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The following questions (in no particular order) which I had submitted have been "Deleted by Community":

2. Is average speed an invariant?

Is the value of average speed an invariant?,
specificly the value of the average speed, with respect to suitable(1) specific participants, say $P$ and $Q$, of some specific participant, say $A$, as $A$ moved from $P$ and $Q$?

Expressing the value of the average speed of $A$ wrt. $P$ and $Q$ as

$$v_{PQ}[~A~] := c~\beta_{PQ}[~A~],$$

where $c$ denotes the signal front speed, and $\beta_{PQ}[~A~]$ is a specific real number,
and where the average refers to the trial from $P$ and $A$ having departed from each other until $P$ and $A$ having reached each other,
does the value of $\beta_{PQ}[~A~]$ depend on the assignment of coordinate values to the relevant unique events $\varepsilon_{AP}$ and $\varepsilon_{AQ}$ (and/or to other events)?

Does the real-number value $\beta_{PQ}[~A~]$ change if coordinate values which are assigned to event $\varepsilon_{AP}$ are being changed, or if coordinate values which are assigned to event $\varepsilon_{AQ}$ are being changed?

Note also, that the real-number value $\beta_{PQ}[~A~]$ can be expressed in terms of intervals "between" certain pairs of the relevant events, e.g.

$$\beta_{PQ}[~A~] = \frac{s^2[~\varepsilon_{AP}, \varepsilon_{AQ}~] - s^2[~\varepsilon_{FQ}, \varepsilon_{AQ}~]}{s^2[~\varepsilon_{AP}, \varepsilon_{AQ}~] + s^2[~\varepsilon_{FQ}, \varepsilon_{AQ}~]},$$

where event $\varepsilon_{FQ}$ denotes the (unique) event of the future ("forward") light cone of event $\varepsilon_{AP}$ in which $Q$ took part (in coincidence with some suitable participant $F$); and that (presumably) the values of intervals are invariant.

(1: Specifily, $P$ and $Q$ remaining separate and at rest with respect to each other; i.e. constituting members of an inertial system in the sense of Rindler: "simply an infinite set of point particles sitting still in space relative to each other".)


Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Look: you seem to have a (rarely used) Wordpress blog; and me, too. I wouldn't mind continuing our debate by those, less limited means. For here and now, I rather concentrate on working out my answer which is a bit complicated, however. Note, btw., that neither there nor in my OP question is any mentioning of "speed".
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "David Wineland of NIST: "[...] when we compare clocks, if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at."" -- Indeed, Nobel Prize winner David Wineland of NIST said so. What a shame he didn't say properly that, if (we have measured that) one clock in one lab is 30 centimeters higher than the clock in the other lab, then we (must) take this (result) into account when trying to compare the (proper) rates at which they run (separately); at the level of their precision NIST has reached.
Jun
13
comment Closed timelike curves in the region beyond the ring singularity in the maximal Kerr spacetime
Timaeus: "[...] a Penrose Diagram as above [...] but the Schwarzschild singularity is [...]" -- I note that the diagram you included contains a mis-spelling of the surname of Karl Schwarzschild. Please consider including the diagram in editable form, e.g. using the appropriate MathJax commands, so it may be edited accordingly. (Also, this might help in distinctly denoting certain vertices in the diagram, for further reference.)
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).