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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?


11h
comment Can Allan variance be generalized such that the “Oscillator model” is not presumed?
+1, I certainly recognize some step towards answering my question. "the same reason that the conventional variance is not a good measure for processes that do not, at least approximately, follow a normal distribution." -- Now it'd be helpful to quantify your notions "good" and "approximately". (Unfortunately, I know next to nothing about statistics; yet.) "applications that I had to deal with" -- You might also be qualified and interested in addressing my question "How to express Allan variance without neglecting clock drift" (PSE/q/132970).
11h
comment “Delayed choice” quantum imaging experiment - why wouldn't it work?
Nathaniel: "thanks!" -- You bet! "Without a subscription I can see the figure, but I can only read the first line or so of its caption." -- Right, me neither. And the figure is shown so damn small that I can't quite make out the labelling either. So, we got to be thankful for what Nature put on their webpage; allowing us to figure out the essentials of the experiment. But perhaps someone could kindly point us to a public/arxiv version of the write-up ... "So I guess that pretty much answers my question." -- As I expected. (Seems always the same trivial question in various guises ...)
21h
comment “Delayed choice” quantum imaging experiment - why wouldn't it work?
It should be instructive to look at the "Schematic of the experiment.", i.e. Figure 1 of the corresponding article "Quantum imaging with undetected photons", G. B. Lemos et al., Nature 512, 409-412 (28 August 2014), which is available online at nature.com/nature/journal/v512/n7515/full/nature13586.html Apparently for any one event $A$ in which the object (cardboard cat) is illuminated, and for the corresponding event $B$ in which some screen element is illuminated, event $B$ is either within, or certainly at least on, the forward lightcone of $A$.
1d
comment Difference between Urca process and $\beta$-decay in neutron stars cooling
Py-ser: "Now, the general expression for the Urca process is: $B_1 \rightarrow B_2 + l + \overline\nu$" -- No; but the general expression for the Urca process is (as far as I understand) instead rather: $$\left\{\sum_{k=1}^N B_k\right\}_{\text{energetic}} \rightarrow \left\{\left(\sum_{k=1}^{N-1} B_k\right) + B_{\text{trans}}\right\} + \ell + \overline\nu \rightarrow \left\{\sum_{k = 1}^N B_k\right\}_{\text{relaxed}} + \overline\nu + \nu,$$ or the conjugate, where in the transition step there appears a $\overline\ell$ together with a $\nu$. (The Wikipedia could be improved correspondingly.)
1d
asked Can Allan variance be generalized such that the “Oscillator model” is not presumed?
1d
comment Two clocks along different worldlines
@Jim: "you were continuing apace at your initial level of speech after several subtextual requests to "tone it down"." -- "Subtext" seems kinda hard to quantify; but I certainly wouldn't disagree with your assessment. Now: What about my untiring subtextual requests to "tone it <expletive_conciliatorily_suppressed> up" ?!? ... "[...] a warning" -- Yeah, thanks. (I had looked up "things Socratic", and not for the first time, after user Void's latest comment. &)
1d
comment Two clocks along different worldlines
@Jim: "think you misinterpreted me. [...] you were being too "formal"" -- Not to worry: I think this was exactly the interpretation based on which I wrote my preceding comment. (The word "too" being perfectly unambiguous; and I'm not quite sure about what you meant by "formal". But I like to believe it refers especially to the catch phrase in our other correspondence above following the OP question.) p.s. Apologies for "cluttering Void's and/or user41616's comment space": If only there were some other more appropriate public and archived venue on PSE ... [to be continued]
1d
comment Two clocks along different worldlines
@Jim: "[...] reluctance to appeal succinctly to your co-conversant's expected level of formality" -- I strive to be as "formal" as I can reasonably muster, because public archived correspondence is not just addressing the incidental co-conversant(s) but posterity; and less "formal" terminology may be established, if desirable. "[...] becomes offensive." -- I consider it my courtesy (even obligation, as a physicst) that I do ask for "formal" underpinnings of incidental terminology. That seems less offensive than presuming outright that co-conversants were "not even wrong".
