Illuminating quantum vacuum quotes

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.”

April 1984: An exchange of letters

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.

And now back to our program

Symmetry and invariance in physics and their relation to conservation laws, both classical and quantum: that's the program, for the most part.  Oh, yeh, and Schrödinger's Cat, also.  And A Serious Man, peripherally, as a sort of springboard.  Remember in the movie there is a very unusual form of the Schrödinger's Cat quantum superposition equation on the board in the non-dream college classroom scene?  An unusually delicate phase relationship is involved in that particular equation.

  

How did we get to where we are now in physics?  Where are we now, anyway?  We're deeply into quantum field theory (QFT), and looking to make it work also for gravity.  I don't like quantum field theory and only barely understand it, so my plan now is to temporarily, in the next few posts, describe it as if I do like it!  I'll be a gauge-invariance/QFT cheerleader for the next month or so and see where that leads. Let's hear it for those hardworking virtual particles and perturbation expansions! 

Ylem, fundamental observers, cosmic time

9· 24· 96  Tuesday; 4:20 pm

Okay – as we describe it nowadays, an event is not something you (or I) can “move away from” or “move toward.”  Why not?  It happens in YOUR frame of reference.  And same for other relatively-moving observers.  

But is it necessary to think of observing this way?  Can you accelerate and leave your ref. frame stationary?  Then you’d imagine light having to catch up with you – maybe.

I’m getting sleepy. . . 

In the Einstein train-and-lightning thought experiment, the two lightning bolts leave marks on both the platform and railroad car, and it is from these marks that calculations of simultaneity (or not) are made by mid-point observers for both frames.  The other observer is always considered to be the one who is moving.  Relative simultaneity, relative length and relative time arise as a result of this distinction.

9 · 26 · 96  Thurs.  12:45 a.m.
 

Okay, I’m awake, with nothin’ to do.  I mean, plenty to do

                         complex analysis probs.

                         thesis work

                         write a letter or two

but nothing that I’m compelled to

                           do.

It does seem like I need to write something.  Maybe just something connected to physics, maybe something more personal.  For lack of other ideas at the moment, I’ll write about Lorentz contraction and cosmic expansion.

             If one accepts redshift phenomenon as due to cosmic expansion, the very-far-away galaxies are moving away from any given observer at relativistically significant velocities.  So, does Lorentz contraction apply to the distance scales attached to the galaxies and moving past us (any observer) at the speed at which the galaxy(ies) is (are) receding?

             In other words, taking the Lorentz contraction seriously (but maybe erroneously?) means the expanding universe suddenly doesn’t seem so big.  It is contracted by its expansion!

             See Steveo Weinberg’s book.  If anybody discusses the issue, I would expect it to be him.

2:30 pm  9/26/96   Begin a novel:  Did you happen to read my previous novel?  It seems improbable since I didn’t write a previous one; thus if you have read it, please let me know as soon as possible.

                (An early morning thought, expressed in the afternoon, and missing some of the truthful oddness I felt in it this morning.)

Photo and caption are from Genesis of the Big Bang (2001) by Ralph Alpher & Robert Herman.

 

9 · 28 · 96  Saturday 1:40 pm   I should do a search for different ideas in the literature about what the Lorentz contraction actually means.

                       In the meantime though, I just opened Cosmological Constants and started reading Alpher & Herman’s paper (p. 117) which mentions in its abstract determining “the time dependence of proper distance.”

                     So I’ll read that first and get back with y’all later about the Lorentz contraction thing.  (I’m in the back room at 4111 Avenue F, where most of my books are.)  This is just a note (at this point) to add:  ylem!   I’d heard of it in some Gamow book, but never have seen it in a research publication until now, in the Alpher & Herman paper “Remarks on the Evolution of the Expanding Universe”:    "According to this theory the ylem (the primordial substance from which the elements were formed) consists of neutrons at a high density and temperature."

                    Ylem – what the universe (and people) are made of; the matter that shrunk into little black holes (electrons).  What about protons (and neutrons, as particles)?                     

10/8/96:  If YLEM is high-density high-temp neutrons, it sounds much like a neutron star.  Which has neutrons as closely packed as they can get, doesn’t it?  (Later.)

                     It’s 4:30 p.m., a Tuesday (Belgium) at 603 Blanco San Marcos Texas USA, Earth (where?), “Sun” solar system, Galaxie 500 or Milky Way or whatever.  Somewhere in space!  HERE.  Somewhere in time!  But who believes in time anyway?  It’s an organizing principle for events.  One could choose to be disorganized and not assign times to events.  Or not assign events to times.  Is there really a history of the universe?  Sure – we created it.  Could we choose disorganization over organization in describing the universe?  Cause and effect don’t seem to allow that.

