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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?


1d
comment Questions about the formalism of Quantum Mechanics
+1 especially for question part "4. How is the potential $V$ evaluated? What are its arguments?". (Even if trying to address this question could take up most of a presentation; or indeed most of a Ph.D. thesis.)
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "[...] for example [...] let $S_p$ and $S_w$ be assigned coordinate times $t=98s$ and $t=107s$ respectively" -- Hmm ... What's putting me off there, at the moment, is the letter "$s$" attached to the suggested $t$-coordinate assignments. (I'm more used to encoutering/challenging $t$-coordinate assignments that are strictly real numbers, as shown above; and generally coordinate tuples being elements of $\mathbb R^4$.) So what you suggest is apparently not meant as "just any (arbitrary) $t$ coordinates", but perhaps (even) as good coordinates of the given set $\mathcal S$.
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "You didn't answer my question about if your idiosyncratic use of "indications" means the same thing as the standard terminology of "clock readings"." -- I addressed your question above; but since you don't find that satisfying you should elaborate your idiosyncratic use of "the standard terminology of "clock readings"", please. Is there something specific that needs to be done before knowing/uttering, for instance ""3:56 pm"" ? Btw.: Let's hope that "the chat" will be supporting MathJax rendering soon, then allowing us to actually consider moving our correspondence there
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "[...] opposed to the 'true' duration [...] along its worldline between [...]" -- Why "opposed"? No, I (merely) object to this quantity being referred to as "(proper) time". Einstein declared at the outset (Ann. Phys. 17, 891-892) that "time" is synonymous to "position of the hand of my watch", so "proper time" is a misnomer for some (related) quantity to be measured. The correct common name is: duration. "MTW §16.4 says [...]" -- MTW Box 16.4 presents the sketch "how to" even twice. (However: How to determine whether a given participant had been "free/geodesic"? ...)
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "Concrete examples would help" -- Well, consider indications of a "biological clock (of a person)"; or of a "forensic clock (of a corpse)" ... Or pretty much anything distinctive having to do with "hands, on a dial". "what does "one specific identifiable participant" mean?" -- Hmm ... What did Einstein mean in writing (about) "recognizable material points"? What did you mean in writing: "you" !? ... That's "(Exp.) Physics/Ontology 101".
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "And would you agree non-ideal clocks" ... in technical jargon one (also) speaks of "bad" clocks, in distinction to "good" clocks (cmp. MTW Fig. 1.9) ... "measure time (approximately)" -- If (big IF) the "degree of approximation", here: the value "$u - 1$", is measured along with that. In other words: strictly, no. That's why we distinguish "measuring" from ... "gauging". Btw., saying "to measure time" (instead of "to measure duration") is a bit of a category error; like saying "to measure cars" while meaning "measuring their gas-milage".
Apr
24
comment Naked Time ( Is there such a thing ?)
We can simply calculate an arithmetic difference between two $t$ values. But determining/evaluating (as a real number value) a particular duration ratio (of the specific participant under consideration; for some of her/his/its specific indications) is a more demanding task (cmp. again MTW §16.4). There's no "given plain arithmetic" way to evaluate "the difference between" any two distinct observed "positions of the little hand" (or for ratios of those). We must first seek, define, and then apply some unambiguous operational method for measuring. That's daily work/fun for (exp.) physicists.
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "And then would $S_w$ and $S_p$ be two different readings" ... indications ... "at two different events" ... yes ... "(whether on the same clock or distinct clocks)" -- No-no! Above you and I were referring to "A (one specific) clock"; so in my understanding this refers to the (ordered) set (e.g. "$\mathcal S$") of indications of one specific identifiable participant, along with one specific coordinate assignment "$t : \mathcal S \rightarrow \mathbb R$". N.B.: [contd.]
Apr
24
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "maybe by "indication" you mean what people usually call a clock reading? (e.g., "3:56 pm")" -- Well, by an "indication" (denoted e.g. "$S_p$") I mean (rather) that what is being read; the observed output of any (analogue or digital) indicator such as a "clock face/dial"; I mean in all generality what Einstein in a famous specific case called "the position of the little hand". I do not mean any numeric (or boolean, or alpha-numeric) value which might be (subsequently) assigned or determined of an indication; such as the/any coordinate time $t[~S_p~]$.
