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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
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.
Aug
25
comment a thought experiment in special relativity theory
@Minimus Heximus: "I think I have to give up. [...] opinions about what'll happen in this experiment. Just a real experiment can be trusted." -- In science it holds, as Bohr put it: "that in each case we must be able to communicate to others what we have done and what we have learned"; and Einstein has provided the necessary means as far as RT is concerned, namely the basic notion ("coincidence") which may be considered sufficiently self-evident and unambiguous. So don't give up on that!
Aug
24
comment Experimental Verification of No Special Frames of Reference
@Nikos M.: "i like the line of reasoning" -- Alright. "but it should also point to experimental tests of SR/GR, as this is what the question asks for [...]" -- Fair enough; this premise shows especially the leading sentence of your question text ("Certainly, there have been numerous tests of both Special Relativity and General Relativity."). So I just added a corresponding remark. p.s. Sorry, I didn't have the chance to respond earlier to your comment.
Aug
24
revised Experimental Verification of No Special Frames of Reference
(v3.1459: some formatting.)
Aug
24
comment a thought experiment in special relativity theory
@Minimus Heximus [Aug 7 at 3:25]: "I deleted my comments." -- Thanks for letting me and everyone know about that. Myself, however, I prefer my comments to stand; including those I had submitted here prior to Aug 7 at 3:25. (Hope this helps.) p.s. Sorry, I didn't have the chance to respond earlier to your comment of Aug 7 [2014] at 3:25
Aug
24
comment A question about special relativity theory
@Minimus Heximus: "in one write the numbers as observer 1 measures and in the other write the numbers a observer 2 measures." -- But how do you propose that any of the directly involved participants listed in my comment above, or all of them, and/or any others should go about measuring any of those supposed "numbers", in order to determine and to express their geometric relations with each other ?? (That's the whole point of RT!, and presumably of your question, too.) p.s. Sorry, I didn't have the chance to respond earlier to your comment of Aug 6 [2014] at 19:17
Aug
24
comment A question about special relativity theory
@Minimus Heximus: "you can draw the picture twice." -- All participants who are directly involved in the setup (ostensibly: the one ("left") "toucher" of "set No 1", the other ("right") "toucher" of "set No 1", the one ("left") "toucher" of "set No 2" the other ("right") "toucher" of "set No 2", the "lamp of set No 1", the "lamp of set No 2"), should be able to understand and agree on their setup relations with each other; provided either of them has the requisit intellectual capability, "like you and me". (Some may find pictures useful to accomplish that.) [to be contd.]
Aug
8
answered Experimental Verification of No Special Frames of Reference
Aug
7
comment Why doesn't the number of space dimensions equal the number of time dimensions?
@Harold: "You could measure time in metres [...] just multiply by c." -- More congruously: Either, referring to SI units, you can express a number of seconds` as the same number of metres, just multiplied by $c/299458792$. Or, referring to quantites: ping duration between two ends (at rest to each other), times $c/2$, is called distance between these ends. On the OP question: If (at least) one identifiable participant took part in several events, we'd call these events pairwise time-like related, and not space-like related. (A basic distinction; some might call it "asymmetry".)
Aug
6
comment Double-slit-experiment but with unobserved alternating opening of slits. Does an interference pattern still arise?
@Sean: "[...] which relates to determining which slit each electron goes through." -- If the "pattern" recorded by the screen is described as "(most probably) due to" source and screen having been separated by a (potential) barrier with "two slits available alternatingly/incoherently" (i.e. the described setup, AFAIU) and only if that pattern consists of two well-separated "blobs", then we can unambiguously attribute all individual entries in the pattern to the corresponding signal "having gone through" either one slit, or the other. Otherwise we can't make that distinction as strictly
Aug
6
comment Double-slit-experiment but with unobserved alternating opening of slits. Does an interference pattern still arise?
@Sean: "There is no large classical device being used [...]" -- Well, it's not explicitly mentioned in the OP description, but there's usually a "screen", or "detector screen" involved; i.e. a device which is suitably persistent (itself, as well as in relation to the signal source) throughout a sufficient number of individual trials to allow recording "a pattern" (based on which the most probable number and "geometry of slits in the barrier between source and screen" throughout the set of trials may be determined). [to be contd.]