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Authors: James Kakalios
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magnetic field, then the rotation of an electrically uncharged object should not generate a magnetic field. 17
Moreover, even if we did not know that neutrons existed, we still could not explain the magnetic field of electrons as arising from their rotation about an axis passing through their center. The magnitude of the measured magnetic field of the electron is such that it would require that these particles spin at a rate so fast that points on their surface would be moving faster than the speed of light!
What experimental question does the proposal of intrinsic angular momentum (that is, spin) answer? In 1922 Otto Stern and Walther Gerlach passed beams of atoms through special magnets, looking for interactions between their laboratory magnet and the internal magnetic field of the atom. They were trying to probe the magnetic field that would arise from the electron’s orbital motion about the nucleus. For atomic systems where they did not expect to see any orbital motion, they nevertheless observed an intrinsic magnetic field of elementary particles and, moreover, that this came in two values. It was if the electron had a built-in magnetic field with a north pole and a south pole that was allowed to point in only two directions, relative to the magnets used in Stern and Gerlach’s experiment. The electron either pointed in the same direction as the external magnet, so that its north pole faced the south pole of the lab magnet, or exactly oppositely aligned, so that the electron’s north pole faced the lab magnet’s north pole.
While Stern and Gerlach’s experiment clearly suggested that electrons possessed an intrinsic magnetic field, spin was actually first proposed to account for features in the absorption and emission of light by certain elements that indicated that there had to be some internal magnetism inside the atom. A variety of careful experiments confirmed that this magnetic field did not arise from the electrons orbiting around the positively charged nucleus, but was somehow coming from the electrons themselves.
So, why do we say that electrons, protons, and neutrons have spin that is associated with their internal magnetic fields? The origins of this phrase go back to, shall we say, a “youthful indiscretion.” Two Dutch graduate students in Leiden, Samuel Goudsmit and George Uhlenbeck, wrote a paper in 1925 suggesting that an internal rotation of the charged electron generated a magnetic field necessary to account for the atomic light-emission-spectra anomalies. They showed their paper to their physics adviser, Paul Ehrenfest, who pointed out various problems with the electron literally spinning about an internal axis. Hendrik Lorentz, Ehrenfest’s predecessor, soon calculated, as the students’ argument required the electron to rotate faster than light speed, that, thanks to E = mc 2 , this would make the electron heavier than the proton. (Neutrons, which would have indicated to them immediately that the observed magnetic field could not result from a spinning charged particle, had not yet been discovered.) Defeated, Goudsmit and Uhlenbeck intended to drop the whole matter. They were surprised when Ehrenfest told them that that he had already submitted their paper for publication. He consoled them, indicating that he had recognized their error but thought that there was merit in their suggestion, and argued that they were “young enough to be able to afford a stupidity.”
On one level it is unfortunate that Goudsmit and Uhlenbeck employed the term “spin” for the intrinsic angular momentum and magnetic field possessed by subatomic particles. The term is so evocative (and the fact that an electron, for example, can have an intrinsic angular momentum of either +(1/2) h /2π or -(1/2) h /2π, but no other values, makes it easy to think of in terms of “clockwise” or “counterclockwise” rotation) that it is difficult to remember that the electron is not actually spinning like a top. The
Moreover, even if we did not know that neutrons existed, we still could not explain the magnetic field of electrons as arising from their rotation about an axis passing through their center. The magnitude of the measured magnetic field of the electron is such that it would require that these particles spin at a rate so fast that points on their surface would be moving faster than the speed of light!
What experimental question does the proposal of intrinsic angular momentum (that is, spin) answer? In 1922 Otto Stern and Walther Gerlach passed beams of atoms through special magnets, looking for interactions between their laboratory magnet and the internal magnetic field of the atom. They were trying to probe the magnetic field that would arise from the electron’s orbital motion about the nucleus. For atomic systems where they did not expect to see any orbital motion, they nevertheless observed an intrinsic magnetic field of elementary particles and, moreover, that this came in two values. It was if the electron had a built-in magnetic field with a north pole and a south pole that was allowed to point in only two directions, relative to the magnets used in Stern and Gerlach’s experiment. The electron either pointed in the same direction as the external magnet, so that its north pole faced the south pole of the lab magnet, or exactly oppositely aligned, so that the electron’s north pole faced the lab magnet’s north pole.
While Stern and Gerlach’s experiment clearly suggested that electrons possessed an intrinsic magnetic field, spin was actually first proposed to account for features in the absorption and emission of light by certain elements that indicated that there had to be some internal magnetism inside the atom. A variety of careful experiments confirmed that this magnetic field did not arise from the electrons orbiting around the positively charged nucleus, but was somehow coming from the electrons themselves.
So, why do we say that electrons, protons, and neutrons have spin that is associated with their internal magnetic fields? The origins of this phrase go back to, shall we say, a “youthful indiscretion.” Two Dutch graduate students in Leiden, Samuel Goudsmit and George Uhlenbeck, wrote a paper in 1925 suggesting that an internal rotation of the charged electron generated a magnetic field necessary to account for the atomic light-emission-spectra anomalies. They showed their paper to their physics adviser, Paul Ehrenfest, who pointed out various problems with the electron literally spinning about an internal axis. Hendrik Lorentz, Ehrenfest’s predecessor, soon calculated, as the students’ argument required the electron to rotate faster than light speed, that, thanks to E = mc 2 , this would make the electron heavier than the proton. (Neutrons, which would have indicated to them immediately that the observed magnetic field could not result from a spinning charged particle, had not yet been discovered.) Defeated, Goudsmit and Uhlenbeck intended to drop the whole matter. They were surprised when Ehrenfest told them that that he had already submitted their paper for publication. He consoled them, indicating that he had recognized their error but thought that there was merit in their suggestion, and argued that they were “young enough to be able to afford a stupidity.”
On one level it is unfortunate that Goudsmit and Uhlenbeck employed the term “spin” for the intrinsic angular momentum and magnetic field possessed by subatomic particles. The term is so evocative (and the fact that an electron, for example, can have an intrinsic angular momentum of either +(1/2) h /2π or -(1/2) h /2π, but no other values, makes it easy to think of in terms of “clockwise” or “counterclockwise” rotation) that it is difficult to remember that the electron is not actually spinning like a top. The
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