Cover Image: October 2010 Scientific American Magazine See Inside

Just How Small Is the Proton?

New findings challenge a basic theory of physics that presumably had been settled















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Physicists have been scratching their heads since July, when a research team announced that the proton, the basic building block of matter, is 4 percent smaller than previously thought. The finding, published in Nature, clashes with theoretical predictions based on quantum electrodynamics, or QED, the fundamental theory of the electromagnetic force that had passed the most stringent tests in physics.

Randolf Pohl of the Max Planck Institute for Quantum Op­tics in Garching, Germany, and his collaborators used a laser to probe exotic, man-made hydrogen atoms in which elementary particles known as muons replaced the usual electrons orbiting the single-proton nuclei. Laser energy made the atoms fluoresce at char­acteristic x-ray wavelengths. Those wavelengths reflected a number of subtle effects, including the little known fact that an orbiting particle—be it a muon or an electron—often flies straight through the proton. That is possible because protons are composed of smaller elementary particles (mainly three quarks), and most of the space inside a proton is actually empty.

By calculating the effects of the proton’s radius on such fly-through trajectories, the researchers were able to estimate the proton’s radius to be 0.84184 femtometer (one femtometer is one quadrillionth of a meter). This figure is smaller than all previous measurements made, which ranged between 0.8768 and 0.897 femtometer. (Either way, the proton is a lot smaller than even a hydrogen atom: if the atom were the size of a football field, the proton would be the size of an ant.)

In dealing with such tiny quantities, the possibility for error always exists. Yet after 12 years of painstaking efforts (“You need to be stubborn,” Pohl says), the team members are confident that some unforeseen subtlety in their apparatus hasn’t thrown off their measurement. Theorists have also double-checked the calculations involved in interpreting the muons’ behavior and predicting the size of the proton, which are relatively straightforward, says Ulrich D. Jen­tschura, a theorist at the Missouri University of Science and Technology in Rolla.

Some physicists have suggested that the interaction between the muons and the proton could be complicated by unforeseen pairs of particles and their antiparticles, which might appear briefly from the vacuum in and around the nucleus. The most likely candidates, Jentschura says, are electron-antielectron pairs, which are not supposed to show up in the everyday physics of atoms, at least not according to the standard theory. “It could be the first indication that something is wrong with our picture” of QED, says Krzysztof Pachucki, a theorist at the University of Warsaw in Poland. The theory might need some tweaking, but likely not a complete overhaul, he says. Whatever the answer, physicists will most likely have plenty to keep scratching their heads about for years to come.



This article was originally published with the title Just How Small Is the Proton?.



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  1. 1. jtdwyer 11:57 AM 9/25/10

    As I understand muons are considered to be much more massive (105.7 MeV) than electrons (0.511 MeV). I would not expect muons to interact with protons identically to electrons.

    While there was little to indicate the actual measurement method employed in the description provided in the article ("By calculating the effects of the proton’s radius on such fly-through trajectories, the researchers were able to estimate the proton’s radius..."), a much more massive orbital may have been able to pass nearer to the proton without its trajectory being affected, leading to the smaller estimate of the proton's size.

    There was no explanation given here for why muon orbital were used rather than electrons, or whether the protons were composed of generation II charm a& strange quarks, which are considered to be more massive than generation I up & down quarks.

    I'd first attribute the measurement difference to the replacement of electrons with muons in this non-standard measurement, rather than presume that this measurement was more accurate than previous measurements.

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  2. 2. candide in reply to jtdwyer 08:52 AM 10/1/10

    "...team members are confident that some unforeseen subtlety in their apparatus hasn't thrown off their measurement. Theorists have also double-checked the calculations involved in interpreting the muons' behavior and predicting the size of the proton"

    I would hope and think that a team of research physicists would have anticipated the effects of the differences between electrons and muons - and would have compensated for it.

    They seem to think that electron-antielectron pairs may be a more like cuplrit, if there is one.

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  3. 3. fubblitious 11:18 AM 10/1/10

    Surely the most logical explanation is that modern particle physics is just breaking all the basic rules that statisticians live by i.e. trying to extrapolate their theoretical models beyond the space to which they are relevant?

    No amount of obfuscated mumbo-jumbo can compensate for the fact that what gets presented in this field in the media can be most accurately be described as "made up" ... errrr I mean "postulation based on cutting edge theoretical mathematics".

    When these guys can tell me in plain english what gravity is, then and only then, might they be onto something. Until then, I suggest we ignore the particle based mythology (whether it fits the self-fulfilling made up "mathematics" or not) and the random directions its conclusions seem to be lurching in.

    I do have another question I'm sure I am not the first to ask: who made the assumption that the LHC would potentially find a "God" particle? It might just as easily find the "Devil" particle. I am somewhat reminded of the general scientific arrogance around the science of GM food crops. In my mind, if the universe doesn't naturally do something, forcing it cannot be a predictable science, so don't be so surprised when the result breaks the model. Selective breeding and GM science are not the same things - it seems traditional physics and particle physics may be developing a similar distinction.

