S05E03: The Pulled Groin Extrapolation

An now, the must-watch exciting conclusion of the axion calculation saga on the whiteboards.

Last week we saw two episodes where upon our heroes’ whiteboards unfolded about making an exciting new particle, “the axion” on Earth. Could axions be made inside an artificial Sun made by the National Ignition Facility?  This summer, I was excited about this, but as you already know by now from reading tonight’s whiteboards, I made a terrible, terrible mistake.

To estimate the rate of axions I used the relative power produced by the Sun versus the small compressed sample produced at the National Ignition Facility.  In both cases a material is made so hot that atoms are ripped apart into their constituents: electrons and nuclei.  Such a gas is called a plasma, and plasma is sometimes called “the fourth state of matter” as it is step hotter than just ordinary gas. It is not unfamiliar.  The glowing orange material in a neon sign is a plasma.

The Northern Lights are an example of a plasma you can see. (National Geographic) The last three episode's whiteboards explored if a dense hot plasma could make the elusive Axion particle.

I was comparing the large far-away plasma in the core of the Sun to the tiny, but close, plasma created in the lab.   It initially looked like the laboratory won.  To understand what was wrong,  you first have to understand how the Sun produces its energy.

The strong nuclear interaction likes to bind protons and neutrons together.   And Martha Stewart says, “It’s a good thing”.  Without it, the only atoms we would ever have are hydrogen.  If hydrogen were our only element, we’d have an unperiodic periodic table–with only one entry, hydrogen. In real life, the nucleus of every atom is held together by this force.  And its strength is impressive.  For example, in helium and every element heavier the protons are repelling each other. Same-sign charges (in the protons’ case, both positive) repel with a force increasing as the square of their distance from each other decreases.  A nucleus is extremely small, and those protons are so close they want to fly apart, badly.   The strong interaction overcomes this repulsion and nuclei stay bound.  That’s why it is called the “strong interaction” (or “strong force”).

But there’s a wrinkle.  If you try to bring just two together (either protons or neutrons) there is only one combination that is stable: a pairing of one neutron and one proton.  The pairing of  two protons or two neutrons is not.

You might think you the strong force could combine any pairing of protons and neutrons. But quantum mechanics only allows a proton and neutron to bind. The result is heavy hydrogen, or "deuterium".

It might seem the reason why two protons are not bound is because of their electric repulsion. But that would not explain why two neutrons are also not bound.  The answer really  lies within the constraints of the quantum mechanics of identical particles.   It turns out that the only way to put two identical neutrons or protons together is if they have angular momentum, but then they are not bound.  We teach our physics majors all about this at UCLA in our introductory quantum mechanics class.  If you can take a quantum mechanics class, I highly recommend it.

The core of the Sun is full of protons but no free neutrons.  So the only way to make energy from them is to convert one of those protons into a neutron so you can bind them.  This bound state of a neutron and proton is still chemically hydrogen, but it has an extra neutron so it is called “heavy hydrogen”, or more technically deuterium.  That’s  the same “heavy” of “heavy water”. “Heavy” water is made with “heavy hydrogen”.   But the reaction does not conserve electric charge so you need a light positively charged particle to fly away, and it turns out to be the anti-matter partner of an electron, which has a positive charge (e+), and so is a “positron”.   But that introduces a new problem.  A positron is a type of particle called “lepton” and for reasons not yet understood, you can’t vioate the number of leptons.   So you also need a neutrino (ν)  to be made as well to not create any net leptons. (These neutrinos were detected from the Sun over the last few decades.  They changed our entire understanding of neutrinos but that’s a story for another day.)    It’s easiest to see graphically:

The first step of making energy in the Sun's core by nuclear fusion.

Ultimately these deuteriums (deuteria?) undergo further reactions and the net reaction in the Sun is:

4 protons  –> 1 helium nucleus (2 protons + 2 neutrons)  + 2 neutrinos + lots of energy.

The released energy heats the core and makes the Sun shine. What happened to the positrons?   They are antimatter and as soon as they find an electron (not long at all!) they annihilate into energy.The problem is that first step:  proton +proton -> proton + neutron + positron +neutrino.    To be a bound state we had to convert a proton to a neutron.  The strong interaction cannot do that, but the weak interaction can.   It is a very weak process and that’s why it is called “the weak interaction”.  It is so slow that this dominates the rate of the total fusion in the Sun.

The rate of energy production in the Sun is so slow that pound-for-pound you produce more energy  than the Sun.  Just sitting in front of your computer, digesting your last meal, you produce about 1 Watt of power per kilogram of your body weight.   The sun produces only about 0.0002 Watts per kilogram.   The Sun is just bigger.  A lot bigger. While it is tempting to think of it as a massive nuclear furnace, it really is just smoldering.   We’re lucky too.  If the Sun’s reactions were not throttled by the weak interaction we would be living next to a nuclear bomb, not a star.

