Of Particular Significance

Why You Can’t Easily Dismiss the Cosmological Constant Problem

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 08/30/2013

I’m still early on in my attempts to explain the “naturalness problem of the Standard Model” and its implications.  A couple of days ago I explained what particle physicists mean by the term “natural” — it means “typical” or “generic”.  And I described how, at least from one naive point of view, the Standard Model (the equations we use to describe the known elementary particles and forces) is unnatural.  Indeed any theory is unnatural that has a

  • a spin-zero particle (in the Standard Model, the newly discovered Higgs particle), which
  • is very lightweight in the following sense: it has a very very low mass-energy compared to the energy at which gravity becomes a strong force, and which
  • isn’t accompanied (in the Standard Model specifically) by other related particles that also have small masses.

But I didn’t actually explain any of this yet; I just described it.

Specifically, I didn’t start yet to explain what causes the Standard Model to be unnatural.  This is important to do, because, as many attentive readers naturally complained, my statements about the unnatural aspect of the Standard Model was based on a rather arbitrary-sounding statistical argument, and story-telling, which is hardly enough for scientific discussion.  Patience; I’ll get there, not today but probably the next installment after today’s.

To see why the argument I gave is actually legitimate (which doesn’t mean it is right, but if it’s wrong it’s not for a simple reason you’ll think of in five minutes), it is necessary to look in a little bit more detail at one of the most fundamental aspects of quantum field theory: quantum fluctuations, and the energy they carry.  So for today I have written an article about this, reasonably complete.

Be prepared — the article runs headlong into the only naturalness problem in particle physics that is worse than the naturalness problem of the Standard Model (the one I wrote about on Tuesday)!  I am referring to the “cosmological constant problem”.  In a nutshell:

  • we can calculate that, in any typical quantum field theory with gravity, the amount of energy in empty space (often called `dark energy’) should be huge, and we know of no way to avoid having it in a typical somewhat-realistic theory of the universe,
  • yet measurements of the cosmos — in fact, the very existence of a large and old universe — assure that, if Einstein’s theory of gravity is basically right, then instead of a huge amount of `dark energy’, there’s just a very small amount — not much more than the total amount of mass-energy [E=mc² energy] found in all the matter that’s scattered thinly throughout the universe.

After you’ve read about quantum fluctuations and the cosmological constant problem, and have a bit of a sense as to why it is so hard to make it go away, we can go back to the Standard Model, and try to understand the naturalness problem that is associated with the Higgs particle and field.  It all has to do with another aspect of quantum fluctuations — the fact that their energy depends on, and therefore helps determine, the average value of the Higgs field.

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43 Responses

  1. Hi Matt,
    I see why this is a real problem, thanks for the illuminating article as always.
    Can I ask a more basic question about the cosmological constant and its consequences? I apologize if this is a hoary old one but I never really found a definitive answer (although you have touched on it in other articles). Here Goes:

    I have no problem with the concept of the expansion of “space” due to some cosmological constant. Can we visualise this as tiny additions to all the quantum fields periodically appearing at random locations?
    While I get that this is not a force between objects, it is nevertheless said to result in objects at large scales moving further apart. If these objects at large scales are being carried along with “space” as it expands, then the objects (or the matter from which they are made) must be interacting with said “space”; the objects are moved relative to one another, “space” does not simply slide through everything.
    So the next logical question people like me ask is something like: ‘what happens to the “space” inside a proton?, and does this affect the proton in any way?’. In other words if large scale objects, like galaxies, move apart as a result of “space” expanding, do those same objects also grow larger? If they do, then is there then a cut-off scale at which this effect no longer applies? I am sure most people are not comfortable with the notion that a proton today could be a different size that it was in the past due to “space” expanding.

    BTW – how do you track these comments in all these articles? is there a time limit for each ‘thread’? it looks as though whenever you add a new article the volume of incoming questions would increase…I hope you are not swamped..

