The Stability and Instability of the Neutron

One of the strange but crucial features of our world is that every type of atom except hydrogen contains neutrons in its nucleus, even though neutrons, on their own, decay (to a proton, electron and anti-neutrino) within about 15 minutes on average.  At first glance this seems puzzling.  At second glance too.  How can stable matter be made from unstable ingredients?

The reason this is possible has everything to do with Einstein’s special relativity, and the way mass and energy are intertwined there.  A crucial role is played by the energy that is most important for binding things together, which I’ve called “interaction energy”.

I’ve now written an article explaining why neutrons inside of nuclei can be stable, giving the example of the deuteron (one proton bound to one neutron) which is the nucleus of “heavy hydrogen”, or “deuterium”.  If you understand this example, you’ll basically understand the point for other nuclei as well.

[For those of you in the New York City area: I’ll be joined by the wonderfully talented singer-songwriter-pianist Andrea Wittgens in giving a physics/music joint performance/presentation at the storied Cornelia Street Cafe, Sunday May 13th at 6 p.m., as part of their Entertaining Science series.  It’s entitled Rhapsody for Piano and Universe, and intended for the general public.  The place is pretty small, so get reservations in advance.]

17 responses to “The Stability and Instability of the Neutron

  1. David Brown

    Prof. Strassler: According to Wolfram Alpha,
    ((neutron mass)/(proton mass)) – (1/(72 * pi**2)) + 1/(352 * pi**4) – 1/(1230 * pi**6) = 1, approximately. In your opinion, is the preceding estimate merely a numerical coincidence without any physical significance?

    • Quantum field theory does a wonderful job of predicting many aspects of physics. In quantum field theory, numerology of this type doesn’t work; or said better, you can always find some fancy equation with fancy numbers in it, but that doesn’t mean it captures the physical phenomena.

      The neutron-to-proton mass ratio is well understood. It comes from (a) the down quark mass being heavier than the up quark mass, compensated in part by (b) the electrostatic repulsion from the proton being electrically charged. The first increases the neutron mass, the second increases the proton mass but by not as much. If you made the up and down quark masses the same and turned off electromagnetism altogether, the neutron and proton would have exactly the same mass. There is deep physics — a symmetry — behind this statement. The formula in Wolfram alpha that you quoted does not in any way exhibit this symmetry and as such is useless at revealing the underlying physical causes, even if it is numerically true.

  2. Mike Anthis

    Now you bring up music, a whole different, amazing universe, intersecting with physics and mind. Not to forget that you’ve been using some musical metaphors already. Have you more thoughts about parallels with harmony and physics?

    • Only artistic and evocative ones. Not appropriate for the technical part of the website. But yes, music is about sound waves, and little ripples in fields (quanta [i.e. “particles”] in particular) are what we’re all made from, so clearly there are going to be things to talk about.

  3. David Brown

    Prof. Strassler: Thanks for the reply. Anyone who wants a good laugh should consider the Bell’s-inequality-denialist entry at the blog Shtetl-Optimized – Scott Aaronson.

  4. Matt, I have seen many papers (some quite recent) where m_u = m_d = 5.5 MeV. I think that certain experimental parameters were used to derive this. Is this no longer a valid possibility?

    • REALLY!? Where? That’s pretty silly, if they were trying to get the details right; maybe they were just giving an average. Because it’s been known the down quark is heavier than the up quark since the 1960s. Since the proton is charged and the neutron is not, equal masses for the up and down quarks would imply a proton heavier than the neutron — in severe conflict with nature!

      In case you wonder whether perhaps we’ve got the sign wrong and somehow charged things would be lighter than neutral ones, we can do a check. There are many pairs of hadrons that differ from each other in the same way as a proton and neutron — by the replacement of an up quark by a down quark. If the neutron-proton mass difference comes not from different quark masses but from electromagnetism, then all of the charged particles in these pairs should all be heavier, or all lighter, than the neutral ones — and since the proton is lighter, the prediction is that all of the charged particles should be lighter than the neutral ones, for all of these pairs.

      On the other hand, if the down quark is heavier than the up quark, then all of the particles that have the down quark should be heavier, regardless of whether they are charged.

