Probabilities of the Quantum World (Pt-6)
Summarizing the Masterpiece by Daniel Danin
[To refresh, text in such square brackets is my commentary. Rest of it is a faithful documentation of the most fascinating story ever told of the Quantum Revolution]
[At the end of Part-5, Niels Bohr had stabilized the atom. Bohr’s ideas raised some more questions, naturally! Did the Electron now have free-will? Why are only these specific discrete orbits available to the Electron as it revolves around the nucleus? We were waiting for Louis de Broglie.]
“Science always proves wrong. It never solves a problem without posing dozens of new ones.”
This had happened with with the discoveries of Planck, Einstein and Rutherford; now it happened with Bohr’s quantum theory of the atom as well.
Rutherford’s question of the the free will of the electron would become the ‘bete noire’ of everybody who was exasperated by the new physical thinking. The imaginary ‘free will’ of the electron was to be joyfully (though mistakenly) taken up by the mysticists, who did not want any determinancy — neither absolute not probabilistic — and were partial only to indeterminate and improbable imaginary events.
Bohr’s theory did indeed have some very strange implications. Assume that the electron has a choice of transitions and performs one of them — from an outer orbit to an inner one. The depth of fall determines the energy of emitted quantum, its frequency or color. That means that the moment a jump starts everything is determined by its end, the distance of the jump. The radiation frequency cannot change during the process; any quantum is of one color, or in the language of physics, monochromatic. In other words, the electron has to choose one of the lower orbits beforehand, to calculate ‘where it is going to stop’. This looks as if it had a free choice — as it it could decide its quantum fate beforehand!
In the spring of 1961, during Bohr’s last visit to Moscow, he told physicists there:
“Rutherford did not say it was stupid, he just couldn’t understand how the electron starting a transition from one orbit to another learned which quantum it had to emit…”
Bohr added: “I told him it was like the ‘branching ratio’ in radioactive decay, but he wasn’t convinced.”
The branching ratio — a strange effect in Radioactivity — was well known to Rutherford. In the Uranium family, two branches developed from the Radium-C: a small portion of the atoms of this element underwent alpha decay, while a greater proportion underwent beta decay; on average three atoms out of 10,000 transformed into Tellurium and 9997 into Polonium. In other words, nature presented each atom of Radium-C with a choice of two fates. It appeared as if the nucleus, underwent exactly similar conditions, could decide beforehand what it would emit — an alpha particle or a beta particle. Rutherford knew this effect and did not show any surprise at it.
Thus, there was a good parallel to justify the new theory. But one fault cannot be justified by the fact that a similar one has already been made. Parallels cannot explain the facts, they only illustrate them.
In March 1913, having read the finished work of Bohr, Rutherford had to recommend it for publication in the Philosophical Magazine; he felt, however, that the very foundations of this work would be questioned. In his letter to Bohr, he mentioned:
“Your ideas as to the mode of origin of spectra in hydrogen are very ingenious and seem to work out well; but the mixture of Planck’s ideas with the old mechanics makes it very difficult to form a physical idea of what is the basis of it all.”
A friend of Rutherford’s, William Bragg, joked later that Bohr’s theory suggested to physicists that they use classical laws on Mondays, Wednesdays and Fridays and quantum laws on Tuesdays, Thursdays and Saturdays. It was all correct mathematically but the picture was ambiguous.
The venerable professor of spectroscopy in Gottingen, Carl Runge, took a dim view of the new theory: “Now the literature of spectroscopy will be permanently contaminated with terrible things” He fulminated against Bohr: “This fellow is definitely mad.”
When the great classicist, Lord Rayleigh, was asked at a scientific meeting in Britain to comment on the quantum theory of the atom he just smiled:
“In my young days I took many views very strongly and among them that a man who has passed his sixtieth year ought not to express himself about modern ideas. Although I must confess that today I don’t take this view quite so strongly, I keep it firmly enough not to take part in this discussion.”
In the autumn days of 1931, when the elderly Raleigh was not able to say much about the quantum theory, at another scientific meeting — this time in Switzerland — thirty-four year olf Max von Laue, a former assistant of Planck, barked: “Rubbish!… The electron at the orbit must emit radiation!”. Luckily, Einstein who happened to take part in the same meeting in Zurich made a similar terse retort: “No, this is remarkable! There is something behind it…” And Einstein was also only thirty-four. Thus we see that age really does not matter — something else is important…
[It is commendable that Rutherford had the broad mindedness to recommend for publication Bohr’s ideas that he thought were not reliable enough. Of course, he must have felt that there was a higher truth which had yet to be revealed behind the Bohr postulates — and he knew from his experience that science could not survive without broad-mindedness and tolerance! For that matter neither can Spirituality.]
The ladder of the stable energy levels in the atom had one highly interesting feature: the further from the nucleus the smaller were the steps of this ladder. This is real as shown by formulae and experimental spectra. The difference between the neighboring allowed energy levels becomes increasingly less noticeable and the electron orbits grow increasingly close to each other. Discreteness is gradually transformed into continuity; the quantum laws give way bit by bit to the classical laws.
As should be expected, there are no border posts in nature declaring ‘Up to here the domain of Galileo, Newton and Kepler, and from here the domain of Planck, Einstein and Bohr.’
Perhaps, it was the first time that a theory was developed in such an illogical way in physics, reported to be a highly logical science. One can barely believe the following admission of one of the geniuses of the quantum physics world, Werner Heisenberg:
“We aimed our efforts not so much at deriving the correct mathematical relations as at making guesses about them, proceeding from their similarity to the formulas of the classical theory.”
