[“Models of the quantum vacuum” series]
A theoretical physicist walks into a bar. The bartender says, “What can I get you?” The physicist says, “Nothing.” The bartender gives the physicist an empty glass. The physicist says, “Thanks, that’s plenty!”
Physicists take emptiness quite seriously. So-called empty space is an important area of study and research. The future of the cosmos, eh.
When I worked at Hughes Space & Communications, visiting the High Bay was a rare opportunity. The scale of the place, … the reflective surfaces of satellites and thermal wraps. Then there was the “shake & bake” area, which included a large thermal vacuum chamber in which satellites were tested in a simulated space environment — vacuum, radiation, and thermal cycling. I’m not sure what vacuum quality that facility achieved (high or ultra high vacuum, for example) — how close the pressure was to that in outer space. The chamber still contained matter particles (other than from any outgassing).
The lowest pressures currently achievable in laboratory are about 10−13 torr (13 pPa). However, pressures as low as 5×10−17 Torr (6.7 fPa) have been indirectly measured in a 4 K cryogenic vacuum system. This corresponds to ≈100 particles/cm3.
Is null outer space truly empty? How about a “perfect” vacuum? Quantum mechanics says not really. There still is energy in the state “(that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space).”
Even if all particles of matter were removed, there would still be photons and gravitons, as well as dark energy, virtual particles, and other aspects of the quantum vacuum.
While that may seem strange — that a complete void is not really empty, there’s something even more puzzling, namely, what physicists call the vacuum energy problem and the “non-zero expectation value.”
I finished reading Sean Carroll’s book about the Higgs boson recently. In chapter 12 “Beyond this horizon,” he talks about the problem with vacuum energy . It has to do with cosmic acceleration, as determined by astronomical measurements in the last 20 years.
To explain the astronomers’ observations, we don’t need very much vacuum energy; only about one ten-thousandth of an electron volt per cubic centimeter. Just as we did for the Higgs field value, we can also perform a back-of-the-envelope estimate of how big the vacuum energy should be. The answer is about 10^116 electron volts per cubic centimeter. That’s larger than the observed value by a factor of 10^120, a number so big we haven’t even tried to invent a word for it. … Understanding the vacuum energy is one of the leading unsolved problems of contemporary physics. — Carroll, Sean (2012-11-13). The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World (Kindle Locations 3603-3608). Penguin Publishing Group. Kindle Edition.
So, astronomers say that we see the universe expanding in a certain way. Theoretical physicists say that we know the density of the universe. Carroll says that the problem is deeper than the energy contributed by any Higgs field. Assuming that we’re not in a GIGO state, how do we model the universe being “pushed apart?”
Wiki: In many situations, the vacuum state can be defined to have zero energy, although the actual situation is considerably more subtle. The vacuum state is associated with a zero-point energy, and this zero-point energy has measurable effects. In the laboratory, it may be detected as the Casimir effect. In physical cosmology, the energy of the cosmological vacuum appears as the cosmological constant. In fact, the energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an erg (or 0.6 eV). An outstanding requirement imposed on a potential Theory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant. 
Quantum field theory states that all fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. A field in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field were like the displacement of a ball from its rest position. The theory requires “vibrations” in, or more accurately changes in the strength of, such a field to propagate as per the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. Canonically, if the field at each point in space is a simple harmonic oscillator, its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. Thus, according to the theory, even the vacuum has a vastly complex structure and all calculations of quantum field theory must be made in relation to this model of the vacuum.
The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light, energy, and so on. According to the theory, most of these properties cancel out on average leaving the vacuum empty in the literal sense of the word. One important exception, however, is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator requires the lowest possible energy, or zero-point energy of such an oscillator to be:
E = hν/2
Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable, much as the concept of potential energy has been treated in classical mechanics for centuries. This argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is handled.
Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. These particles are always created out of the vacuum in particle-antiparticle pairs, which in most cases shortly annihilate each other and disappear. However, these particles and antiparticles may interact with others before disappearing, a process which can be mapped using Feynman diagrams. Note that this method of computing vacuum energy is mathematically equivalent to having a quantum harmonic oscillator at each point and, therefore, suffers the same renormalization problems.
Additional contributions to the vacuum energy come from spontaneous symmetry breaking in quantum field theory.
The Casimir attraction between uncharged conductive plates is often proposed as an example of an effect of the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by Milonni (1994) as validly, though unconventionally, explaining the Casimir effect with a model in which “the vacuum is regarded as truly a state with all physical properties equal to zero.” In this model, the observed phenomena are explained as the effects of the electron motions on the electromagnetic field, called the source field effect. … This point of view is also stated by Jaffe (2005): “The Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant, α, goes to zero.”