    Lets hope Gandalf, Asandir, or even Mr. Potter (the REAL Magicians) have got their ears to the ground ready to save us from the consequences of "well, I really didn't expect that to happen ..."

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  4. 4. jtdwyer in reply to candide 11:19 AM 10/1/10

    You might like to presume that scientists don't make errors and dismiss my suggestion out of hand. In doing so you could be discarding the solution to this problem. Everything must be questioned!

    You see, otherwise these expert scientists are contradicting the most accurate theory in existence and all prior evidence, as stated:
    "The finding, published in Nature, clashes with theoretical predictions based on quantum electrodynamics, or QED, the fundamental theory of the electromagnetic force that had passed the most stringent tests in physics."

    According to Wikipedia/Moun under the heading "Muonic atoms":
    The muon was the first elementary particle discovered that does not appear in ordinary atoms. Negative muons can, however, form muonic atoms (also called mu-mesic atoms), by replacing an electron in ordinary atoms. Muonic hydrogen atoms are much smaller than typical hydrogen atoms because the much larger mass of the muon gives it a much smaller ground-state wavefunction than is observed for the electron. In multi-electron atoms, when only one of the electrons is replaced by a muon, the size of the atom continues to be determined by the other electrons, and the atomic size is nearly unchanged. However, in such cases the orbital of the muon continues to be smaller and far closer to the nucleus than the atomic orbitals of the electrons."

    Since muonic atoms are known to be smaller than normal hydrogen atoms, this radical, unstable variant is the most likely candidate source of error. If you must solve the problem, question everything!

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  5. 5. candide 01:42 PM 10/1/10

    I absolutely agree with questioning everything.
    That and repetition are the foundation of science.

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  6. 6. gesimsek 01:49 PM 10/1/10

    They said there was light of the big bang in the begining and there will be the dust of entropy at the end. However, somehow I knew this already. They say there is the tree, look closely there are molecules inside, more closely there are atoms inside the inside, then there are particles, then there are quarks, then there is energy at the end. What is energy? It is the ripples of the first bang flowing according to the law of entropy. Who are we? Ripples moving against the law of entropy. Why? The answer lies inside us.

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  7. 7. ormondotvos 05:17 PM 10/1/10

    Ah, yes, the new anti-scientific outlook: if I don't understand it instantly, it must be claptrap.

    What a bunch of arrogant commentators we've raised!

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  8. 8. llewellyn 05:49 PM 10/1/10

    Good job, fubblitious!
    Particle schmarticle.
    Get thee a cheapo throw away yahoo Edress and mail me at:
    elseaminor@yahoo.com
    The gravity of the situation demands it!
    l

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  9. 9. gesimsek 12:20 PM 10/2/10

    Excuse me for being anti-science. I thought this was a public forum for us to present our opinions. As this is Scientific AMERICAN I thought I could be a little arrogant.

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  10. 10. limitfree1 01:10 PM 10/2/10

    perhaps we need to examine how the size of a proton might possibly have different "sizes" in different regions of spacetime. does a proton, or an electton expand in size along with expanding spacetime, meaning that as matter curves spacetime like einstein postulated in his theory of gravity, we can also see how expanding spanding spacetime makes it possible for two protons in separate regions of the universe where spacetime is expanding at different rates, to be of different sizes relative to each other. then the question arises is the expansion of spacetime analog, or is it digital. is there a quanta of time?

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  11. 11. limitfree1 01:12 PM 10/2/10

    does a proton stay the same size as it travels through spacetime, or does it stretch or contract with the exansion of or spacetime?

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  12. 12. limitfree1 01:13 PM 10/2/10

    if spacetime curves in response to the presence of matter, does matter then change in size or shape due to the nature of expanding spacetime.?

    Reply | Report Abuse | Link to this
  13. 13. edromar 06:09 PM 10/2/10

    Funny comedy, but not what I expect from SciAm!

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  14. 14. edromar 06:11 PM 10/2/10

    Is a muon biger than a cow?

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  15. 15. edromar 06:15 PM 10/2/10

    Ididn't know scientists used meaningless terms refering to unobservable entities like "gods and anti-gods (devils)

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  16. 16. edromar 06:17 PM 10/2/10

    Now rthat ia not a FRIENDLY THING TO SAY!

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  17. 17. edromar 06:26 PM 10/2/10

    Now rthat ia not a FRIENDLY THING TO SAY!
    bUT i THOUGHT "SIZE" W2AS AN IRRELEVANT CONCEPT WHEN IT COMES TO ATOMS AND LESS MASSIVE TINGS WHERE "MASS" IS THE OPERATIVE CONCEPT AND OTHER EQUALLY6 RELIGIOUS TERMS OF THINGS TAKEN BY FAITH!

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  18. 18. edromar 06:27 PM 10/2/10

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  19. 19. edromar 06:29 PM 10/2/10

    IF MY LAST COMMWNT WWAS NOT MASSIVE ENOGH TO MEASURE, MAYBE IT WAS WAS JUST NOT WEIGHTY ENOUGH!

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  20. 20. jtdwyer in reply to robert schmidt 06:33 PM 10/2/10

    Why do you rarely have any comment regarding the subject of the article, only comments berating commentators?

