Revealing the hidden connection between pi and Bohr's hydrogen model
Posted on Sunday, November 22, 2015 @ 00:26:38 GMT by vlad
WGUGLINSKI writes: To: Dr. Carl R. Hagen, University of Rochester, Dr. Tamar Friedmann, University of Rochester
Cc: Dr. Drew Milsom, University of Arizona
Dears Dr. Hagen and Dr. Friedmann
Very interesting your work on the hidden connection between pi and Bohr’s hydrogen atom, because your work awakens an old unanswered question of Quantum Mechanics, regarding the incompatibility between the Bohr’s model of atom and the model of atom adopted in Quantum Mechanics.
Revealing the hidden connection between pi and Bohr's hydrogen model
Dr. Drew Milson comments the work saying:
“It is ultimately unsurprising that the pi formula emerged from the quantum solution because, as Friedmann herself points out, "mathematical formulae come up in physics all the time". She adds that finding the link "is a manifestation of the ultimate connection between math and physics", but whether there exists some deeper, fundamental correlation between the two remains unknown.”
However, the link you found between pi and Bohr's hydrogen
model has not any chance to be considered seriously as a connection
between the math and the physics, because the Bohr’s atom model is
considered to be wrong by the whole community of physicists, since his
model is incompatible with the atom model of Quantum Mechanics, which is
the theory considered to be correct. Therefore, as the Bohr model is
considered wrong, from this viewpoint his model cannot have any
connection with the physical structure of the atom existing in the
Nature, and thereby it makes no sense to look for a link between pi and
the Borh’s hydrogen atom, because the physical structure of the atom
existing in the Nature cannot have connection with pi, as consequence
that the atom model of Quantum Mechanics cannot have connection with
The link found by you, dears Dr. Hagen and Dr.
Friedmann, makes sense only if the atom Model of Quantum Mechanics can
be replaced by a new model of atom, compatible with pi.
In short, the link found by you requires to consider that the atom model of Quantum Mechanics is incomplete.
there are strong evidences suggesting that the atom of Quantum
Mechanics cannot be entirely correct, and I discuss them ahead.
of all, there is need to mention the fact that Schrödinger Equation
cannot be applied to the atom model of Quantum Mechanics, as I
emphasized along a discussion with the Nobel Laureate in Physics Dr.
Brian Josephson, in the beginning of 2015. My argument shown to Dr.
Josephson is published in the Book Description of my book “The Evolution of Physics”, published in Amazon.com:
resume, the reason why the Schrödinger Equation cannot be applied to
the atom model of Quantum Mechanics is obvious, because he developed his
equation by considering a free electron, and therefore his equation
cannot be applied to an electron moving within a potential, as happens
when the electron is moving in the electrosphere of an atom.
In my book “The Missed U-Turn” it is shown that the Schrödinger Equation must be actually applied to my new model of hydrogen atom:
the new hydrogen model of atom the electron moves with helical
trajectory (zitterbewegung discovered by Schrödinger in the Dirac’s
equation of the electron) within the electrosphere of the proton, while
the space of the electrosphere about the proton is non-Euclidian (and
this is the reason why the electron moves with constant speed within the
electrosphere, and so it justifies why the Schrödinger Equation can be
applied to the electron moving into the atoms). So, when Schrödinger
has discovered his equation 90 years ago, he actually had discovered the
equation for the electron moving with helical trajectory within a
But there is other unsolved puzzle
proving that the atom model of Quantum Mechanics is incomplete, as
explained in my book The Missed U-Turn, in the Chapter 19, entitled “END OF THE MYSTERY OF BOHR’S SUCCESSES”,
regarding the mystery of the successes of the Bohr’s hydrogen model of
atom. Because one of the most astonishing mysteries of Physics is the
why is the Bohr’s theory
able to supply so many spectacular successes, since his model is wrong,
and incompatible with the atom model of Quantum Mechanics?
emphasized by Schrödinger, the successes of the Bohr theory of the atom
cannot be accidental. Something must be correct in the Bohr model,
concerning the instant when the atom emits a photon. However the
mechanism of photon emission by the atom model considered in Quantum
Mechanics can be 100% correct only if the mechanism of photon emission
in the Bohr model is 100% incorrect, because the two mechanisms are
totally incompatible, since in the Bohr model the centripetal
acceleration on the electron plays a role in the photon emission, and
the centripetal force on the electron cannot exist in the atom model of
Quantum Mechanics. As the Bohr model cannot be 100% incorrect, it means
that Quantum Mechanics cannot be 100% correct. This is one of the most
intriguing paradox of Quantum Mechanics. But the physicists do not use
to mention it, since it implies that the atom model of Quantum
Mechanics cannot be correct.
