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Empty dumpty

[“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 [1]. 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. [2]

[1] Wiki:

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.

[2] Wiki:

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.”

13 thoughts on “Empty dumpty

  1.‘s Spaceman1 on March 3, 2016, wrote:

    Have an empty box? Poof, like magic, they can appear! Or disappear! Whatever! Of course, if they do appear, they’ll disappear right away — stealing energy from the vacuum to exist for just a little bit; that’s all they can muster. But if you already have something — say, a photon zipping about — it can turn itself into an electron and positron without even realizing it. And those particles can turn themselves back into a photon if they feel like it. It’s seriously just that easy. Matter and energy are really the same thing, and can change forms as easily as you change your shirt.

    [1] 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’s Expert Voices: Op-Ed & Insights.

  2. This 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.

    Dark energy may emerge from fluctuations in the nothingness of empty space, a new hypothesis suggests. … The new study proposed that the expansion is driven by fluctuations in the energy carried by the vacuum, or regions of space devoid of matter. The fluctuations create pressure that forces space itself to expand, making matter and energy less dense as the universe ages, said study co-author Qingdi Wang, a doctoral student at the University of British Columbia (UBC) in Canada.

    An idea in process.

  3. Another recent (9-4-2017) article “What Does Space Look Like Under a Microscope?” discusses “gazing deeper and deeper into empty space.”

    That something is a roiling collection of virtual particles, collectively called quantum foam. According to quantum physicists, virtual particles exist briefly as fleeting fluctuations in the fabric of spacetime, like bubbles in beer foam.

    “The ‘bubbles’ in the quantum foam are quadrillions of times smaller than atomic nuclei and last for infinitesimal fractions of a second — or in ‘quantum-speak,’ the size of a Planck Length for a Planck Time,” Eric Perlman, a Professor of Physics and Space Science at Florida Institute of Technology, says.

    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.]

  4. Physicists Just Measured Quantum ‘Nothingness’ at Room Temperature (Mar 30, 2019)

    By now most of us know that there’s nothing empty about the vacuum – it’s actually filled with quantum fluctuations. We can’t ‘hear’ these fluctuations, but for the sensitive equipment scientists use to measure the minute distortions of space-time, they can create subtle effects that can be deafening.

    This experiment looked at a phenomenon called quantum radiation pressure, which arises when particles interact with detectors such as LIGO – the Laser Interferometer Gravitational-Wave Observatory in the US, responsible for confirming the existence of gravitational waves a little over three years ago.

    But a team of researchers from Louisiana State University managed to actually measure this quantum effect in real-world conditions – at room temperature.

    Which is useful because it means we may now be able to apply the findings to real-world equipment.

    This experiment was done using miniature versions of LIGO …

    This research was published in Nature.

    Wiki: Radiation pressure

  5. Fluc­tu­a­tions in the void (April 11, 2019)

    In quantum physics, a vacuum is not empty, but rather steeped in tiny fluctuations of the electromagnetic field. Until recently it was impossible to study those vacuum fluctuations directly. Researchers at ETH Zurich have developed a method that allows them to characterize the fluctuations in detail.

    Jérôme Faist, professor at the Institute for Quantum Electronics at ETH in Zurich, and his collaborators have now succeeded in characterizing those vacuum fluctuations directly for the first time.

    “The vacuum fluctuations of the electromagnetic field have clearly visible consequences, and among other things, are responsible for the fact that an atom can spontaneously emit light,” explains Ileana-Cristina Benea-Chelmus, a recently graduated Ph.D. student in Faists laboratory and first author of the study recently published in the scientific journal Nature.

    … they used a detector [cooled to -269 degrees centigrade] based on the so-called electro-optic effect. The detector consists of a crystal in which the polarisation (the direction of oscillation, that is) of a light wave can be rotated by an electric field – for instance, by the electric field of the vacuum fluctuations. In this way, that electric field leaves a visible mark in the shape of a modified polarization direction of the light wave. Two very short laser pulses lasting for a fraction of a thousandth of a billionth of a second are sent through the crystal at two different points and at slightly different times, and afterward, their polarisations are measured. From those measurements, the spatial and temporal correlations between the instantaneous electric fields in the crystal can finally be calculated.

