LESSON NO. 2
These lessons teach the physics that governs Aether Science
theory
COLLISIONS
© Harold Aspden, 1997, 2002
Electric Particles in
Action
In Lesson No. 1 we discussed the principles governing the
motion of a particle of mass m when acted upon by a force. In this Lesson No. 2
the same approach based on energy conservation will be applied to the collision
of two particles. We are, however, going to complicate the problem by declaring
that all particles of matter are, at the truly fundamental level, not just
something having a mass we can denote as m and then proceed by using Newtonian
principles. Instead, we shall see them in their true form as being minute
particles of electric charge concentrated into a small volume of space so as to
have an energy which we know governs their mass.
Eventually we will need
to explain how charge derives its polarity in terms of energy, space and time,
in order to justify our master plan of reducing everything in fundamental
physics to these three dimensions. However, we are obliged to proceed step by
step and so we will accept that those fundamental charges each have the unitary
charge e equal in magnitude to that of the electron. Indeed, I admit that I
cannot, as yet, solve the riddle of charge polarity. It lies in unexplored
territory and, apart from a few brief excursions into that territory, I see it
as uncharted ground.
Though electricity is everywhere in us and around
us, just as is the aether, the question of what determines whether an electric
charge is positive or negative and why like polarity charges repel and unlike
polarity charges attract is a mystery. Note that I could say that the measure of
energy density is the square of field strength, that the polarity of the charge
is the direction of that field and that, since there are positive and negative
square roots to a positive energy density expressed as the square of field
strength, so there must be two polarities of opposite sign. If that level of
explanation satisfies your curiosity then we can move on without concern but, if
you share my thoughts, you would still wonder whether there is an oscillation
mode at the universal Compton electron frequency and whether phase relationships
are the governing factor.
Indeed, I see that question of charge polarity
as a challenge and possibly the final frontier of our conquest of physics. It
surprises me that the subject is not even mentioned by physicists as something
warranting research investigation. It seems that it is easier to explore what
happened in the first moments of the 'Big Bang' than to look into what is
happening within us and all around us here and now on Earth.
Note also
that I shall not be bringing relativistic mass increase into this enquiry. When
two charged particles come into collision at high speed they are normally moving
'freely' and my comments in Tutorial No. 1 concerning relativistic mass increase
do apply. Indeed, as I explained in my book 'Physics without Einstein' on
pp. 17-18 under the title 'Fast Electron Collision' I can draw attention to an
experimental study which confirms this in an interesting way. See the paper by
F. C. Champion, Proc. Roy. Soc. Lond., v. 136A, p. 630 (1932). There are
two points of special interest raised by this paper. One is the statement by
Champion that:
"Considering the total number of collisions measured it would
appear that, if any amount of energy is lost by radiation during close
encounters, the number of such inelastic collisions is not greater than a few
per cent of the total number."
Yet, your teachers will persist
in telling you that there is such energy radiation, as given by the Larmor
formula, even though one cannot do the mathematics of deriving the formula for
mass increase with speed if there is such radiation. They know that energy is
radiated by a radio antenna where, if there are billions of electrons (say, N)
all oscillating together as current, then that current squared is a measure of
the strength of that radiation. However, they do not seem to comprehend the fact
that the individual electrons will not radiate on their own. They can only act
collectively and so the energy radiated by that antenna is proportional to
N(N-1) and not proportional to N2. To the radio world, with N
measured in billions, or rather many billions of billions, these two quantities
are as good as the same, but the individual mass of each of those electrons is
quite small and that small difference in energy radiated is what accounts for
the inertial mass of the electron. Champion's experiment proved that they do not
radiate the energy that gives them that inertial mass. Even Einstein had to
assume that, but teacher's have swept the problem aside and they still teach
that energy is radiated by the electron when accelerated. Then, when confronted
with electron acceleration within the atom, they hide behind the notions of
quantum theory to say that the electron only radiates when it jumps between two
stable states of motion in the atom.
The other point is rather subtle.
There is some evidence hidden in the experimental data obtained by Champion
which leads me to think that there is a statistical chance that a hidden jitter
motion, that of the aether, can get involved in those fast electron collisions.
Perhaps one day I shall discover my old notes on that theme and put my findings
into my Web pages.
