Updating the textbook: Is the radius of a proton wrong?

Feb 26, 2013 by Jonathan Carroll, The Conversation
We thought we knew the radius of the proton to within 0.8%. Perhaps not. Credit: Ludie Cochrane/Flickr

Striving for agreement between theory and experiment and pushing the boundaries of precision are important parts of the scientific process.

With each step in this process we move closer to enlightenment but things get interesting when theory and experiment diverge.

Such was the case following a series of recent experiments investigating the radius of the .

As the author once said:

The most exciting phrase to hear in science, the one that heralds , is not "Eureka!" ("I found it!") but rather "hmm … that's funny …"

The simplest atom

is a simple atom, right? It's an electron bound to a proton. Who knew it would cause such a stir in the physics community?

A recent article in Science provides an update to a 2010 announcement that fit the usual pattern: a grand claim of a large between established theory and a new experiment, followed by a wide range of explanations of varying levels of .

Usually these updates are to clarify that the problem has been resolved and that, once again, something innocuous was to blame for the unexpected result. Updating three years later to say "it's still broken!" is something of an oddity.

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Listen to hydrogen?

The announcements in question here are about a finding that the radius of the proton differed from the "textbook" value by 4%. This doesn't sound like much, but we thought we knew the radius to within 0.8%, making 4% sort of a big deal.

Physicists only count something as a "discovery" if it's five "standard deviations" (5σ) significant. This measurement is now at 7σ and more than ten times more precise than the previous value, with an error of just 0.05%.

What made it all the more important though, was that the radius of the proton wasn't some value that comes from reading it off a ruler. The theory behind the textbook value is quantum electrodynamics (QED), probably the most refined and accurate theory in all of physics. It describes the way that light and matter interact at the fundamental scale.

Quantum electrodynamics

This is the theory that leads to predictions of the "anomalous magnetic dipole moment" of the electron (and muon), one of the most precisely measured quantities in physics. In a perfect world, electrons would have a "g-factor" of exactly g=2. Combining theory with experiment for this value leads to a unitless quantity that differs from g=2 by a very well understood amount:

g/2 = 1.001 159 652 180 76 ± 0.000 000 000 000 27

That is, we know g/2 to better than one part in 3x1013, equivalent to knowing the distance of the heliopause (the "edge" of our solar system) to the nearest metre.

This also has implications for the fine structure constant – a quantity for which even a minute change would render life in our universe impossible. This constant has also been verified experimentally to better than one part in a billion.

The point here is that QED works really well. So it's a really, really big problem if it's broken.

Hydrogen spectrum. Credit: http://en.wikipedia.org/wiki/File:Hydrogen_transitions.svg

Radius of the proton

Science wins when theory agrees with experiment. But it moves ahead when they don't. In the case of the proton radius, the theory involves a quantity known as the Rydberg constant, R.

We thought we had a good idea about its value. In fact, it is the most accurately measured fundamental constant.

The beauty of this constant is that it can be related to just a few other basic fundamental constants such as the mass and charge of an electron, and also a unit of energy:

1 Ry = h c R = 13.605 692 53 (30) eV.

That energy might be familiar to you if you've studied hydrogen at all – it's the energy of the ground (lowest energy) state, and it's critical to our understanding of atomic spectra – the range of discrete frequencies given out or absorbed by atoms based on their electrons' energy levels.

Atomic spectra

We think we understand spectra pretty well. The "21cm" line of hydrogen is reasonably well known in science culture. It's the wavelength that SETI scans in looking for signals from other worlds.

It was also used as the standard scale for the diagrams on the gold plaques sent out on Pioneer 10 and 11 and gold records on Voyager 1 and 2, along with a diagram explaining its significance (in case you're wondering, it's the energy of a spin-flip of the ground-state electron in hydrogen, also known as the hyperfine splitting).

Pioneer 10 plaque showing (top-left) the hydrogen spin-flip (hyperfine) scale (marked |) on which all other distances in the images are based in binary (e.g. | – – – for 8 x 21cm = 1.68m for the heights of the people). Credit: http://en.wikipedia.org/wiki/File:Pioneer10-plaque.jpg

Calculating the hydrogen ground state energy, or the 21cm line, precisely relies on quantum electrodynamics, but these don't depend on the value of the proton radius very strongly. Why? Because in the case of hydrogen, the electron spends most of its time a very long way away from the proton.

On average (and we're talking quantum mechanics here) the electron sits about 50,000 proton radii away from the proton itself when in the energy state relevant to the 21cm line. This is why we say that atoms are "mainly empty space".

The important difference comes when you replace the electron in hydrogen with a muon, the electron's heavier cousin. The muon's mass is about 200 times that of the electron, and because of this it spends a lot of its time 200 times closer to the proton.

Being so much closer, its energy levels are more sensitive to the radius of the proton (specifically, how the proton's charge is distributed over its volume).

People have been making predictions of the spectrum for 40 years using the "textbook" radius as an input, but we lacked experimental verification.

In review

Which brings us back to what a team of did at the Paul Scherrer Institute (PSI) in Switzerland in 2010 and again recently – they measured the energy spectrum of muonic hydrogen very precisely and found that it didn't match what they expected.

Using , they unravelled the dependence on the proton radius, and found that a value 4% smaller than the "textbook" value fixes the problem entirely.

Previous experiments which led to that value all involved "normal" hydrogen, mostly extracting the proton radius from energy shifts in the same way as muonic hydrogen. A few experiments used electron-proton scattering to determine the proton radius, but there are fundamental issues with this extraction that complicate the matter.

