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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?


Mar
4
reviewed No Action Needed Derivation of relativistic uniformly accelerated motion
Mar
4
asked Did a racer on a “restless” course race at some particular average velocity? (1: Starting blocks, finish line moving uniformly wrt. each o.)
Mar
3
comment The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light?
Emilio Pisanty: "This post describes the case where they share unlimited copies of perfectly pure, completely known, maximally entangled states." -- Can the assertion be communicated (foremost between "Alice and Bob") that this particular case did indeed apply in some experimental trial(s) under consideration, rather some other "degraded case"? If so, such communication is not superluminal either. (And I meant that this consideration ougth to be added to what your post describes already.)
Mar
2
awarded  Excavator
Mar
2
comment The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light?
Emilio Pisanty: "[...] The problem with this sort of scheme is that Alice has no control over the results of her measurements, since those are random. [...] To make this more precise, consider the standard case where they share a Bell triplet state" -- The problem is (surely) compounded by the difficulty (even impossibility) for Alice and Bob to find out "soon enough" whether (or to which accuracy) the described "standard case" had indeed been applicable in an actual trial under consideration.
Mar
2
comment A vertical variation of modern versions of Michelson-Morley
aepryus: "In 2003, Müller et al. performed a normal (2 horizontal orthogonal arms) modern MMX using cryogenic optical resonators [... arxiv.org/abs/physics/0305117 ]" -- There (p. 2) it is claimed "In our experiment (Fig. 1), we use two $L = 3 ~ \text{cm}$ long COREs (cryogenic optical resonators)". How did Müller et al. measure whether (or to which accuracy) this setup condition was and remained actually satisfied throughout the trial? (Surely that's not only a worry in case in a "vertical variation" of the setup?)
Mar
2
revised What are the generators of spherical symmetry?
Identified the required at least six characters to correct; arguably legitimately. (No claim of factual accuracy or pertinency implied.)
Mar
2
revised About the complex nature of the wave function?
Identified the required at least six characters to correct legitimately. (No claim of factual accuracy or pertinency.)
Mar
2
suggested suggested edit on What are the generators of spherical symmetry?
Mar
2
suggested suggested edit on About the complex nature of the wave function?
Mar
2
comment “String” infinity paradox
anna v: "[...] predict all possible outcomes of experiments." -- Well, that's seems conjugate to the (true! ;) experimentalist's approach of first ridding oneself entirely of any expectations. "Experimental physics is the chore of gathering the data" -- ... that's the easy/inevitable part. The hard part (I repeat) is to derive Boolean values; or at least real values; or at least finite real confidence intervals from that. "and validating or falsifying physics theories." -- No; but as you suggsted yourself (see quote in my previous comment): validating or falsifying physics models.
Mar
2
comment How can a black hole have spin?
@Noah: "[...] (intuition doesn't belong here!)" -- Surely it doesn't belong "beyond the horizon". (An that is admittedly pretty much all I know, or can confidently claim, about that.)
Mar
2
comment “String” infinity paradox
anna v: "Physics is the discipline of modeling measurements (called data) with mathematical theories." -- No: that's at most some part of physics (and indeed a part of physics about which I admittedly know little). However: Experimental Physics is the discipline of deriving measured values (in particular: real number values or Boolean values) from given/incidental observational data.
Mar
2
comment How can a black hole have spin?
Noah: "How is it possible, or even meaningful, to say that a black hole has spin? (Tangentially, if the singularity is assumed to be a point, it must have either zero or infinite angular momentum [...])" -- If it is indeed questionable (at least to you, since you ask this question yourself) whether the former possible, or even meaningful, then what makes you presume the latter being meaningful enough to say "it must [have some particular characteristic]"? "but even so, [TMALK] spacetime cannot be twisted, only bent" -- Doubtful; there are Gram determinants of 6th as well as of 5th order.
Mar
2
answered Two clocks along different worldlines
Mar
2
comment Two clocks along different worldlines
user41616: "If you mean [both clocks] started out at same time [at being separated] ... yes" -- Fine, that's answering the requirement "(3)" I had asked about above; thanks, so far. "If you mean [both clocks] were 100% accurate ... yes" -- This may refer to requirements "(1)" and/or "(2)". So: what exactly do you mean by "a clock having been **accurate**" (or by quantifying some deviation from "accurate", in percent?) "and they increased at same rate" -- Well, do you understand and agree that this is precisely and only requirement "(2)" being satisfied?
Mar
2
comment Two clocks along different worldlines
user41616: "Let's say we have two clocks. I leave one at home and keep one in my pocket. Then, I started running [...] then come back to my house. If I compare those two clocks how would they differ in time?" -- You should clarify: (1) Did each of these two clock remain good during the separation (or how did they differ from having been good)? (2) If they had remained good individually, were they "running" at equal coordinate rates $\frac{d}{d \tau_A}[t_A] = \frac{d}{d \tau_B}[t_B]$? (3) What were the values $t_A[ \text{at separation from B} ]$ and $t_B[ \text{at separation from A} ]$?
Mar
2
revised Relativistic Doppler effect on gamma rays
Identified the required at least six characters to correct formally. Refer to submitted answer for additional factual corrections.
Mar
2
suggested suggested edit on Relativistic Doppler effect on gamma rays
Mar
1
answered Relativistic Doppler effect on gamma rays