But the good people at the National Ignition Facility cannot wait around for such slow reactions.  Instead, they use heavy hydrogen (deuterium). and an even heavier hydrogen with two neutrons and proton, or “tritium”. Their  net reaction is:

deuterium+ tritium -> helium + neutron + energy.

No neutrons or protons changed their identity. They just change who they hang out with.   This proceeds by the strong interactiona nd also releases massive energy.  This reaction is about 1025 times faster than the proton+proton fusion in the Sun. And there’s the rub.  You can’t compare the two Sun’s directly.  The boys’ calculation was off by “only” a factor of 1025.

Before the taping of tonight’s episode, many of the crew members asked me why there was an unhappy face :( at the end of one of the whiteboards.  Now you know why.

55 Responses to “S05E03: The Pulled Groin Extrapolation”

  1. charlesculp Says:

    Thanks for the post, I really enjoyed it, even if the whiteboard was only visible for a few seconds this episode.

  2. feldfrei Says:

    Many thanks for the explanation – though I’m familiar with fusion processes from my former nuclear physics background I was not really aware that the axion production has to do with the hot plasma rather than directly with the fusion reaction. Thus, the total axion rate indeed scales with the volume and makes the rather inefficient fusion plant Sun a powerful potential axion source since it’s just huge. As a matter of chance, a few weeks ago I prepared an illustration for a press release about solar neutrinos from the ‘pep’ process detected by the BOREXINO experiment at the Gran Sasso underground lab in Italy: http://www.mpi-hd.mpg.de/mpi/typo3temp/pics/b60b0aeb3d.png

    Best greetings from Mallorca (at a severe storms conference)

  3. Chris Says:

    Sheldon would never had made that mistake!

  4. Lord of the Sheaf Says:

    It’s a pity that it is so terribly difficult to spot those whiteboards during the episodes. I fear a little that tbbt is transforming more and more into a ‘normal’ sitcom. Would be boring and redundant. It feels a bit, that the producers grew a little tired on this prominent science stuff and the prominent nerdiness. But instead of transforming their handling of the science, they seem to try keeping it out more and more.

    I am just waiting for that one episode, when sheldon meets a mathematician, who is at least as obnoxious as sheldon is and who kind of pokes sheldons work around^^ as mathematically inexact and therefor not true^^.

    On the other hand there is much more to the lives of science people than sheldon, raj, howard and leonard are exposing. On the one hand you are travelling much, but more importantly there often comes a point where you have to leave a place and seek opportunity/failure elsewhere.

    For instance: My perception it is, that most married professors at the universities I have visited so far, have a partner who is likely to have a degree but gave up his/her science career for that of the partner. (Ok this is a problem every profession has to face nowadays)

    There are so much more topics, which people in science positions have to handle. I guess this would make for some great episodes, than this constant gibble, gabble of boy-girl relationsships every sitcom as examined very closely so far.

  5. Andrius Rudeičiukas (@churchill1874) Says:

    Is this site dead or just BBT lost their scientific side ?

  6. Pomita Says:

    Really looking forward to your updates about the more recent episodes (the Russian rocket and Schrodinger’s friendship/Heisenberg in 5, Saul Perlmutter and cosmology in 6, Sheldon’s whiteboard musings with a CPT operator in 7, FTL neutrinos in 8)..

    Who says BBT doesn’t have enough current science nowadays?

  7. Our Bodies Create More Energy than the Sun « Thus Spoke Jon Says:

    [...] The URL for David Saltzberg’s blog is http://thebigblogtheory.wordpress.com/ and for this specific post is http://thebigblogtheory.wordpress.com/2011/09/30/s05e03-the-pulled-groin-extrapolation/. [...]

  8. Documented_Prism Says:

    Very cool blog :)

  9. mathias Says:

    When can we expect some more new, interesting blog entries? While season 5 is still running?
    I am looking forward to read exciting background information again. keep it up!

  10. Gareth Williams Says:

    I just saw the episode in season one in which Leonard does the olive and glass trick. (For readers who have not seen it, the glass is placed over the olive and moved rapidly in a circle so the olive is picked off the table and spins around inside the glass). The glass used appeared to have a constant outward taper towards the rim (ie a frustum of a cone).

    I do not see how it would be possible to do the trick with that sort of glass (and indeed I can’t get it to work!) I have seen a youtube video where the glass used is a brandy sniffter, which tapers inwards.

    The reaction force on the olive, normal to the glass, must have a horizontal component (the centripetal force) and a vertical component to balance its weight. This is possible only if the glass tapers inwards towards the rim. In an outward tapering glass the vertical component of the reaction force is downwards and the olive falls out. It will not spin inside the glass even for a short time, as it did for Leonard. I think they cheated when they filmed this!