      Let’s look at the data:

      Pair: particle containing up quark : particle containing down quark

      nucleons : proton 938 MeV : neutron 939 MeV

      kaons : charged kaon 494 MeV: neutral kaon 498 MeV

      D mesons : neutral D 1865 MeV : charged D 1870 MeV

      B mesons : charged B 5279.2 : neutral B 5279.5 MeV

      chi baryon : neutral chi 1315 MeV : charged chi 1322 MeV

      charmed chi baryon : charged 2468 MeV : neutral 2471 MeV

      The pattern is completely clear, and convincing: the particle containing the up quark is always lighter than the particle containing the down quark, no matter whether the hadron itself is charged or not.

      • Those two B mesons are very close in mass. So the electrostatic repulsion between the quarks in the charged B raise its mass a lot, but not quite as much as the difference in down quark and up quark mass?

        Why is the difference between the neutral chi and charged chi much greater than the others? That’s 7 MeV, which is much more than the difference in mass between and up quark and a down quark (I’m getting my numbers from wikipedia… please excuse me if I’m wrong).

  5. Not that it proves anything, but material will come up if you google “m_u = m_d = 5.5 MeV”. I think it is called the NJL (Nambu, Jona, Lasinio) model. I know of hundreds of papers that employ this model or variants thereof, but they all have the statement m_u = m_d = 5.5 MeV…

    • Right — this has nothing to do with the NJL model.

      When you read physics papers, you have to pay very close attention to whether people are *trying* to match the real world precisely or not. These papers are focused on issues where the difference between the up and down quark masses is a tiny little effect that doesn’t matter for the physics that they are studying. If you can understand the physics when the two masses are equal, everyone knows how to put in the small corrections from the fact that they are not equal.

      For example,

      Effect of magnetic field on chiral symmetry breaking in a 3-flavor Nambu Jona Lasinio (NJL)
      model at finite temperature and densities is considered here using an explicit structure of ground
      state in terms of quark and antiquark condensates. While at zero chemical potential and finite
      temperature, magnetic field enhances the condensates, at zero temperature, the critical chemical
      potential decreases with increasing magnetic field.

      These authors are interested in certain phenomena that are very insensitive to the fact that m_u isn’t equal to m_d, so they simplify their problem by taking the masses equal, knowing that there will be small but (for their problem) unimportant effects due to the fact that m_u and m_d aren’t equal.

      It’s not so different from assuming the earth is a sphere. It’s not, but for many questions it doesn’t matter that it isn’t a perfect sphere. On the other hand, if you want to know exactly where your satellite’s orbit is going to be, it may matter to you to be more precise.

      In the same way, you can learn a lot of information about the world by just setting m_proton = m_neutron. The difference in the masses is very unimportant if you want to understand the density of ordinary materials; if you keep track of the difference, you’re just making the problem harder and messier for no good reason.

      On the other, if you’re interested in why protons don’t decay and neutrons do, then you definitely need to know there’s a difference. And if you want to know the lifetime of the neutron, you need to know the difference rather precisely.

      So it is all a matter of knowing when it’s important. But every professional physicist knows that when you’re trying to describe the real world completely, rather than just get a rough idea about a small piece, you need to take m_d > m_u.

  6. hello Proffesor,
    I have a question related to the higgs.
    Hello professor,

    A few times I have been hearing the claim that the LHC had to discover something- either a higgs or new physics to unitarize WW-scattering.
    Is this true?
    aren’t there any scenarios which would have been completely missed even after 20 years of LHC running?

    For example- scenarios with an invisibly decaying higgs..

  7. David Brown

    Prof. Strassler: In connection with my laugh comment I think that Joy Christian has the laugh at the expense of Scott Aaronson and me. Prof. Strassler, would you like to make a bet? I bet you $100.00 (payable by check) that Joy Christian will win the Nobel prize by the end of the year 2022 CE? Do you accept the bet?

  8. It is good to see a quarkologist analysing particle masses. Both the positive and neutral vector B mesons are quoted as having a mass of 5325.1 MeV, with an uncertainty of 0.5 MeV. Can you use quark theory to predict whether they really do have exactly the same mass, or to say which is heavier and by how much?

  9. David Brown

    What is meant by a “physics/music joint performance”?

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