  2. Thank you Mr. harryjohnston, we know the “energy”, that was something burning. Moment of inertia and gravity cannot be separated.
    (.) The explosion (combustion) of gunpowder:
    4KNO3(s)+7C(s)+S(s) —> 3CO2(g)+3CO(g)+2N2(g).
    (.) The explosion (Decomposition or Detonation) of Nitroglycerin:
    4C3H5(NO3)^3 (s) —-> 12CO2(g)+10H2O(g)+6N2(g)+=2(g).
    Nitroglycerine contains its own oxidant. One gram of TNT produces about one liter of gas, which is a 1000 fold sudden increase in volume – that produces the blast pressure. For instance, when a particle and its antiparticle annihilate and vanish in a puff of electromagnetic radiation, comparatively little matter is transformed into rather a lot radiation.
    The explosions is due to strained “chemical” bonds in the molecules which have stored potential energy.

    That does not mean, “matter is converted to gas”. Only energy is changing its one form to another.

    This is also true for sudden increase in the volume of “new space” – because “space” is a form of energy.

    (.) Nuclear explosion: Equivalence or transformation? : For Einstein, mass (more precisely: relativistic mass; the property that determines how difficult it is to change a body’s speed or its direction of motion) and energy are simply two different names for one and the same physical quantity.
    The angular momentum “c^2” (in quantum mechanics h-bar) is already changed the speed and direction of “inertia”. Thus producing a new kind of energy called the “rest mass”.
    So Einstein’s formula explains the power of the nuclear bomb – and that the large conversion factor c2 is responsible for the immense amounts of energy released?

    Binding energies: nuclei vs. molecules: When hydrogen and oxygen explosively combine to make water, the sum of the rest masses of the initial hydrogen and oxygen atoms is just a little bit less than the sum of the rest masses of the resulting water molecules. The same is true for the chemical reactions involving spontaneous oxydation – in other words: burning. The same formula applies: The mass difference, multiplied by c2, gives the energy set free during the chemical reaction.
    This clearly shows that the difference between nuclear and chemical reactions must be due to something other than E=mc2.

    This is wahat explained by Nima Arkani-Hamed, “the difference between massive and massless particles. If we understand that, we can tilt the “vase” from unnaturalness (rest mass) to naturalness (relative mass).

  3. /1. Is supersymmetry equivalent to a singularity?/ – Oak Tree.

    Is vacuum in vacuum fluctuations is almost a singularity?

  4. Thank you professor Strassler for a very interesting article. This is one of many topics I am trying to understand.

    Just out of curiosity: in mid-April you wrote a very good description of the interior of protons and neutrons and mentioned there would be a more detailed follow-up (second and third layer). I was wondering if this is still in plan. Thank you.

  5. The cosmological constant is based on particles from nothing and the quantative easing is based on moneyfrom nothing. I am afraid that they share the same problem.

        1. It is quite the opposite. Detailed observations of the universe (e.g. the recent Planck mission) show that the universe is apparently expanding at an increasing rate. One way to make our models of the universe consistent with these observations is to put the so-called cosmological constant into the equations. In this sense it is required for consistency with reality. (There could be other ways to make the models fit reality, and scientists are investigating those, too.)

          Now the other end of the question is: How can we explain the existence of the cosmological constant and its value (that we can estimate from observations) from microscopic physics? This is were vacuum fluctuations come in, and there we hit upon a really big and fascinating problem, which Prof. Strassler explains in the article.

          1. …”to make the models fit reality”…

            …”explain the existence of the cosmological constant”…

            I rest my case.

            Apart from cosmology: Bernanke and Dragi use a model which does not fit reality. The Dow Jones for instance is about 3000 points above intrinsic. Money for nothing is MTV, not economy.

    1. Soothing Mr martenvandijk,
      vacuum in vacuum fluctuations is filled by “The 1%” with virtual particles, evolutionary theory, money and theorems based on this as “Peace and Truce of God” – running their own Roman Empire ?

    2. That’s why they’re called “virtual particles” – they’re not really particles at all. But the energy should be real if you trust the math. Ultimately, of course, the problem is somewhere in the maths; either the excess energy isn’t really there, or it is cancelled out, or it doesn’t interact with gravity for some reason. The point is that we can’t just ignore the problem, we need to figure out how to make the math work properly. Otherwise we’re not doing physics.

