Physicists make most precise measurement ever of the proton's magnetic moment(phys.org)
phys.org
Physicists make most precise measurement ever of the proton's magnetic moment
https://phys.org/news/2017-11-physicists-precise-proton-magnetic-moment.html
55 comments
First-principles predictions of properties of baryons are only in their infancy. Even the best lattice QCD calculations of mesonic properties at the physical pion mass are good to 1 part in 10^(4ish), nothing approaching the accuracy needed to detect new physics in the baryon sector.
Calculations with baryons suffer from a severe signal-to-noise problem, and the latest calculation of a substantially-easier-to-compute quantity, the nucleon isovector axial coupling, is only at ~1% precision: https://arxiv.org/abs/1710.06523 (full disclosure: one author of said calculation).
I don't know of a calculation of the proton magnetic moment with physical parameters.
Calculations with baryons suffer from a severe signal-to-noise problem, and the latest calculation of a substantially-easier-to-compute quantity, the nucleon isovector axial coupling, is only at ~1% precision: https://arxiv.org/abs/1710.06523 (full disclosure: one author of said calculation).
I don't know of a calculation of the proton magnetic moment with physical parameters.
Why is the precision so low? I assume it's not due to lack of computing resources. Is it due to the limited accuracy of inputs? inherent instability of the model, like with weather prediction?
Particle physics simulations are one of the areas where quantum computers would be exceedingly useful, dropping many calculations from exponential-time to, in the best case, linear. That's if you're trying to find exact solutions. Which you can't, but even the approximations we've got are frankly awful.
So, basically a lack of computing resources. QCs aren't generally that much faster than classical ones, but in this particular case they are--understandably so, given the universe runs on quantum mechanics. Turing machines are not good enough for this, and no number of Intel CPUs will let us overcome that barrier.
Physicists try really hard anyway, but the approximations are... Well. As I said, awful.
So, basically a lack of computing resources. QCs aren't generally that much faster than classical ones, but in this particular case they are--understandably so, given the universe runs on quantum mechanics. Turing machines are not good enough for this, and no number of Intel CPUs will let us overcome that barrier.
Physicists try really hard anyway, but the approximations are... Well. As I said, awful.
> Turing machines are not good enough for this, [...]
Usually we only bring up Turing machines for decidability, ie when the only thing that matters is whether it takes finite or infinite amounts of time.
(Yes, I know, you can also calculate exact runtimes with Turing machines, but nobody really cares, I think?)
I guess you mean to say classical computer or so?
> [...] and no number of Intel CPUs will let us overcome that barrier.
Or at least that's everybody's best guess. On similar footing to the empirical evidence for P != NP. It's still theoretically possible that BQP = BPP, if memory serves right. (https://en.wikipedia.org/wiki/BQP vs https://en.wikipedia.org/wiki/BPP_(complexity))
Usually we only bring up Turing machines for decidability, ie when the only thing that matters is whether it takes finite or infinite amounts of time.
(Yes, I know, you can also calculate exact runtimes with Turing machines, but nobody really cares, I think?)
I guess you mean to say classical computer or so?
> [...] and no number of Intel CPUs will let us overcome that barrier.
Or at least that's everybody's best guess. On similar footing to the empirical evidence for P != NP. It's still theoretically possible that BQP = BPP, if memory serves right. (https://en.wikipedia.org/wiki/BQP vs https://en.wikipedia.org/wiki/BPP_(complexity))
The best 'physical' model of computation is probably the reversible 3D mesh (R3M) model: http://iopscience.iop.org/article/10.1088/0957-4484/9/3/005/....
Of course, it depends a bit on what you are trying to model.
Most of the time the different ways to model computing only have a polynomial slowdown to emulate each other. In that sense, quantum computers are different from Turing machines: the best way we know to emulate quantum computers on Turing machines has exponential slow downs.
Most of the time the different ways to model computing only have a polynomial slowdown to emulate each other. In that sense, quantum computers are different from Turing machines: the best way we know to emulate quantum computers on Turing machines has exponential slow downs.
