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New crack in QED?

  1. Jul 8, 2010 #1

    Apparently the proton is about 4% smaller than thought, which is somewhat challenging for QED. It could be new effects or experimental error of some sort. Any such guessing is speculative at this time, but what would you think?
  2. jcsd
  3. Jul 8, 2010 #2


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    (New crack? I didn't know there was an old one ;) )

    QED has successfully calculated the Lamb shifts for hydrogen and helium to a high degree of accuracy, so it would appear QED 'works'. And has for some time - it's not very new stuff, calculating the Lamb shift of hydrogen - but muonic hydrogen, on the other hand, is relatively new stuff. And there's room for mistakes when going from hydrogen to muonic hydrogen, since the relative masses are very different, and the Lamb shift energy includes mass-dependent recoil corrections.

    So that's my offhand guess - errors in the recoil corrections.
  4. Jul 8, 2010 #3
    Yeah well it was just sensationalism :devil:
    I suppose the vacuum catastrophe might sort of qualify for one :biggrin:
  5. Jul 9, 2010 #4


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    Hmm, looking deeper into this, I'm not so sure - it seems the recoil corrections are overall too small to be able to account for the discrepancy. Of course, if a guy like me could find a correction that could possibly account for this, it should be immediately obvious to the people working on this thing, and we might not be having this discussion ..

    The opinion I'd most like to hear is that of http://www.fuw.edu.pl/~krp/" [Broken], since he's the one who's done most of the calculations used for the muonic Lamb shift.

    Me, I'm just a chemical physicist, so as far as I'm concerned the nucleus is a point charge, and the Lamb shift is just a rounding error! :biggrin:
    Last edited by a moderator: May 4, 2017
  6. Jul 9, 2010 #5
    It's not something I'm seeing any obvious way to correct either. My first thought was binding energy, but... still seems the large mass difference highly likely has something to do with it. I'm stuck on this one without even any really reasonable guesses.
  7. Jul 9, 2010 #6
    If the size of the proton is actually smaller does this imply that other quantities such as proton mass are different?
  8. Jul 9, 2010 #7
    QED does not deal with protons.

  9. Jul 9, 2010 #8


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    Not likely. Basically they're talking about the charge radius here. This is measured using scattering (typically), and this number is then used calculating the Lamb shift. The mass is also used, but this is determined independently, and better. (For instance, you have to use it to get the unshifted values of hydrogen to begin with, it's several orders of magnitude larger).

    What on Earth do you mean by that?

    Lamb-shift calculations, which are done using QED include a whole host of corrections which are dependent on the properties of the nucleus/proton. (charge radius, mass, polarizability, etc) Everyone agrees it's not likely to be a fundamental failure of QED here, but it's at least a distant possibility.
  10. Jul 9, 2010 #9
    Look up form factors. The Lamb shift calculation does not use QED, but effective field theory where the proton is a "black box" with some phenomenological parameters associated to it.
  11. Jul 9, 2010 #10
    Thanks alxm.My feeling is that it's early days yet and we can't rule out the possibility of other surprises cropping up.Interesting stuff.:biggrin:
  12. Jul 9, 2010 #11


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    I know about the form factors (in fact I thought it was the experimental determination of them we were talking about), I don't know why you think that that means it doesn't use QED. What would that imply?

    All I can say that your definition of 'using QED' must be different from everyone else's, because it certainly seems everyone else thinks that QED corrections are used, including the people who wrote the paper in question, and the people who did the Lamb shift calculations that they refer to, and the textbooks, and Wikipedia.
  13. Jul 9, 2010 #12
    I would even argue that QCD has very little theoretical relevance in this context : not only most of the Lamb shift corrections are just QED, but in addition form factors which could in principle be calculated from QCD in fact are not manageable (non-perturbative), and are just experimentally measured using QED probes (DIS) !
  14. Jul 9, 2010 #13
    Size can take on different meanings depending on the context. It's not necessarily a simple geometric volume in space. Would you call a charge radius a size? It really makes no difference what ontological notions you attach to size in this case, it's about 4% smaller than what we can account for.
  15. Jul 9, 2010 #14
    Is it true that the Rydberg constant is used to calculate the size of the proton?
  16. Jul 9, 2010 #15
    The charge radius is defined consistently in electron scattering, ordinary hydrogen Lamb shift and muonic hydrogen Lamb shift. The definition chosen is the round-mean-squared of the charge 1-D distribution as a function of radius.

    We already expect from models that the mass radius (by which I mean : the RMS of the mass 1-D distribution; also other radii, such as from angular momentum density or force density) are different BTW.
  17. Jul 9, 2010 #16
    The root-mean-square charge radius is, and that goes into defining the Rydberg constant.
  18. Jul 9, 2010 #17
    A qoute from the introduction to the paper:

    The references used here are:

    • 3. Mohr, P. J., Taylor, B. N. & Newell, D. B. CODATA recommended values of the
      fundamental physical constants: 2006. Rev. Mod. Phys. 80, 633–730 (2008)
    • 11. Pachucki, K. Theory of the Lamb shift in muonic hydrogen. Phys. Rev. A 53,
      2092–2100 (1996)
    • 12. Pachucki, K. Proton structure effects in muonic hydrogen. Phys. Rev. A 60,
      3593–3598 (1999)
    • 13. Borie, E. Lamb shift in muonic hydrogen. Phys. Rev. A 71, 032508 (2005)
    • 14. Martynenko, A. P. 2S Hyperfine splitting of muonic hydrogen. Phys. Rev. A 71,
      022506 (2005)
    • 15. Martynenko, A. P. Fine and hyperfine structure of P-wave levels in muonic
      hydrogen. Phys. At. Nucl. 71, 125–135 (2008)

