Historical research guide · 0449 · 1984
Classical spinning magnetic dipole in classical electrodynamics with classical electromagnetic zero-point radiation
Timothy H. Boyer
In one minute
Space quantization is one of the strangest things a physics student meets: put a spinning magnetic object in a magnetic field and quantum mechanics says it cannot simply lie at any angle it likes. Timothy Boyer asks whether a purely classical calculation can produce the same behaviour, provided you grant that empty space carries a real random electromagnetic field — the classical zero-point radiation of stochastic electrodynamics. He takes a classical spinning magnetic dipole, puts it in an arbitrary spectrum of random radiation, and works out the steady-state probability of finding it at each angle to an applied magnetic field. Feed in the classical thermal spectrum and out comes the ordinary Boltzmann distribution, exactly as it should. Feed in the zero-point spectrum instead and something else happens: the distribution of alignment angles no longer depends on the strength of the magnetic field at all, and a large spin sits with its component along the field short of its full value by exactly half of h-bar. Boyer notes the resemblance to space quantization.
Connection
Chapter two’s case is that the zero-point field is a real physical medium, and the strongest form of that case is a calculation where changing the field’s spectrum changes the answer in a way experiment can see. Chapter three then takes the same field and asks it to carry inertia and gravity, so it matters a great deal that the field can already reproduce a signature as quantum-looking as space quantization without quantum mechanics being assumed anywhere.
From the source
A classical spinning magnetic dipole is considered within classical electrodynamics with classical electromagnetic zero-point radiation.Abstract, first sentence
The stationary probability distribution for the angle of alignment between the spinning magnetic dipole and an external magnetic field is calculated when the system sits in an arbitrary spectrum of random classical radiation — the spectrum is an input, not an assumption.Abstract, second sentence
For the Rayleigh–Jeans spectrum, the probability distribution for alignment is just the Boltzmann distribution.Abstract, third sentence
In classical zero-point radiation, by contrast, the alignment probability distribution is independent of the magnetic field causing the alignment.Abstract, fourth sentence
For classical spin angular momentum much larger than h-bar, the average component of the spin in the direction of alignment equals the spin magnitude minus one half of h-bar, where h-bar is Planck’s constant divided by two pi and is used here only to set the scale of the classical zero-point radiation spectrum.Abstract, fifth sentence
The results seem suggestive of the idea of space quantization in quantum theory; the model discussed was first considered by S. Sachidanandam, unpublished.Abstract, sixth and seventh sentences
The way in
https://doi.org/10.1103/physreva.29.2389How to cite it
Timothy H. Boyer (1984) Classical spinning magnetic dipole in classical electrodynamics with classical electromagnetic zero-point radiation doi:10.1103/physreva.29.2389