phenomenologist Mark Goodsell's comments nearly that, summation his argumentation why the number has to cancel. Influenza A virus subtype H5N1 fraction of these problems is plenty to conclude that the Japanese papers are just some mathematical masturbation that yous shouldn't read inward especial because it's a waste materials of time. After some fourth dimension yous pass amongst the paper, yous volition acquire almost sure that they just tried to honour a formula that numerologically agrees amongst the muon anomaly. Gravitational potentials looked attractive to them, they conduct maintain used them, too they cooked (more precisely, kooked) a rationalization afterwards. Well, this query strategy is driven yesteryear random guesses too a wishful thinking too it's non surprising that it fails most of the time.(I handgrip amongst phenomenologist Mark Goodsell, however, who says that this "inverse" approach is oft right because query is a creative process. Of course of study I oft attempt out to guess the large results starting fourth dimension too and hence consummate the "details", too. One just needs to avoid fooling himself.)
But I desire to provide to the title. Defenders of the paper, similar TRF commenter Mike, say us that experiments commonly mensurate lots of coordinate-dependent effects etc. Well, this is the key claim that shows that Mike – too sure others – completely misunderstands the pregnant of the equivalence regulation too approximate symmetries inward modern physics.
The pregnant of coordinate redefinitions inward the full general theory of relativity is that those are the group of local, approximate transformations of that theory too exclusively "invariant" quantities that are independent of these transformations may live measured! Only the invariant quantities are "real". That's genuinely the betoken of the adjectives such equally "invariant". That's how approximate transformations differ from whatsoever other transformation of observable quantities. They're transformations that are purely imaginary too accept house inward the theorist's imagination – or, to a greater extent than precisely, inward the intermediate stages of a theorist's calculation. But the lastly predictions of the experiments are ever coordinate-independent.
In particular, stiff rulers too perfect clocks may exclusively mensurate the proper distances too proper times. It's totally similar amongst the coordinate dependence of other quantities beyond distances too times – too amongst all other approximate invariances inward physics.
The instance of electromagnetism is completely analogous. Electrodynamics has the \(U(1)\) approximate symmetry. The 4-potential \(A_\mu\) transforms equally \[
A_\mu \to A_\mu + \partial_\mu \lambda
\] which is why it depends on the selection of the approximate – or changes after a approximate transformation defined yesteryear the parameter \(\lambda(x,y,z,t)\). That's why experiments can't mensurate it. The selection of \(\lambda\) is upwards to a theorist's complimentary will. You tin pick out whatsoever approximate yous desire too experimenters can't mensurate what yous want. They mensurate the actual object you're thinking about; they don't mensurate your complimentary will.
On the contrary, the electromagnetic acre pull doesn't transform,\[
F_{\mu\nu}\to F_{\mu\nu}.
\] That's why electrical too magnetic fields at a known betoken inward the spacetime may live measured yesteryear experiments – their magnitude may appear on the displays. Also, the Araronov-Bohm experiment may mensurate the integral \(\oint A_\mu dx\) over a contour surrounding a solenoid modulo \(2\pi\). That seemingly depends on \(A_\mu\) but the contour integral of \(A_\mu\) modulo \(2\pi\) (in proper units) is genuinely equally invariant equally \(F_{\mu\nu}\). After all, \(\oint A_\mu dx=\int F\cdot dS\) is the magnetic flux through the contour. And that's why it tin live measured (even if the particle avoids the "bulk" of the contour's interior) – yesteryear looking at the stage shift affecting the location of some interference maxima too minima.
The instance of coordinate dependence is completely analogous. One tin pick out coordinates inward many ways inward GR – they're similar the selection of gauges inward electromagnetism. But the experiments can't mensurate artifacts of a selection of coordinates. They tin exclusively mensurate existent effects – effects that may live discussed inward damage of gauge-invariant (including coordinate-independent) concepts. For example, when LIGO sees seismic noise, the seismic dissonance isn't just an artifact of someone's selection of coordinates. The seismic activity is a genuine fourth dimension dependence of the proper distances betwixt rocks within public – too the "time" inward this judgement could live defined equally some proper time, e.g. 1 measured yesteryear clocks attached to these rocks, too.
