Historical research guide · 1070 · 2015
Quantum ground states as equilibrium particle–vacuum interaction states
Harold E. Puthoff
In one minute
A hydrogen atom in its lowest state ought to be a disaster in classical physics. The electron is accelerating, accelerating charges radiate, and the atom should collapse almost instantly. Quantum theory simply declares that it does not, and most working physicists leave the matter there. Harold Puthoff, of the Institute for Advanced Studies at Austin, asks what actually balances the books, and answers that the atom is not alone in the room. It sits in the zero-point field, the restless electromagnetic background that fills empty space even at absolute zero. Working semiclassically, in the approach called stochastic electrodynamics, he computes the power a bound charge radiates away by Larmor’s formula and the power it absorbs from that background, and finds the two exactly equal. A ground state is not a state where nothing happens; it is a state where emission and absorption cancel. He then shows the same balance holds for any confining potential that does not change with time, making it a general constraint on quantum ground states rather than a special feature of the oscillator.
Connection
Chapter 2 needs a vacuum that does continuous, load-bearing work on ordinary matter, and this is the cleanest statement of that case: the stability of every atom in the universe is an energy balance struck against the zero-point field. Chapter 13’s unified picture — quantum behaviour as the visible signature of a real background field — turns on exactly this result, and Puthoff draws the same conclusion the site does, that atoms are open systems in permanent exchange with the vacuum.
From the source
For a one-dimensional harmonic oscillator immersed in the vacuum zero-point field, a purely classical calculation reproduces the standard quantum results with no quantum postulate: the mean square position is Planck’s reduced constant divided by twice the mass and the natural frequency, the mean square momentum is the mass times the reduced constant times the frequency over two, the ground-state energy is half the reduced constant times the frequency, and the position-momentum uncertainty product is the reduced constant over two.Section 2, Equations 15 to 20
The power the oscillating charge absorbs from the zero-point field is exactly the power it radiates away by the Larmor formula, so the stationary ground state is a dynamic equilibrium rather than an absence of motion — and the balance is independent of the charge, which cancels from both sides, so it survives even in the limit of a vanishingly small charge.Section 2, Equations 21 to 24 and the closing paragraph
The balance is not special to the harmonic oscillator. Starting from the generalised equation of motion with radiation damping, the electric and magnetic zero-point forces and any confining potential that does not depend on time, the requirement that the state be stationary forces the time-dependent term to vanish, and what remains is precisely the statement that radiated power equals absorbed power.Section 3, Equations 25 to 27
The zero-point spectrum used is the Lorentz-invariant one whose energy density rises as the cube of the frequency, corresponding to half of Planck’s reduced constant times the frequency in every normal mode of the field — the same distribution measured through the Casimir force and derived by Boyer without quantum assumptions.Section 2, Equation 2 and the Lorentz-invariant spectral energy density
The same equilibrium explains why an atom in its ground state does not on net absorb zero-point radiation and so stays in that state; ground-state structures are therefore open systems in continuous dynamic interaction with the vacuum, and the vacuum field is formally necessary for the stability of atoms in quantum theory.Section 3, closing paragraph; Section 4, Concluding remarks
Puthoff flags the open item himself: long numerical stochastic-electrodynamics simulations of hydrogenic atoms have so far been only marginally successful at confirming that the time-dependent term vanishes, with self-ionisation often the outcome, and work continues on adding terms beyond the dipole approximation, spin-orbit coupling and relativistic effects.Section 3, footnote 1
The way in
https://doi.org/10.1007/s40509-015-0055-5How to cite it
Harold E. Puthoff (2015) Quantum ground states as equilibrium particle–vacuum interaction states doi:10.1007/s40509-015-0055-5