    “Still, the measured signal is absolutely tiny,” ETH-professor Faist admits, “and we really had to max out our experimental capabilities of measuring very small fields.” According Faist, another challenge is that the frequencies of the electromagnetic fluctuations measured using the electro-optic detector lie in the terahertz range, … the scientists at ETH still managed to measure quantum fields with a resolution that is below an oscillation cycle of light in both time and space.

    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].

  6. 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.

    … empty space holds perhaps the top spot when it comes to a phenomenon that defies our intuition. Even if you remove all the particles and radiation from a region of space — i.e., all the sources of quantum fields — space still won’t be empty. It will consist of virtual pairs of particles and antiparticles, whose existence and energy spectra can be calculated. Sending the right physical signal through that empty space should have consequences that are observable.

    In 2016, scientists were able to locate a neutron star that was close enough and possessed a strong enough magnetic field to make these observations possible. Working with the Very Large Telescope (VLT) in Chile, which can take fantastic optical and infrared observations, including polarization, a team led by Roberto Mignani was able to measure the polarization effect from the neutron star RX J1856.5-3754.

  7. 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, 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 an article to be published in Physics Letters B, a researcher from the University of Geneva (UNIGE), Switzerland [Lucas Lombriser, assistant professor, Department of Theoretical Physics, UNIGE’s Faculty of Sciences], proposes an approach that may seemingly resolve this inconsistency. The original idea in the paper is to accept that another constant – Newton’s universal gravitation G, which also forms part of the equations on general relativity – may vary. This potentially major breakthrough, which has been positively received by the scientific community, still needs to be pursued in order to generate predictions that can be confirmed (or refuted) experimentally.

  8. 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?

    Our everyday world is accurately modeled as stuff, distributed through three-dimensional space, evolving with time. That’s something to be thankful for! But we can also wonder why it is the case.

    I don’t mean “Why is space three-dimensional?”, although there is that. I mean why is there something called “space” at all?

    Space is probably emergent rather than fundamental, and the ultimate answer to why it exists is probably going to involve quantum mechanics, and perhaps quantum gravity in particular.

    But rather than answer it, for the purposes of thankfulness I just want to point out that it’s not obvious that space as we know it had to exist, even if classical mechanics had been the correct theory of the world.

    … from the Hamiltonian perspective, positions and momenta are on a pretty equal footing. Why then, in the real world, do we seem to “live in position space”? Why don’t we live in momentum space?

    As far as I know, no complete and rigorous answer to these questions has ever been given. But we do have some clues, and the basic principle is understood, even if some details remain to be ironed out.

    That principle is this: we can divide the world into subsystems that interact with each other under appropriate circumstances. And those circumstances come down to “when they are nearby in space.” In other words, interactions are local in space. They are not local in momentum. Two billiard balls can bump into each other when they arrive at the same location, but nothing special happens when they have the same momentum or anything like that.

    … on the “Why is there space?” question. The answer is “Because space is the set of variables with respect to which interactions are local.” Which raises another question, of course: why are interactions local with respect to anything? Why do the fundamental degrees of freedom of nature arrange themselves into this kind of very specific structure, rather than some other one?

    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.

  9. 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 research, published recently in Nature Physics, was jointly led by Professor Michael Tobar, from University of Western Australia‘s School of Physics, Mathematics and Computing and Chief Investigator at the Australian Research Council Centre of Excellence for Engineered Quantum Systems and Dr. Jacob Pate from the University of Merced.

    Professor Tobar said that the result allowed a new way to manipulate and control macroscopic objects in a non-contacting way, allowing enhanced sensitivity without adding loss.

    “If you can measure and manipulate the Casimir force on objects, then we gain the ability to improve force sensitivity and reduce mechanical losses, with the potential to strongly impact science and technology,” Professor Tobar said.

