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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
23
answered Is the speed of light in vacuum constant or does the math just happen to work out?
Jul
22
answered Why does the speed of light in vacuum have no uncertainty?
Jul
16
revised Why do we use Mie scattering to describe light scattering off large objects?
spelling corrected
Jul
16
suggested approved edit on Why do we use Mie scattering to describe light scattering off large objects?
Jul
16
answered A way to determine if a body accelerates or loses speed at a certain time
Jul
11
comment How do I sum up speed though space and time to obtain c (in terms of units)?
@Chris Drost: "That was the most complicated way I have ever seen to observe that the 4-velocity $\gamma~[c,\vec v]$ has 4-magnitude speed $c$, such that [...]" -- Perhaps you mean compared to any number of other ways which cut short on deriving that the relation between speeds such as $c$ and $v$ and a third one in terms of their "magnitudes" takes a particular (algebraic) form; namely related to that by $\gamma$ you mean $1 / \sqrt{1 - (v/c)^2}$? (In my college days we used to observe that "The sum of all difficulties is a constant.". Google doesn't seem to know that anymore ...)
Jul
10
comment If all motion is relative, how does light have a finite speed?
GreenBeans: "Nature doesn't care how we label points in space-time." -- Right on. (But we may want to use distinct labels for distinguishable events.) "Some relations are [...] geometry itself, and are independent of coordinate systems." -- Right on; among them: "the geometric lengths of a straight path between two points", and related, the quantities $s^2$ (or at least ratios between them). "speed itself is a coordinate system dependent concept" -- ??? Can "speed" (e.g. of participant $A$ wrt. the members of system $\mathcal S$) not be expressed through relevant $s^2$ values?
Jul
10
comment Doppler shift for a uniformly accelerating observer
Rob Jeffries: "NB: In my answer, the unit system is such that $c=1$" -- That's alright, I suppose; mostly since $1$ is explicitly different from $0$; and as long as you (can) steer clear of expression that would "mix apples and oranges" (i.e. not to use expressions such as "$(a / \omega_0) - (\omega_0 / a)$", or somesuch). But in any case, to be consistent, you should therefore remove any reference to the unit "$\text m$" from your answer, too.
Jul
10
comment Doppler shift for a uniformly accelerating observer
Rob Jeffries: "[...] ok so long as the speed of the observer does not change significantly during the time between wavefronts." -- