Wednesday, March 11, 2015

What physics says about the vacuum: A visit to the seashore.

[Image Source:]
Imagine you are at the seashore, watching the waves. Somewhere in the distance you see a sailboat — wait, don’t fall asleep yet. The waves and I want to tell you a story about nothing.

Before quantum mechanics, “vacuum” meant the absence of particles, and that was it. But with the advent of quantum mechanics, the vacuum became much more interesting. The sea we’re watching is much like this quantum vacuum. The boats on the sea’s surface are what physicists call “real” particles; they are the things you put in colliders and shoot at each other. But there are also waves on the surface of the sea. The waves are like “virtual” particles; they are fluctuations around sea level that come out of the sea and fade back into it.

Virtual particles have to obey more rules than sea waves though. Because electric charge must be conserved, virtual particles can only be created together with their anti-particles that carry the opposite charge. Energy too must be conserved, but due to Heisenberg’s uncertainty principle, we are allowed to temporarily borrow some energy from the vacuum, as long as we give it back quickly enough. This means that the virtual particle pairs can only exist for a short time, and the more energy they carry, the shorter the duration of their existence.

You cannot directly measure virtual particles in a detector, but their presence has indirect observable consequences that have been tested to great accuracy. Atomic nuclei, for example, carry around them a cloud of virtual particles, and this cloud shifts the energy levels of electrons orbiting around the nucleus.

So we know, not just theoretically but experimentally, that the vacuum is not empty. It’s full with virtual particles that constantly bubble in and out of existence.

Vizualization of a quantum field theory calculation showing virtual particles in the quantum vacuum.
Image Credits: Derek Leinweber

Let us go back to the seashore; I quite liked it there. We measure elevation relative to the average sea level, which we call elevation zero. But this number is just a convention. All we really ever measure are differences between heights, so the absolute number does not matter. For the quantum vacuum, physicists similarly normalize the total energy and momentum to zero because all we ever measure are energies relative to it. Do not attempt to think of the vacuum’s energy and momentum as if it was that of a particle; it is not. In contrast to the energy-momentum of particles, that of the vacuum is invariant under a change of reference frame, as Einstein’s theory of Special Relativity requires. The vacuum looks the same for the guy in the train and for the one on the station.

But what if we take into account gravity, you ask? Well, there is the rub. According to General Relativity, all forms of energy have a gravitational pull. More energy, more pull. With gravity, we are no longer free to just define the sea level as zero. It’s like we had suddenly discovered that the Earth is round and there is an absolute zero of elevation, which is at the center of the Earth.

In best manner of a physicist, I have left out a small detail, which is that the calculated energy of the quantum vacuum is actually infinite. Yeah, I know, doesn’t sound good. If you don’t care what the total vacuum energy is anyway, this doesn’t matter. But if you take into account gravity, the vacuum energy becomes measurable, and therefore it does matter.

The vacuum energy one obtains from quantum field theory is of the same form as Einstein’s Cosmological Constant because this is the only form which (in an uncurved space-time) does not depend on the observer. We measured the Cosmological Constant to have a small, positive, nonzero value which is responsible for the accelerated expansion of the universe. But why it has just this value, and why not infinity (or at least something huge), nobody knows. This “Cosmological Constant Problem” is one of the big open problems in theoretical physics today and its origin lies in our lacking understanding of the quantum vacuum.

But this isn’t the only mystery surrounding the sea of virtual particles. Quantum theory tells you how particles belong together with fields. The quantum vacuum by definition doesn’t have real particles in it, and normally this means that the field that it belongs to also vanishes. For these fields, the average sea level is at zero, regardless of whether there are boats on the water or aren’t. But for some fields the real particles are more like stones. They’ll not stay on the surface, they will sink and make the sea level rise. We say the field “has a non-zero vacuum expectation value.”

