The Quantum Quandary: Electron Spin Defies Classical Rotation
Introduction
It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates.- G.E. Uhlenbeck.
In the realm of quantum mechanics, many of our classical intuitions are challenged. One of the most perplexing concepts is that of electron spin, which defies traditional notions of rotation. Though the term ‘spin’ suggests that the electron behaves like a tiny rotating sphere, this is a misleading analogy. Quantum spin is a deeply intrinsic property of particles, exhibiting behaviour that cannot be fully explained by classical physics. So before we start let’s have a look at the timeline that highlights the key moments in the history of electron spin discovery.
Timeline
- Bohr’s Quantum Model (1913)
He suggested that electrons revolving around the nucleus can only occupy certain stable orbits, for which their orbital angular momentum is quantized. These orbits correspond to specific energy states, and electrons do not radiate energy while in these stable states. The transition between two orbits provided an accurate explanation for the quanta of light seen in spectroscopic emissions of hydrogen.
- Stern-Gerlach Experiment (1922)
To test Bohr’s theory they shoot the beam of silver atoms through a nonuniform magnetic field. If the Bohr’s model was correct the atoms would be deflected into two discrete lines on the detector plate rather than forming a single continuous band. Indeed, the experiment revealed that the silver atoms took only two distinct paths through the field, confirming the quantization of angular momentum. Initially, it was assumed that this splitting was due to the orbital angular momentum of the electrons. However, it was later understood that the splitting was actually caused by the quantization of the electron’s intrinsic angular momentum—known as spin.
- Pauli Exclusion Principle (1924)
It states that no two electrons in an atom can have the same set of quantum numbers. This means that each electron in an atom must occupy a unique quantum state. The principle also implied the existence of an additional quantum number, which was later identified as spin.
- Ralph Kronig (1925)- He independently proposed the idea of electron spin to explain fine structure (splitting of spectral lines, caused by the interaction of the electron’s spin with its orbital angular momentum) in atomic spectra. However, he refrained from publishing his idea due to skepticism from prominent physicists at the time.
- Uhlenbeck & Goudsmit (1925)
While studying the fine structure of atomic spectra, they proposed that the electron is an electrically charged particle spinning on its own axis, with its spin angular momentum given by a specific quantized value. However, this physical spinning model was later replaced by the concept of the electron as a point-like particle possessing an intrinsic property called spin, which is a quantum mechanical phenomenon rather than a literal rotation.
- Paul Dirac (1927)- Initially, the idea of spin was met with resistance from physicists. These theoretical objections were resolved when the Dirac equation provided a relativistic foundation for electron spin, demonstrating that it was a natural consequence of quantum mechanics and special relativity.
Why Not classical rotation? Faster than light!
Initially, the electron was imagined as a tiny marble spinning about its own axis. However, this idea implied that its surface would rotate faster than the speed of light—a concept that defies physical laws. Let’s calculate the surface speed of a classically rotating electron using classical mechanics to explore this paradox.
For a classical spinning object (with radius r), the angular momentum (L) is related to the moment of inertia (I) and the angular velocity (ω) by,
The linear velocity at the surface of the electron (v), is related to the angular velocity (ω) by,
The intrinsic angular momentum (S)(or spin) of an electron is given by,
Clearly, this result indicates that electron spin challenges and redefines our understanding of reality.
Shortly after Niels Bohr’s quantum theory was introduced, Otto Stern and his colleague Max von Laue famously declared, “If this nonsense of Bohr should in the end prove to be right, we will quit physics!” However, Stern later embraced quantum mechanics and won the Nobel Prize in 1943. Reflecting on his journey, he remarked, “I still have objections to the ... beauty of quantum mechanics, but she is correct.”
Reference
- https://www.quantamagazine.org/the-often-overlooked-experiment-that-revealed-the-quantum-world-20231205/
- https://lorentz.leidenuniv.nl/history/spin/goudsmit.html