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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".)


Jun
26
comment Is magnitude of velocity same as speed?
diracpaul: Concerning the two equations (which had been added after I made my first comment), I'm struggling already to follow the equations and implications with tag "$(01)$". Is there perhaps a "$\lt$" sign missing somewhere? And is there perhaps a version of these equations and implications in terms of "differences $\Delta$" instead of "infinitesimals $d$", to provide at least some plausibility?
Jun
26
comment Is magnitude of velocity same as speed?
p.s. My request for making the given sketch editable is also driven by the desire to easily and unambiguously reference its salient "graphic" features (with even better resolution than to note the "color of the dots", because there seem to be several "dots" of the same color in the sketch as presently provided). Especially: How would you call the blue "dot" by which the two red arrows are connected (and two of the black arrows happen to be connected, too)? And (perhaps more importantly): why did you draw these two red arrows at all?
Jun
26
comment Is magnitude of velocity same as speed?
diracpaul: "The two positions of a moving particle in Figure are at a differential distance apart" -- Hmm ... A "differential (infinitesimal) distance", $d$, i.e. that there is no way to measure "it"? Or instead a "differential distance", $\Delta$, which is still in the (physical) realm of "the measurable", characterizing a geometric relation between distinguishable "ends", commensurate to other (incl. "large") distance values? (Then we may consider ratios, and take limits.)
Jun
25
comment Is magnitude of velocity same as speed?
diracpaul: The notation used in the sketch you provided can be confusing, because you use the symbol $d$ "by itself"; and apparently not as the OP, only within a pair $\frac{d}{d}$ for denoting a derivative operator. It seems advisable that your letters $d$ be replaced (individually) by the symbol $\Delta$; writing in particular $$\|\Delta\mathbf r\|\ne\Delta\|\mathbf r\|.$$ Also, please consider formatting and including your sketch by means of appropriate available MathJax commands for easier editing by us, the Physics Stackexchange contributors.
Jun
25
comment Why are neutrino and antineutrino cross sections different?
Paganini: "[...] $u,v$ [denote] the spinors for particles and anti-particle. [...] Squaring the amplitudes, averaging over the spin of the initial quark and summing over the spins of the outgoing quark and lepton yields: [...]" -- It would be really terrific if you could spell out these calculations in a bit more detail, making their difference for $u$ vs. $v$ more explicit. (You should edit your post anyways wrt. spelling the surname of N. Cabibbo.)
Jun
25
comment Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent?
@chharvey: "I think he used the word "theoretical" per its colloquial definition: meaning "speculative"" -- I think so, too. (This applies both to dmckee's usage in the comment to which I replied, and to the OP's title choice.) And that's surely one of my pet peeves: the diminishing or even denial of understandable, committable principles and definitions (incl. their logical consequences), by the (only) appropriate word available for referring to them being (ab)used otherwise.
Jun
25
answered Is magnitude of velocity same as speed?
Jun
25
comment Why is the momentum of a particle $\gamma mv$?
@Kyle Kanos: "You've given a definition of the phase, but shown nowhere where it ought to be." -- Hmm ... (I hadn't persued the mentioned afterthought up to this point) ... I suppose the "phase" $\phi_A$, as specified above, might/should be part of the state description/representation (colloquially a.k.a. "wave function") of object $A$; formally: $$|\psi_A\rangle := |\phi_A~\varphi_A\rangle = \phi_A~|\varphi_A\rangle,$$ where $|\varphi_A\rangle$ is (the part of the description of $A$ which is) explicitly independent of $\Delta \tau_A$ (in the suitable, short trial under consideration).
Jun
25
comment Why is the momentum of a particle $\gamma mv$?