On the seashore, you now have to wade through the water, which will slow you down. This is what the Higgs-field does: It drags down particles and thereby effectively gives them mass. If you dive and kick the stones that sunk to the bottom hard enough, you can sometimes make one jump out of the surface. This is essentially what the LHC does, just call the stones “Higgs bosons.” I’m really getting into this seashore thing ;)

Next, let us imagine we could shove the Earth closer to the Sun. Oceans would evaporate and you could walk again without having to drag through the water. You’d also be dead, sorry about this, but what about the vacuum? Amazingly, you can do the same. Physicists say the “vacuum melts” rather than evaporates, but it’s very similar: If you pump enough energy into the vacuum, the level sinks to zero and all particles are massless again.

You may complain now that if you pump energy into the vacuum, it’s no longer vacuum. True. But the point is that you change the previously non-zero vacuum expectation value. To our best knowledge, it was zero in the very early universe and theoretical physicists would love to have a glimpse at this state of matter. For this however they’d have to achieve a temperature of 1015 Kelvin! Even the core of the sun “only” makes it to 107 Kelvin.

One way to get to such high temperature, if only in a very small region of space, is with strong electromagnetic fields.

In a recent paper, Hegelich, Mourou, and Rafelski estimated that with the presently most advanced technology high intensity lasers could get close to the necessary temperature. This is still far off reality, but it will probably one day become possible!

Back to the sea: Fluids can exist in a “superheated” state. In such a state, the medium is liquid even though its temperature is above the boiling point. Superheated liquids are “metastable,” this means if you give them any opportunity they will very suddenly evaporate into the preferred stable gaseous state. This can happen if you boil water in the microwave, so always be very careful taking it out.

The vacuum that we live in might be a metastable state: a “false vacuum.” In this case it will evaporate at some point, and in this process release an enormous amount of energy. Nobody really knows whether this will indeed happen. But even if it does happen, best present estimates date this event into the distant future, when life is no longer possible anyway because stars have run out of power. Particle physicist Joseph Lykken estimated something like a Googol years; that’s about 1090 times the present age of the universe.

According to some theories, our universe came into existence from another metastable vacuum state, and the energy that was released in this process eventually gave rise to all we see around us now. Some physicists, notably Lawrence Krauss, refer to this as creating a universe from “nothing.”

If you take away all particles, you get the quantum vacuum, but you still have space-time. If we had a quantum theory for space-time as well, you could take away space-time too, at least operationally. This might be the best description of a physical “nothing” that we can ever reach, but it still would not be an absolute nothing because even this state is still a mathematical “something”.

Now what exactly it means for mathematics to “exist” I better leave to philosophers. All I have to say about this is, well, nothing.

If you want to know more about the philosophy behind nothing, you might like Jim Holt’s book “Why does the world exist”, which I reviewed here

This post previously appeared at Starts With a Bang under the title “Everything you ever wanted to know about nothing”.


  1. A very good paper that seems to address the heart of the issue. I hope our intuitions have not diverged... then again between all the theoreticians it may be a good thing. The seashore is a great metaphor as Newton knew. As I said, the equations written in the sand and the tides that wash them away - at least a few have seen them.

  2. The statistical behaviour of virtual-particles-sea has bugged me for a long time.
    If e.g. electric field is fluctuating, it's distribution around zero is symmetric (I guess), yielding to zero cumulative value (over time).

    But for energy, the allowable values are always non-negative (or are they), leading to non-zero accumulated value over time. Or average mass over volume of vacuum being positive.

    Is there any neat explanation making this to look as "beautiful" as laws of nature typically tend to? (conservation of energy-momentum instead of energy; combined mass of virtual-pair being zero; energy being square of something which averages to zero; the Higg's-boson-thing just explained in the post; ...)

  3. Check out the paper by Bianchi and Rovelli if you are interested in the quantum vacuum and its relationship to the cosmological constant.

  4. Defectively postulated vacuum background fails as theoretical predictions. Vacuum blind to massless bosons versus massed fermion quarks is unendingly patched. Achiral (but Ashtekar and Immirzi) spacetime curvature also contains chiral spacetime torsion (Einstein-Cartan-Kibble-Sciama, Fernparallelismus, Weitzenböck. Hayashi and Nakano, etc.). The Equivalence Principle fails within geometric challenges outside GR.

