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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?


Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "optical clocks go slower when they're lower" -- Any meaningful, grammatical comparative phrase would still require (one or even more instances of) the word "than". So: "one optical clock went slower than" what ??, measured how ?! (Standard insufficient answer: "Slower than any equal LC.". Standard reply: "Equal by which measure?" Standard insufficient answer: "Equal by separation between their pairs of mirrors." Standard reply: "Separation -- what's that (how to measure)?". On to the PCoincP.)
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "the people who tell you that VSL ideas are untenable are contradicting Einstein" -- The people who tell you that VSL ideas are untenable are contradicting Einstein's statements on VSL (e.g. as referenced). Einstein's own epistemological demands and insights (e.g. as referenced) are contradicting Einstein's statements on VSL! (Why do you think there's still debate after 100 years?) "velocity is the common-usage [...] Read it as speed." -- Fine. How do you propose it ought to be measured?!
Jun
12
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "[...] So if I placed you at the event horizon, you don't fall down." -- Hmm ... I admit that spectators "remaining outside" have the appearance of "things approaching and getting stuck at the EH"; though "it looks" less like, say, "a feather approaching the surface of a pond"; but more like a Rindler horizon that one "sees" when accelerating (constantly, long enough). Well, that's why, especially in RT, we consider proper quantities and characterizations; asking what the participants themselves observed of each other, and derive/measure from that, in mutual agreement.
Jun
12
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Now, Einstein is obviously on record emphasizing the importance of defining "how to measure", but he also acknowledged that some of his efforts remained somewhat "Preliminary, imprecise". And apparently he didn't quite recognize that "his" point-coincidence principle provided just the required final, precise, defensible underpinning of geometric measurement; even though he used it in "his" definition of "simultaneity" (arguably even already in 1905 as the requirement of simultaneity being transitive).
Jun
12
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "people will tell you he gave up this VSL idea in [1911]. He didn't." -- The ref. you gave above indicates that, indeed, around 1919/20, Einstein had not. But people (can) also tell you that "VSL ideas" are plainly untenably to begin with: they fail to consider and to address how "speed" ought to be measured at all; they couldn't even justify and answer for instance whether two constituents of an "embankment" were "at rest to each other", or to quantify if they weren't (other than just being called "two ends of a ruler", out of the blue); they are "classic" in the worst sense.
Jun
11
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Rob Jeffries: "[ plato.stanford.edu/entries/spacetime-holearg ] Sec. 1 begins by discussing coordinates and "4-D manifolds"?" -- Math as such is manageable, isn't it. But did you get to read the Section on Physics/Geometry/GR (8.2)?: "finally {Einstein} published what John Stachel calls the “point-coincidence argument.” This argument, well known from Einstein's (1916, p.117) review of his general theory of R, amounts to a defense of Leibniz equivalence. He urges that the physical content of a theory is exhausted by the catalog of the spacetime coincidences it licenses."
Jun
11
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Rob Jeffries: "If you could arrange for a clock to be stationary at the EH (you can't)" -- Case closed. (As far as @John Duffield's above remark is concerned; I'll respond to him elsewhere.) "[...] seen from the diagrams I've drawn". -- I already wrote that they're useful for what they're worth. Now, I'm pondering how to fit in 2 or 3 of those
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Rob Jeffries: "[A ticking light clock is not at the EH.] is not true for a falling observer." -- That's at least my reading of your statement. Should this be a mis-representation then I apologize; clarify in any case, please. My understanding: if and while constituents of a light clock are "falling" then they cannot (strictly) be said to have been "at" the EH; but (merely) "having been passing through" the EH. (Sorry for spamming "your" correspondence.) "GR is all about Coord-Ss" -- Eventually even Einstein thought otherwise.
Jun
10
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v3.14159265: Extraneous HTML source code removed. (Point kept.))
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
@Kyle Kanos: "this Meta.SE post ["Can we clarify to the OP that their Q is not yet closed and the Ds are only suggestions?" (M^SE/q/250922)]" -- Well, I do find it incredibly irretating that (perfectly civil) submissions to SE would have to face being closed; instead of being (merely) suitably redirected, or tagged, or just being left (with their typically deplorable score) as examples calling for improvement. And feeling pressed to accomodate repetitive quibbles by pain of having the publication not only of the own question revoked, but even of other contributors' answers and comments.
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
@John Duffield: "A light clock at [the event horizon] doesn't tick." -- Well, sort of, but: therefore anything at the ÉH shouldn't be called "light clock" to begin with. (And it may already be a stretch to speak of "any thing at the EH".) So, A ticking light clock is not at the EH. (And that's a coordinate-free statement.) "John Rennie's answer [...]" -- Well, I've generally stopped paying much attention to John Rennie's contributions since he seems pre-occupied with coordinates, coordinate speeds, manifolds, and somesuch; and he has been (practically) always irresponsive about that.
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "what Einstein said is clear." -- What Einstein wrote is on record (apparently; as far as reasonable) and now thankfully even free online. Unfortunately, but naturally however, Einstein's writings seem rather to show some development and even inconsistencies and changes of arguments and opinon, rather than one consistent treatment and testament. Therefore the exegesis in the SEP article and its references. "There's no motion in spacetime because [...]" -- But there's a definition (within GR/SR) of (how to measure) "speed" values (e.g. "of a train wrt. an embankment"), right?
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "Re your hole-argument link, there's no references to what Einstein actually said" -- There's just one explicit reference listed in the SEP article (mentioned above), namely: Einstein, Albert (1916), “The Foundation of the GToR,”; from which I quote tirelessly: "All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more material points.".
Jun
10
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v3.1415926: Edit in response to ... anonymous modifications. Added tag [tag:equivalence-principle].)
Jun
10
revised What is the heaviest stable element in the center of the sun due to Photodisintegration?
added tag "astrophysics"
Jun
10
suggested approved edit on What is the heaviest stable element in the center of the sun due to Photodisintegration?
Jun
10
comment What is the heaviest stable element in the center of the sun due to Photodisintegration?
Related: "Which nucleus is the most resilient against gamma-induced fission?" (PSE/q/119544).
Jun
10
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Rob Jeffries: "Non-radial displacements are outside my expertise." -- Please consider developing such expertise and sharing it by expanding your answer; which would thus become acceptable to me. "I'd guess there would be little difference from [...] ." -- I have a different hunch (though specifically only recently): 4 or 5 participants maintaining "normal relations" amongst each other should have to meet. "coordinates are quite standard" -- But I understand and trust only assertions about coincidence, or sequence. "John's answer" -- @John's missing a few arrows (in his quiver), IMHO.
Jun
9
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "See einsteinpapers.press.princeton.edu/vol7-trans/… " -- Fair enough; but I don't presume that I can understand Einstein where he's discussing coordinates instead of geometry ("space-time propositions") itself, i.e. specificly as it boils down to observations and determinations concerning space-time coincidences. Indeed, Einstein himself seems to have been sufficiently suspicious about any arguments involving coordinates to expound the "point-coincidence argument" instead.
Jun
9
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "the answers with most votes contradict Einstein, who said "the law of the constancy of the speed of light no longer holds, according to the general theory of relativity"." -- I don't find any mentioning of "velocity" (or of "speed") in answers there (PSE/q/187917). And that is sensible, AFAIU (due to the definition of "velocity" requiring "distance between start and finish"; and thus requiring "start and finish" to be at rest wrt. each other, i.e. in a flat region). [contd.]