The quantum vacuum: an introduction

Older than the idea of virtual particles (see previous post) is the idea of zero-point energy fluctuations of a field such as the electromagnetic field.

These days virtual particles are considered to be the medium through which real particles communicate with each other.  Virtual photons, for example, are considered to be the carriers of the electromagnetic force. Only the effects they cause are detectable.  Virtual particles themselves are undetectable.

The idea of the quantum vacuum is similar in that it postulates the existence of fields in what was formerly considered to be empty space.  Here's the beginning of the preface to Peter W. Milonni's excellent book, The Quantum Vacuum: An Introduction to Quantum Electrodynamics, published in 1994:

According to present ideas there is no vacuum in the ordinary sense of tranquil nothingness. There is instead a fluctuating quantum vacuum.  One purpose of this book is to survey some of our most important ideas about the quantum vacuum.  A second is to describe, based on fundamental vacuum processes, the physical concepts of quantum electrodynamics (QED).

Why bother?  Few people doubt the reality or significance of vacuum field fluctuations, and the formalism for perturbative QED calculations can already be found in many books.  My answer is that, if QED is indeed the nonpareil physical theory, and if [as P.C.W. Davies says in Superforce, p. 104] "the vacuum holds the key to a full understanding of the forces of nature," then it is worthwhile to look carefully at the physical ideas underlying QED vacuum effects, including not only such things as mass and charge renormalization, Lamb shifts and Casimir efffects, but even more "elementary" things such as spontaneous emission, van der Waals forces, and the fundamental linewidth of a laser.  Phenomena of the latter type, primarily nonrelativistic, are basic to quantum optics and other aspects of modern, applied QED.  All of them involve the vacuum electromagnetic field in one way or another.  All of them, furthermore, can be described physically in ways that involve source fields.  A third purpose of this book is to exhibit and explain the relation between vacuum and source fields.

But I may be getting ahead of where I should be at this point.  I need to say, first, that "communication" between particles is through forces, and forces are carried by fields.  What do forces do?  That's pretty simple:  push or pull, via repulsion or attraction.  The problem that led to the concept of fields as carriers of forces is this:  if there is really nothing in the space between two objects that exert forces on each other, how can the fact of measurable attraction or repulsion be explained?  In other words, how can there be "action at a distance"?  This was a major philosophical problem in the 17th and 18th centuries, and was given much thought by Newton, Descartes, and others.  But I won't go into that, yet.

In the 1800s, Michael Faraday came up with the idea of fields, starting with the magnetic field. The pattern of the magnetic field  of a bar magnet can easily be observed using iron filings. The field idea is still around but it has been significantly altered as a result of two 20th century theories: Einstein's description of the force of gravity as a curvature of spacetime, and quantum field theory's description of all forces (all fields) as being carried by virtual particles.  Just how compatible these two ideas are remains to be seen, but "quantum gravity" theories postulate that gravity's attraction occurs via virtual  gravitons, and the other forces--strong & weak nuclear forces, and electromagnetism--are also considered to be due to the curvature of spacetime, so there is an overlap of the curvature idea and the virtual particles idea. And, besides that, real particles are now considered to be made of "matter fields" that are represented in the equations of quantum mechanics by wave functions.

Here's Milonni again, in chapter 2 of his Quantum Vacuum book:

According to contemporary physics the universe is made up of matter fields, whose quanta are fermions (e.g., electrons and quarks), and of force fields, whose quanta are bosons (e.g., photons and gluons).  All these fields have zero-point energy.  The oldest and best known quantized force field is the electromagnetic one.  It is important for us to understand the main features of the quantized electromagnetic field, not only because quantum electrodynamics is "the best theory we have," but also because it is in many ways characteristic of all quantum field theories.

And here are some comments along the same lines from Anthony Zee:

That the exchange of a particle can produce a force was one of the most profound conceptual advances in physics.  We now associate a particle with each of the known forces: for example, the photon with the electromagnetic force and the graviton with the gravitational force; the former is experimentally well established and the latter, while it has not yet been detected experimentally, hardly anyone doubts its existence.

-- from the book Quantum Field Theory in a Nutshell, by A. Zee, 2003.

The photons that allow you to read these words are real photons, although the word "photons" may not be the best description of what is going on in the process of light emission and absorption.  No one has yet  come up with a replacement for the word "photon," however.

Photons are said to be quanta of the electromagnetic field, but there's much more involved in this terminology than meets the eye. First of all there's the setting up of the harmonic oscillator model for the electromagnetic field.  At the lowest level of approximation, a "normal mode expansion" results in an idealized, linear model in which photons are independent vibrations of this harmonic oscillator field.  The thing to keep in mind is that the variables are called normal mode coordinates, and are not the coordinates of a particle moving in the x, y, z coordinates of what we normally think of as space. Photons are oscillating normal modes that are used to model in a quantum mechanical way the actual space and time variations of an electromagnetic wave.  We can all picture a wave, because we've all seen waves on strings--if not in actuality, at least in a drawing.  But nobody can picture a photon!