    Quantum mechanics arises from momentum. Noether's theorems conserve angular momentum given isotropic vacuum. Vacuum trace chiral anisotropy leaks Milgrom acceleration. Dark matter is another patch. Quantum gravitation, at scale, has an incomplete founding postulate.

    Theory is Aquinas' 3500 pages versus Spinoza's 200. Physics (DOI: 10.5281/zenodo.15107) and chemistry (DOI: 10.5281/zenodo.15439) measure spacetime torsion as Equivalence Principle diastereomeric geometric violation. Look.

  5. « But for energy, the allowable values are always non-negative ». But dark energy is a perfect example against. The entropic explanation is so natural. The Big Bang is a big fluctuation of the vacuum creating a decompression (negative energy), this decompression extract vacuum energy by a positive-feedback mechanism. More energy is extracted more the loan balance becomes big. We are living on borrowed time-space.

    That said, stimulating space without fully knowing its properties of excitement may not be such a good idea ;-)

  6. SH: "So we know, not just theoretically but experimentally, that the vacuum is not empty. It’s full with virtual particles that constantly bubble in and out of existence."

    1. Yes and NO! We have good experimental evidence that something pervades the "vacuum", but "virtual particles" are completely hypothetical and the something may turn out to be other entities. Until we have empirical evidence for the something pervading the vacuum, it would behoove you and other physicists to not hype the "virtual particle" liturgy, but rather admit that it is an open problem.

    2. The cosmological constant problem, aka the vacuum energy density disparity/crisis, tells us in unambiguous terms that there is are one or more serious flaws in our current set of fundamental assumptions.

  7. It's my understanding that virtual particles would be better described as not even hypothetical: they have no ontological status, they are lines drawn in diagrams. See also “psiontology” and this.

  8. Paul,

    That is correct, yes, but it's similarly correct for "real" particles and thus a rather pointless statement.

  9. Robert:

    1. You're wrong. Virtual particles are simply a technical phrase that describes a particular calculation device, in this case it's higher-order correction to certain cross-sections. That this works has been confirmed to excellent precision, it is no longer hypothetical. I think it should be clear to you and to everybody else that this post of mine is heavy on metaphors, of course that's not how one really works with virtual particles.

    2. This too is wrong. Consider for a moment the cosmological constant had turned out to be zero. Nobody would have found anything strange about it. Now for what I am concerned a zero followed by dot and an infinite amount of zeroes is equally finetuned as a zero followed by 120 zeroes, a 1 and infinitely many other numbers. Most of my colleagues would disagree with me of course, but then they live from creating problems and trying to solve them.



  10. Practical:

    Fluctuations are by definitions fluctuations around some mean value. That mean value could be zero or something else. They're symmetric in the sense that otherwise the mean wouldn't be the mean (or it might be ill-defined). A non-zero electric field has also quantum fluctuations around it.

    As I wrote in my post, you shouldn't think of the vacuum energy as the energy of a particle. It doesn't work. That's not how it is. When we speak of 'virtual particles' what we actually mean are higher-order contributions to certain Feynman diagrams. Best,


  11. The article contains no math and it's also fringe from perspective of dense aether model logics. The photon-photon scattering amplitudes were already measured with using of strong lasers and these results can be also interpreted as a manifestation of virtual particles of vacuum under high energy density conditions. In another words, the physicists are speculating about things, which were already observed and measured before ten years. Their only interest is continuation of jobs, until money are going - so they're willing to measure the same things again and again, just under another names.

  12. BTW the animated picture above illustrates the gluon field - i.e. the density fluctuations inside of atom nuclei, not the vacuum.

  13. "Energy too must be conserved, but due to Heisenberg's uncertainty principle, we are allowed to temporarily borrow some energy from the vacuum, as long as we give it back quickly enough." Is gravitational energy conserved at the level of the Newtonian approximation? I say "NO" — google "peter woit fqxi essay 2015" and read my comment on Woit's essay. Perhaps my thinking is wrong but, in any case, the empirical evidence backs Milgrom's MOND. I think the string theorists fail to realize that acceptance of MOND has been slow because the money flows to the anti-MOND researchers while the pro-MOND camp is impoverished. Google "witten milgrom".