@Kyle Kanos: "But you don't seem to invoke your phase [...]" -- Correct, IIUYC. "Invoking the phase" is explicitly done only in the equation of my above comment. In my answer itself, "invocations" are only of $$\frac{d}{d \mathbf r_{\mathcal S} }[~\Delta \tau_A~],$$ or incl. conventional coeff.s: $$-m_A~c^2~\frac{d}{d \mathbf r_{\mathcal S} }[~\Delta \tau_A~].$$ "Phase" (and "energy") are considered merely as afterthoughts; though adding e.g. the equation mentioned above may not hurt. Btw.: I trust you're aware of the distinction between "operator" (with a "hat") and "(measured) value".
Jun
25
comment Why is the momentum of a particle $\gamma mv$?
@Kyle Kanos: "How does your $i\hbar$ magically disappear?" -- You mean the $i\hbar$ in operator $$\hat E_{\mathcal S}:=i~\hbar~\frac{d}{d\mathbf\tau_{\mathcal S} }[~]$$? This (magically! ;) **cancels** against the coefficient $\frac{-i}{\hbar}$ which had been (cleverly! ;) first inserted into the "phase": $$\phi_A :=\text{Exp}[~-i~\frac{m_A~c^2}{\hbar}~\Delta\tau_A~],$$ such that $$\hat E_{\mathcal S}[~\phi_A~]=m_A~c^2~\frac{d}{d\mathbf\tau_{\mathcal S} }[~\sqrt{(\Delta\tau_{\mathcal S}[~A~])^2-(\Delta \mathbf r_{\mathcal S}[~A~] / c)^2}~]~\phi_A=m_A~c^2~\gamma_{\mathcal S}[~A~]~\phi_A.$$
Jun
24
answered Why is the momentum of a particle $\gamma mv$?
Jun
19
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v1.61803: identification corrected. (The ping being considered were between separated participants; not the trivial coincidence of one participant with itself.))
Jun
18
answered Why do we need coordinate-free descriptions?
Jun
18
answered Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Jun
14
comment On the no-faster-than-light in special relativity
Related: "Understanding the “π” of a rotating disk" (PSE/q/121889)
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
Look: you seem to have a (rarely used) Wordpress blog; and me, too. I wouldn't mind continuing our debate by those, less limited means. For here and now, I rather concentrate on working out my answer which is a bit complicated, however. Note, btw., that neither there nor in my OP question is any mentioning of "speed".
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "David Wineland of NIST: "[...] when we compare clocks, if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at."" -- Indeed, Nobel Prize winner David Wineland of NIST said so. What a shame he didn't say properly that, if (we have measured that) one clock in one lab is 30 centimeters higher than the clock in the other lab, then we (must) take this (result) into account when trying to compare the (proper) rates at which they run (separately); at the level of their precision NIST has reached.
Jun
13
comment Closed timelike curves in the region beyond the ring singularity in the maximal Kerr spacetime
Timaeus: "[...] a Penrose Diagram as above [...] but the Schwarzschild singularity is [...]" -- I note that the diagram you included contains a mis-spelling of the surname of Karl Schwarzschild. Please consider including the diagram in editable form, e.g. using the appropriate MathJax commands, so it may be edited accordingly. (Also, this might help in distinctly denoting certain vertices in the diagram, for further reference.)
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "optical clocks go slower when they're lower" -- Any meaningful, grammatical comparative phrase would still require (one or even more instances of) the word "than". So: "one optical clock went slower than" what ??, measured how ?! (Standard insufficient answer: "Slower than any equal LC.". Standard reply: "Equal by which measure?" Standard insufficient answer: "Equal by separation between their pairs of mirrors." Standard reply: "Separation -- what's that (how to measure)?". On to the PCoincP.)
Jun
13
comment Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
John Duffield: "the people who tell you that VSL ideas are untenable are contradicting Einstein" -- The people who tell you that VSL ideas are untenable are contradicting Einstein's statements on VSL (e.g. as referenced). Einstein's own epistemological demands and insights (e.g. as referenced) are contradicting Einstein's statements on VSL! (Why do you think there's still debate after 100 years?) "velocity is the common-usage [...] Read it as speed." -- Fine. How do you propose it ought to be measured?!