Apr
23
revised What is the proper time used in relativistic non-equilibrium statistical physics?
(consistent spelling of the title)
Apr
23
suggested approved edit on What is the proper time used in relativistic non-equilibrium statistical physics?
Apr
23
revised Can I say that physical entities do not exist and everything is observed “as if” they exist?
Some copy-editing. (YMMV.)
Apr
23
suggested approved edit on Can I say that physical entities do not exist and everything is observed “as if” they exist?
Apr
23
comment Are there computerized ontologies for Relativity and (Experimental) Physics? How to contribute?
@rob: "It stuck out at me because it's the only other question I've seen here about o." -- In the strictest sense of "Ontology (information science)", apparently. I did the obvious search admittedly only soon after your "standard comment". (I claim and hope this doesn't make this question of mine "duplicate".) "If you find several you might create a tag [...]." -- How many "several"?? (I've created tags even on, at first, singular topics; just so I could spell it out.)
Apr
23
comment Are there computerized ontologies for Relativity and (Experimental) Physics? How to contribute?
@rob: "Related: [ PSE/q/131076 {etc.}: Lexical/ontological/semantic knowledge base for physics...]" -- Wow!, that's really sort of related. (Never underestimate a sufficiently diverse bunch of PhysSE contributors ... &). (Well, that guy who (elsewhere) first posted $$\frac{11.86~\text{a}}{2} =\! \approx \!= 5.9~\text{a}$$ had beat me to the punch, too ...)
Apr
23
comment Naked Time ( Is there such a thing ?)
Hypnosifl: "OK, but are you arguing that there aren't good ways to determine which real clocks are better approximations of ideal clocks?" -- Hardly: I just wrote down the relevant formula for you in my above comment; and the answer on which we're commenting lists a (the!?) reference of how to determine duration ratios: MTW. "the word "operational" in "operational def." has nothing to do with the definition of "operators" in QM" -- Only for a sufficiently narrow conception of "having to do". The point being: certain applicable operational/thought-experimental definitions don't commute.
Apr
23
asked Are there computerized ontologies for Relativity and (Experimental) Physics? How to contribute?
Apr
23
comment Naked Time ( Is there such a thing ?)
It's of course the task of (experimental) physicists to quantify or to delimit, trial by trial, how bad an approximation. (W/o that you don't even have any serious estimates; right?). Here: to evaluate the (otherwise unknown) number $u$, case by case. And this requires knowledge and appreciation of how to determine duration ratios properly in the first place. "All continuous physical quantities are assumed to have a "true" value" -- All physical quantities have likewise an operational definition; and thus a definite range of values. But as you surely know: not all such operators commute.
Apr
23
comment Naked Time ( Is there such a thing ?)
@Hypnosifl: "A real clock is an approximation to an ideal clock," -- Sure: any real/observed set (or already even: sequence) "$\mathcal S$" of watch indications together with pretty much any coordinate assignment "$t : \mathcal S \rightarrow \mathbb R$" constitutes some "approximation to an ideal clock". Concretely, for any three (distinct) indications $S_b, S_p, S_w~\in\mathcal S$ there sure is some real number value $u$ such that $$(t[~S_w~]-t[~S_p~]) = u~t[~S_p~] - t[~S_b~])~\frac{\text{Duration}_{\mathcal S}[~S_w, S_p~]}{\text{Duration}_{\mathcal S}[~S_p, S_b~]}.$$ [continued]
Apr
23
comment Naked Time ( Is there such a thing ?)
@David Hammen: "A watch is a measurement device" -- No. A watch is a (typically easily portable) generator of distinctive, conspicuous indications (to watch and remember). The measurement of durations of a given watch (resp. its "wearer"), between pairs of its indications, is (only, by definition) accomplished by "ideal clocks", such as sketched in MTW §16.4. (p.s. Sorry for not having replied earlier; I nearly missed your comment ...)