  14. /* Is gravitational energy conserved at the level of the Newtonian approximation */

    Newtonian approximation is based on energy conservation, so any model based on Newtonian approximation cannot violated energy conservation laws or this model isn't Newtonian anymore.

  15. David,

    Depends on what you mean exactly. Energy of what is conserved? And in which approximation? The Newtonian approximation in GR is quite general, and then it depends on whether you do or don't take into account backreaction. If you don't, then you can violate all kinds of conservation laws. Energy is conserved whenever you have a 'conservative force', which means essentially that the rotation of the field vanishes. This is certainly the case if you take the Newtonian limit of point sources, and thus also for linear superpositons, so I don't know what you mean. Best,


  16. "But there are also waves on the surface of the sea. The waves are like “virtual” particles; they are fluctuations around sea level that come out of the sea and fade back into it."

    Vacuum fluctuations are not the same thing as virtual particles. Vacuum fluctuations can be likened to the tiny ripples on the surface of the sea, and a photon can be likened to an oceanic swell wave. But the powerful attraction between an electron and a proton is not some Casimir effect. It's more like the way counter-rotating whirlpools move towards and around one another. A virtual photon is a calculation device for the way they "exchange field" such that the hydrogen atom doesn't have much in the way of field. But it isn't a real photon. Hydrogen atoms don't twinkle, and magnets don't shine.

  17. /* Vacuum fluctuations are not the same thing as virtual particles */

    Yes, they are. They're representing the density fluctuations of underwater in the water surface analogy of space-time.

  18. /* But it isn't a real photon. Hydrogen atoms don't twinkle, and magnets don't shine. */

    We cannot see the photons with using of light, so it doesn't matter whether this photon bounces between Earth and Sun or between electron and atom nuclei. Even the long distance photons aren't stable due to decoherence, as they decay fast under formation of another photons. The twinkling of atoms it's called quantum zitterbewegung.

  19. re the "virtual particle" discussion, Matt Strassler's blog post seemed helpful to this layman,
    "Virtual Particles: What are they?"

    BTW, the popular metaphor/description of a black hole's "Hawking radiation", doesn't make any sense, either. ie, often it's written that a virtual particle pair appears at the edge of the event horizon, one of the pair "falls in", leaving the other to become "real" and escape -- a metaphorical mashup of quantum mechanics & general relativity & newtonian physics ;-)
    If there's some layman-accessible explanation of how & why Hawking radiation is supposed to work, I'd appreciate a reference.
    (PS, I don't know why this blog software is calling me "unknown", I am signed in with my Google account).

  20. I have never accepted "What Me Worry" hand-waving arguments as satisfactory from a scientific standpoint.

  21. /* If there's some layman-accessible explanation of how & why Hawking radiation is supposed to work, I'd appreciate a reference */

    The strong curvature of space-time works like the density gradient of water surface, which undergoes total reflection like the mirror and most of radiation is reflected back. The density fluctuations of vacuum serve like the scratching of this mirror and enable the long wavelength portion of radiation to pass through.

  22. Sabine,

    Would it really be “similarly correct” to say that real particles have no ontological status?! There are two separate issues here - the utility of the particle concept and the reality of virtual... fluctuations - and I was making a point about the latter, in response to Robert L. Oldershaw. He was taking issue with your statement:

    "So we know, not just theoretically but experimentally, that the vacuum is not empty. It’s full with virtual particles that constantly bubble in and out of existence."

    And I thought [and think] that he was questioning the general ontological validity of that (i.e. irrespective of the particle concept business). That Bianchi and Rovelli paper Phillip Helbig linked to also suggests that we do not in fact know experimentally that the vacuum is not empty of vacuum fluctuations.

  23. The concept of "virtual" seems unclear to me. Here "virtual" means "formally non-observable" but "mathematically necessary". The status of "virtual" could apply to many concepts as the "field" only observable by the trajectories deviations or the wave function that is not really a wave ...

  24. Loved the article,

    The universe is amazing, and the fact that mathematics might be at its very foundations is incredible.

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  26. Thank you for the formalization but I especially wanted to raise the fact that in physics, the number of masked concepts (computational) used to obtain real experimental results are in a state of mystery as to their physical reality.

