Natural Science Forum / Physics / General Physics / July 2008

There's a couple ways to talk about this. One way is that the
wavefunction of the proton actually has a tail that extends outside
the barrier, and because its position is only determined insofar as
the magnitude of the wavefunction (squared) tells you, then there is a
certainly probability it will be found outside the barrier. This
statement applies without any consideration whatsoever to how it gets
from "inside" to "outside" and therefore crossing the barrier. That
is, because the wavefunction is nonzero outside, then the proton is
*already* partially outside the barrier and doesn't cross at all.

The second way is that energy is not strictly conserved inside a
finite time interval, and so you don't have to go looking for places
to "borrow" energy from in order to conserve energy. This is what the
energy form of the uncertainty principle means: that the energy only
is constant within a band of fluctuation that is constrained by the
time window that you're looking in. The shorter the time window, the
more fluctuation in energy is tolerated without violating the
conservation of energy.

PD

Quantum Mechanical Tunneling (not):
In 1928 Gamow suggested that alpha particles were held inside the
nucleus by a potential barrier.  Gamow was a skilled mathematician and
theorized that the "wave function" allowed the alpha particle to
"tunnel out" through a forbidden zone of higher energy.  This idea was
accepted by the quantum mechanics and even today mistakenly forms the
basis for modern quantum mechanical theory. See the original Gamow
paper, "Quantum Theory of the Atomic Nucleus"  G. Gamow  ZP, 51, 204
(1928).

The Gamow mystical (magical) alpha particle tunneling theory
completely breaks down in the decay of the Beryllium eight (Be8)
nucleus.
The Be8 isotope decays "neatly" into two alpha particles, so nothing
else is left of the Be8 nucleus. This clean Be8 decay, into only two
alpha particles, should have been a test bed for the theory of alpha
particle tunneling decay, from the first, but no one could calculate
the binding energies involved.

Now, since the year 2000, calculation of binding energy has been
possible.  Simply, the Be8 is composed of two pre-alpha (each with two
protons and two neutrons) that tighten up into two alpha particles.
The formation of two alpha particles creates an extra binding energy
release of (Be8 – 2(alpha) = -0.092 MeV) making decay of Be8
energetically possible.

This reaction shows that new atomic energy is created when nucleons
rearrange their null patterns, from a pre-alpha to an alpha
configuration, and it is the resulting newly created atomic energy
that forces the alpha particle decay.  Because it is now possible to
calculate the binding nuclear energy between various arrangements of
protons and neutrons, the intimate details of Be8 decay can be shown.
The two Be8 pre-alpha "inter" binding energy is ~34.045 MeV, and then
these two pre-alpha are bound together with an "intra" binding energy
of ~22.454 MeV. The "inter and intra" binding energies total to give
the Be8 its (measured) binding energy (mass defect) of ~56.499 MeV.

The Be8 decay (into a lower mass energy state) occurs as the two pre-
alpha tighten up into the two greater "inter" binding energy (mass
defect) between nucleons in the alpha structure.  The new atomic
energy created is a substantial ~22.546 MeV.    This newly created
atomic energy is just enough to replace the "intra" ~22.454 MeV
binding energy (mass defect) holding the two pre-alphas structures
together in the Be8 with 0.092 MeV to spare. Thus the measured Be8
decay energy of 0.092 MeV is supplied, from the newly created alpha
formation binding energy, after replacing the energy binding the two
pre-alpha together in the Be8.  The extra 0.092 MeV energy forces the
Be8 to alpha decay.
The quantum mechanical notions of square wells, wave functions and
tunneling have nothing to do with any alpha particle decays what-so-
ever.

The idrea that the electron "tunnels"  and causes the Josephson effect
falls apart under close inspection.  A JJ consists of two
superconductors (SC) separated by a gap of a few nanometers, OR A
NANOWIRE WEAKLINK.   What happens in an insulating gap is the
electrons form Cooper pairs and bridges the gap.   In the case of the
nanowire conducting weak link is the Cooper pairs are simply conducted
across the junction.

You can Google and see the JJ works (not on electron tunneling) but
with weak links (tiny restrictions, microscopic point contacts, and
weakly conducting layers or certain grain boundaries.

Sorry to destroy long standing "Quantum Mechanical Tunneling myths"
that started in 1928 when I was 2 years old!

Regards; Tom;

See;  www.amazon.com   096315463X     (2008)   for more complete
details.

warm-up  rajaniyer

   It is quite interesting to note that Gamov's text on 'one, two,
three ..... infinity' motivated me at a young age, especially
imaginary number i that somehow mystically solves treasure puzzles.
Then quantum physics wave equation including Schroedinger equation
have the i factor which makes the mathematics of sinusoidal waves
possible.

   Quite simply with this, the physical significance of i will be
that it is algebraically representing logarithmic fluctuation, i.e. i
= log(fluctuation). We can show that it implies signal as a function
of noise noting that fine structure constant is also logarithmic
function with energy & mass, thereby representing energy in parametric
form as signal. We now have method quantifying the grand unified
theory of everything vacuum genesis of universe modeling starting with
signal = f(noise). I have derived this equation performing signal
analysis as well as mathematical physics to connect with quantum
probability si quantifying quantum physics of quantum tunneling.

The barrier tunneled through is an energy barrier.

As one lay person to another, I think sometimes the professional
physicists in here tend to have become immune to try to picturise
phenomenon in their own minds. This is due to years of education which
tends to indoctrinate them in a numb don't-ask-questions mindstate. They
are in a different state of mind from the rest of us, they are in the
"my professor told me this is the way it is, and his professor before
him, thus it is always thus."

Obviously it would be the Electroweak force that makes a proton escape
the clutches of the Strong force within a nucleus, in a fission process.
 The Electoweak is several times weaker than the Strong, however, that
comparison only applies to their strength relative to each other when
the Strong is at its strongest. The interesting thing about the Strong
is that it has a peak in strength at a specific distance between the
nucleons; its strength drops off considerably both above and below that
distance. However, the Electroweak just keeps getting stronger and
stronger the closer and closer you make things come together. At some
point if some nucleons are pushed too close together and their
Electroweak repulsion becomes strong enough to overcome the peak
strength of the Strong, and then you can see nuclei fly apart. Much like
a pinball breaking through a barrier -- it may not break through all of
the time, but do it enough times and eventually it'll find a hole in
there somewhere.

    Yousuf Khan