terms.
In physics, when we have the Maxwell Equations with the facts of
Chemistry as the axioms, there are primitive axiom terms involved,
such as duality, rest-mass, electricity, magnetism, energy, time,
space, momentum, charge, spin.
I need to spend a little bit of time discussing the primitive term
equality and equivalence of mathematics and its misuse and
understanding in mathematics and then its horrible flagrant misuse in
physics.
In mathematics, equality is sameness. So to say that 2 = 2 means one
is the same as the other. But what about 2 = 1 + 1? Well, in
mathematics, since math is abstraction and not physical objects, that
2 = 1 + 1, is just as acceptable as 2 = 2. So what about equivalence?
In math, equivalence is something like 1/2 equivalent to 3/6. Now in
physics, if we have a pie cut in 2 parts and a pie cut in 6 parts,
that 1 part of the one pie is the 3 parts of the other pie. Which is
not exactly sameness of math but similarity of math, but for physics,
equality and equivalence are used when there is no equality nor
equivalence.
Now I am not here to straighten out math and physics as concerns
equality and equivalence. I am here to draw attention to this thorny
troubling problem that is in both mathematics and physics. There is no
clear way of dismissing as to what is equal and what is equivalent,
because 1/2 = 3/6 and
1/2 equivalent to 3/6.
But major problems do occur in physics when we think that equality is
everywhere in physics. The equality or equivalence in E = mc^2. It is
not really equality at all, nor is it equivalence.
In physics, often the concept of "proportional" is used. Now let us
try that on mathematics. Is it better to say 1/2 is proportional to
3/6, rather than say it is equal or equivalent. It is safe to say that
2 = 2, because equality is identity. But in physics is it safe to say
the Coulomb force is a equality? Or is there equality in the Maxwell
Equations?
When physicists use "proportional" they still have some linear factor
to include before they can put in a equal sign. So that in Faraday law
emf is proportional to -dB/dt. Once we include the N windings do we
have equality, emf = -N dB/dt.
But do we really have equality in physics as in mathematics? I would
say no, because mathematics is not physical objects and physical
structure but rather abstraction divorced of physical objects and
structure, whereas physics is all about objects and structure. An
electron at point A in space is different from electron at point B in
space, simply because they are at different locations. The share the
same charge of -1 and other attributes but they are not the same and
identical.
So that in physics we just borrow the concept of equality from
mathematics to allow us to make deductions.
So I guess I can help a little bit, by saying there are terms better
suited than equality or equivalence for physics. Terms such as
"transforms" or "proportional" or "becomes" or "changes" or "dual".
So that in the formula E = mc^2 we can say energy changes to mc^2 or
the neutron in this formula:
Neutron = proton + electron + neutrino
we can say Neutron tranforms into proton + electron + neutrino
In the formula E = mc^2, perhaps the best term for that is that Energy
is the dual of mc^2. So if we symbolize duality with a O symbol and a
arrow in that O such as the arrow in -->, that the equation looks like
this E Q mc^2, (sorry the keyboard cannot do the symbol, but the
letter Q imagine that slash bar as a arrow in the circle), meaning
that energy is the dual of mass * c^2.
And so the four Maxwell Equations have no equal sign but a sign of
duality.
I do not want to spend much time on this because someone can devote
their entire life on just this topic with no guarantee of success or
improvement.
I do want to point out the gray and prickly area of logic of
"primitive axiom terms".
And it should be obvious to all who master physics that although we
should not use equality symbol in physics, we do so anyway, since it
is the most practical means of going forward. So as long as we keep it
back in our minds that equality is a symbol for mathematics, but not
really for physics.
--
Google's archives are top-heavy in hate-spew from search-engine-
bombing. Only Drexel's Math Forum has done a excellent, simple and
fair archiving of AP posts for the past 15 years as seen here:
http://mathforum.org/kb/profile.jspa?userID=499986
Archimedes Plutonium
http://www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
|
|
|
|
