Atomic Circus: Jumps and Spins

Atomic spectra was used to support the idea that electrons can jump between energy levels or ‘stationary states’ in the atom. Schrödinger rejected this and thought a more natural explanation was to view the electron as a standing wave changing frequencies. The notion of the ‘spin’ of an electron was an example of mathematical expediency at work, rather than anything physically real.

Transcript

Atomic Circus: Jumps and Spins

Hello, I'm Kay Strang. You can check me out at my website, quantumid.science, where you can find more detailed analysis and material on my series of six podcasts, Hunting the Identity of the Quantum. The previous podcasts highlighted the rivalry between Heisenberg and Schrödinger, the former supporting the discontinuity of the new quantum physics, and the latter a proponent of the continuous wave theory of light and matter. Heisenberg, with the help of Max Born and others, sabotaged Schrödinger's work by hijacking his wave equation to apply to particles rather than waves. He used his criticism of their incoherent philosophy of the superposition of states of particles as support for it, and I will cover this in podcast six. They also relied on atomic spectra to support the idea that electrons can jump between energy levels or stationary states in the atom. The first part of this podcast will look at the arguments against jumps, and the second part will try and unravel the notion of spin and show that it is mathematical expediency at work rather than anything physically real. 

   So let's look at the atomic circus of jumps and spins. Schrödinger argues that photons and the line spectra of atoms are useful mathematical shorthand but do not reveal reality, which he maintains is continuous and is better described by wave mechanics. If you look at the emission spectra of any atom, you will see a black background punctuated by coloured lines of progressively lower wavelengths. The absorption spectra is a series of black lines with similar intervals against a background of the colour spectrum. Bohr's model of the atom is of a nucleus at its centre and orbiting electrons in a series of shells representing increasing energy levels. Absorption of a photon by the atom will make an electron jump from a lower energy level to a higher one. Equally, emission of a photon will cause the electron to jump down at an energy level. Schrödinger's criticism of this model is best summed up in his own words taken from his paper Are There Quantum Jumps? 

‘For having shut our eyes to its one great deficiency, while describing minutely the so-called stationary 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 quantum jumps, 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 three or four feet in length, as can be observed in an interferometer, would use up just about the average interval between two transitions, leaving the atom no time to be in those stationary states, the only ones of which the theory gave a description. The achievement of wave mechanics was that it found a general model picture in which the stationary states of Bohr's theory take the role of proper vibrations, and the discrete energy levels the role of the proper frequencies of these proper vibrations. The principle of superposition not only bridges the gaps between the stationary states and allows nay compels us to admit intermediate states without removing the discreetness of the energy levels, because they become proper frequencies, but it completely does away with the prerogative of the stationary states. 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 Planck's constant h and a frequency as a bundle of energy lost by one system and gained by another. How else should one understand the exact dovetailing in the great double entry bookkeeping in nature? I maintain that it can in all cases be understood as a resonance phenomena.’

  Think of the piano with definite notes which equate to proper frequencies, and a violin where the violinist can slide up and down between these notes. This combined with harmonics, where one set of vibrations is triggered by similar vibrations, and a much clearer picture emerges of the behaviour of the electron. In any event, Schrödinger was proved correct in an experiment written up in an article by Z. K. Miner and others To catch and reverse a quantum jump mid-flight in Nature magazine in 2019. Unfortunately, I do not believe this has triggered a reappraisal of Schrödinger's wave mechanics. 

   Turning to spin, when electron spin was first mooted, it was dismissed by Henrik Lorentz and Wolfgang Pauli as unphysical. However, expedience dictated it was used as a fourth quantum number to save Pauli's exclusion principle and explain the Zeeman effects, which were additional line spectra of atoms when a magnetic force is applied and which cannot be explained by the so-called jumps. Pauli's exclusion principle states that no two identical fermions, that is electrons, can exist in the same quantum state. Unlike two classical objects such as two billiard balls, which are similar but not identical, all electrons are identical. Classical objects can follow well-defined trajectories, whereas if two electrons identified as P and Q because of their different locations cross paths or collide, it is impossible to determine afterwards which is which. In quantum mechanical terms, when their wave functions overlap, the particles become indistinguishable. Pauli’s principle identifies uniquely each electron in a system, that is an atom, by its four quantum numbers. The first three, namely energy level, angular momentum, and the magnetic property, were accepted, but the fourth, spin, was shoehorned into the picture because the model of the atom and the mathematics involved needed a fourth attribute. 

  The two electrons in the helium atom share the first three numbers, so for the exclusion principle to work, a fourth distinguishing feature was required. The Stern Gerlach experiment, which I believe actually predated the advent of spin and used silver atoms, is usually cited as proof that such a mysterious quantity exists. I do not believe it does for the same reason as many experiments in quantum mechanics fail. The presumption at the start of the experiment is that one is already dealing with a discrete particle, whereas in reality one is dealing with waves. It strikes me that it's the scientists who are in a spin here. I have included additional material on the website titled The Atom and the Brighton Rock, which covers the problems arising from a theory of identical particles. All the ad hoc additions in quantum mechanics to the standard particle model seem very similar to Ptolemy's epicycles, where he had to keep adding more mechanisms to save his planetary model. Look at how the current standard model of the elementary particles has mushroomed and weirdly includes particles that may not even exist or for which there is no evidence. 

   If you want to find out more, please visit my website at quantumid.science, where you will find more in-depth downloadable essays, book lists, and original papers by some 19th and 20th century physicists. The next podcast is titled Magic Particles, which examines the concept of entanglement or spooky action at a distance, as Einstein called it.

© K. Strang 2025