Why Action equals Reaction
Moving on,
our reason for introducing electric charge in motion is the physical reality
that energy involved in all collision events between particles, as seen at the
ultra-microscopic level, is essentially in electrodynamic form and spreads over
the field environment of the collision. It is not just something that is seated
in one or other of the particles and which gets pooled only at the instant of
contact in the collision. The dominating fact is that energy is conserved and,
now assuming that the masses of the individual particles do not change because
the speeds involved are so low compared with the speed of light, we will proceed
here by relying on a force formula that we shall derive from first principles in
the next Lesson No. 3.
That formula declares that the electrodynamic
force between two charges e, e' acts directly along the line joining them and is
proportional to ee', inversely proportional to the square of their separation
distance and directly proportional to the square of their relative velocity. Two
electrically neutral particles really comprise numerous such charges of opposite
polarity and it is easy to suppose that those individual forces between the
numerous pairs of charges approaching collision will cancel out because they all
share the motion of their parent particle. However, our sole concern is what
happens at the moment of each individual impact between two charges as the
parent particles crash into one another. Each colliding pair will have a Coulomb
potential ee'/x, if x is the distance between their charge centres at the moment
they suffer the change of speed. That remains the same, whether the collision is
about to occur or whether it has just occurred. The electrodynamic potential,
according to our above formulation, will similarly need to remain the same under
these circumstances, since energy is conserved, and so the square of relative
velocity of the charges is unchanged as well. However, as you know from
mathematics, the square of a negative quantity is the same as the square of its
positive equivalent. This means that the event of collision can reverse the sign
of the relative velocity as between the two colliding charges.
What is
here suggested is that two electrically neutral particles of matter can enter a
collision and, given no loss of energy in the process, emerge from that
collision with their relative velocities reversed. Yet the reason for this is
their microscopic composition as an aggregation of numerous fundamental
component electric particles, such as electrons and positively charged atomic
nuclei. This proposition has been deduced by applying a force formula that we
shall in turn derive from first principle analysis in Lesson No. 3.
To
proceed, the task at hand is to analyze in terms of mechanics the energy
involved when two particles of different masses m, M come into collision at
velocities of u, U, respectively and emerge from that collision at velocities v,
V, respectively, assuming no loss of energy by radiation or otherwise. We
proceed, basing our analysis solely on the energy conservation requirement and
the reversal of the relative velocities in the collision.
Write:
U-u = v-Vand rearrange to give:
U+V = v+uEquate the combined kinetic energies of the two
particles before and after the collision:
mu2/2+MU2/2 =
mv2/2+MV2/2Now multiply throughout by 2,
rearrange and factorize the terms to get:
m(u-v)(u+v) = M(V-U)(V+U)Next, use the second equation to
simplify the above expression and obtain:
m(u-v) = M(V-U)Again rearrange:
mu+MU = mv+MV
The equation now obtained says that the
combined linear momentum of the two particles before impact is equal to that of
the particles after impact and so shows that momentum is conserved when two
particles interact. In mechanics particle interaction is by contact and so,
since rate of change of momentum is a measure of force, we can say that no net
force is generated by particle interaction. In other words, if one part of a
mechanical system acts on another part to set up forces between those parts, the
action equals the reaction because the two forces must sum to zero.
It
follows that we have derived Newton's Third Law of Motion by applying first
principles based solely on energy conservation and a law of force involving
relative motion.
Take note that the conservation of energy applies to the
whole system and that the system is, in its microcosmic sub-structure, comprised
of electric charges, as is the aether itself. Therefore, at all times, in
applying Newton's Third Law of Motion, one must not be unduly surprised if
anomalies are encountered because the aether itself has got into the act. Isaac
Newton had no authority to rule out possible circumstances where, with energy
conserved, the reaction of the aether intrudes into the picture and asserts
forces on matter. Indeed, it must if it is to shed energy that finds its way
into the matter form as by creating protons and electrons.
The starting
point for determining what is possible and what is not possible concerning
unbalanced forces is the conservation of energy without the help of Newton's
Third Law of Motion. The territory where the force anomalies are to be found is
that known as electrodynamics, which in turn gets us into the world of
gravitation. So let us proceed by moving to Tutorial No. 3 and deriving that
electrodynamic formula introduced above.
To progress to the next Tutorial press:
Tutorial
No. 3
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