                   Anyway, I’m 42 years old.  I should get to work.  I haven’t done that except in a need-for-money fashion, part-time for the most part.  It seems to me I have a resistance to becoming an authority, among other things.  But if one keeps doing something, like physics in my case, becoming an authority is inevitable.  What I’ve always been mainly interested in is asking questions about things.  Becoming an authority is to give in to a mild form of brainwashing.  But it’s still possible to raise questions, provided seeds were planted at some time in the past, possibly.  Maybe – most of the time it seems now that I think about it – questions seem to pop out of nowhere. 

                   My question posed in this journal on p. 135 (9· 26· 96) seems to be answered by the concept of “cosmic time.”  There must be a lack of synchronization of clocks between two relatively moving observers in order for length contraction to exist (if we accept that idea, rather than the idea that it’s impossible to do a length measurement of a moving rod, which I call the Einstein length measurement problem).

                   As M.S. Longair writes in Theoretical Concepts in Physics, p. 317, “We now introduce a set of fundamental observers, defined as observers who move in such a way that the Universe appears to be isotropic to them.  Each of them has a clock and proper time measured by that clock is called cosmic time.  There are no problems of synchronisation of these clocks carried by fundamental observers because, for example, they could be told to set their clocks to the same time when the Universe has a certain density.”

                   But it sounds like too much of an idealization.  Who will tell them to set their clocks?  God?  Even if a clock is automatically set at a certain density, that means density measures time.  But I’ll accept that idea of cosmic time, for the time being.

10/9/96  8:50 pm   However, the renowned Hermann Bondi, MA, FRS, in Cosmology p. 125, says, when discussing Milne’s kinematic relativity, 

In general relativity, the equivalence of the laws of nature is postulated for all observers whatever their positions and their state of motion.  Such a formulation is clearly inappropriate in kinematic relativity.  At the stage at which the cosmological principle is required laws of nature have not been defined.  As was discussed in Chapter 1, the distinction between the actual motions and the laws of motion can hardly be drawn in cosmology, and is presumably  quite inappropriate.  The cosmo prinzip [my abbreviation] has therefore to be defined with respect to the actual aspect of the universe rather than with respect to the laws of nature.  Now a good deal is known from purely terrestrial physics about observers at the same place in different states of motion.  From this we know that although the laws of nature may be the same, the aspect of the universe will be different for observers in the same place in different states of motion.  Accordingly, it is impossible to define the cosmo prinzip  as implying that all observers, irrespective of their position and state of motion, obtain the same aspect of the universe.  It becomes necessary to select a set of ‘fundamental observers’ of whom there is always one at each point.  The cosmo prinzip, the contents of which will be discussed later, applies only to this set of observers.

          Longair makes no such distinction in calling into service the fundamental observers—he doesn’t say it is for purposes of satisfying the cosmo prinzip in kinematic relativity, just for making time defined equivalently for observers throughout the U.  Cosmic time.

        But, I see now Bondi mentions fundamental observers in other contexts.  First, particles:  “Any particle moving with the substratum is called a ‘fundamental particle’.”  Substratum = the theo. construction that implies or states that the cosmo prinzip applies in detail and not just statistically.  (See pp 65, 66.)

       Then H. B. says:  “In order to apply the cosmological principle to the construction of the substratum it is necessary to compare the physical aspect of the universe from various points in it.  For this purpose imaginary observers have to be introduced, present at all points of space-time.”  . . .

          These observers are just a way of making specific what the cosmo prinzip says:  “any observers like ourselves anywhere would obtain equivalent results from equivalent observations.”  Hoo boy – observations or measurements, or are they the same?  The same, apparently.

         An observer going by Earth at high speed is not a fundamental observer, because he or she doesn’t see (see? observe? measure?) isotropy of U.  So only observers to whom the U looks isotropic (“no first harmonic deviation from isotropy”) are fundamental observers.  Real motions are the only ones allowed, whereas in special relativity “equivalent observers means equivalent for testing the laws of motion” – all possible motions, eh?  Milne gets mentioned here (p. 67), too:

                     

 "The precise way in which these fundamental observers are introduced varies somewhat between different theories, but their distribution and general characteristics are always the same.”  Oh, no!  It’s the consistent observer—the horror of the universe (paraphrasing Brenda Ueland)!  “An argument given by Milne which appears to be of rather restricted applicability shows that the observers must form a continuous rather than a discrete set, but in any case every current theory assumes them to form a continuous set.

   "The cosmological principle may now be stated as:  Every member of the 3-parameter set of fundamental observers obtains the same result of corresponding observations of the universe as every other member."

              My question from p. 135 herein is definitively answered by Bondi on p. 71:  “The universe itself therefore acts as a synchronizing instrument which enables A and B (and hence all observers) to synchronize their clocks.”  Also:  “Kinematic relativity also has a cosmic time, and that cosmic time can only be dispensed with in a theory which adopts the perfect cosmological principle, i.e., in the steady-state theory.”  World map and world picture are also mentioned on this page (Milne’s terms).

           And next Bondi discusses whether cosmic time actually applies to the U and not just to idealized models of it!  He says:  “This question is common to all theories other than the steady-state theory, but very little attention seems to have been paid to resolving this problem which is relevant to the logical foundations of all these theories.”