Absurdities in Modern Physics:A Solution

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*8-9 Physical Reality
of Quantum Tunneling.*

Let us
look
now at another case in which the quantum mechanical
interpretation
leads
to nonsense. It is quantum tunneling. Quantum tunneling is the
traversal
of a particle to the other side of a potential barrier, even
though its
energy is less than the height of the barrier. In standard
textbooks,
it
is claimed that tunneling is a part of quantum mechanics that
cannot be
explained in a rational way. We are told that there is no
alternative
to
believing in imaginary velocities and negative kinetic energy to
cross
the classically forbidden region of the barrier. In other words,
we
have
to use the absurdities of the Berkeley-Copenhagen
interpretation. Since
kinetic energy is the product of a mass (positive number) times
the
velocity
squared (also necessary positive), the result cannot give a
negative
value
of kinetic energy. Then, the particle should not be able to
cross the
potential
barrier.

The
reason
for such an apparently contradictory description of tunneling is
due to
restrictions unconsciously applied during the description of the
phenomenon.
For example, let us use for a moment the same terms as in
quantum
mechanics.
We calculate the probability of finding the particle in
different
regions
of space by setting up the Hamiltonian. Then, we use operators
to
obtain
the equation of the particle. Then, the square of the amplitude
of the
wave function tells the probability of finding the particle.

In this
description,
perhaps we did not notice that the word "particle" implies a
point
particle.
We all know however, that matter is made out of "waves", as
required by
the de Broglie wavelength. If particles have a "real" existence
and
have
wave properties compatible with realism, they cannot have the
size of a
mathematical point.

*8-10 Demonstration
of
Classical
Tunneling.*

For
over
twenty
years I have had to teach the basic principles of quantum
mechanics and
the tunneling of particles through potential barriers. The
questions
raised
by many students about the interpretation of the mathematics of
quantum
physics were quite interesting. Physics students do not accept
absurdities
easily. Their fresh and unbiased minds deserve better
explanations
since
the interpretation of tunneling as the real passage of a
particle
through
a tunnel drilled in the potential well is absurd. For many years
I have
illustrated the problem in a way reproduced by the drawing on
Fig. 8-C.

In the
upper
part of Fig. 8-C I show a rubber band held at about half the
height,
inside
a glass beaker. It is assumed that in this position, the rubber
band
has
no kinetic energy. There is only the gravitational potential
between
the
base of the beaker at this half height. At the bottom of the
beaker,
the
object would then have a positive kinetic energy. We know that
the
energy
is conserved. Therefore, the sum of the potential and kinetic
energies
of the rubber band is too small, to allow to take the rubber
band out
of
the beaker since no external energy is available. At the top of
the
beaker
the rubber band would have negative kinetic energy.

It is
interesting
to challenge physicists to take the rubber band out of the
beaker
without
increasing the total energy of the rubber band. They are
absolutely
convinced
that nobody can do it. In fact, no physicist has ever done it in
my
presence.
This is what they have been told when they were students.

Figure 8-C

However,
a
rubber band is a deformable body, and it is possible to raise
one end
of
the rubber band while lowering the other end so that the center
of
gravity
is not raised. Then, one end of the folded rubber band is
allowed to
creep
above the edge of the beaker without raising the center of
gravity of
the
object, as illustrated on the central part of Fig. 8-C. Then the
rubber
band can fall freely outside the beaker.

Without
external
energy, the center of gravity of the rubber band was never risen
above
the half height line, as in the case of "tunneling". Since we
know that
a real particle in physics is not a point, as shown by the de
Broglie
wavelength,
it is clear that electrons come out of a potential well the same
way
the
rubber band does.

Even if
no
material moved through the beaker walls, the center of gravity
moved
through
it. Let me add that I have also used other versions of that
rubber band
"tunneling" experiment. One is to substitute the rubber band
with a
paper
clip. However, a commercial paper clip cannot be bent easily but
we can
make our own easily-pliable paper clip, indistinguishable from a
standard
paper clip, by using a piece of soft solder tin wire from the
electronic
shop. It is fun to unroll the tin paper clip inside the beaker
before
taking
it out without raising the center of mass. The creeping of the
malleable
object that allows reaching the outside of the beaker is not
described
by an appropriate word when using "tunneling" since there cannot
be any
tunnel. The expression "tunneling" is pedagogically misleading.
This
crossing
of the barrier is achieved successfully by skilled high jumpers.
It
would
be more compatible with reality and rationality to call it the
"high
jumper
effect". This would avoid the misleading expression "tunneling".

*8-11 Physical
Realism
in
the Description of the "High Jumper Effect"*

One can
find
several examples to show that the "high jumper" model is a
better
description
of the phenomenon than the "tunneling" model. There are two main
variables
in establishing a comparison between the two models. The model
of
tunneling
implies the crossing of the potential barrier by making a tunnel
through
it. In such a model, the energy required to go through the wall
is
completely
independent of the height of the barrier. It simply depends on
its
thickness.
In the case of classical tunneling however, the difficulty of
crossing
a barrier depends on the barrier height as well as on the
barrier
thickness.
Furthermore, the existence of a tunnel into a potential barrier
does
not
make sense, since there exists no description of the material
from
which
the potential barrier is made.

In the
case
of a "high jumper" effect, the difficulty of jumping over an
obstacle
is
a function of both the height and the thickness of the barrier.
The
problem
of the material of the wall is irrelevant since the jumper moves
above
it, even if its center of gravity moves through it.
Consequently, the
analogy
between quantum tunneling and reality does not hold. We have
seen that
the "high jumper" model requires the same parameters (thickness
and
height)
as mathematical physics requires.

The
mathematical
probability of having the *high jumper effect* (classical
tunneling)
has been calculated recently by Cohn and Rabinowitz [8.1],
[8.2].
These
authors calculate the probability of crossing an obstacle with
different
shapes. Cohn and Rabinowitz show that the probability for ropes
of
varying
lengths to cross the potential barrier of different height and
thickness
is in excellent agreement with the quantum mechanical
calculation. Cohn
and Rabinowitz [8.1],
[8.2] mention:

We must conclude that there is no magic in tunneling nor anywhere else in science. Forever, particles have been using the same "high jumper" method to cross potential barriers. Primitive peoples have always taught sorcery and witchery, claiming magic to explain what they could not understand. It is time for science to get rid of those activities. We must start admitting that what we do not understand is not caused by the lack of logic in Nature; it is due to our ignorance. Nature is always logical; only humans can behave illogically.

**References**

8.1 Cohn, Arthur, Rabinowitz, Mario, in

8.2 Rabinowitz, Mario, "Do the Laws of Nature and Physics Agree on What Is Allowed and Forbidden?", in

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