    (It might be possible to get this to work with an outward tapering glass, but only by tilting it so the side of the glass in contact with the olive is at a less then vertical angle. The axis of the glass would have to be rotated at the same rate as the olive moving around, to keep it in. This would be very difficult and I do not think Leonard was doing that).

  11. feldfrei Says:

    @Gareth Williams: It might work if stiction is not neglected.

  12. Pooja Desai Says:

    Dear sir. Am writing a script for a small feature in India where the characters all have backgrnds on various branches of physics and was wondering @ what stage of the scripting process do you come in…

  13. WorkingSlaveUSA (@WorkingSlaveUSA) Says:

    David – I have to admit to never being being a very good student when it came to math and science. I excelled in English and Social Studies, but had to go to work early in life, so most of this is like trying to read Klingon to me! BUT – I have to say that at least once a week now I learn *something* from the show. I’ve even started watching the older seasons and when I hear something that confounds me, I come here to look it up or check for more info on the web. Just wanted you to know that the science you put into the show, even though it goes way over my head, still spurs me to learn more each week. Thanks for helping in my continuing education, even at 52 years of age!

  14. lurker Says:

    The professor has permanently abandoned this blog, maybe because the whiteboards didn’t get enough airtime.

    • Gareth Williams Says:

      Airtime hardly matters – I always pause to look at the whiteboards :-)

  15. dh Says:

    One factor that is being overlooked in the quest for fusion is gravity. To me, it is as key a component in a star’s formation as is the amount of mass in a given area of space.
    Once the mass creates enough gravity to get atoms to begin exchanging their components the reaction will continue until the star runs out of fusible atoms.
    You can not sustain fusion if the matter you’re using as fuel has insufficient mass to create a gravity well strong enough to hold the reaction together.
    Following that logic, a quantum singularity cannot have more mass than the star from which it formed, at least at its birth.

  16. Rodrigo Maximo Says:

    Please come back and write more of your amazing posts! One of the best things to do after watching a new episode of Bg Bang Theory used to be reading your blog!

    • David Saltzberg Says:

      Thank you! Your message is motivating. I was just too busy this year. I will get back to it. Either I will start with season 6 or I will go and back-fill over the summer.

      • feldfrei Says:

        Thanks, David, for the promising reply :-) If (as stated above) at least once a week something can be learned from the show, it’s worth to have the science in the show and more science behind the science here. We’re looking forward to it!

      • Marc Says:

        David – if you write again, we’ll you a copy of the new book due out next month: “The Big Bang Theory
        and Philosophy: Rock, Paper, Scissors, Aristotle, Locke” (ISBN: 978-1-1180-7455-8)

  17. Ria Gandhi Says:

    this might help:

    http://deadducksalive.wordpress.com/2012/04/29/karmatube-aurora-borealis/

  18. Gennaro Says:

    Professor does not know how I missed his science!
    I am the founder of an Italian page of “The Big Bang Theory” and I would love to be able to contact, would be willing to send me an email to this address: gennaromaisto1@alice.it

    She to me is a GOD! ;-)

  19. Liz Says:

    I appreciate your explanation and I hope you return to post more on your blog. It really helps me understand both physics and the characters on the show.

  20. Madhu (@madwho92) Says:

    Please continue this blog for season 6!!!

  21. Francois Says:

    Hope you will be more active for Season 6 David! There are a few things to be placed in the show with some boson… ;-)

    Francois

  22. Daniel Quinn Says:

    Hi!
    I love the show and your blog, and I’m looking forward to some great Higgs boson stuff soon!

    I know you’re not a writer, but I was wondering if the writers could do an episode at some point that dealt with the relationship between faith and reason. It would be easy because they already have some Jewish characters to play with, and Sheldon’s mother (not much in the way of a meeting of faith and reason there). They could make use of a whole Catholic-sponsored world of scientists, such as the Jesuit astronomers at the Vatican observatory in Arizona (http://vaticanobservatory.org/) and The Pontifical Academy of Sciences. Theology would also provide a whole new field of technical jargon to babble on about! (i.e. “My dissertation was an exegetical analysis of the pentateuch through a hermeneutic of pneumatology.”)

    I think it would be especially appropriate since the first person to propose the theory of the expansion of the universe and the big bang theory itself was a Catholic priest and astronomer, Georges Lemaître (http://en.wikipedia.org/wiki/Georges_Lemaitre).

    I look forward to the blog resuming!

  23. Big Bang Theory LOL (@BigBangTheoryLO) Says:

    I just discovered this blog and I am startled. How can you even write these long details on a Comedy show episode?

  24. Canadian Dart Fan Says:

    Just putting it out there, the dart board hung on the door is hung at the wrong height for a standard dart board. For how precise Sheldon is about everything in his place, he would not have missed this detail. Proper height should be 5’8″ at the center of the red bull’s eye.