  6. The logic of charles darwin ‘s evolutionary natural selection (idea) is valid only in local symmetry conditions like “Rest mass” – but it is not a physical reality.
    We cannot switch off Higgs field is sounds like “we cannot stop all the relative movements of planets and stars”. Indeed we cannot stop, it need very high energy. Cosmological constant is vacuum energy + negative energy ? – and the matter is positive energy ?

    But the “rest mass is not a physical reality” – so the Higgs field also. This arise as a mathematical necessities in models using rest mass in their calculations. We cannot avoid consistency particle theory, but wave theory is more realistic – but we cannot calculate in QFT without manipulating (virtual particles) Quantum fluctuations of a field – like in law of quantum physics by Louis de Broglie.

    The Uncertainty Principle states that for a pair of conjugate variables such as position/momentum and energy(mass)/time(dilation), it is impossible to have a precisely determined value of each member of the pair at the same time. For example, a particle pair can pop out of the vacuum during a very short time interval.
    An extension is applicable to the “uncertainty in time” and “uncertainty in energy” (including the rest mass energy mc^2). When the mass is very large like a macroscopic object, the uncertainties and thus the quantum effect become very small, and classical physics is applicable.

    Thus the non zero cosmological constant, space expansion, the creation of new space by cancellation of negative and positive energies were related to the energy withstanding capacity of spacetime (membrane)?

  7. Well, physicists love measurable predictions. I want to remind that on October 9 happens Juno Earth flyby. Naturally physicists are watching closely possible flyby anomaly. Contemporary physics can’t explain the phenomenon not to mention predict its value!

    But as I have claimed (arrogantly by Matt) previously, my pet theory can. Here is a quote from my blog (including predictions). This comment concerns very much the naturalness discussion going on here.

    “Quote from SPACEFLIGHT101:

    During its mission, Juno spins at different rates depending on mission maneuvers. During Cruise, Juno makes one rotation per minute, during science operations, the spin rate is 2rpm and for Main Engine Burns, the spin rate is increased to 5rpm.
    Ok, what will be the spin frequency during the flyby? Probably that 2 rpm. After all, they are going to do some science operations near Earth, right? And why would they use the Main engine (even though it would give the biggest boost 🙂 )? Anyway, here are the predictions for all those three different spin frequencies. Total anomalous acceleration is in case of

    1 rpm: 0.278 mm/s^2
    2 rpm: 1.111 mm/s^2
    5 prm: 6.944 mm/s^2
    Calculations are based purely on a spin frequency of the spacecraft. Contemporary physics includes factors other than the effect from spin frequency of the spacecraft. Some very small deviations from predictions might emerge due to possible spin frequency changes right before or after the closest part of flyby.”

      1. You give some “anomalous acceleration”, but what is that supposed to refer to? Presumably the anomalous acceleration would vary continuously from small, to large, and back to small again as the flyby progresses. It can’t be a constant, or the anomaly would not be limited to the flyby, it would continue on forever and also still be happening long before the flyby. There would be an unlimited gain in kinetic energy rather than a finite, measurable gain as has always been the case for flybys in the past.

        1. Good point! Acceleration surely varies during the flyby. I won’t go into mathematical details here but the most significant acceleration is gained during the time when the spacecraft’s spin plane is towards Earth. There is an acceleration gained before and after the closest part of flyby but it’s very much weaker (distance & spin plane angle in relation to Earth).

          My pet theory can be used also in the cases of Pioneer anomalies.

          1. You didn’t answer my question. Are the numbers you gave supposed to represent the maximum acceleration reached at any point during the anomaly, or what?

          2. Also, does your pet theory predict any detectable anomalous acceleration for the Pioneer flyby, or an undetectably small amount?

          3. Yes, they are maximum values.

            (Pioneer anomalies) Naturally detectable. You pretty much need only the Pioneer spacecraft spin plane angle in relation to Sun and spin frequency of the spacecraft. There has been naturally changes both in angle and spin frequency so in order to calculate the exact value I should know all history data regarding spin plane angle and spin frequency.