    Reference: “Casimir spring and dilution in macroscopic cavity optomechanics” by J. M. Pate, M. Goryachev, R. Y. Chiao, J. E. Sharping and M. E. Tobar, 3 August 2020, Nature Physics.



    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].

    Summing over all possible oscillators at all points in space gives an infinite quantity. Since only differences in energy are physically measurable (with the notable exception of gravitation, which remains beyond the scope of quantum field theory), this infinity may be considered a feature of the mathematics rather than of the physics. This argument is the underpinning of the theory of renormalization. Dealing with infinite quantities in this way was a cause of widespread unease among quantum field theorists before the development in the 1970s of the renormalization group, a mathematical formalism for scale transformations that provides a natural basis for the process.


    On 4 June 2013 it was reported that a conglomerate of scientists from Hong Kong University of Science and Technology, University of Florida, Harvard University, Massachusetts Institute of Technology, and Oak Ridge National Laboratory have for the first time demonstrated a compact integrated silicon chip that can measure the Casimir force.

  10. 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 electromagnetic vacuum is the absence of a medium that can slow down light. And a gravitational vacuum lacks any matter or energy capable of bending space. In each case the specific variety of nothing depends on what sort of something physicists intend to describe.

    But physicists learned that the universe’s fields are quantum, not classical [in which a field’s value can be zero], which means they are inherently uncertain. You’ll never catch a quantum field with exactly zero energy.

    When fields pile up, they interact, influencing each other’s pendulums and establishing new mutual configurations in which they like to get stuck. Physicists visualize these vacuums as valleys in a rolling “energy landscape.”

    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.

    Only finite regions of space would stop inflating, becoming bubbles of relative stability separated from each other by inflating space in between.

    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.

    [But] Physicists may not have hit on the right way to handle positive vacuum energy within string theory [particularly regarding so-called “tiny” dimensions].

    Multiverse bubbles
    Credit: Pixabay/CC0 Public Domain

  11. Expanding universe

    Another go at the topic … cosmic epochs … the cosmic web … dark energy … the future of the Universe via its past … enduring background radiation, a “glass” that is never empty – so, eternal energy, eh.

    There’s some hand-waving regarding modes of radiation. A mash-up. With evolving epochal dominance.

    Wiki > Radiation

    • Big Think > “Our Universe wasn’t empty, even before the Big Bang” by Ethan Siegel (July 27, 2023, from the Starts With A Bang archives) – No matter how much you take out of it, the Universe will always generate new forms of energy.

    It’s like the Universe itself doesn’t understand our idea of “nothing” at all … No matter how “empty” we artificially make the expanding Universe, the fact that it’s expanding would still spontaneously and unavoidably generate radiation.

    In a sense, you’d just have empty space itself: still expanding, still with the laws of physics intact, and still with the inability to escape the quantum fields that permeate the Universe.

    In a Universe with dark energy, a cosmological constant, or the zero-point energy of quantum fields, there’s no reason to infer that the zero-point energy would actually be zero.

    The earliest light that’s arriving right now, 13.8 billion years after the Big Bang, is from a point that’s presently about 46 billion light-years away.

    And just like the existence of a black hole’s event horizon results in the creation of Hawking radiation, the existence of a cosmological horizon must also — if the same laws of physics are to be obeyed — create radiation [thirty orders of magnitude weaker than the current CMB].

    But there’s another time in the Universe — not in the future but in the distant past — when the Universe was also dominated by something other than matter and radiation: during cosmic inflation. … the field energy of inflation.

    So long as the fabric of space itself has a non-zero amount of energy intrinsic to it, it will expand.

    Insisting that the laws of physics remain valid is enough to do away with the idea of a truly empty Universe.

  12. Nothingness vacuum

    Hey, what’s a “false” vacuum? When is “nothing” genuine? To paraphrase the Beatles’ “With a Little Help from My Friends” song:

    With a Little Help from Quantum Physics

    what do you have when you empty all space?
    i can’t tell you, but i know it’s energy

    Is the notion of absolute vacuum (stillness) just as undefinable as absolute acceleration? Reality vibrates regardless.

