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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".)


13h
revised Angle sum of triangle in Schwarzschild solution
corrected spelling the name of K. Schwarzschild (also in the title);cmp. https://en.wikipedia.org/w/index.php?title=Schwarzschild_Solution
14h
comment Angle sum of triangle in Schwarzschild solution
@John Rennie: "How are you going to define the straight lines that make up the sides of your triangle?" -- This is a worthwile question by itself; and it is closely related to the OP question as well as to the (arguably more basic) question "What is the notion of a spatial angle in general relativity?" (PSE/q/108359). (The latter question has been answered already, possibly providing the means of addressing the OP question directly).
14h
suggested approved edit on Angle sum of triangle in Schwarzschild solution
14h
comment Is momentum an invariant?
@Danu: "This is a trivial question for first year courses [...]" -- Your assessment suggests that you (too) know a plain, unambiguous answer to my question. So which is it: "Yes.", or "No."? If "No." then please consider expanding and submitting this as an answer. (The answer "Yes." has been issued already.) "[...] The "usual notation" is clearer and you would do well to learn to use it." -- What exactly do you consider the "usual notation" for denoting the momentum of one specific particle (such as a $\Lambda^0$) with respect to one specific reference system (such as "the lab"), please?
1d
comment In a CMCS 2-body system, why does the speed of the particles after collision stay the same?
Greg: "Changing to a moving coordinate system, the Center-of-mass Coordinate System (CMCS), we now have [...]" -- The equations and the speed values $v$ and $v_c$ given in your question don't seem to involve any coordinates at all. So instead of referring to coordinate systems, perhaps you mean a comparison of two reference systems; i.e. first considering the inertial reference system of which particle $m_2$ was a member, and then changing to considering the Center-of-mass Reference System (CMRS).
1d
answered Does entanglement have to be verified synchronously
1d
comment Will two clocks moving in opposite directions measure the same time as one at rest?
Well, what could you know or demand of the tick rates of various clocks at all if you didn't understand and use the relativistic methods for comparing them in the first place?
2d
comment Why is a silicon ball with an exact number of atoms a bad measure of mass?
ton.yeung: As @Shaurya Bhave's answer indicates, the more pertinent question might be to ask, whether and why it is a bad idea to attribute some particular value of "mass" so some (non-zero) number of artefacts (concretely: to attribute a "mass of 12 grams" to the Avogadro number of C12 atoms. (And I'd say that's bad because it precludes asking and measuring whether two exemplars of "C12 atoms" had equal "mass", or whether the "mass" of one particular exemplar of "C12 atom" had remained constant, or not.)). Anyways: +1 to your question.
2d
comment Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?
dmckee: Re your recent edit, with several "counter examples": Yes, these seem indeed examples of events whose causal relations do not imply specific interval ratios. (I'd foremost think of "arbitrarily many events which are pairwise timelike to each other".) But may I remind you: I had been asking in the OP about a suitable set of events $\mathcal S$, i.e. if such a set may be thought of at all. Taking (again) a hint from Synge's more or less well-known "five point curvature detector" (GR, p. 408), I'd guess that such a set should have a whole lot more than 4 elements, suitably related.
2d
comment Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?
@Slereah: "As the causal relationships will be identical for two conformally related metrics" ... perhaps related to "$\Omega^2(x) \gt 0$" in the other answer mentioned above ... "the interval will also be conformal, since it is ~ g". -- Can you prove that (in the sense of my question, the corresponding interval values due to either metric tensor are "scaled isometric", with a non-zero proportionality constant) even allowing that neither $g$ nor $\Omega$ are necessarily constant? If so, please consider submitting that as an answer; and please don't forget the "how to go about".
2d
comment Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?
dmckee: "[...] but the intervals in the second set are 4 times as large." -- Please note the phrase "up to some (non-zero) constant" in the OP question statement. The two example cases described in your answer are in so far to be considered equivalent (with the applicable constant of value 4, or 1/4); and your answer is therefore (trivially) incorrect.
2d
comment Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?
@Slereah: "As that is knowing all the causal structure of spacetime, the answer is the same as physics.stackexchange.com/q/196496" -- Perhaps you're referring specificly to the (your) answer physics.stackexchange.com/a/196500 given to PSE/q/196496 ? If so, note that the answer given there apparently does not at all mention values of intervals ($s^2$), or at least their ratios (between interval values which are not "null"); nor does it seem to address explicitly "how to go about" obtaining the requested determinations.
2d
asked Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?
2d
comment Is momentum an invariant?
user37496: "[...] you need a way to get from spacetime events to real numbers." -- Correct. The "canonical way" to achieve this is to count successive pings (a.k.a. "signal roundtrips") between participants; as shown e.g. in MTW Box 16.4 (part of which happens to be publicly visible in this link). These counts are of course integer numbers; their ratios provide rational values; their limits in turn reals. So: do you suppose that counting pings is in any way contingent on coordinates (which may or may not be assigned to the events under consideration)?
2d
comment Is momentum an invariant?
user37496: "How do you measure a distance without a ruler? How do you measure a time without a clock?" -- Well, when it comes to off-the-shelf rulers and clocks, the pertinent questions are how to determine whether a given pair of ruler ends were and remained "at rest to each other" (or at least "rigid to each other"); and whether a given clock was "good". That's (of course) addressed by the "Marzke-Wheeler method"; see also MTW §16.4. But returning to my question: What do you suppose this might have to do with coordinates??
2d
comment Is momentum an invariant?
user37496: How do you suppose that the measurements of distance values, or of duration values, might be contingent on coordinates??
Jul
28
comment Is momentum an invariant?
user37496: "no such thing as "the speed" of a particle independent of coordinates." -- Why involve any coordinates at all?? Relevant and necessary are (e.g.) values of certain distances and durations; which (btw.) can be expressed as values of intervals $s^2$ "between" certain pairs of the relevant events (e.g. "the passage of the beam pipe wall" and "the passage of the first inner detector plane"). Do you claim "observers using different coordinates may measure different interval values" of this event pair?
Jul
28
comment Is momentum an invariant?
user37496: "observers using different coordinates may measure different speeds" -- Suppose that the described specific lab constituents (of beam pipe wall etc.) had measured the speed value of the specific $\Lambda^0$ baryon wrt. those lab constituents (themselves) as $$ \beta_{\text{lab}}[~\Lambda^0~]~c = 0.2~c.$$ Which value do you suppose that "observers using different coordinates" might obtain instead for the speed $\beta_{\text{lab}}[~\Lambda^0~]~c$ of the specific $\Lambda^0$ baryon wrt. those lab constituents?? (Or do you use the word "speed" improperly??) And: ...
Jul
27
comment Is momentum an invariant?
user37496: "If I measure the speed of a particle in the lab and then write down in my notebook the value" ... as real-number multiple of $c$ ... "an observer in a different inertial frame reads [...] the same" -- Correct. Real numbers are presumed unambiguous; they can be copied; +1. "(although [...])" -- Their graph structure (or topology) should remain distinctive enough. "context that led you" -- Foremost this: "speed itself is a coordinate system dependent concept"; then that.
Jul
27
comment Is momentum an invariant?
@Kyle Kanos: "[...] transformation [...] into a different reference frame" -- I wonder whether that's even a proper notion. As far as it is meaningful at all, remember that such "transformation" should be applied both to the specific $\Lambda^0$ baryon "of whom" the momentum value is to be obtained as well as to the constituents of the specific lab equipment by whom and with respect to whom the value is obtained. p.s. Admittedly, since "bases" had been brought up, the notion of "vectors" cannot be denied either.