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The following questions (in no particular order) which I had submitted have been "removed from PSE for reasons of moderation":

  1. Which geometric relations obtain between two distinct rest systems?

Consider, as a thought experiment, a set of participants who measure throughout the experiment having been at rest to each other; among them explicitly participants ${\mathbf A}$, ${\mathbf B}$ and ${\mathbf F}$ who determine the ratios of their (chronogeometric) distances between each other as real number values $\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}$, $\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}$, and $\frac{{\mathbf A}{\mathbf B}}{{\mathbf B}{\mathbf F}} = \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} / \frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}$.

Further let there be another set of participants (of which neither ${\mathbf A}$, nor ${\mathbf B}$, nor ${\mathbf F}$ are a member) who measure throughout the experiment having been at rest to each other as well; among them ${\mathbf J}$, ${\mathbf K}$ and ${\mathbf Q}$, who determine the ratios of their (chronogeometric) distances between each other as real number values $\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}$, $\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}$, and $\frac{{\mathbf J}{\mathbf K}}{{\mathbf K}{\mathbf Q}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} / \frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}$,

such that

  • ${\mathbf J}$ passed ${\mathbf A}$, then passed ${\mathbf B}$,

  • ${\mathbf A}$ passed ${\mathbf J}$, then passed ${\mathbf K}$,

  • ${\mathbf Q}$ passed ${\mathbf F}$, in coincidence with ${\mathbf Q}$ and ${\mathbf F}$ observing ${\mathbf J}$ and ${\mathbf A}$ having passed each other,

  • ${\mathbf B}$ and ${\mathbf F}$ determined that ${\mathbf B}$'s indication of the passage of ${\mathbf J}$ was simultaneous to ${\mathbf F}$'s indication of the passage of ${\mathbf Q}$, and

  • ${\mathbf K}$ and ${\mathbf Q}$ determined that ${\mathbf K}$'s indication of the passage of ${\mathbf A}$ was simultaneous to ${\mathbf Q}$'s indication of the passage of ${\mathbf F}$.

Question:
Is thereby guaranteed that for these distance ratios obtains

(1)
$\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}$ ?,

and (moreover)

(2)
$\left( \left(\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}\right)^2 + 1 - \left(\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}\right)^2 \right) \left( \left(\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}\right)^2 + 1 - \left(\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}\right)^2 \right) = 4 \left( 1 - \left( \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} \right) \left( \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} \right) \right)$ ?

Or otherwise:
What could be concluded if (1) and/or (2) were not found satisfied?