When success isn't …

I myself spent the past two years calculating the QED values more precisely, and reached the same conclusion as the PSI team. I've come to realise during this time that hydrogen is anything but simple, requiring extremely precise calculations at this level.

Diverging results. Credit: http://www.sciencemag.org/content/339/6118/405

The update in Science verifies the PSI team's experiment with a second value which agrees perfectly with their first, suggesting they didn't have a problem with their set-up initially.

In a lot of cases, outrageous claims of beyond-five-standard-deviation discoveries vanish with the discovery of an overlooked contribution or even a loose wire (as some predicted). In this case though, the result has withstood intense interrogation and remains undamaged.

Time to re-evaluate

What comes next is a re-evaluation of the "textbook" value, and updated experiments are underway to probe this. There's still the problem with the Rydberg constant and the other experiments, but there is a horrible phenomenon whereby experiment and theory tend to agree with established values until they are challenged firmly enough, at which point they "drift" towards updated values.

Nonetheless, the journey that has lead to this point encapsulates for me the motivation for science: "Let's measure X and see if it's any different to what people got last time." When things don't agree, we learn something and make progress.

Again, Asimov puts it better than I can:

When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.

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User comments : 11

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HannesAlfven
1.3 / 5 (12) Feb 26, 2013
Rupert Sheldrake has interviewed metrologists on similar discrepancies for the gravitational constant and the speed of light, with hilarious results (see his YouTube talks). There does seem to be a problem here with our choice of the term, "constant". After all, one possible explanation is that the values are not actually constant. So, to insist that they *must* be due to theory, and to not take the alternative seriously, would seem to not exactly be a "scientific" approach.
Antoweif
1.8 / 5 (10) Feb 26, 2013
First Asimov tells you not to judge others views, then he judges your view. Figures.
cantdrive85
1.9 / 5 (17) Feb 26, 2013
Not sure why the pornography on the Pioneer 10 plaque, it's not as if the aliens are going to see us without clothes on. Well, not until they get to know us a little better... Sagan was a slut!
EyeNStein
2.8 / 5 (9) Feb 26, 2013
Why should the proton be a fixed radius like a ball bearing? Perhaps its average shape is perturbed by the proximity of the big fat muon in close orbit, more than by an electron relatively far away.
ValeriaT
1 / 5 (9) Feb 26, 2013
Perhaps its average shape is perturbed by the proximity of the big fat muon in close orbit, more than by an electron relatively far away
Of course, the intuitive solution of this problem is easy, but its quantification may be difficult. There you can find a checklist of already known QED effects, which must be accounted into calculation of proton diameter. For me for example this classical effect is apparently missing in this list - but to analyze it qualitatively is fortunately not my problem.
ValeriaT
1 / 5 (7) Feb 26, 2013
Maybe the above effect is contained in "recoil-like" corrections, who knows. It's difficult to say without seeing the exact physical model of these corrections.
gurloc
2.3 / 5 (3) Feb 26, 2013
Why should the proton be a fixed radius like a ball bearing? Perhaps its average shape is perturbed by the proximity of the big fat muon in close orbit, more than by an electron relatively far away.


Its not, the proton is a seething mass of virtual quarks and gluons, but you can still define an average radius (like defining an average sea level even though the surface consists of waves). The muon does effect the proton via exchange of photons which is what the QED calculations are used to determine, but that only depends on the charge of the muon not its mass so is identical to that of an electron.
EyeNStein
1.8 / 5 (5) Feb 26, 2013
My point is that the dance of the quarks is more purturbed by the proximity of the muon than a distant electron. I dont believe that dynamic effects are factored in the standard model except as an average of cloud probability distributions. Perhaps the quarks high tide is 4% higher.
EyeNStein
1.8 / 5 (5) Feb 26, 2013
I see no reason why a charged quark group couldn't polarise and become re-oriented toward the muon; as water molecules do when charge-neutral water drops are atracted to a static charged object.
Silverhill
5 / 5 (9) Feb 27, 2013
Not sure why the pornography on the Pioneer 10 plaque
"Pornography: writings, pictures, films, etc, designed to stimulate sexual excitement" (from Greek terms meaning "writing about prostitutes"). FYI: The plaque has neither illustrations nor text involving prostitutes.
Nor was it designed for the purpose of sexual excitement, though if you get your jollies from a simple drawing of two unclad adults, be my guest.

it's not as if the aliens are going to see us without clothes on. Well, not until they get to know us a little better...
Indeed. Exchanges of information, including comparative anatomy, will be fascinating if they ever happen.

Sagan was a slut!
By whose perverse definition, eh? BTW, Linda Sagan did the drawings of the humans, not Carl. (Adjusted accusation that *she* was a slut in 3...2...1...)

Grow up, cantdrive85. Remember Oscar Wilde's observation: "If man was meant to be nude, he would have been born that way."
rubberman
2 / 5 (4) Feb 27, 2013
"The important difference comes when you replace the electron in hydrogen with a muon, the electron's heavier cousin. The muon's mass is about 200 times that of the electron, and because of this it spends a lot of its time 200 times closer to the proton."

"Using quantum electrodynamics, they unravelled the dependence on the proton radius, and found that a value 4% smaller than the "textbook" value fixes the problem entirely"

By swapping the electron for the muon they have increased the atomic density and binding field strength of the atomic components, essentially "compressing" the proton. Given the mass ratio of 200/1 the compression would be higher if the muon could be accelerated to electron velocity...roughly 10.8%, but the slower muon derates the compression to observed 4%. I would surmise that the diameter is correct in both cases for the proton and is dependant on the overall atomic mass in this case...

But of course this is a guess....

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