    I see three (of the many) authors:

    Laboratoire Kastler Brossel, École Normale Supérieure, CNRS, and Université P. et M. Curie-Paris 6, 75252 Paris, Cedex 05, France

    Eric-Olivier Le Bigot, Paul Indelicato,

    Institut für Teilchenphysik, ETH Zürich, 8093 Zürich, Switzerland

    Franz Kottmann

    who 'did work on QED theory', according to the paper.
  19. Jul 9, 2010 #18
    Yes, but by how much and at what variance from the muon data?
  20. Jul 9, 2010 #19
    Here's something that may help:
    http://engineering.library.cornell.edu/node/4510 [Broken]
    Last edited by a moderator: May 4, 2017
  21. Jul 9, 2010 #20
    Wow the implications here are really interesting.:tongue2:
    Last edited by a moderator: May 4, 2017
  22. Jul 9, 2010 #21
    Thank you my_wan.:biggrin: Well, I followed up by also searching for further information that pertains to the Nature "News" article. I am fond of Dr. Randolf Pohl of Max Planck Institute of Quantum Optics. Max Planck Institute provides added insight: PRESS RELEASE - Garching, 08.07.2010, How small is the proton?

    Here are two consecutive quotes from the press release from Max Planck Institute, though I encourage people to read the entire press release. I have highlighted in red what I thought was important to remember.

    [QUOTE]Finally the experiment has been realized in a joined effort in which each team brought in its own expertise in the fields of accelerator physics, atomic physics, laser technologies and detectors. First measurements in 2002, 2003 and 2007 were not encouraging. Although the experiment seemed to work as planned, there was no sign of the expected resonance. “First we thought our lasers were not good enough, so we rebuilt large parts of the laser system using the new disk laser technology developed at the University of Stuttgart. But then it turned out that we had simply looked at the wrong place: apparently the theoretical prediction of the transition frequency was wrong”, explains Dr. Aldo Antognini from PSI.

    The breakthrough happened in the summer of 2009. After three months of set up time and three weeks of data taking – day and night – the scientists could unambiguously observe the signal on the evening of July 5, 2009. After a long and careful analysis of this signal, the deduced value of the proton radius is ten times more precise, 0.84184 femtometers (1 femtometer = 0.000 000 000 000 001 meter), but in strong disagreement with the international accepted value (0.8768 femtometers) deduced from previous experiments. The scientists are still discussing the possible reasons for the discrepancy. Everything is under scrutiny now: Previous high-precision measurements, complicated calculations, and maybe at some point even the world’s most precise and best-tested fundamental theory itself: quantum electrodynamics. “[COLOR="Red"]However, before we question the validity of QED theorists have to check their calculations”, says Dr. Pohl. A hint, which interpretation could be correct, may come from the new project, planned for 2012. Then, the researchers want to perform the same kind of experiment with muonic helium. The required muon source and lasers, says Randolf Pohl, are already available. .[/COLOR] Meyer-Streng(MPQ)/Piwnicki(PSI)[/QUOTE]

    It appears to me to be an ongoing work-in-progress. I'm excited! The new project planned for 2012 should give us further information. Wow! I'll be looking forward to tune-in on this topic in 2 more years. :biggrin:
    Last edited by a moderator: May 4, 2017
  23. Jul 9, 2010 #22


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    The Rydberg constant is naturally necessary for determining the absolute values of the the electronic levels, but the "classical" Lamb shift, being the relative shift of the 2S and 2P levels, is independent of the Rydberg constant; it cancels out.

    But the accuracy of the Rydberg constant is limited by the accuracy of these lower (1S, 2S, 2P) levels, which in turn is limited by the Lamb shift. As I read it, they're saying that if their value of the Lamb shift is correct, and the charge radius calculated from it is correct, then the Rydberg constant will be changed by an improbable amount.
  24. Jul 9, 2010 #23
    Changed by an improbable amount but does improbable mean zero?

    Can someone please confirm,clarify or otherwise the following.As far as the whole atom is concerned the most probable radius is the Bohr radius(for ground state) and muonic hydrogen has a much smaller radius than ordinary hydrogen(for the non reduced mass equation the radius being inversely proportional to the lepton mass)
  25. Jul 9, 2010 #24


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    No, their calculated value differed by "−110 kHz/c (4.9 standard deviations)".
    It's a very large deviation, and given that there are lamb-shift independent means of determining it, I suspect they simply mean it's impossible. So they're basically doing the old "either the calculations are wrong or <something impossible> is true" argument. Of course the theorists will inevitably raise the additional possibility of experimental error.

    In this context (extremely accurate hydrogen calcs) I would have to say no. These days, the Bohr radius is defined as the non-relativistic value for a fictional hydrogen with infinite nuclear mass. It does not take into account reduced-mass, or relativistic effects, or indeed the Lamb shift. So it's not exactly the most probable radius, and the ground-state energy is not exactly 0.5 a.u.

    Entirely correct, for the ordinary clamped-nucleus Schrödinger equation a change in electron mass is just a linear scaling of coordinates. So the muon 'orbits' about 200x closer to the nucleus, hence nuclear structure effects have a correspondingly much, much larger effect. Which is why this experiment was done.
  26. Jul 9, 2010 #25
    Great stuuff alxm,thanks a lot.I need to look more into the Bohr radius thing.
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