LQCD is approximation-free, once you take the continuum and infinite-volume limits (if you're operating with physical parameters). But I obviously agree that large-scale universal quantum computers (or even specialized quantum emulators) would be extremely useful! For example, you can solve many notoriously difficult fermion sign problems, or study real-time dynamics with one.
Not an expert but I think it is actually due to a lack of computing resources, lattice QCD calculations seem to be extremely demanding based on what I read.
It's a classic example of combinatorial explosion making something untractable. Going to one more order in perturbation theory is such an incredible increase in computational expense.
Solving chess (in the strict sense) is a similar example. E.g. all 6-piece endgames were known in 2005; by 2012 we had the complete 7-piece endgame tablebase, but the 8-piece endgame tablebase is such a hard problem that we're nowhere close even with Moore's law; the sheer size of that tablebase is estimated to be ~10 petabytes.
Solving chess (in the strict sense) is a similar example. E.g. all 6-piece endgames were known in 2005; by 2012 we had the complete 7-piece endgame tablebase, but the 8-piece endgame tablebase is such a hard problem that we're nowhere close even with Moore's law; the sheer size of that tablebase is estimated to be ~10 petabytes.
Lattice QCD does not rely on perturbation theory, and so it doesn't suffer from a combinatorially explosion in the way you think. However, we do attempt to perform many-millions-dimensional (scaling with the spacetime volume grid size) integrals stochastichally.
Huh, can you explain more? I always assumed this stuff was done by expanding the action or the S-matrix or something using some relevant diagrams to some loop order? (I must confess it's too long since I did QFT.)
(Disclaimer: not a QCD expert, but I did read a paper or two back in grad school from the perspective of someone who liked numerical linear algebra. Don't rely on this advice.)
I believe the core difference here between QCD and QED (the classical perturbative QFT) is that QED has a very small coupling constant (it's the fine structure constant, so ~1/137) whereas QCD has a large one (comparable to or greater than one.) It turns out that a perturbative expansion is effectively in powers of the coupling constant, so QED expansions converge rapidly...and QCD expansions converge not at all.
I believe the core difference here between QCD and QED (the classical perturbative QFT) is that QED has a very small coupling constant (it's the fine structure constant, so ~1/137) whereas QCD has a large one (comparable to or greater than one.) It turns out that a perturbative expansion is effectively in powers of the coupling constant, so QED expansions converge rapidly...and QCD expansions converge not at all.
This explanation ought to be correct at low energy, just where most LQCD work occurs (attempting to predict even lower-energy observables, like the proton mass, etc.).
At high (collider) energies, it is okay to work perturbatively.
At high (collider) energies, it is okay to work perturbatively.
I'm going to put in some explanations of things that it sounds like you already know, for the sake of any other readers.
One way of calculating observables in quantum field theory is by performing a path integral. That is, an integral over all configurations of the fields in your system. We start with a partition function
We can calculate expecation values of an observable O, which is a functional of the fields, by taking averages.
This produces an ensemble of N configurations. Because our configurations are generated according to the weight e^{-S} we can estimate simply:
Once we have an ensemble of field configurations, we can measure all sorts of observables on them. Typically one measures order parameters or correlation functions, but it depends on what physics you're interested in.
What approximations have I made? First, I calculate on a finite, discrete spacetime volume. Second, I don't have an infinite budget, so I have statistical uncertainty in my result, much like an experimentalist. In fact, we usually say we "measure" the observable O. Of course we're not interrogating nature, but a system of axioms (or something). For our purposes, a computer is like a telescope, but it lets you see into the Platonic world.
To control the continuum limit, you need to redo the above Monte Carlo procedure a few times with different lattice spacings (holding the hadronic spectrum fixed). To control the infinite-volume extrapolation you need to redo the above MC procedure a few times with different numbers of lattice sites but otherwise fixed parameters.