Virtual photons, and virtual electrons and positrons, come into use at an even higher level of abstraction and a higher level of approximation. They allow a more precise calculation of what are called radiative corrections to the motion of electrically charged particles--electrons mainly--and it's these calculations that have proved to be so impressive in predicting and verifying experimental results. 

The basis for physicists' audacity in predicting the existence of particles that are not observable is Heisenberg's uncertainty principle.  Or rather the flip side of the uncertainty principle.

On Side A we have the lower limit of ħ on any simultaneous measurement of the uncertainty (Δ) in both the position x and linear momentum p of a particle: ΔxΔp ≥ ħ.  And, still on Side A, we have the same limitation on the energy uncertainty that a particle can have and the time during which that energy is measured, ΔEΔt ≥ ħ.  This side of the principle tells us what supposedly can't happen.  We can't  have an arbitrarily small value for the product of the uncertainties in these measurements like we could in classical physics.

The B side of the uncertainty principle says--according to current ideas--that particles of a certain energy ΔE must pop into and out of existence for a certain time period Δt given by the lower limit of the uncertainty principle:  ΔEΔt = ħ.  In terms of the time period a virtual particle can exist, this would be re-written Δt = ħ / ΔE.

For describing the distance limit of a force field, this time limitation translates into the distance that virtual particles with a given energy can transmit a given force. Also, by E = mc², the  mass of the virtual particle transmitting the force can be predicted.

In the 1930s, based on the necessarily short range of force inside a nucleus, the strong nuclear force that holds nuclei together was predicted by Hideki Yukawa to be carried by a virtual particle with a mass about 200 times that of the electron.  Lo and behold, in the 1940s real particles of the predicted mass were discovered in cosmic rays.  (Once a real particle is known to exist, its virtual counterpart is assumed to exist). They were given the name pi-mesons, which soon was shortened to pions.   Yukawa was awarded the 1949 Nobel prize in physics.

The carriers of the weak nuclear force (the W-plus, W-minus, and Z bosons) were similarly predicted and later discovered in high-energy accelerators.  Like the Higgs boson, however, these are very short-lived "resonances," which would not be considered particles by anyone but a physicist who considers particles to be transmitters of forces. The detection of the predicted particles such as electrons, muons, and photons that result from the decay of these resonances is the basis for declaring that the two W's, the Z, and the Higgs have been discovered.  The fact that the numbers and types of these decays can be predicted is very impressive!

In contrast to the short-range strong and weak nuclear forces, gravity and electromagnetism are long-range forces. Their force equations (Newton's law of gravity and Coulomb's law of electrostatics) predict that the range of influence of masses and electric charges extends to infinity. Therefore...well, think about it.  We have an inverse linear relation between the range (distance) of influence of a force and the mass of the virtual particle that carries the force.  If the range is huge (infinite!), the particle's mass must be very small (zero!).  Photons do have zero "rest mass" (they only exist at the speed of light), and gravitons are predicted to have zero rest mass also.

Finally, to tie together these ideas, Side A of the uncertainty principle is considered to be responsible for the vacuum fluctuations of a field:  the field cannot have an arbitrarily small value of uncertainty in its position and momentum values, or in its energy and time-of-measurement values, and that means the particular value of zero without fluctuations for these variables is prohibited. Side B of the uncertainty principle, as described above, claims that virtual particles are undetectably swishing back & forth throughout what we formerly thought of as empty space.

Calculations based on these ideas have been quite amazing at predicting the results of experiments, including the prediction of the existence and approximate mass of the recently discovered Higgs boson.

Art and envy, and following your dream

Before I start my cheerleading routines in support of quantum field theory, gauge invariance, renormalization, virtual particles and all that, I want to mention a note I wrote that I found a few days ago stuck in Steven Weinberg's book The Quantum Theory of Fields, Vol. I,  published in 1997.  (There are three volumes, of which I only have the first.)  The note begins with a quote from the book, related to Richard Feynman's formulation of quantum field theory:  "... the nature of the infinities becomes transparent."  After I'd copied that on the slip of paper, I wrote this comment:  "Heehaw!  Can't see it, then!  Blinded by Feynman.  Oh envy, thou are art."

There's never been any doubt in my mind that envy and wanting to be the one who corrects the errors of the late 20th century quantum theorists are reasons I do physics research.  But the main reason is an inborn curiosity, and I really have no choice in the matter.

I take some inspiration for following this dream of mine from the late Julian Schwinger, who shared the 1965 Nobel Prize in physics with Feynman and Sin-Itiro Tomonaga.  Schwinger didn't agree with the mainstream of field theorists who followed the path blazed by Feynman, and he wrote his own set of books about quantum theory called Particles, Sources, and Fields, which also was published in three volumes, prior to Weinberg's 3-volume set.  As an epigraph at the beginning of each of the three volumes, Schwinger says, "If you can't join 'em, beat 'em." In the spirit of the early 1970s, when Schwinger's book was first published, I say, "Right on, Julian!" Schwinger's biggest disagreement with the mainstream theorists, as I understand it, was his disbelief in virtual particles, and I'm of the same mind as he was in that regard. Nevertheless, next time I will post with the intention of praising virtual particles, not burying them.