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Bohr's Physics

  1. Jan 13, 2005 #1
    Hans Dehmelt (Nobel Prize 1989), with others in 1979, measured the
    ratio of the electron's intrinsic magnetism to its intrinsic "spin". Bohr and the quantum community had essentially declared this to be impossible.

    David Wick in his book "The Infamous Boundry" provides a picture of
    the Bohr's science at work:
    "Dehmelt's measurements refuted claims made originally in the 1930s
    on grounds of principle. Niels Bohr, his disciple Wolfgang Pauli, and other proponents of the Copenhagen interpretation thought they had conclusively demonstrated that the magnetic moment of a free electron - one not bound in an atom - could never be observed. Bohr's argument was widely accepted in the 1970s; some theorists were supporting it as late as 1985. As today this quantity may be the best measured number in all of science, Bohr's "proof" must take it's place in the entrance hall of the Impossibility Hall of Fame, ahead of such celebrated demonstrations as the impossibility of heavier-than-air flight, space travel, or (for that matter) seeing an atom
    with your unaided eyes.
    Now I return to Bohr's claim that the spin of a free electron would never be observed. Bohr first formulated this notion around 1928, the year Dirac's theory appeared. The spinning electron hypothesis had been put forward in 1925 by R. Kronig to explain the splitting of certain spectral lines, but he let himself be talked out of it by Pauli partly because, if the spinning electron had the radius some people calculated for it, a point on its surface would move considerably faster than light - an ironical argument given the
    present picture. Consequently, the Dutch physicists Samuel Goudsmit
    and George Uhlenbeck, who received better advice from Ehrenfest, were
    able to publish the idea. Bohr's work was prompted by a paper of Leon Brillouin, who examined various possibilities for measuring the magnetism of a free electron, including shooting electrons straight at the north pole of a magnet. (The ones with spin pointing toward the magnet would be repelled.) He concluded that success was unlikely, but not impossible. Bohr, however, had a different view. "It does not appear to be generally recognized," wrote Bohr in 1929, "that the possibility of a direct observation of the magnetic moment of the electron would be inconsistent with the fundamental principles of quantum theory."

    With the exception of Pauli, few physicists understood what Bohr was
    talking about. Part of the trouble was Bohr's lecture style: his assistant Rosenfeld described Bohr's talks as "masterpieces of allusive evocation of a subtle dialectic," which audiences found hard to follow. Here is Rosenfeld's description of a lecture given by Bohr in 1931 about spin:

    "He had begun with a few general considerations calculated, no doubt,
    to convey to the audience that peculiar sensation of having the ground suddenly removed from under their feet, which was so effective for promoting receptiveness for complementary thinking. This preliminary result being readily achieved, he eagerly hastened to his main subject and stunned us all (except Pauli) with the unobservability of the electron spin. I spent the afternoon with
    Heitler pondering on the scanty fragments of the hidden wisdom which we had been able to jot down in our notebooks."

    The general drift of Bohr's reasoning was not difficult to follow - it was the details that baffled Rosenfeld and friend. Recall that Bohr based the complementarity principle on the assertion that all experiments must ultimately be described in classical terms. Electron spin, however had no classical analogue. (Pauli originally opposed the use of the suggestive term "spin" for what he called "peculiar not classically describable two-valuedness" and thought of as something almost mystical.) True, for an electron bound in a magnetic atom, the electron's spin did make a contribution
    to the atom's overall magnetism, as Stern and Gerlach had shown. But the principles of quantum mechanics prevented this decidedly unclassical phenomenon from being detected in a free electron. "This," recalled Rosenfeld, was "the point [Bohr] ineffectually tried to make in his talk."

    Luckily, one of the physicists in the audience, Nevill Mott, could make sense of the details and published the argument a year later, with Bohr's blessing. Mott and H. Massey incorporated the argument in their well-known text, *The Theory of Atomic Collisions*, whose third edition appeared in 1965. It is typical of arguments based on uncertainty, although a trifle more complicated than most: an electron is made to pass through an inhomogenious magnetic field as in the EPRB experiment. Since the electron is charged, it experiences a force whenever it moves perpendicular to any component of the magnetic field. (The force on a charged particle in a magnetic field, first described by the Dutch physicist H. Lorentz in the last century, acts perpendicularly to both the particle's velocity and the direction of the magnetic field lines.) One tries to minimize this effect by shooting the particle straight down a field line, but the tilting of the lines - they cannot be perfectly aligned since the field is spacially varying - combined with uncertainty in the particle's position yields a force that perturbs the particle's trajectory. This perturbation is just sufficient to produce a blurring of the pattern on a photographic plate one hopes to observe. In other words, quantum uncertainty is mated to classical pictures as usual to yield a "no go" theorem for a free electron in the conventional geometry of the Stern-Gerlach experiment. No doubt one really cannot carry out a spin measurement *in this unimaginative way* with free electrons.

    Unfortunately, Mott and Massey jumped to an unwarrented
    conclusion: "From these arguments we must conclude that it is
    meaningless to assign to the free electron a magnetic moment." Mott
    and Massey, like von Neumann, Bohr, Pauli, and others in this
    century, fell into a trap set for those people who desire to prove
    their ideology."

    All the best
    John B.
  2. jcsd
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