I must add together a disclaimer. Coordinates may be defined equally some proper distances too proper times based on some real-world objects. For example, yous may specify a house inward continental Europe (at whatsoever height upwards to kilometers) equally the place's proper distance from a betoken inward Yekaterinburg, inward Reykjavik, too Cairo. Three proper distances \((s_Y, s_R, s_C)\) are a practiced plenty replacement for the Cartesian \((x,y,z)\) – 1 must live careful that such maps aren't ever one-to-one, soundless (for example, points higher upwards too below the airplane of the triangle conduct maintain the same value of the 3 proper distances).
So nosotros could live worried that the 3 rulers – that mensurate proper distances from these 3 cities – are a counterexample to my declaration nearly the coordinate independence of measurable quantities. Experiments straight measured some coordinates. But that's exclusively because nosotros had to define the coordinates to live the proper distances inward the starting fourth dimension place! So the starting fourth dimension stair inward an experiment, the measuring of the proper distances of an object inward Europe from the 3 cities, shouldn't fifty-fifty live considered a measuring yet. It should live considered a calibration. Experiments that probe laws of physics – e.g. a proposed number that depends on the house of Europe – may exclusively laid out 1 time yous mensurate something else on superlative of the 3 proper distances! And Federal Reserve notation that when coordinates are equal to 3 proper distances too experiments mensurate these 3 numbers for an object, it's soundless truthful that "experiments exclusively mensurate invariant quantities". The quantities are both invariant too (someone's especial chosen) coordinates.
So Mike uses lots of the right words from the physicist's toolkit but the deep statements are just wrong. He completely misunderstands the equivalence regulation too approximate symmetries – principles that underlie much of modern physics too allow us to live sure nearly hence many things despite the apparent complexity of many situations too gadgets. One may say lots of things too write Japanese papers but they're virtually guaranteed to live wrong.
The muon \((g-2)\) anomaly hasn't been explained away. Properties of unproblematic particles measured within localized labs cannot depend on the gravitational potential. And fifty-fifty if something depended on the gravitational potential, the Sun's contribution would live dominant. If the equivalence regulation holds – too at that spot are lots of confirmations too reasons to scream back it's truthful – the muon's magnetic 2nd is a universal constant of Nature hence it just cannot depend on the environs (the quantities describing the local gravitational field).
One could soundless live worried that the experimenters who mensurate the muon's magnetic 2nd conduct maintain made a fault too they also included some corrections that depend on the gravitational acre that they shouldn't, too the damage from the Japanese papers should live interpreted equally the "fixes" that subtract these specious corrections. But I don't scream back that this worry is justified because the equivalence regulation says that it's genuinely impossible to see, inward a unopen lab, whether you're within the Earth's gravitational acre or inward outer space.
You tin exclusively mensurate the acceleration (using accelerometers on your smartphone, for example) or the non-uniformities of the acre (if the lab is sufficiently large). But those effects exclusively influence the unproblematic particles to a tiny extent that isn't measurable. So if 1 believes this declaration – or if he believes that the number should live proportional to a gravitational potential – the muon \((g-2)\) experimenters cannot innovate the gravitational-potential-dependent fault fifty-fifty if they wanted.
(Well, if they genuinely wanted, they could just add together the error deliberately. "We desire the muon magnetic 2nd to depend on the gravitational potential, hence nosotros just adjusted the readings from our apparatuses to conduct yous a incorrect result. Our friend is a NASA astronaut too nosotros wanted to brand her too women inward scientific discipline to a greater extent than relevant, hence nosotros added her height to the muon's magnetic moment." Well, I don't scream back that they're doing it. They just ignore the gravitational field-related issues too the basic principles of physics demonstrate why this strategy is consistent too the results are genuinely relevant inward whatsoever gravitational field. It's just incorrect to "adjust" results straight measured inward unopen localized lab yesteryear whatsoever gravitational potentials too similar factors. This disagreement may conduct maintain almost "moral" dimensions. Some people would desire the experimenters to add together lots of corrections which makes it "very scientific", they think. But inward practiced science, experimenters never add together corrections of the type they don't fully sympathise or they don't fully written report – they are supposed to live comprehensible too written report the readings of their displays or procedure them inward ways that they conduct maintain completely mastered too described. In this context, experimenters just never accommodate whatsoever readings yesteryear whatsoever Earth's gravitational corrections too theorists sympathise that too why the results obtained inward this agency are soundless relevant fifty-fifty exterior Earth's gravitational field.)
