Historical research guide · 0494 · 2019
Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics
Daniel C. Cole
In one minute
Daniel Cole takes on the objection that stops most readers at the door of vacuum energy: if empty space really holds an enormous, formally infinite store of energy, why does nothing run away with it? Cole writes from stochastic electrodynamics, the classical theory in which the zero-point field is a real electromagnetic field — as real as sunlight or heat — rather than a bookkeeping device. His answer is that we already extract energy from the vacuum, constantly, and call it chemistry. If the zero-point field is what holds electrons in their configurations, then every bond that forms or breaks alters that field and moves energy between field and matter: cement setting, a battery discharging, TNT detonating. Two Casimir plates closing are the same transaction, only smaller and cleaner. Nothing violates thermodynamics; what changes is the equilibrium state, and restoring it costs work. Cole then supplies a new calculation — the full probability distribution of the zero-point field values in closed form, with the recipe for extending it to oscillators.
Connection
This is the cleanest published answer to chapter 6’s first objection, and it comes from inside the physics rather than around it: energy taken from the vacuum is ordinary bookkeeping, not a violation, and the reason it does not look miraculous is that it is happening in every chemical reaction already. It also states chapter 2’s premise in its strongest form — the zero-point field is not a virtual accounting term but the thing holding matter together.
From the source
Energy can be taken from the vacuum without any violation of thermodynamics. Two neutral conducting plates closing under the Casimir force either do configuration work on stops and springs, in the reversible case, or radiate the energy away as their fluctuating charges accelerate, in the irreversible case — energy is conserved throughout, and the process cannot repeat because the configuration has changed and work must be done to pull the plates apart again.Section 2, ‘Extracting Energy from the Vacuum’, opening pages
If stochastic electrodynamics is the foundation of quantum theory, then extracting energy from the vacuum is a daily commonplace: the zero-point field is what holds electron configurations stable in atoms and molecules, so every chemical reaction that rearranges those configurations alters the field and transfers energy between field and matter — TNT exploding, cement hydrating, a battery discharging.Section 2, from ‘We will now attempt to go beyond this restriction’; Section 4, Concluding Remarks
Zero-point radiation is what keeps the classical atom from collapsing. Without it the Rutherford hydrogen electron spirals into the nucleus in about 1.3 × 10⁻¹¹ seconds from the Bohr radius; with it, simulations of the classical electron in the zero-point field show collapse resisted on average, though a random-walk ionisation is also seen and is not yet resolved.Section 1, Introduction, third and fourth pages
The zero-point spectrum is forced, not chosen: it is the only classical radiation spectrum that is Lorentz invariant, and the only one that satisfies the physical definition of zero temperature — that no heat flows during isothermal quasistatic changes — so thermodynamic equilibrium at absolute zero requires non-zero radiation to be present.Section 1, Introduction; the Lorentz-invariance and T = 0 conditions
The two theories put the vacuum in different structural roles. In quantum electrodynamics the vacuum perturbs atomic states already given by the wave equation, producing effects such as the Lamb shift; in stochastic electrodynamics the field in stochastic equilibrium with the charges is what produces the stable states in the first place. Cole’s reading is that the classical stochastic theory can deduce the quantum results while the reverse does not hold, as statistical mechanics yields thermodynamics but not the other way round.Section 2, ‘How does this compare with QT?’; Section 1 closing paragraph
A new calculational route gives the entire probability density of the zero-point-plus-Planckian electric field in closed form — a product of three Gaussians whose widths are the mean squared field components along each axis — and the same recipe extends to joint distributions of the field at several points in space and time, and to linear electric dipole oscillators in the field.Section 3, ‘A Calculational Method within SED’, Equations 25 and 27; extensions at Equations 28 and 29
The way in
https://doi.org/10.3390/atoms7020050How to cite it
Daniel C. Cole (2019) Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics doi:10.3390/atoms7020050