In 1926, after failing to convince Bohr and Heisenberg that wave
mechanics can get rid of quantum jumps, SchrΓΆdinger exclaimed:
πΌπ π€π βππ£π π‘π ππ ππ π€ππ‘β π‘βππ π ππππππ
ππ’πππ‘π’π ππ’πππ , π‘βππ πΌ'π π ππππ¦ π‘βππ‘ πΌ ππ£ππ
πππ‘ πππ£πππ£ππ. --πΈ. ππβππππππππ
26 years later, in 1952, SchrΓΆdinger returned to this question in the
paper: 'π¨ππ πππππ πΈππππππ π±ππππ?'
https://web.archive.org/web/20210914022807/www.ub.edu/hcub/hfq/sites/default/files/Quantum_Jumps_I.pdf
[SchrΓΆdinger reiterates that one of his main motivations for his intense research into a more detailed atomic model was that the atomic jumps of
the Bohr model didn't sit well with him]:
------------------------------------------------------------------------------- Bohrβs theory held the ground for about a dozen of years, scoring a
grand series of so marvelous and genuine successes, that we may well
claim excuses for having shut our eyes to its one great deficiency:
while describing minutely the so-called βstationaryβ states which the
atom had normally, i.e. in the comparatively uninteresting periods when
nothing happens, the theory was silent about the periods of transition
or βquantum jumpsβ (as one then began to call them). Since intermediary states had to remain disallowed, one could not but regard the transition
as instantaneous; but on the other hand, the radiating of a coherent
wave train of 3 or 4 feet length, as it can be observed in an
interferometer, would use up just about the average interval between two transitions, leaving the atom no time to βbeβ in those stationary
states, the only ones of which the theory gave a description.
This difficulty was overcome by quantum mechanics, more especially by
Wave Mechanics, which furnished a new description of the states;
... [Wave mechanics] is most easily grasped by the simile of a vibrating
string or drumhead or metal plate, or of a bell that is tolling. If such
a body is struck, it is set vibrating, that is to say it is slightly
deformed and then runs in rapid succession through a continuous series
of slight deformations again and again. There is, of course, an infinite variety of ways of striking a given body, say a bell, by a hard or soft,
sharp or blunt instrument, at different points or at several points at a
time. This produces an infinite variety of initial deformations and
accordingly a truly infinite variety of shapes of the ensuing vibration:
the rapid βsuccession of cinema pictures,β so we might call it, which describes the vibration following on a particular initial deformation is infinitely manifold. But in every case, however complicated the actual
motion is, it can be mathematically analysed as being the superposition
of a discrete series of comparatively simple βproper vibrations,β each
of which goes on with a quite definite frequency. This discrete series
of frequencies depends on the shape and on the material of the body, its density and elastic properties. It can be computed from the theory of elasticity, from which the existence and the discreteness of proper
modes and proper frequencies, and the fact that any possible vibration
of that body can be analysed into a superposition of them, are very
easily deduced quite generally, i.e. for an elastic body of any shape whatsoever.
The achievement of wave mechanics was, that it found a general model
picture in which the βstationaryβ states of Bohrβs theory take the role of proper vibrations, and their discrete βenergy levelsβ the role of the proper frequencies of these proper vibrations; and all this follows from
the new theory, once it is accepted, as simply and neatly as in the
theory of elastic bodies, which we mentioned as a simile. Moreover, the radiated frequencies, observed in the line spectra, are in the new
model, equal to the differences of the proper frequencies; and this is
easily understood, when two of them are acting simultaneously, on simple assumptions about the nature of the vibrating βsomething.β
But to me the following point has always seemed the most relevant, and
it is the one I wish to stress here, because it has been almost obliteratedβif words mean something, and if certain words now in general
use are taken to mean what they say. The principle of superposition not
only bridges the gaps between the βstationaryβ states, and allows, nay compels us, to admit intermediate states without removing the
discreteness of the βenergy levelsβ (because they have become proper frequencies); but it completely does away with the prerogative of the stationary states. The epithet stationary has become obsolete. Nobody
who would get acquainted with Wave Mechanics without knowing its
predecessor (the Planck-Einstein-Bohr-theory) would be inclined to think
that a wave-mechanical system has a predilection for being affected by
only one of its proper modes at a time. Yet this is implied by the
continued use of the words βenergy levels,β βtransitions,β βtransition
probabilities.β
The perseverance in this way of thinking is understandable, because the
great and genuine successes of the idea of energy parcels has made it an ingrained habit to regard the product of Planckβs constant β and a frequency as a bundle of energy, lost by one system and gained by
another. How else should one understand the exact dove-tailing in the
great βdouble-entryβ book-keeping in nature?
πΌ πππππ‘πππ π‘βππ‘ ππ‘ πππ ππ πππ πππ ππ ππ
π’πππππ π‘πππ ππ π πππ ππππππ πβππππππππ.
One ought at least to try, and look upon atomic frequencies just as
frequencies and drop the idea of energy-parcels. I submit that the word 'energy' is at present used with two entirely different meanings,
macroscopic and microscopic. Macroscopic energy is a ' quantity-concept
'. Microscopic energy, meaning βΞ½, is a 'quality-concept' or 'intensity-concept'; it is quite proper to speak of high-grade and
low-grade energy according to the value of the frequency v. True, the macroscopic energy is, strangely enough, obtained by a certain weighted summation over the frequencies, and in this relation the constant β is operative. But this does not necessarily entail that in every single
case of microscopic interaction a whole portion βΞ½ of macroscopic energy
is exchanged. I is believe one allowed to regard microscopic interaction
as a continuous phenomenon without losing either the precious results of
Planck and Einstein on the equilibrium of (macroscopic) energy between radiation and matter, or any other understanding of phenomena that the parcel-theory affords.
The one thing which one has to accept and which is the inalienable
consequence of the wave-equation as it is used in every problem, under
the most various forms, is this : that the interaction between two
microscopic physical systems is controlled by a peculiar law of
resonance. This law requires that the difference of two proper
frequencies of the one system be equal to the difference of two proper frequencies of the other:
(Eqn. I) Ξ½_1 - Ξ½_1' = Ξ½_2' - Ξ½_2
The interaction is appropriately described as a gradual change of the amplitudes of the four proper vibrations in question. People have kept
to the habit of multiplying this equation by β and saying it means, that
the first system (index 1) has dropped from the energy level, βΞ½_1 to
the level βΞ½_1', the balance being transferred to the second system, enabling it to rise from βΞ½_2 to βΞ½_2'. This interpretation is
obsolete. There is nothing to recommend it, and it bars the
understanding of what is actually going on. It obstinately refuses to
take stock of the principle of superposition, which enables us to
envisage simultaneous gradual changes of any and all amplitudes without surrendering the essential discontinuity, if any, namely that of the frequencies. -------------------------------------------------------------------------------
Obviously, my interest in SchrΓΆdinger's picture, is that it is
compatible with an aether, while discrete quantum jumps make no sense
from an aether point of view.
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