In some wide sense, the same comments apply to global symmetries, too. The special theory of relativity has the Lorentz too Poincaré symmetries. The Lorentz symmetry (a modern deformation of the Galilean symmetry) guarantees that yous can't experimentally create upwards one's hear whether the educate where yous perform your experiments is moving. So if somebody measured the muon magnetic 2nd within a uniformly moving train, he couldn't mensurate whatsoever damage proportional to the educate speed \(v\) fifty-fifty if he wanted! That's just impossible yesteryear the symmetry – yous just can't meet whatsoever \(v\) or a non-trivial role of \(v\) on your experimental apparatuses' display.
You could exclusively mensurate \(v\) or things that depend on \(v\) if yous did something amongst results of experiments done both inside the moving train too inside the railway station – too on superlative of that, these 2 labs (static too moving) would conduct maintain to interact or communicate amongst each other inward some way. The muon experimenters (and their colleagues whose results needed to live relied upon) haven't done whatsoever experiment exterior the Earth's gravitational acre where \(\phi\approx 0\), I think, hence they couldn't conduct maintain made whatsoever comparing similar that, which is why their results – functions of readings on their displays – just can't depend on \(\phi\). Again, the argue is analogous to the argue why the experiments done inward the educate cannot depend on the educate speed.
These are some really general, basic, precious principles underlying modern physics. Every practiced theoretical physicist loves them, knows them, too appreciates them (and appreciates Albert Einstein who has genuinely brought us this new, powerful agency of thinking that's been extended inward hence many amazing ways). The Japanese papers are an instance of ambitious piece of occupation yesteryear self-confident people who don't know these rudiments of modern theoretical physics too who desire to pretend that it doesn't matter. But it does affair a slap-up deal. When it comes to the framing of the papers yesteryear many, the papers aren't anything else than just some other attempted assault on theoretical physics equally a discipline. Look how stupid the theoretical physicists are, using all the overly complex mathematical formalism too overlooking the obvious things that may live discussed using the undergraduate formalism. (Tommaso Dorigo makes this excited claim inward betwixt the lines too a reader of his weblog makes it explicitly.) Except that the graduate schoolhouse formalism is needed to hash out the magnetic moments of leptons at the state-of-the-art precision.
And after all, it's fifty-fifty untrue that the professional person particle physicists – amongst their Feynman diagrams too loops etc. – are making things to a greater extent than complicated than they bespeak to live too than the Japanese folks. Unlike the Japanese men too similar folks, the competent theoretical particle physicists maximally utilize the deep principles such equally symmetries that greatly simplify situations too calculations. It's genuinely the Japanese men who dedicate dozens of pages to the calculation of an number that is known to live null yesteryear a straightforward symmetry-based argument!
In other words, if yous don't know the tools of mathematics too modern theoretical physics, you're jump to pass most of your fourth dimension yesteryear existence lost within seemingly complicated materials too expressions that the competent folks right away meet to equal null – or some other simple value (and you're almost guaranteed to do lots of errors inward that context). Competent theoretical physicists soundless pass lots of fourth dimension amongst complicated stuff, but that's because everything that could live conduct maintain been simplified has been simplified.
If yous desire to live a practiced or at to the lowest degree decent theoretical physicist, yous just bespeak to larn those methods too principles too yous bespeak to larn them properly. If yous scream back that experiments "usually mensurate gauge-variant or coordinate-dependent quantities", yous conduct maintain learned almost null from modern physics yet.