I have neglected some details. For example, there are different ways to discretize, and some ways are better than others (but typically that corresponds to a more expensive method). Depending on your discretization you may have different input parameters you can fiddle with. In QCD, the QCD coupling constant and the quark masses are the ones you can fiddle with. Take some set of parameters and compute, for example, the hadronic spectrum. If the ratios of the masses match those we see in nature, we rejoice. We can then compare the mass computed from the lattice (which is a dimensionless number) and compare it to the masses in the real world (which are measured in GeV). The conversion factor is the lattice spacing (usually on the scale of .1 to 0.05 fm, which we convert to GeV using hbar=1), m_lattice = m_physical * a_lattice. If you are near the continuum limit, anything dimensionful you need to measure on the lattice will simply be converted by the correct powers of the lattice spacing, and any errors will scale like some higher power of the lattice spacing. That this is true is essentially a reflection of the fact that QCD has a negative beta function and becomes weakly coupled / perturbative at large energies / short distances. In theories without a UV fixed point you cannot take a continuum limit---in perturbative language, this is the Landau pole coming to bite you.
As an aside, from this perspective, Wilson's renormalization program is much less mysterious: if you want to hold physics fixed and change your lattice spacing, you'd better change the bare, dimensionless parameters you stuck into your action.
One way of calculating observables in quantum field theory is by performing a path integral. That is, an integral over all configurations of the fields in your system. We start with a partition function
Z = ∫ D[fields] e^{i S[fields]}
S[fields] = ∫ dSpacetime L[fields[spacetime]]
We can calculate expecation values of an observable O, which is a functional of the fields, by taking averages.
< O[fields] > = 1/Z ∫ D[fields] e^{i S[fields]} O[fields]
< O[fields] > = 1/Z ∫ D[fields] e^{-S[fields]} O[fields]
S_lattice[fields] = ∑[Spacetime] L[fields[spacetime]]
This produces an ensemble of N configurations. Because our configurations are generated according to the weight e^{-S} we can estimate simply:
< O[fields] > = 1/N ∑[field configuration] O[fields]
+ error of order 1/sqrt(N)
Once we have an ensemble of field configurations, we can measure all sorts of observables on them. Typically one measures order parameters or correlation functions, but it depends on what physics you're interested in.
What approximations have I made? First, I calculate on a finite, discrete spacetime volume. Second, I don't have an infinite budget, so I have statistical uncertainty in my result, much like an experimentalist. In fact, we usually say we "measure" the observable O. Of course we're not interrogating nature, but a system of axioms (or something). For our purposes, a computer is like a telescope, but it lets you see into the Platonic world.
To control the continuum limit, you need to redo the above Monte Carlo procedure a few times with different lattice spacings (holding the hadronic spectrum fixed). To control the infinite-volume extrapolation you need to redo the above MC procedure a few times with different numbers of lattice sites but otherwise fixed parameters.
I have neglected some details. For example, there are different ways to discretize, and some ways are better than others (but typically that corresponds to a more expensive method). Depending on your discretization you may have different input parameters you can fiddle with. In QCD, the QCD coupling constant and the quark masses are the ones you can fiddle with. Take some set of parameters and compute, for example, the hadronic spectrum. If the ratios of the masses match those we see in nature, we rejoice. We can then compare the mass computed from the lattice (which is a dimensionless number) and compare it to the masses in the real world (which are measured in GeV). The conversion factor is the lattice spacing (usually on the scale of .1 to 0.05 fm, which we convert to GeV using hbar=1), m_lattice = m_physical * a_lattice. If you are near the continuum limit, anything dimensionful you need to measure on the lattice will simply be converted by the correct powers of the lattice spacing, and any errors will scale like some higher power of the lattice spacing. That this is true is essentially a reflection of the fact that QCD has a negative beta function and becomes weakly coupled / perturbative at large energies / short distances. In theories without a UV fixed point you cannot take a continuum limit---in perturbative language, this is the Landau pole coming to bite you.