    Here’s another useful recap on the topic: theoretical physicist Isabel Garcia Garcia [New York University and the Institute for Advanced Study] explains what a “true vacuum” is. And, yeah, she does mention quantum field theory (at least with the metaphor of quantum harmonic oscillators – “pendulums” – at every point in spacetime). And some hand-wavy accommodations by physicists.

    Like Ethan Siegel’s recent article on this topic, the key idea is an expanding universe. Energy density.

    Yet, I was left wondering about energy density and quantum fields (in the sense of Wilczek’s Grid). Emptiness as no energy diffusion whatsoever, the absence of all quantum interactions, the absence of all superpositions (including entanglements). If spacetime is emergent, …

    • Quanta Magazine > “Does Nothingness Exist?” by Steven Strogatz (July 26, 2023) – The concept of nothingness figures at least implicitly into almost every theory of modern physics.

    [from transcript of interview]

    If you make an electromagnetic vacuum, you’re sort of just assuming that, you know, you’ve removed all the photons [wavepackets] in a certain region, perhaps in a cavity. And you make it free of any type of photons in this way.

    Heisenberg’s uncertainty principle … a quantum particle [ahem] can never be, sort of, exactly at complete rest [still].

    … in the context of quantum field theory we cannot actually measure the absolute value of the energy of the vacuum. … we can measure energies relative to the energy of the vacuum.

    [The Casimir effect] The plates need to be very close together. In order for us to see this effect. The pressure that acts on the plates is inversely proportional to the fourth power of the distance between the plates.

    … we have to go beyond quantum field theory into what is called quantum gravity … our universe is expanding … That tells us that experimentally, the vacuum energy density of our universe is a positive quantity. … extremely tiny. … So there is this puzzle by the name of the cosmological constant [the energy density of the vacuum] problem …

    There are other properties of our vacuum that are also somewhat mysterious. And the origin of them, we don’t understand.

    [Vacuum decay] … quantum mechanics has a way … where a system that is not in its preferred state can actually sort of tunnel quantum mechanically [cross an energy barrier] by nucleating sort of, like, bubbles of this new vacuum into this new state, which will be the true vacuum.

    [Uh-ho, string theory] … typically string theory has to be formulated in 10 space-time dimensions [compactified]. … a string theory landscape … in theories that have extra dimensions, a vacuum could actually decay to something that is true nothing. And by true nothing, we actually mean, a region where not even space-time is defined.

  13. Photon quantum scattering
    Credit: J. Sommerfeldt/Technical University of Braunschweig

    “Punching” emptiness … the interaction of localized energy densities …

    Success in “hitting” a target depends on its effective surface area – the cross section presented to an impinging projectile. For example, in archery, hitting a target edgeways is harder than frontways.

    Cross sectional models are critical to analysis of photon-scattering experiments which explore atomic structure. Modeling interactions between photons and bound electrons, and between photons and the “empty” field around nuclei.

    This article is about modeling the practical, real effects of the quantum vacuum.

    • > “Quantum Deflection Unraveled” by Ryan Wilkinson (August 8, 2023) – Improved calculations of a quantum phenomenon called Delbrück scattering resolve a long-standing discrepancy between theory and experiment.

    The sky owes its color to a process known as Rayleigh scattering, in which light bounces off [is scattered via interactions with] electrons bound to atoms. Quantum physics permits an analogous effect, dubbed Delbrück scattering, whereby photons deflect from [interactions with] the electrostatic field around atomic nuclei.

    According to quantum theory, empty space is not actually empty but teeming with particle–antiparticle pairs that flit in and out of existence. Delbrück scattering occurs when photons interact with such [virtual] pairs in the electrostatic field of a nucleus.


    • Wiki > Cross section (physics) – Quantum scattering, Scattering of light

    In physics, the cross section is a measure of the probability that a specific process will take place [occur] when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). … In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

    It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the [geometric] cross section relative to some physical process.

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