May
29
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
"The ruler is essentially a scaled-up H atom" -- If you agree calling (any) one H atom "a ruler" outright (with its unique "Max" and any "Max/e^2" part as two relevant ends/marks) then ... what/how should be "monitored" at all?? "stipulating that the relative size of [distinct] atoms could measurably change" -- In reference to M-W measurement this can at least be contemplated. But less so by "atomic artifact rulers". "I'll be happy for the protocol to fail" -- Which "protocol"? M-W, or "your a/m-ically minded" one? And importantly: What is "failure of a protocol", in your view?
May
29
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Emilio Pisanty: "[...] skim read" -- Apologies; relevant is: each of the H atoms of your "atomistically/metreologically minded ruler" shall have distinguishable parts "Max" and "Max/e^2". And AFAIU you suggest monitoring whether "Max/e^2 parts of neighboring Hs" were coincident. (In principle, "before each trial"; why not during, too. And what do you mean by a "linear arrangement" of several such parts, btw.?) Now: Do "pieces of equipment" which are thus monitored/seleted therefore remain "proportional" in reference to M-W comparison? (Not even to mention anything "atomic" in general.)
May
28
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Emilio Pisanty: "follows from the special considerations I took regarding my ruler." -- Such as? Considerations ("diligence") applicable in each individual trial?, or (only) expectations extrapolating previous trials? "not really achievable by a mere change in $\alpha$." -- That's considering just one "known unknown" (dismissing its "being responsible by itself"). But what about any/all "unknown unknowns" (wisely mentioned elsewhere), and even any/all other "known unknowns"?? "(The alternative is that not all hydrogen atoms are alike.)" -- Some being "ends"; some "bulk" etc.
May
28
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Emilio Pisanty: "if my ruler has "shrunk" then so have I (as I'm made of atoms) and so has every piece of equipment in my lab and elsewhere on Earth." -- How so?? Different artefacts (you, "your ruler", other "pieces of equipment") which have no relation with each other except for all being in turn made/constituated "of atoms" don't necessarily have any particular geometric relations with each other at all. There's surely no expectation that they should remain "proportional" to each other, trial by trial. (But in the exceptional case that they all did you may call them "undisturbed".)
May
28
answered Is it possible to speak about changes in a physical constant which is not dimensionless?
May
27
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Emilio Pisanty: "I have little to add beyond recommending a thorough reading of Duff and Duff, Okun and Veneziano." -- Having done so (already almost when those arXiv "preprints" had appeared), I'm still and again struck that they don't even seem to consider the solution provided by Einstein (Kretschmann?, Comstock?, Poincaré? ...) in the guise of "point coincidence"; much less endorse and promote it (as I try to do). Now: How to turn this observation into a PSE question? ...
May
27
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
@Emilio Pisanty: "[...] you have failed to meaningfully engage with the kernel of my contributions." -- Well, I've been focussing on what's my own kernel of interest and competence. (It would perhaps have led too far afield to ask you further e.g. "How is the ground state of a Cs133 atom defined?".) And it seems you're not intending to address my rather urgent (return-) question ("How so??") either. Since PSE is about asking questions: I'm quite confident that I'll succeed, too, in extracting some from "the Marzke-Wheeler article (1964)" (which I haven't gotten a hold of yet, however).
May
27
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Now, our epistemiological preference is arguably to base such methods on determinations of "coincidence" vs. "non-coincidence" ("sequence"). This leads to the "chrono-geometric" definition of "distance" (as finally spelt out by Sýnge, but arguably already recognized by Einstein) as equivalent to the (mutually agreed) half ping duration (half "signal roundtrip" duration) of participants who were and remained at rest to each other; conventionally (just for the purpose of distinction from any other durations) with a purely formal/symbolic non-zero prefix "$c_0$". Which cannot "change by 10 %".
May
27
comment Is it possible to speak about changes in a physical constant which is not dimensionless?
Emilio Pisanty: "[...] examples?" -- I sketched two in the preceding comment. You seem to be (sort of) discussing one already: "you can only set $c=1$ if you have solid empirical evidence that the speed of light is constant and independent of e.g. the relative speed of the source and the detector.)" -- Well, there would have to be a (comprehensible/communicable/reproducible) method declared how to gather solid empirical evidence (how to measure) "speed" in the first place. (Related: How to measure whether e.g. source and the detector had been "at rest" wrt. each other.) [contd.]
May
27
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
4, 6: "Your perspective ("$c$ is constant") [...] The other [...] (atomic time is constant) [...] Epistemologically, they are on equal grounds." -- I disagree: There seem no "unknown unknowns" when it comes to plainly comprehending the notion (and communicating findings) of "coincidence" vs. "non-coincidence". In contrast, assertions such as "all the lightest charged leptons always have exactly equal charge" are empirical; model dependent. "you have decoupled the speed of light from that symbol." -- How so?? With the usual definitions follows: $c_0$ is identified as "signal front speed".
May
27
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
"You simply cannot postulate that the mirrors are on exact geodesics" -- Well, the problem is rather: Is there any ("operational") method at all for determining whether a given mirror had been "(sufficiently) exactly on a geodesic", or not?; i.e. some method based explicitly and exclusively on determinations of coincidence, or sequence. (I, for one, have been unable to recognize such a method being described explicitly in MTW. I can only presume that it can be constructed nevertheless; motivated mainly by Einstein's quoted assertion.)
May
27
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
3, 5: "The mirrors in your MTW implementation [...] In practice there are fundamental limits to contend with, starting with the radiation pressure on them." -- Again, foremost, there's no strict need of an actual implementation. The Marzke-Wheeler construction may already be useful as idealized reference (similar to the "0 K" reference, or the notion of "inertial frames"). Applicable mirrors appear indeed less "magical" than "caesium 133 atoms at 0 K" because it is at least imaginable that the relevant "radiation pressure" might be found suitably compensated ("due to other reasons").
May
27
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
@Emilio Pisanty: Thanks for your comments which I'll try to address point by point in my following four (total). (There seems no related need for me to edit my answer; but I've added two "Notes" which may provide more perspective.) 1, 2:"why you're so hung up about the mention of blackbody radiation." -- Several reasons: The SI definition is mentioning it explicitly; it provides an example where reference to an idealization is sensible and acceptable even if it cannot be found/implemented at all; and: the notion "ground state of the caesium 133 atom" seems now even more difficult to me.
May
27
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
(v3.141: Removed in appropriate tag "[tag:time]"; restoration of the appropriate tag "[tag:duration]" is pending.)
May
27
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
(v3.14: Added two "Notes (p.s.)". Also: (trying to) restore the appropriate tag "[tag:duration]".)
May
26
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
Emilio Pisanty: Please consider this answer my attempt at a reply to several issues raised in your answer here, and in related comments. (Of course I'd welcome you commenting there in turn.) p.s. "I expect you to do your due diligence and check whether I have edited my answer when I say I have." -- I certainly agree to that. But I note, as a final remark on this curious matter, that there is no explicit mentioning of "your answer" in the comments following my OP question. And I apologize for not having been dilligent above and beyond that.
May
26
answered Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
May
22
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
p.s. On first looks this answer of yours, especially the "Addendum" seems very interesting, thoughtful, substantial, and ... well ... very much debatable/contestable. (Indeed closely along the lines of physics.stackexchange.com/q/78684 where I put my two cents already). Indeed too interesting for me to get hung up too much about your preceding comment. (And, therefore, it may take rather until mid next week to express a reply; perhaps best in form of an own separate answer to my question; of which I plan to notify you explicitly, because, thankfully, you seem interested in the Physics.)
May
22
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
Emilio Pisanty: "Yes, that was intentional." -- Are you suggesting that I was lying in my preceding comment, and/or that I didn't in good conscience carry our correspondence right below the OP question since yesterday?? (<outrage streniously suppressed>) Well, no. Think again about the working conditions and habits of PSE contributors. I had been curious (and I had asked) when you mentioned "your edit" the first time (I considered whether you had referred again to that); the second time "your edit" came up I discovered this answer here right away.
May
21
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
Emilio Pisanty: Very sorry, only just now I noticed that you had posted this lengthy answer. (Btw., AFAIU its URL is specificly " physics.stackexchange.com/a/184999 "). So, thanks for that; I'll need to take a while to read it ... And, due to weekend etc. I may be able to submit some additional comment (as I surely may want to) only late on Monday.