  27. Nicolas,

    Maybe, yes. I don't really know what you mean with 'physical reality' though. What is real anyway? Best,


  28. The physical reality that I consider is the experimental reality (phenomenological reality) while there within the calculation exists a non-experimental reality as, for example, temporary transient particles in the Feynman diagrams (noumenal reality). Here, form of the algorithmic trick describes a process supposedly real but not observed because only the end result is observable. Thus, I find it difficult to separate the notion of "computational artifice" of the noumenal reality (unobserved but assumed real).

  29. This comment has been removed by the author.

  30. Indeed, it is a questioning having been an important part of my hobbies. About the reference of Eugene Wigner's it's infinitely sad. Probably equivalent to a monkey using a computer or me trying myself to physics.

    By cons regarding the previously mentioned technicality it is rather philosophy of knowledge or truth.

  31. I once read a Frank Close book on Nothing.
    This article says on one page for what Frank needed some 200 pages or so, and quite profoundly too.
    Thank you!

  32. Nicholas:
    "Unobserved but assumed real" seems to me a somewhat theological approach. :)

  33. Bee,
    Thank you for the interesting post and the guided tour along a seashore we are unlikely to visit. It seems such a mysterious place that one can almost hear a soundtrack ominously reminiscent of “Jaws.” It provokes a long list of questions for the naive sightseer. Among the strange phenomenon is one you do not directly address and that I find most curious.

    “Virtual particles have to obey more rules than sea waves though.”

    It’s about these rules. As you explain, quantum physics has discovered that within any quarter-teaspoon of ‘empty’ space there is a latent and extensive energy that is simmering at the edge of becoming and yet somehow constrained by rules of strict accounting that apply equally across vast reaches of space and every hummingbird’s heartbeat of time.

    Whence this universal governance?

    Further, since this image of nature is evoked by the rule of a well-tested equation, is it possible to identify and name that factor within the equation that brings about this constraint, this governance?



  34. IMHO, I think that Hawking did not calculate with the possibility of a chiral oscillating Higgs field vacuum lattice combined with propeller shaped Fermions. Electrons and positrons both pushed away from the BH horizon at different distances, forming TWO different charged separated spheres. With quark ( plasma) formation in between.
    WHY is this possible?
    ONLY if the oscillating Higgs vacuum Lattice (tetrahedral shaped) has a preferred chirality. So in our MATERIAL universe, all the Planck lattices ( the edges of the tetrahedrons) FORM A LEFT HANDED SPIRAL. As a result all neutrinos are left handed! because the neutrino information travels in the form of an Higgs oscillation along these edges.
    SEE: <a

  35. See also:

  36. As a non-physicist I have no right to ask, but I'll go ahead anyway.

    Is there any chance that when virtual particles emerge, however briefly, that the intervening distance between them is a source for the expansion; i.e. dark energy?

    It seems to me that the presence of matter/energy 'generates' spacetime, such that expansion is never 'into' a surrounding nothingness. Could virtual particles be what cause greater expansion in relatively empty regions of space, as compared to 'matter and particle rich' regions which contract under gravity?

    Pls forgive the word salad. Any replies most welcome. Not insulted if half-butted ideas called ridiculous!

  37. "Is there any chance that when virtual particles emerge, however briefly, that the intervening distance between them is a source for the expansion; i.e. dark energy?"

    Maybe. Some people see zero-point vacuum energy (which is related to virtual particles) as a source of "dark energy". It is perhaps not the only source, though.

    However, dark energy is responsible for the current accelerated expansion of the universe. Even if it didn't exist, there would still be expansion.

  38. This comment has been removed by the author.

    1. ? Don't know what you mean. I have credits and a reference on the image.

    2. This comment has been removed by the author.

    3. Hi Joel,

      I really don't know what you mean, the reference is right below the animation.

    4. This comment has been removed by the author.

  39. This comment has been removed by the author.

    1. Joel, which simulation are you talking about? Yes, I am talking about the Derek Leinweber simulation. The credits are below it. What are you talking about?

    2. This comment has been removed by the author.



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