So, the mystery of the
successes of the Bohr’s model has an important virtue: it proves that
the Quantum Mechanics cannot be correct, because while the most
physicists use to consider that the successes of the Bohr’s model is
accidental, however it is hard to believe it, as pointed out by
Schrödinger in Chapter 4 page 89 at “On a Remarkable Property of the Quantum-Orbits of a Single Electron”, regarding the successes of the Bohr atom, where he said:
is difficult to believe that this result is merely an accidental
mathematical consequence of the quantum conditions, and has no deeper
In the Chapter 19 of my book The Missed U-Turn, entitled “END OF THE MYSTERY OF BOHR’S SUCCESSES” it is explained why the atom model of Quantum Mechanics cannot be entirely correct, as follows:
Note that, although the Bohr model is wrong, it contains a modicum of truth: the centripetal acceleration really exists
at the instant the photon is emitted. The error of the model is to
consider that this centripetal acceleration is directly tied to the
mechanism of the photon’s emission and this is not true because the
emission occurs due to a mechanism of resonance, in which the
centripetal acceleration does not participate because the electron,
moving in a helical trajectory, is subjected to centripetal acceleration
all the time; that is, it is always affecting the electron’s motion.
However, at the moment when the photon is emitted the radius, RHT, of
the helical trajectory is equal to the Bohr radius and the force, FP of
proton-electron attraction is equal to the ether’s force, FP on the
electron. These coincidences are responsible for the success of his
On the other hand, the model of Quantum
Mechanics, in spite of being wrong, also contains a modicum of truth.
It is correct first because, from the mathematical viewpoint, it makes
sense to consider that the electron has no trajectory, since the
electron’s position along the helical trajectory can be viewed as a
probability distribution about the axis of the helical trajectory.
Second because the model is correct in considering that the mechanism of
emission is due to a process of resonance. But the model is wrong
because there is no chance of the electron having centripetal
acceleration and, therefore, there is no way of justifying the
coincidences of the Bohr model. That is why most theoreticians suport
the viewpoint that the successes of Bohr are accidental, mere
coincidences, and his model has not a grain of truth. This is an
uncomfortable position because, from the viewpoint of mathematical
probability, it is impossible that it be mere coincidence. So, the
theoreticians prefer to bet that the impossible can happen and that the
mathematics can be wrong rather than accept that the model of Quantum
Mechanics can be wrong. In an article(16) in which the helical
trajectory of the electron for unifying the relativity with the quantum
theory is proposed, the physicist Natarajan writes, commenting on the
success of Bohr theory in explaining the spectral bands - “But this
significant success along with the other spectacular successes of
Bohr’s theory of the hydrogen atom is now considered by physicists as
‘accidental’ after the development of Quantum Mechanics”.
new model of atom proposed in my theory conciliates the Bohr’s theory
of the atom with the Schrödinger Equation, and the reason why Bohr model
of atom is so successful is explained in the Figures 46 and 47 of my
book The Missed U-Turn, shown ahead:
Dears Dr. Hagen and Dr. Friedmann.
work is an additional strong evidence showing that the atom model of Quantum Mechanics
cannot be correct, since the number pi is connected to a circular trajectory of
the electron when an atom emits a photon (while the atom model of Quantum
Mechanics is incompatible with the circular trajectory). As already explained
before here, as the successes of the Bohr’s theory cannot be accidental, and as
the centripetal force appears in his calculations, then obviously the centripetal force plays a
fundamental role in the mechanism of emission of the atom existing in the
Nature. Therefore the atom model of Quantum Mechanics cannot be
hundred percent correct, since it makes no sense to consider the centripetal
acceleration on the electron in the atom
model of Quantum Mechanics.
your work is very interesting, because it reinforces the need of considering a
new model of atom, working with new fundamental principles (where the
centripetal force plays a fundamental role in the mechanism of the photon
emission, as occurs in the actual
atom existing in the Nature), as proposed in my Quantum Ring Theory,
published in 2006:
perhaps my new hydrogen model of atom may help both you to understand the
missing link which "is a manifestation of the ultimate connection between
math and physics" regarding the atom, proving that concerning the atom there
exists a deeper strong fundamental correlation
between the two, since the math is just a description of the physical reality existing
within the actual atom existing in the Nature,
unknown up to now by the community of physicist. As the true physical reality existing in the
Nature does not exist in the atom of Quantum Mechanics, it is impossible to
find the link by considering the atom model of Quantum Mechanics. You found the link in the Bohr’s atom because
his model is physically closer to the
physical reality existing in the Nature than the atom model of Quantum
Mechanics, in spite of other laws postulated by Bohr are wrong.
we have the duty of persecuting the true, no matter whether in the end of the
persecution we find that Quantum Mechanics is not entirely correct.
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