As an aside, from this perspective, Wilson's renormalization program is much less mysterious: if you want to hold physics fixed and change your lattice spacing, you'd better change the bare, dimensionless parameters you stuck into your action.
Thanks for the time to write that out. It was very insightful for this armchair physicist.
Thank you!
To be fair, it's a quantum example.
I seem to recall reading that some calculations complexity were dramatically reduced with a new method having something to do with volumes of n-dimensional polyhedra. Can't find it with google because I don't recall enough.
Maybe you are thinking of the amplituhedron [1] which can make calculations of interaction amplitudes much easier than summing up a large number Feynman diagram.
[1] https://en.wikipedia.org/wiki/Amplituhedron
[1] https://en.wikipedia.org/wiki/Amplituhedron
That's it I think. No infinite nesting of diagrams for virtual particles.
[deleted]
It is due to computing resources. LQCD calculations consume a large fraction of all the world's supercomputing, and there's never enough to go around.
The procedure is essentially an evaluation of a millions-of-dimensions-large integral via Markov-chain Monte Carlo. Each step in the Markov chain requires inverting extremely large ill-conditioned matrices, which we can make better-conditioned by moving away from physical parameters (and then trying to extrapolate). People are glad to have only hundreds or thousands of independent samples in an ensemble. You need ensembles for multiple lattice spacings and spatial volumes in order to ensure you can control your discretization and finite-volume artifacts when you extrapolate to the continuum and to infinite volume.
What is generated in the Markov chain is essentially the configurations of the gluons and quark loops. With these configurations in hand we can measure physical observables on each.
Observables with baryons have an exponentially bad signal-to-noise problem in the temporal direction (time on the grid, not Monte Carlo time) and you either need an exponentially large computer, an exponentially long time, or an exponentially wealthy funding agency. There are attempts to circumvent this issue, we'll see how successful they prove...
The procedure is essentially an evaluation of a millions-of-dimensions-large integral via Markov-chain Monte Carlo. Each step in the Markov chain requires inverting extremely large ill-conditioned matrices, which we can make better-conditioned by moving away from physical parameters (and then trying to extrapolate). People are glad to have only hundreds or thousands of independent samples in an ensemble. You need ensembles for multiple lattice spacings and spatial volumes in order to ensure you can control your discretization and finite-volume artifacts when you extrapolate to the continuum and to infinite volume.
What is generated in the Markov chain is essentially the configurations of the gluons and quark loops. With these configurations in hand we can measure physical observables on each.
Observables with baryons have an exponentially bad signal-to-noise problem in the temporal direction (time on the grid, not Monte Carlo time) and you either need an exponentially large computer, an exponentially long time, or an exponentially wealthy funding agency. There are attempts to circumvent this issue, we'll see how successful they prove...
Is it really necessary to invert those matrices? Often that is possible, but not the best way to find the solution of the problem:
https://www.johndcook.com/blog/2010/01/19/dont-invert-that-m...
Presumably, an ensemble of nuclear theorists, particularly those dedicating their lives to making big LQCD calculations, would avoid inverting large ill-conditioned matrices, if that was a clever thing to do.
I know a few QFT types - they tend to be decently intelligent and mathematically capable. Ok, they're more like wickedly smart...
I know a few QFT types - they tend to be decently intelligent and mathematically capable. Ok, they're more like wickedly smart...
It depends on the computational step. Often we "just" need to compute the determinant, in which case we use a trick. In some other cases, we do only need linear solves. Exact inversion of the whole thing is often prohibitive.
Not a prediction, but comparison with previous work:
Accepted value [1]: µ = 2.792847351 ± 0.000000009
New value: µ = 2.79284734462 ± 0.00000000082
Nice that the new interval completely lies within the old.
I remember from college that there was an important physical constant where a new, more precise measurement was pretty far outside the range of the previous best measurement. I don't remember which one..