    Perhaps I could have phrased it differently to spare some readers' faith in the general infallibility of all scientists, but it may be beneficial to criticize the article.

    In this case, there was no explanation that the massive muon could affect the measurement of or even the size of the nucleon being measured. Muonic hydrogen atoms are more massive and their spatial displacement is less than normal electron hydrogen atoms. I insist that it may be an effect of the muon in the measurement process that has produced this measurement result. If it has already been considered and evaluated then it should have been mentioned in the article.

    Typically, such an influence on their measurement process would have to be addressed in the research. Since it was not mentioned here I think it warrants my mention. If these brilliant researchers would obviously already considered and previously disproved my assertion, why is it not even mentioned to the science reporter who wrote this article? It should have been a primary concern to the researchers.

    Why would I care that you chose to defend these researchers who are contradicting the work of many much more significant contributors to this field?

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  21. 21. robert schmidt 08:15 PM 10/2/10

    @jtdwyer, "Why do you rarely have any comment regarding the subject of the article, only comments berating commentators?" I am humble enough to know what I don't know. The articles don't give enough information to discuss whether or not the conclusions are justified. For that one needs to go to the source and look at the data. What I take exception to is those that speak with absolute authority about things they know nothing about or people that deliberately misrepresent the facts to further their agenda. People are free to make whatever statements they like (with some limitations) but it doesn't mean they should not be challanged. If a person holds a proposition that is in error it would be wrong not to point it out, just like it would be wrong not to point out to someone that there fly is open.

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  22. 22. jtdwyer in reply to robert schmidt 09:28 AM 10/3/10

    In that case please feel free to point out precisely which statements I made were incorrect. Otherwise you are simply objecting to the precise statements I make, which I do not think not be objected to a particle physicist. I can assure you that my attempt to precisely state my assertions is not an attempt at self-aggrandizement but simply an attempt to clearly communicate.

    I don't have to be a particle physicist to know that the distinctions between muons and electrons physical characteristics (mass) could affect measurement results. In fact that must be the reason why it chosen for use rather than the electron.

    That there was no explanation for this is this article is a shortcoming, limiting the understanding that can be gained from it.

    Since Scientific American is not journal limited to an audience of particle physicists, but a more general audience, it is incumbent on its authors to minimally explain the information being presented. That there is no explanation of the reasons muons are selected or their precise effects on measurement makes it impossible for the readership to understand why the discrepancy between these measurement results, QED theory and past measurement results could occur. SA should not be used as a teaser to sell $32 Nature articles.

    I suggest that the author of this article, Davide Castelvecchi, follow up by interviewing some particle physicists, perhaps the reviewers of the paper published in Nature, to explain how the use muonic hydrogen atoms affected the measurement of proton size and assess the possibility that additional effects not accounted for by the researchers could have produced the reported discrepancy.

    If my remarks suggesting that the use of muons could be responsible for producing measurement effects that were not accounted for was inappropriate I will apologize to the author of this report, the researchers and the SA readership.

    Davide Castelvecchi and SA, can you please assist with this continuing dispute? Thanks in advance...
    James T. Dwyer

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  23. 23. robert schmidt 11:18 AM 10/3/10

    @georgeferhardt, good question! I'd be interested to know the answer to that. Would the quarks be as densly packed in the soup as in the proton or more so? At what point (density / pressure) do the quarks start to form protons? Where did the electrons come from and at which point did they start attaching themselves to protons? It would be an interesting article for sciam to produce, showing the process of the precipition of matter after the big bang.

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  24. 24. jtdwyer in reply to georgeferhardt 09:54 PM 10/3/10

    georgeferhardt: I suggest you begin your investigation at:
    http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang

    Maybe there is some initial estimate of the total number of quarks, which would be required for the estimation you suggest, even if there is some estimate for the size of free quarks in the initial universe.

    I think it's hypothesized that the initial universe contained only energy; that matter condensed from that energy as the universe expanded and cooled per E=mc^2. As a result, the number of particle of varying types may have varied as the universe quickly developed. Of course, there is no fixed quantity for the number of photons at any moment in time, for example.

    Keep in mind that, according to the Wikipedia reference, "all ideas concerning the very early universe (cosmogony) are speculative." As a result, only a consensus speculation can be represented as the current 'standard model of cosmology'.

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  25. 25. jtdwyer in reply to georgeferhardt 10:00 PM 10/3/10

    George, I strongly recommend to you and everyone else that you not give out even seemingly innocuous personal information over the internet. You never know...

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  26. 26. jimfusco 10:10 AM 10/5/10

    In this article, Davide Castelvecchi makes the eerily familiar remark: "Most of the space inside the proton is empty".

    I remember reading the EXACT same thing about the atom; That it was mostly empty space, and that most of it's mass resides in the nucleus.

    Well the proton(along with the neutron) ARE the nucleus, and we are now told that THEY are mostly empty space.

    So it raised a question: "What kind of particle or state of matter would have NO empty space?".

    I have an idea, but want to know what others think.

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