Quote
One
What is the physical significance of these
vacuum-state expectation values ... ? One
thing they indicate is that the electromagnetic vacuum is a stationary state of the field with statistical fluctuations of the electric and magnetic
fields. As far as measurements are
concerned, however, it is often argued that the entire universe is evidently
bathed in a zero-point electromagnetic field, which can add only some constant
amount to [non-vacuum] expectation values … .
Physical measurements will therefore reveal only deviations from the vacuum state.
… This is especially reasonable
in the case of the field Hamiltonian [an “operator” representing the total
energy of the field], since the zero-point term merely adds a constant energy
which can be eliminated by a simple redefinition of the zero of energy. Moreover, this constant energy in the
Hamiltonian obviously commutes with a
and a† [the annihilation and creation operators for photons] and so
cannot have any effect on the quantum dynamics described by the Heisenberg
equations of motion.
So the argument goes. However, things are not quite that simple,
for in general relativity the zero of energy is not arbitrary. Furthermore we shall see that it is possible
to attribute measurable effects, such as the Casimir force and the Lamb shift,
to changes in zero-point energy. And finally, as discussed in Section 2.6, the
zero-point field is not eliminated by dropping its energy from the Hamiltonian.
--Peter Milonni,
The Quantum Vacuum (1994), from Section
2.4, titled “Quantization of a Field Mode.”
Quote
Two
This energy may be attributed to unavoidable
fluctuations in the electromagnetic field. … it is not possible for the vector
potential at any point in space to vanish (or take any definite fixed value)
for a finite time interval; if the field vanishes at one moment, then its rate
of change at that moment cannot take any definite value, including zero. The energy density has no effect in ordinary
laboratory experiments, as it inheres in space itself and space cannot normally
be created or destroyed, but it does
affect gravitation, and hence influences the expansion of the universe and the
formation of large bodies like galaxy clusters.
Needless to say, an infinite result is not allowed by observation. Even if we cut off the integral at the
highest wave number probed in laboratory experiments, say 1015 cm-1,
the result is larger than allowed by observation by a factor roughly 1056. The energy due to fluctuations in the
electromagnetic field and other bosonic fields can be cancelled by the negative
energy of the fluctuations in fermionic fields, but we know of no reason why
this cancellation should be exact, or even precise enough to bring the vacuum
energy down to a value in line with observation. Since E0/Ω [the vacuum energy density]
was known to be vastly smaller than the value estimated from vacuum
fluctuations at accessible scales, for decades most physicists who thought at
all about this problem simply assumed that some fundamental principle would be
discovered that imposes on any theory the condition that makes E0/Ω
vanish. This possibility was ruled out
by the discovery in 1998 that the expansion of the universe is accelerating, in
a way that indicates a value of E0/Ω about three times larger than
the energy density in matter. This
remains a fundamental problem for modern physics, but can be ignored as long as
we do not deal with effects of gravitation.
--Steven
Weinberg, Lectures on Quantum Mechanics
(2013), from Section 11.6, titled
“Photons.”
A “photon,” by the way, is the same thing as the “quantization of a field mode” in QED (Quantum ElectroDynamics). Our final illuminating
quote compares photons with phonons, which result from quantizing the
acoustical field modes in a solid. "Modes" means "normal modes," normally. See the last few paragraphs of my November 19 post. The
theory of the acoustic and electronic behavior of electrons and atoms in solids is known as condensed
matter physics or solid state physics.
In contrast to the vacuum, interactions in a solid take place in a
medium: the atoms and fields of the material. Which leads us up to quote three ...
–DT
Quote
Three
In QED there is, apparently, no medium to provide
the interactions which, for the electron in a solid, alter its effective
charge. In relativistic quantum
mechanics, however, the remarkable possibility exists of quantum fluctuations
in the vacuum. The process we are
considering [an electron interacting with a muon, both of which are leptons] is
a typical example of such a vacuum fluctuation.
The photon exchanged between the two leptons can create, from the
vacuum, a virtual electron-positron pair.
This pair has only a fleeting existence; it lives on borrowed time, in
the sense that the energy necessary to call it into existence, ΔE ≈ 2mc2,
is only available for a time of order Δt ≈ ħ/2mc2 (we are using the so-called ‘energy-time
uncertainty relation,’ which states that there is a spread ΔE in the energy of
a quantum system given by ΔE ≥ ħ/Δt, where Δt is the time over which the
system’s energy is measured; over short times quite large energy fluctuations
are possible). In relativistic quantum
mechanics, therefore, we must beware of thinking of the vacuum, too naively, as
being ‘nothing’. Even when a particle is
supposedly free and propagating in the vacuum, the parameters describing it
(such as the charge) are changed, from the values appearing in the original
one-particle Hamiltonian, to ones which include the effect of its interactions
with the virtual particles produced from the vacuum.
--I. J. R. Aitchison and A. J. G. Hey, Gauge Theories in Particle Physics, 2nd ed. (1989), from Section 6.10, titled “Higher-order calculations:
renormalization and tests of QED.”