I remember from college that there was an important physical constant where a new, more precise measurement was pretty far outside the range of the previous best measurement. I don't remember which one..
I think the story was that the first experiment was borked but done by someone famous, so the new experimenters didn't want to disagree too much.
This happened (allegedly) with the the Millikan oil drop experiment[0] which measured the charge of the electron.
[0] https://en.wikipedia.org/wiki/Oil_drop_experiment
[0] https://en.wikipedia.org/wiki/Oil_drop_experiment
Depending on when you went to college, you may be thinking of the proton radius puzzle https://en.wikipedia.org/wiki/Proton_radius_puzzle which (to gloss over an enormous amount of detail) amounts to tension between two different ways of measuring the same property of the proton.
Other possibilities: Neutron lifetime, Newton's constant (twice!)
This is a case when it's convenient to use the following notation:
Accepted value: µ = 2.792847351(9)
New value: µ = 2.79284734462(82)What's that notation called, and how does it work when digits overlap, e.g. in
0.123±0.004In your example one writes 0.123(4). I don't know what the notation is called, but it's discussed here: https://en.wikipedia.org/wiki/Uncertainty#Measurements
Makes sense, thanks.
> Doesn't seem to mention how this value agrees or not with predictions
I don't think there are any theoretical predictions with anywhere close to this level of precision for nucleons.
I don't think there are any theoretical predictions with anywhere close to this level of precision for nucleons.
The main interesting thing about a high-precision measurement of the proton's magnetic moment is to compare the result to the magnetic moment of the antiproton. Depending on your string theory of choice, you should be able to see a difference between those two values. So far, they are identical within the measurement uncertainty.
The proton team (Mooser et al in Mainz) and antiproton team (Ulmer et al at CERN) are collaberating very closely, so any improvement in one apparatus leads to an improvement in the other.
The same groups are closely related to a group (Sturm et al in Mainz/Heidelberg) that measures the magnetic moment of the electron near a nucleus. The measurement precision is even higher, and QED gives predictions of similar precision, so these measurements are used as tests of QED.
The proton team (Mooser et al in Mainz) and antiproton team (Ulmer et al at CERN) are collaberating very closely, so any improvement in one apparatus leads to an improvement in the other.
The same groups are closely related to a group (Sturm et al in Mainz/Heidelberg) that measures the magnetic moment of the electron near a nucleus. The measurement precision is even higher, and QED gives predictions of similar precision, so these measurements are used as tests of QED.
The article specifically mentions precision, but not accuracy.
FTA: ...finding it to be 2.79284734462 plus or minus 0.00000000082 nuclear magnetons...
Ok, physicists can measure this quantity to 10 decimal places and Computer "Scientists" cannot understand the systems _we built_ well enough to reliably measure a 1% speedup.
/sigh
Ok, physicists can measure this quantity to 10 decimal places and Computer "Scientists" cannot understand the systems _we built_ well enough to reliably measure a 1% speedup.
/sigh
That’s because “speedup” is a hard thing to measure of the variance of what you’re trying to measure is more than the accuracy you’re trying to achieve. The comparison doesn’t make sense here: physicists are trying to measure a constant while execution time depends on the input data, system load, etc.
Interestingly enough, even the physical constants are all over the map in terms of their experimental uncertainty. The gravitational constant is only good to around 5 digits.
https://physics.nist.gov/cgi-bin/cuu/Value?bg
https://physics.nist.gov/cgi-bin/cuu/Value?bg
Science in CS is an abused term.
No, computer science is not the same thing as software development. There is a lot of science in computer science, you probably just haven't been exposed to it.
I think there is a lot of math in computer science and not as much science.
Math and logic may be called "formal sciences" as opposed to "natural sciences".
Benchmarking programs is runnimg an empirical experiment. There is a lot of science in computer science.
The systems we built are a lot more complicated than one proton.
The G-2 experiment at Fermilab is coming online soon and they're investigating the Muon's magnetic moment, which is suspected to not match the current predictions