[General] Electron Size in a Collision

[John Macken]

Vivian and All,

 

We all agree that collision experiments indicate that the size of an
electron is smaller than the resolution of the collision experiment.  Since
some experiments have been done at about 50 GeV, this means that the
electron appears to be smaller than about 10-18 m. We have different models
of an electron and they have different explanations for how an electron can
appear to be a point particle.  In a previous post you say, "I prefer the
answers given by John W, Richard G, myself and others that the radius of an
electron decreases with its energy, giving it a point like property as it
travels at sufficiently high velocity."  I will address this point.  You
seem to be saying that a fundamental particle changes its radius in X, Y and
Z dimensions as it propagates.  As I recall, the radius decreases with 1/γ
in one model and 1/γ2 in another model.  Also as I recall the decrease in
radius is accompanied by an increase in the electron's Compton frequency in
some models.  Perhaps I do not understand this concept correctly, but the
change in radius and frequency appears to violate the covariance of physical
laws.  All frames of reference should have the same physical laws.  Here is
the problem.  In order for the laws of physics to be the same in all frames
of reference, Lorentz transformations have to hold between different frames
of reference. The changes you propose do not correspond to Lorentz
transformations.  

Suppose that we designate the Z axis as the direction of propagation between
two frames of reference. Then the expectation is that an observer in frame A
would perceive that an electron in frame B retains its original radius in
the X and Y dimensions while the Z axis dimension decreases by r = ro/γ.
Also, the rate of time in frame B appears to slows down by 1/γ as seen from
frame A.  The Compton frequency can be considered a clock beat.  Therefore
the observer in frame A should perceive that the electron's Compton
frequency in frame B has slowed down rather than speed up.  If the changes
you propose take place, then an observer in frame B would perceive that an
electron has different properties than the properties observed in frame A.
This would be a violation of the basic assumption of invariance in spacial
relativity.

Perhaps, the most important point is that the changes that you propose do
not even achieve the goal of making the electron appear to be a point
particle in a collision.  Here is the reasoning.  Suppose that we have two
electrons accelerated to 50 GeV and propagating in opposite directions in an
accelerator.  I am in the acceleration frame of reference and the electrons
will collide in front of me.  If the collision is head-on, both electrons
momentarily are stopped in my frame of reference at the moment of closest
approach.  Therefore at that moment neither electron is moving relative to
me.  They might have been small when they were moving, but when they have
stopped in the collision, in your model they should have their original
radius equal which you believe to be ½ the reduced Compton wavelength.
Since the scattering is taking place in my frame of reference, the
scattering should indicate this full size.

Contrast that to my model.  I say that the electron appears to be the same
size and have the same Compton frequency when viewed as a "stationary"
electron in any frame of reference.  This means that Lorentz transformations
hold between frames. An electron in frame B retains the same radius in the X
and Y dimensions but appears to shrink in the Z direction.  Also the Compton
frequency appears slower when observed from frame A.  

However, the important point is not the size during propagation, but the
size during collision.  In my model, the size of each electron physically
decreases when the two electrons collide and momentarily are stopped in my
frame of reference.  The kinetic energy carried by each electron has been
converted to the internal energy of the waves that make up the two
electrons.  At the moment of collision, the wave amplitude increases and
wave frequency increases.  The Compton wavelength decreases, therefore the
radius decreases when the colliding electrons are momentarily stopped.  If
the collision is at 50 GeV then γ = 100,000 and the radius decreases by this
factor.  The calculations are done in the "foundation" paper, in section
4.5, titled Point Particle Test. This section of the paper concludes that
the reason that electrons appear to be point particles is that "It is a
classic case of the experiment distorting the property being measured and
invalidating the measurement". 

I also have other arguments supporting my electron size and characteristics,
but this is enough for one post.

 

John M.

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