    • David Saltzberg Says:

      I’ll measure it next week.

    • David Saltzberg Says:

      It’s 4’5″. But most of the characters are not very tall, so perhaps they invented their own rule.

      • Gareth Says:

        Sheldon is 6’2″ (if he is the same height as Jim Parsons). Leonard and Howard are then 5’5″ and 5’4″, but that hardly seems to justify a dart board at 4’5″.

        This is a conundrum. I can’t imagine Sheldon would play on a board the wrong height. But I can’t imagine Sheldon playing darts at all. That is too much like excercise, and we know from the Sheldon vs Kripke basketball match that he can’t throw. Have we ever seen any of the cast playing on the board? I think Sheldon has it there for some other reason. It may not even be a dart board! I hope we will find out :-) :-)

  25. Erubey Says:

    I’m currently studying physics and calc II, and this blog is a nice way to spend time in between problem sets. I like your writing style and it’s really hard to find blogs about physics like this.

    Looking forward to talking to my professor who is an astrophysicist about the rate of the reactions in the sun!

    • David Saltzberg Says:

      Thanks. Knowing that people read and enjoy this gives me (much needed) motivation to continue. I will try for Season 6. Starts Sept 27. “Check your local listings”

  26. feldfrei Says:

    Speaking of neutrinos (besides axions) – here’s a nice interview with Prof. Boris Kayser (Fermilab) by K-State Physics Videos.

  27. Gennaro Says:

    Professor said he was beginning to write his book of science at the beginning of the sixth session of TBBT ….. because he has not written anything yet on the episode 01×06?? I am looking forward to that she starts!

  28. Akshay Says:

    Please start this blog again. I learnt something after every episode!

  29. NeoTechni Says:

    1) What happened? You haven’t updated in a year!

    2) What happened? The newest ep was completely unrealistic with the holographic technology. Leonard would be a billionaire overnight with that

  30. Anonymous Says:

    @NeoTechni

    http://phys.org/news168797748.html

    Science FTW!!!

    • NeoTechni Says:

      And you’ll note that looks nothing like the one in the show.

      • Anonymous Says:

        And you should note that that article and video was from 2009. Or is it implausible to you that a simple modification of the graphics software on it could not very well be used to change that bouncing ball to a globe or to a galaxy?

        Point is, the tech exists and is reproducible. Feasible, currently, no, but probable? Definitely so.

      • NeoTechni Says:

        such tech does not exist now.

  31. David Dilworth Says:

    Excellent explanation of how we deduce there is a Strong force

    One tiny suggestion : I read “plasma is sometimes called “the fourth state of matter” as it is step hotter than just ordinary gas.”

    To be fair, plasma does not need to be hot or even warm. Plasma can and does exist in the icy realms of space between our planets and between galaxies where matter is barely above absolute zero.

  32. lurker Says:

    I’m finally going to delete this web site from my TV favorites folder. You could post blog entries that aren’t so elaborate, which would of course not take up very much time.

  33. Alex Says:

    I think that the science connection nowadays on tbbt is lost… or the proportion between science and a vampire tv show is 1 to 20 (in minutes)

    • Aife Says:

      It’s a disapontement. It has redunded into a romantic comedy for pseudo-brainiacs…

      Makes me puke… bleeeuurrgh…

      It seems nowadays hat if you use glasses or read a comic book you must be a geek… No space for diferential analysis, assembly programming or experimenting with weird food in your kitchen…

      The nerds became turds.

  34. BadHabit Says:

    What were those blue squares on Sheldon’s whiteboard while he was in his parking space in the Parking Spot Escalation?? Never seen them before! I really hope this blog comes back!!

    • DM Says:

      Prof. S, I would love to know what the squares were in the Parking Spot Escalation too. A full explanation would be great, but if not, would you have time for a quick reply to a pointer where I could read more at a basic level? I’m only an engineer ;-) Thanks!

      • David Saltzberg Says:

        They are calculations in quantum chromodyamics. The diagrams are very difficult Feynman diagrams.

        On Mon, Dec 3, 2012 at 5:24 PM, The Big Blog Theory

  35. shekh rabbani Says:

    Are you know, how i love your science? It really help me understand about science. I really enjoyed it.

  36. Victor Rutledge Says:

    Please try not to laugh too hard. I was discussing the discovery of mass in neutrinos with my brother and he suggested that the change of ‘flavor’ over time might be caused by an undiscovered property of the particle. His idea was that the particle had spin not only in space/time as we think of it but across multiple dimensions so that it changes flavor depending on its orientation to the dimensions we normally observe. I (obviously) can’t dispute this because I’m math challenged (slightly autistic) but it seems that such a case would only be possible if string theory be accurate and it would have repercussions beyond my ken.

  37. Big Bang Theory Says:

    Hi David, looking forward to you starting this blog again, when do you think that will be? Gregg

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