We have covered some of the fundamental problems with the Atom and looked at how the Structured
Atom Model solves many of these problems. We have also wondered what exactly a charged
particle, either a proton or an electron is. The electron has some very strange properties
that defy many aspect of accepted science. While researching I came across this paper
by Michael Singer who put together a very comprehensive piece outlining some of these
issues.
Let’s run through his paper and get a better understanding of what these issues are.
We know that charged particles emit electromagnetic radiation as a function of their acceleration.
There are however some rather glaring exceptions to this. Some believe that classical electromagnetism
cannot be used to describe atomic behaviour because it requires that an electron radiates
energy under acceleration and this would mean the electron would eventually fall into the
nucleus. But why would a charged particle radiate under one condition but not the other?
Any complete model of the universe must be able to predict precisely which behaviour
occurs or accept that that model of the universe cannot be complete.
The original concepts that particles radiate electromagnetic energy seems to have arisen
in an attempt to describe how X-rays occurred back in 1895. At the time Thomsons plum model
was used and it was believed that electrons smashed into the plum pudding and came to
a dead stop. Using this model the only possible explanation for the X-ray was that the extreme
deceleration during the impact had generated the radiation. This idea has become so embedded
in the scientific consciousness that little critical analysis has ever been carried out
to determine if this does in fact occur in this way. The first real challenge to this
concept came with the theory of relativity and then later on by Rutherford when he proposed
a different model for the atom with a positive central charge orbited by negatively charged
electrons.
Applying Relativity to linear accelerative radiation
If we consider the simple scenario where an electron is accelerated from the observer’s
rest frame up to a velocity v and then decelated back to zero in the observers rest frame.
Lets also assume that this acceleration produces radiation.
There is a certain amount of energy required to accelerate the electron to velocity v - lets
call this Ek. There will also be a certain amount of energy that is radiated by the particle
lets call this Er. This means that the amount of energy required to get the electron up
to the velocity v is Ek + Er if the Principle of the Conservation of Energy is to apply.
This radiation will escape the system. So we have supplied Ek + Er and are left with
only Ek after Er escapes.
Next we will decelerate the electron. According to relativity from the electrons’s frame
of reference it is simply undergoing more acceleration, just in a different direction.
So again we must supply an amount of energy to slow the electron down, Ek and once more
the electron will radiate a fixed amount of energy Er. The radiation escapes leaving the
electron at rest in the observers rest frame.
So the total amount of work done in the observer’s rest frame in the first step is Ek+Er and
the same amount of work is returned to that frame in the second step. So overall there
is no net work done in that frame. But 2Er escapes the system. This process either violates
the Principle of Conservation of Energy and an accelerating charged particle is a source
of free energy, or Er must be zero. In other words there is no accelerative radiation.
If accelerative radiation did exist we would be avle to create a source of infinite energy
by simply having a charge particle bounce back and forth between charged end plates,
radiating energy as it does so.
For accelerative radiation, when the particle is being acclerated by an outside force, momentum
consideration would require it to be radiated more or less in the direction of acceleration.
By contrast a particle slowing down by itself due to radiative loss would radiate energy
in the opposite direction to the acceleration in order to conserve momentum. Relativity
does not allow us to pick and choose like this.
Applying Relativity to circular accelerative radiation
Lets now consider an electron orbiting around a positively charged central point. The question
now becomes does classical electromagnetism demand that the electron radiates and thereby
loses kinetic energy, spiralling into the central charge?
The electron is orbiting because the force it experiences towards the central charge
causes its path to be constantly charged created a circular path. It’s velocity is constant
but it displacement meaning it is accelerating. If it were to slow down and spiral into the
central charge it would have to radiate along the direction of its velocity so that it would
carry momentum away from the electron.
Lets consider this from the electrons frame of reference. It feels a force towards the
positive charge. For the electron to decelerate it must emit radiation in the forward orbital
direction. This is not only at right angles to the acceleration but in one specific direction
out of the 360 degrees of possible directions that are at rights angles to the acceleration.
Now consider an electron that was not orbiting but simply accelerating towards the positive
charge. Now the electron would radiate energy at right angles in one specific angle and
this would cause the electron to start orbiting!
If we now apply the same results from the previous section on linear acceleration but
assume radiation occurs then the work done in radiating the energy must be provided by
an increased centrifugal force, so the electron would orbit at a lower speed for any specific
distance from the central charge. It would not fall into the central charge but emit
radiation continusouly towards it. Hence in this model we would see continuous radiation
coming from atomic structures and a consequential violation of the Principle of Conservation
of Energy
The possibility of an underlying flaw
These issues imply that there might be a fundamental flaw in this concept. Accelerative radiation
is assumed to a lossy mechanism that takes energy from the accelerating charge. If we
consider a simple spring system with a mass on one end. When the system oscillates the
spring provides a force which changes depending on the position of the end in relation to
the attached point. The mass provides a force that is a function of its acceleration or
deceleration. Together these would allow the spring to oscillate forever in a perfect system
where there is no loss associated with any part of the system. If we introduce a damper
then we can remove energy from the system over time but this amount the damper can extract
is directly related to the velocity.
If we therefore consider this with respect to the electron then there must be some sensitivity
to velocity. The problem is that any accelerative radiation is a function of the electron’s
acceleration in its own reference frame, but it is always travelling at zero velocity in
its own reference frame so such radiation cannot be lossy. Consequently any radiation
emitted cannot act to remove energy from the system.
In part 2 we will examine some known examples that are thought to radiate energy through
acceleration and see how this may not actually be the