10 thoughts on “Empty dumpty”
Space.com‘s Spaceman1 on March 3, 2016, wrote:
 Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center. Sutter is also host of Ask a Spaceman, RealSpace and COSI Science Now. He contributed this article to Space.com’s Expert Voices: Op-Ed & Insights.
This Space.com article “Dark Energy May Lurk in the Nothingness of Space” published on May 31.2017, is an example of the continuing saga about so-called empty space.
An idea in process.
Another recent (9-4-2017) Space.com article “What Does Space Look Like Under a Microscope?” discusses “gazing deeper and deeper into empty space.”
What evidence is there for this stuff? The Casimir Effect. But conclusively demonstrating its existence is another matter, as recent experiments disagree. Planck world gotcha.
On the other hand, Lawrence Krauss argues that the ability to “come up with the best, most accurate prediction in all of science” — the spectrum of hydrogen — demonstrates that virtual particles exist. [Krauss, Lawrence. A Universe from Nothing: Why There Is Something Rather than Nothing (p. 68). Atria Books. Kindle Edition.]
Physicists Just Measured Quantum ‘Nothingness’ at Room Temperature (Mar 30, 2019)
Wiki: Radiation pressure
Phys.org: Fluctuations in the void (April 11, 2019)
Wiki: Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 380 to 740 nanometers. In terms of frequency, this corresponds to a band in the vicinity of 430–770 THz [terahertz].
This Forbes article by science communicator Ethan Siegel is a helpful overview of the mind-boggling quantum vacuum: “Yes, Virtual Particles Can Have Real, Observable Effects” by Ethan Siegel, Forbes Contributor (Jul 12, 2019) [Starts with a Bang Contributor Group | Science | The Universe is out there, waiting for you to discover it.]
The article contains some good visuals and discusses how the behavior of virtual particles in strong magnetic fields — like around some neutron stars — can polarize light, a measurable effect called vacuum birefringence.
Regarding the vacuum energy problem described by Carroll [ “… we can also perform a back-of-the-envelope estimate of how big the vacuum energy should be. The answer is about 10^116 electron volts per cubic centimeter. That’s larger than the observed value by a factor of 10^120, a number so big we haven’t even tried to invent a word for it. … Understanding the vacuum energy is one of the leading unsolved problems of contemporary physics.”], this August 29, 2019, Phys.org article “Providing a solution to the worst-ever prediction in physics” describes research “that finally makes it possible to harmonize theory and observation on the cosmological constant.”
In the latest of his “Thanksgiving” series of blog posts, Sean Carroll this year gives thanks for space: “Thanksgiving” (November 28, 2019).
Space is an important area of study and research (as noted above). And the notion of space has evolved over time. Aristotle. Newton. Hamilton. Einstein, etc.
So, what are we really talking about? The everyday notion of moving about in a 3D landscape, a mathematical framework for describing the motion of things, a spacetime continuum, or an emergent characterization of quantum entanglement?
Without a better grasp of Hilbert space and eigenvalues, Carroll’s closing discussion eludes me. However, he poses a question about something that we typically take for granted – that there’s dispersed stuff which interacts, that energy states change with time. Sort of the philosophical question “Why is there something rather than nothing at all?” – why the universe is not some bland arena.
Are there practical applications for “harvesting” the quantum vacuum? This SciTechDaily article discusses some research using the Casimir force.
• SciTechDaily > “A Force From ‘Nothing’ Used to Control and Manipulate Objects” by University Of Western Australia (October 13, 2020)
The Casimir effect as due to vacuum energy [re post on renormalization] vs. as result of the relativistic van der Waals force [so need to understand the evidence that atomic and molecular effects, such as the van der Waals force, are distinct from but variations on the theme of the Casimir effect].
Nothing is a major something, eh.
• Wired > “How the Physics of Nothing Underlies Everything” by Charlie Wood (Aug 28, 2022) – The multiverse hypothesis says there are false vacuums in a rolling “energy landscape” of vacuum bubbles.
The multiverse hypothesis
1. Compared to standard quantum field models, our (observed) universe has a puzzling “ultra-low” positive vacuum energy.
2. String theory allows nearly countless vacuums. (Cf. references to string theory in “Is supersymmetry dead?“)
3. Once started, cosmic inflation might continue, with most of the vacuum violently exploding outward forever.
4. On a vast cosmic timescale, the stability of positively energized space (like our bubble) might be uncertain – metastable. Not one of reality’s preferred states.
Credit: Pixabay/CC0 Public Domain
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