2d
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
p.p.s. I appreciate that you let your answer stand despite my criticism; thus allowing my comments to stand.
2d
revised How to express Allan variance without neglecting clock drift
(v3.14: trying to optimize the appearance on the http://physics.stackexchange.com/questions page ...)
2d
asked How to express Allan variance without neglecting clock drift
2d
comment Two clocks along different worldlines
@Jim: "I agree." -- Splendid. ... Now, considering again the recent answer below and subsequent follow-up questions and responses would it be too much asked for user Void to kindly weigh in? ...
Aug
27
comment Two clocks along different worldlines
@Jim: "Einstein probably recognized his own insight, but he wrote with such effective simplicity in his works that most of almost everyone could understand exactly what he was saying." -- This seems rather questionable; hence the OP's question and related activities, such as our's. But the relevant, grokable subject matter of "(being able to judge) coincidence (vs. sequence)" had surely been communicated effectively as: If the observer perceives the two flashes of lightning at the same time, then ...
Aug
27
comment Two clocks along different worldlines
@Jim: ""not even the OP may know what the OP meant". This seems rather questionable." -- I'll assume you understand that the sentence tail you quoted from my comment above is to be understood together with its sentence head: "Without such a foundation [...]". "given that the meaning is subjective to intent [...]" -- True. I should rephrase/correct myself: Without such a foundation (as that of Einstein, linked above) not even the OP may know what the OP meant, apart of the basic (baby-like!) intent of wanting to grasp at something outside the OP's present reach. [to be continued].
Aug
26
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
p.s. Btw., some more or less rigorous derivation of how to "correct for the shift due to ambient radiation" might be gathered for instance from "Black Body Radiation Shift of the 133Cs Hyperfine Transition Frequency". But, again, that's not at all what I like to know ...
Aug
26
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
Ben Crowell: "I don't know if I'm right, but here is an attempt to estimate one effect that might be relevant." -- Well, you've completely missed the intended point of my question ... Perhaps it's helpful to contrast rather symbolically: Your answer seems to be concerned with "reasoning out" $$\frac{\partial}{\partial~T}[~f~]~|_{~T =0~ \text K,~f = f_S} \times (T - 0~\text K) $$ while I like to know about (how to determine experimentally) $$f - f_S,$$ where $f_S$ denotes the "standard transition frequency of a plainly and exactly unperturbed Cs133 atom", and $f$ is "of the given sample".
Aug
26
comment Two clocks along different worldlines
@Jim: "I am sure the usage of the term "good clock" has interpretations that allow you to point out ambiguities in any statement [...]" -- It's indeed frustrating that not even you seem to appreciate Einstein's insight that All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more recognizable material points. Without such a foundation not even the OP may know what the OP meant, if anything specific at all.
Aug
26
comment Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
@Ben Crowell: "This seems like two different questions to me." -- Well: the present OP question text contains (even) three separate question marks. "Most of the question is about the perturbing effect of blackbody radiation" -- Not at all. I'll accept for the purpose of my question that "the perturbing effect of blackbody radiation" is settled, e.g. with results as seen in arxiv.org/abs/1107.2412 (Tab. 2). Instead, I am (only) trying to ask about "the perturbing effect of anything else" not listed e.g. in that table. Is that called "(due to) anomalous (reasons)"?
Aug
26
comment Two clocks along different worldlines
Void: "Is there something you want to actually clarify [...]" -- Yes, of course, namely: Whether questions which occur to me in consideration of your answer (in its present version) and your subsequent responses would lead you to reconsider and rework your answer to the OP question; and how. This could obviously only be answered by you yourself.
Aug
26
comment Two clocks along different worldlines
@Jim: "from context, it is easy to see that the clocks are assumed ideal for the purpose of the question." -- If the OP made any such possible assumptions explicity they might be easier, more reliable "to see", IMHO. Either way: any two "ideal clocks" e.g. as defined via MTW Box 16.4 do not necessarily have equal proper "tick" rates. "focusing on whether they remain good and the like falls under the umbrella of not seeing the forest for the trees" -- The focus is strictly conceptual: What it means (how to measure) in the first place whether two given clocks had been equal.