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Comment by sundarurfriend | Hacker News Reader

Ignorant outsider to the field here: I've often heard the claim that quantum mechanics has been verified to amazing accuracy, that its predictions match with reality to the maximum degree that our instrumental precision allows, etc. A 5% difference seems big enough that at least some of our experiments should have error limits less than that. So how is it that this is only now being found, and there's still uncertainty surrounding it?

I feel like I'm missing something fundamental here, and I'd like to know what it is.

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Real physicists can correct me, but here's my understanding of it: if only the electromagnetic force is involved, the numbers provided by QED are amazingly accurate (for example, calculating the magnetic moment of an electron). But when the strong force is involved, as for the radius of the proton, the calculations are much more difficult: you can't calculate what the radius should be.

That's correct. It's very hard to calculate the proton radius ab initio, even with LatticeQCD approaches.

What does "very hard" mean here? e.g., the math is advanced? The calculations are onerous? You need too many potentially risky assumptions? etc.

Good question. According to Wikipedia, Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationally intensive.

Yeah, for form factors at small Q^2, you need large lattices and the convergence isn't very good --> very computational intensive.

I am a LQCD practitioner. “Very hard” means that even with a nontrivial fraction of all the available leadership-class supercomputing in the world we don’t have enough computer power.

Part of this is also that a proton isn't a elementary particle. And in fact it's not only the three quarks typically ascribed; that's just only a little over 1% of it's mass. The rest is a maelstrom of virtual particles.

Defining the radius anything more than extremely statistically runs up against the uncertainty principle of all these constituent particles.

There are lots of different numbers that you can use quantum mechanics to predict. It turns out that the size of the proton is both harder to predict and harder to measure than many of those other numbers.

Meanwhile we can measure the fine structure constant to 12 decimal places (https://en.wikipedia.org/wiki/Electromagnetic_coupling_const...) and that measurement is in very close accord with the predictions of quantum mechanics.

I thought the fine structure constant was primitive: there is no theory arguing what it's value should be.

The fine structure constant can be measured in two different ways.

One is to measure the g-factor of the electron in a Penning trap. This can be related to the fine structure constant using quantum electrodynamics (QED).

The other is to measure the recoil that an atom receives when it absorbs a photon in an atom interferometer. By combining the result with another well known constant, the fine structure constant can be calculated.

The results of both methods agree to 12 digits, which shows that the QED calculations of the electron g-factor are correct on that level.

thanks for clarifying. That makes a lot more sense than GP's phrasing.

Yes, that is rather clearer than what I wrote!

That maximum precision had a confidence interval. The new smaller 5% value is within that confidence interval, which is now also tighter.

That 5% smaller value was between 4 and 7 sigma away from the old value (depending how you average measurements). It's absolutely not within expectation.

Quantum theory has the largest error between theory and prediction (120 orders of magnitude). See https://en.wikipedia.org/wiki/Cosmological_constant_problem

That’s just a back-of-the-envelope calculation. Nobody knows how to do a bone-fide calculation because we don’t have an accepted quantum theory of gravity.

I guess that's why they invented slide rules. I could get within 3 significant digits on a slide rule (and compute the exponent in my head), whereas I guess the margin of this envelope is too small to contain the calculation.

The size of the proton is a very poorly defined measurement.

The amazing accuracy you have read about is the anomalous magnetic moment of the electron, which is a very clear cut measurement.

Well this 5% is the instrument precision.

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