[And, they made correct guesses!]
Einstein himself wondered in his typical mildly ironical fashion: “If I only knew which nuts and bolts God uses here!”
A letter written by Sommerfeld to Einstein reflects his trust in the keen insight of the man who had created the quantum theory of light:
“You are thinking about the fundamental problems of the light quanta. But I, who do not feel strongly enough about it, am satisfied with an understanding of the details of the quantum miracles in the spectra… I cannot suggest anything to account for their physical meaning. I can only help to develop the techniques of the quanta. You must build their philosophy.”
However, Einstein’s fate was to become a life-long enemy — a tireless, inventive, tenacious but ultimately futile opponent of the quantum theory. This fate seems even more dramatic when one recalls that Einstein was present at the cradle of the ‘philosophy of quanta’; in fact, it was he who had placed in this cradle the baby who would grow stronger and stronger. The baby was a centaur — it combined the properties of both particles and waves.
The concept of these submicroscopic centaurs — the particle-waves — was not needed at all for saving the planetary model of the atom from instability. It was irrelevant to such and extent that Niels Bohr allowed himself to deny the reality of the particles of light suggested by Einstein and recognized only the quanta suggested by Planck — the portioins in which nature measures up the electromagnetic energy of radiation.
“At many stages in its history, science closed its eyes for the time being to groups of factors and entire ranges of phenomena which complicated the task.”
Bohr was eventually satisfied that it was nature that furnished us with the concept of particle-waves, rather than Einstein himself. Bohr wrote the following prophetic words at this hour of heightened awareness:
“In this situation one should be ready for a resolute restructuring of the concepts on which the description of nature has hitherto been based.”
There was another significant event in physics that had significant effect on Bohr at the time. It took place in Paris.
In the late autumn of 1924 a thesis entitled ‘Studies in the Theory of Quanta’ was submitted at the Sorbonne. It was by the thirty-two year old Louis de Broglie. In 1923, at the fourth Solvay Congress, the jovial Frenchman Paul Langevin, who has been a student of J. J. Thomson together with Rutherford, told Ioffe about the study of a student of his in Paris:
“His ideas, of course are nonsensical but he develops them with such elegance and brilliance that I have accepted his thesis.”
But of course, Langevin, outstanding scientist that he was, felt deep inside his heart that no nonsense could be presented with elegance and brilliance; the elegance of the theory warranted its deep-seated significance.
De Broglie suggested that the electron was related to some wave. A simpler though stranger suggestion was that the electron itself had some wave like property.
[While sitting on a beach one can absent-mindedly could the waves — one, two, three… But we never think that this count describes a continuous process discretely. Another example is the ticking of a pendulum clock which gives a discrete count of the continuous oscillations of the pendulum. Oscillations and waves result in periodic repetition of the same states.]
Take an electron travelling along one allowed orbit. Its motion is stable — it does not acquire nor loose anything. The stability means that after each revolution around the nucleus, everything is repeated precisely as before. This means that the mysterious wave should at this point have the exact same form as the revolution before. To provide for this constancy — this stability — the orbit should accommodate an integral number of the electron waves along its length. The number must be integral. If this condition is violated even to a very small extent — the ‘phase shift’ in the parlance of physics — the electron will return to the given point in a state different from that of the previous time. The stability will be violated; the orbit will be forbidden.
De Broglie traced a possible reason for the strange fact of the existence of allowed pathways for the electron within the atom. Only those orbits are allowed whose length is a multiple of the wavelength of the electron!
This concept immediately explains the appearance of why the allowed orbits are discrete: the closest together differ by at least one wavelength of the electron wave so that a circular gap appears between them.
It throws some light on the mystery of the quantum jumps too. The electron indeed cannot find a stable state between the allowed orbits since there are no pathways there which would be a multiple of its wavelength; it thus has to cross the instability gap in one jump which cannot be subdivided into smaller jumps… When Langevin told Ioffe that de Broglie’s ideas were presented with brilliance he meant, above all else, that they gave a simple and elegant derivation of a clear formula for the suggested electron wavelength. This he achieved using the relativity and quantum theories.
De Broglie had found that the wavelength of the electron is equal to Planck’s constant, h, divided by the electron mass and electron velocity. Indeed, what could be simpler and more elegant!
Now the obvious thing to do was for the X-ray spectroscopists to conduct experiments and find out whether the electron waves were real or not.
Davisson and Thomson discovered the wave-like behavior of electrons in 1927 independently of one another. It was found later that Davisson has observed the electron diffraction six years earlier: but he had not understood the significance of the strange patterns he had obtained in his experiments with electrons and nickel crystals, he just could not imagine that what he saw was a wave pattern. Once again one recalls the amazingly astute words of Einstein:
“Only theory decides what it is that we manage to observe!”
George Thomson, son of the old J. J., specially conducted sensitive experiments knowing beforehand what he would see; he thus managed to make photos showing wave behavior of the electron. So, the father took all the credit for the discovery of the electron as a particle and the son was given half-share of the credit for discovery of the electron as a wave.
Even stubborn skeptics had to accept the de Broglie theory after the successful experiments of 1927. In 1929 he was awarded the Nobel Prize!
[The culmination of the ‘Strum und Drang’ period is now near. Adjectives like ‘amazing’, ‘strange’ or ‘queer’ will appear with increasing frequency.]
… To be Continued
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