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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".)


Jul
1
answered Accuracy and Error of Atomic Clocks
Jul
1
comment I know light's speed in vacuum is constant, but what about its velocity?
Michael Seifert: "the velocity of a light ray" -- Is "velocity" really attributable to an "entire light ray", or not rather (only) to a particular "piece of it" (e.g. the signal front as "tip of the ray")? "any particle that follows a geodesic in a curved spacetime is, in a very real sense, moving with "constant velocity"" -- Agreed (thus "free motion", from event to event, is made geometric-kinematically comprehensible in general); but light-like geodesics are moreover definitive of "(straight) direction between participants".
Jul
1
comment Hafele-Keating revisited with a gravity clock
aepryus: "[...] The timing of such a fall would be [...]" -- Here it gets interesting: How, specificly (in terms of a thought-experiment), do you propose to "time a fall"?? Is there also a "top sensor" involved, besides a "bottom sensor"? Are they supposed to be and to remain in some particular geometric relation to each other; and how is such a relation to be measured, or "tuned" as desired? (Btw., eventually such a geometric characterization may also allow to determine, trial by trial, whether a given ball bearing "moved freely" through a "drop chamber", or in how far it did not.)
Jul
1
comment Hafele-Keating revisited with a gravity clock
aepryus: "[...] the device I have imagined above is almost entirely independent of EM (and other standard model) phenomena." -- "Almost entirely"?? It's perfectly justified to worry whether any "device" (ball bearings, Cs133 atoms etc.) is being disturbed electromagnetically, or weakly, or strongly, or due to what's not even considered in the SM; throughout each trial. Your only decisive idea is about that the "tuning" (before each trial, and certainly also troughout each trial). That is: to consider and select only such devices and such trials as "valid" for which ... what exactly??
Jun
30
comment Hafele-Keating revisited with a gravity clock
aepryus: "gravity clock [...] Such an apparatus could be tuned such that each cycle took exactly one second to occur." -- We may think of all sorts of pendulum clocks, e.g. with pendulum "sizes" varying in any ways imaginable, and either being "left swinging passively" or "being jiggled actively"; and among them those being selected which maintain constant "cycle periods" (each itself) and equal "cycle periods" (pairwise between separated clocks), as measured by the Marzke-Wheeler method, throughout each and any trial. (Which pretty much determines anything else you've been asking.)
Jun
30
revised Why are neutrino and antineutrino cross sections different?
Corrected spelling the surname of N. Cabibbo; together with some minor copy-editing to reach the required change of at least six characters.
Jun
30
comment Why are neutrino and antineutrino cross sections different?
Paganini: "I've added few lines of explanations that might help." -- They do; thanks, +1. "thanks for the typo" -- Well, looks like I should still lay hand on it myself. Also, there's still an entire sentence left which I find difficult to grasp as it stands: "[...] So necessarily this configuration cannot be possible explaining the null cross-section at this angle!" -- Is this perhaps supposed to mean (rather, as far as I understand the argument described): "[...] So this explains that the cross-section of this process at this angle ($\theta = \pi$) is null."?
Jun
30
suggested approved edit on Why are neutrino and antineutrino cross sections different?
Jun
29
revised Has anyone tried Michelson-Morley in an accelerated frame?
corrected spelling the last name of A. A. Michelson; cmp. https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment (NB: also consistent with the spelling used in R. A. Mould, "Basic Relativity".)
Jun
29
suggested approved edit on Has anyone tried Michelson-Morley in an accelerated frame?
Jun
29
answered I know light's speed in vacuum is constant, but what about its velocity?
Jun
28
comment Is it possible for two events happen at the exact same time?
@Gennaro Tedesco: "[...] measure [...]" -- By Einstein description: The indication of "piece of embankment A" being hit by lightning, and the of "B" being hit by lightning may (or may not) be determined having been simultaneous to each other. (Where A and B shall remain separate and at rest to each other.) "times to be the same" -- No: Either way these are distinct indications; not the same. (Don't confuse "times" with "time coordinate values".)
Jun
28
answered Is it possible for two events happen at the exact same time?
Jun
27
comment Is magnitude of velocity same as speed?
@Tim Krul: "what does double modulus mean?" -- That's the notation for "norm". (Having seen this in diracpaul's answer I find it more appropriate than "modulus, or absolute value".) "what does square bracket signify?" -- In square brackets I usually enclose arguments to functions, or operators; here e.g. the argument to which the differential operator is applied. (That's "Mathematica style"; reserving parentheses for grouping only).
Jun
27
comment Is magnitude of velocity same as speed?
Tim Krul: "what do you people mean by two moduli ?" -- The double bars which appeared in @diracpaul's answer and which I subsequently used as well (in comments and in editing my answer) is the notation for "norm". I think that's more appropriate for denoting a distance value (which in geometry/physics usually has some dimension: "length") than using only single bars which denote "modulus, or absolute value" (which is just some non-negative real number).
Jun
27
revised Is magnitude of velocity same as speed?
(v3.14159: Note on the distinction between "speed before reaching the evaluation point" and "speed afterwards"; particularly in response to the example in yuggib's answer PSE/a/191299.)
Jun
27
comment Is magnitude of velocity same as speed?
Tim Krul: "Is magnitude of velocity same as speed?" -- If by "speed" you specificly mean the left term of your equation then apparently you don't mean to distinguish between "speed on the journey before reaching" e.g. some particular "origin" of the description, and "speed afterwards". However, the right term of your present equation, $$ \frac{d}{dt}[\| ~\vec r \|~], $$ makes this distinction; and some answers make a point of that. So consider asking instead about $$\left\lvert \left\lvert \frac{d}{dt}[~\vec r~] \right\rvert \right\rvert =?\!\!= \frac{d}{d|t|}[~\|\vec r\|~].$$
Jun
27
comment Is magnitude of velocity same as speed?
yuggib: I've just suggested to the OP to ask instead about $$\left\lvert \left\lvert \frac{d}{dt}[~\vec r~] \right\rvert \right\rvert =?\!\!= \frac{d}{d|t|}[~\|\vec r\|~].$$ (I wonder if that's going to happen. Or which title I would choose if I'd try to ask this question myself, eventually ...)
Jun
26
comment Is magnitude of velocity same as speed?
2 (Re: eq. (01)) diracpaul: "In (01) we differentiate the first equation." -- Ah, thanks, that helps (me trying to follow your argument). So: How exactly would you argue in the particular case that $$\mathbf r \mapsto \mathbf{r_0},$$ where $$\|\mathbf{r_0}\|=0$$ ?? (Btw., this seems more or less the "subtlety" which I was concerned about in much of my own answer to the OP.) p.s. "$y=x^2$ by differentiation yields $dy=2~x~dx$" -- I find it reassuring, and even necessary to know in the first place, that $$2~x=\text{lim}_{\{\Delta x\rightarrow 0\}}[\frac{(x+\Delta x)^2-x^2}{\Delta x}].$$
Jun
26
comment Is magnitude of velocity same as speed?
1 (Re: the Figure) diracpaul: "What are then $dy,dx$ ???" -- A pertinent question, deserving of a specific answer. But what I question specificly goes moreover to the consequence: Is it therefore appropriate to use "$d$" (rather than "$\Delta$") for labelling elements of your Figure, as it presently stands?!? "Sorry, but I don't know how to create editable sketches with MathJax" -- And I'm sorry, too: I don't know much more about that than to google "MathJax" and "pstricks". But consider the possibilities ...