Re: [math-fun] Dimensional analysis (was Re: Gimbal lock??)
Brad Klee <bradklee@gmail.com> wrote:
I alluded to metrology of SI by mentioning Caesium hyperfine. This is a justification for projective formalism: there is an agreed upon standard for how to set absolute value 1 in each dimension.
Right. Time is really several similar but subtly different concepts. The cesium clock pins down which one we're using. Also, the time of day is given, not just by any cesium clock, but only by one on the geoid (roughly speaking, at mean sea level). In principle, time as measured by each of the four forces could be different, in which case the cesium clock implies we're using time based on the electromagnetic force. Similarly, the original definition of the gram implied that "pure water" is well defined. Actually, it can have a varying isotopic composition, hence a range of densities.
As for time dependence of fine structure, Ralston discusses this in his article on Planck?s constant:
https://arxiv.org/abs/1203.5557 ( worth the time to read )
He was against the recent decision to fix Planck?s constant.
I could make no sense of that paper. I can't figure out what he means by abolishing the Planck constant. Setting it to 1? The Planck system of units does exactly that, as it sets it, c, G, and k-sub-B to 1. But its usefulness is limited by the low precision to which G is known, and by the inconvenient sizes of most units. Obviously the Planck constant can't be set to 1 within SI, as that would radically change the sizes of lots of units. Perhaps he means it should be regarded as dimensionless? That would make action and angular momentum dimensionless, meaning that energy and frequency would be considered the same thing. And so would distance and momentum. That doesn't sound useful to me. Anyhow, the Planck constant would still exist, though it would become a mere conversion factor, the number of hertz in a joule, like the number of feet in a mile. If he's arguing that its numerical value is arbitrary, a mere artifact of our system of units, I don't know of anyone who disagrees. He argues that if it was abolished, other constants could be determined better. But that's exactly what the 2019 SI changes did, and a large part of why they were adopted. And you say he was against those changes. Not having gone to college, I'm reluctant to argue with people with doctorates, especially doctorates in hard sciences. Does the fact that he misspells Rydberg and calls Kelvins "degrees Kelvin" count against him, or does it just mean I have the soul of a proofreader? So, is he confused, or am I? If the latter, can someone explain his central thesis to me? Thanks.
Hi Keith, If you haven't gone to college, shouldn't you be more inclined to argue with the entitlement crowd? What gives them the right to vote and not you? The gist of Ralston's argument is that classical quantities energy and mass are not useful in the quantum regime, and that they should not appear in formal equations of quantum mechanics, such as Schroedinger equation. Personally, I would have moved some of the content from p.25 up to the introduction, and started with Einstein on the photoelectric effect. The following video shows great design and procedure, and great results: https://www.youtube.com/watch?v=Eyp38Uh38sE However, the analysis is misleading, because the extracted parameter *is not* Planck's constant, rather h/e or the "magnetic flux quantum". Ralston's argument on page 25 says that the flaw in unit handling is even worse. We have "e*V=h*nu" from photoelectric effect and "e*V=h*nu" from more precise hydrogen ionization data. By division, "E2/E1 = nu2/nu1". Now if we measure photoelectric nu2 on a Hydrogen standard nu1, we get photoelectric band gap E2 relative to hydrogen standard E1, *without mentioning Planck's constant*. That is to say, the photo-electric effect is another version of the Rydberg Hydrogen experiment (with a hell of a lot more uncontrolled variables and uncertainties. Also with less of an intelligible level structure.). Once the hangup with photoelectric effect is sidestepped, there is still often an objection about electron mass. This is a concept that makes some amount of sense in terms of the oil drop experiment. Again, this is not a direct measurement of electron mass, it is an inference of electron mass from classical physics involving gravitational and electric fields. Thus the extracted parameter is a mess of other constants besides m_e. Section 2 of the paper does an admirable job showing that Planck's constant (1900) was over-promoted relative to the fine structure constant (Sommerfeld 1916), and and the Compton wavelength (1923). It all drives to the conclusion of equation (24) that: including Planck's constant and electron mass introduces an extra, perhaps delusional, degree of freedom. In electron experiments, we only need Compton wavelength to set scale, and fine structure constant to search through the perturbation hierarchy (alpha as an expansion parameter is discussed in most QM textbooks). This analysis of quantum pre-history doesn't exactly answer the question about generality. If you want to look at other quantum transitions. In general, for each experiment, you need to find a value analogous to Compton wavelength, which sets the overall scale of whatever particular matter waves you are working with. ( These wavelength values would take the place of mass values in the S.E.) The article argues solely for the elimination of Planck's constant, and does not seem to be an endorsement of BIPM, who have decided to keep Planck's constant, and to elevate its importance. Practically speaking, the weight of history is more difficult to ignore than "Le Grand K". We certainly don't want to become holocaust deniers, nor should we ourselves become fascists in an attempt to eradicate any mention of Planck's constant. So it can be conceded, on pragmatic grounds, that the current scenario with h constant achieves the most important experimental goal of improving precision, even if it does not address issues with the formal theory and teaching. --Brad PS. QM has "Symplectic symmetry", so position and momentum are treated as fully equivalent variables. The Schroedinger EQ itself can be written in either position or momentum basis, and nothing much changes. Frequency-valued Hamiltonian functions make sense relative to reams and reams of spectra that have been collected over the years. On Sun, Feb 2, 2020 at 3:55 PM Keith F. Lynch <kfl@keithlynch.net> wrote:
Brad Klee <bradklee@gmail.com> wrote:
I alluded to metrology of SI by mentioning Caesium hyperfine. This is a justification for projective formalism: there is an agreed upon standard for how to set absolute value 1 in each dimension.
Right. Time is really several similar but subtly different concepts. The cesium clock pins down which one we're using. Also, the time of day is given, not just by any cesium clock, but only by one on the geoid (roughly speaking, at mean sea level). In principle, time as measured by each of the four forces could be different, in which case the cesium clock implies we're using time based on the electromagnetic force.
Similarly, the original definition of the gram implied that "pure water" is well defined. Actually, it can have a varying isotopic composition, hence a range of densities.
As for time dependence of fine structure, Ralston discusses this in his article on Planck?s constant:
https://arxiv.org/abs/1203.5557 ( worth the time to read )
He was against the recent decision to fix Planck?s constant.
I could make no sense of that paper. I can't figure out what he means by abolishing the Planck constant. Setting it to 1? The Planck system of units does exactly that, as it sets it, c, G, and k-sub-B to 1. But its usefulness is limited by the low precision to which G is known, and by the inconvenient sizes of most units. Obviously the Planck constant can't be set to 1 within SI, as that would radically change the sizes of lots of units.
Perhaps he means it should be regarded as dimensionless? That would make action and angular momentum dimensionless, meaning that energy and frequency would be considered the same thing. And so would distance and momentum. That doesn't sound useful to me. Anyhow, the Planck constant would still exist, though it would become a mere conversion factor, the number of hertz in a joule, like the number of feet in a mile.
If he's arguing that its numerical value is arbitrary, a mere artifact of our system of units, I don't know of anyone who disagrees.
He argues that if it was abolished, other constants could be determined better. But that's exactly what the 2019 SI changes did, and a large part of why they were adopted. And you say he was against those changes.
Not having gone to college, I'm reluctant to argue with people with doctorates, especially doctorates in hard sciences. Does the fact that he misspells Rydberg and calls Kelvins "degrees Kelvin" count against him, or does it just mean I have the soul of a proofreader?
So, is he confused, or am I? If the latter, can someone explain his central thesis to me? Thanks.
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Keith F. Lynch