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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?


Aug
28
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 ...)
Aug
28
asked How to express Allan variance without neglecting clock drift
Aug
27
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.
Aug
26
revised Two clocks along different worldlines
edited tags: adding the tag `duration` ((Note that "duration" is the relevant term being used in at least one answer and in comments by several users).
Aug
26
suggested suggested edit on Two clocks along different worldlines
Aug
26
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
edited tags: restored the tag `duration` (Note that "duration" is the relevant term being used in the OP question as well as in the quote; while "time" is not).
Aug
26
comment Two clocks along different worldlines
Void: "stopwatches have a display which shows duration elapsed between certain events." -- Stopwatches I know about have displays indicating numbers. (ints, rationals,...) What do you propose those numbers might have to do with durations (of that stopwatch, between indication pairs)? And: do you suppose this was specified by the OP question?? "any kind of physical watch based on a physical principle will show less time elapsed when in the runners pocket." -- No: only clock pairs of equal proper rates. So: how to compare in the first place?.
Aug
26
comment Two clocks along different worldlines
Void: "The friend at home has established a coordinate system wrt. himself [...]" -- Why sprinkle any coordinate tuples on the setup at all?! Surely the (suitable) friend and suitable "(mutually static)" landmarks may determine (from the ratios of their mutual ping duations) ratios of their "distances" between each other; and surely the (magnitude of the) quantity $v$ of your answer represents speed, not just some "coordinate speed"? "[...] if someone else measured the distance, the result might be different" -- ?? Is "distance" not a proper attribute of suitable two landmarks?
Aug
26
comment Two clocks along different worldlines
Void: "[...] landmarks [...]" -- Ah, right: landmarks. (Or by MTW's terminology of Box 13.1: "principal identifiable points".) Surely landmarks such as "the friend's home"; or even that friend him/her/itself; or even "the traveller", too. "sending signals to landmarks he has observed as static and measuring the time delay of the returning signal." -- How should be defined/determined which landmarks had been (mutually?) "observed as static", or not? By measuring whether the (mutual) "time delays" (a.k.a. "ping durations") had been constant, or not? [comment parts 2 and 3 to follow]
Aug
26
comment Two clocks along different worldlines
Void: "Ok, so you start [...] when you arrive home again [...] compare your times. Your proper running time" -- ... a.k.a. "your duration (from start indication until arrival indication)" ... -- "will be [...] $\sqrt{0.75} ~ (t_2 - t_1)$" -- Rather: $\sqrt{0.75} \simeq 0.87$ of the duration of the stay-at-home friend from his indication of your departure until his indication of your return. "your stopwatch would show $0.87$ times less runtime than the stopwatch left at home." -- What should the durations have to do with what these stopwatches "show"?? Are they supposed to be good??
Aug
26
comment Two clocks along different worldlines
Void: "a friend staying at home measuring the time and observing you [...] his measure of distance $x$" -- Distance of that "friend staying at home" with respect to whom? (Do you claim that the geometric and/or kinematic relation of "a friend staying at home" and some specific "travelling protagonist" could be characterized in terms of a "measure of distance $x$"? Or are there additional participants involved which you haven't named explicitly yet?) [to be continued]
Aug
25
comment Experimental Verification of No Special Frames of Reference
@Nikos M.: "same can be said for Newtonian/Galilean relativity as an axiomatic system" -- How so?, What's axiomatic about "Newtonian/Galilean relativity"?? Einstein's axiomatic notion ("being able to distinguish and decide about who coincided, or not") is presumed applicable and unambiguously understandable to each and every particpant; and the definitions of (how to measure) kinematic relations between participants in RT (namely "joint membership in an inertial frame", "distance ratios", "speed values $\beta$") are to be expressed in terms of that one basic axiomatic notion.