            However, rough estimate is easy to calculate.

          4. OK, then I guess your theory has been knocked out. When the radiative anisotropy of the RTG was finally factored into the calculations in 2012, the anomaly disappeared. There is no longer any detectable Pioneer anomaly. A quote from one of the last papers on the subject:

            “”We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains.”

            Better luck next time.

          5. And this same reason is behind ALL the cases where this anomaly is detected? There are other cases than Pioneer 10/11. Besides, flyby anomaly and Pioneer anomaly are related. And the contemporary explanation for the flyby anomaly is…?

            Other than that, modified Cavendish experiment and generating particle annihilations without high energy supports my case.

          6. It’s very simple. Your theory made a prediction regarding the Pioneer anomaly. That prediction was false, therefore your theory has been shown to be false.

            1. That’s true. But only in the case that mr. Anderson made his case correctly (which I doubt). Also, it’s possible that those spacecrafts had the exact 90 degrees angle between spin plane and Sun hence no “ToEbi effect”. But getting that angle absolutely 90 degrees, without any deviations, sounds impossible. Therefore I put my money on my case.

          7. “Mr. Anderson”? The result regarding the effect of the thermal recoil force was reached by several research groups independently. What reason do you have to suspect that they have each independently made an error in their analysis?

            1. There is a simpler explanation for the acceleration and I prefer Occam’s razor. There is uncertainties with that modeling and we both have our own views regarding Pioneer anomalies, that’s ok. We need a better example for the “new” physics.

              But things are going to be *much* more interesting in the case of Juno Earth flyby! There the effect is a very strong compared to Pioneer. What is your suggestion as the cause for the flyby anomaly? It surely ain’t thermal recoil force, right? 😉

  8. Dear Professor: I recently saw a video of a talk given by Dr Fay Dowker given at the Perimeter Institute in which she claimed the cosmological constant problem had been solved long before dark energy was discovered by theorists working on the Causal Set structure of spacetime. What do you think about that? Thanks.

  9. Anon
    If asking the most fundamental questions is trolling , then all of our investigations are mere nonsense.
    But we are already calling it un-natural , extra-normal , not expected , so the more we know the more we will see its huge un-naturalness. That is point 2.
    Point 3proves design.
    Point 1 proves your extreme lack of understanding the fundamental attributes of GOD.

    1. Boys and Girls —

      to all: atheists, agnostics and devout believers are all permitted here on this website. However, attempts to convince others of one’s opinion on a non-scientific question are discouraged.

      aa.sh — it seems that every time I write anything at all, your reply is “it’s obvious from what you say that God exists”. I don’t need to hear this every time, nor do my readers; we all know that there are always questions about science, truth, origin of the universe, etc., and we all know that people have different opinions, and any of us who have been on this site already know your opinion.

      Actually, if you want to convince people of things, it is a good idea not to be unpleasant as a person. And a commenter who says the same provocative thing again and again, and generates a whole host of useless back-and-forth comments on a regular basis, becomes an impolite annoyance on a website. I would prefer not to ban you from this site, but if you persist in this not very nice behavior, I will do so.

      So — out of politeness — please desist from discussions of God on posts that have nothing to do with God. If you happen to think my post about scientific reasoning has something to do with God, keep it to yourself, please. We can discuss these issues in more appropriate settings — specifically, when the question is raised by the post or article, and not by you. .

  10. Design is not the only solution. But it is one. When (if) we finally answer all there is to answer about the origin of everything there will be only three answers:
    1. It was created by some God like being(s).
    2. It occurred naturally without the existence of a God
    3. We will prove we can never figure it out.

    1. Designer had no beginning and will have no end. Designer exists from before everything else. Your mind is too tied up with what your eyes see here on earth and the idea that universe had a beginning. Maybe it did, maybe it didn’t, but the one that created it out of the energy that belongs to its body is not affected by time or this universe. thus, Eternal, Omnipresent, Omnipotent, Omniscient. http://www.youtube.com/watch?v

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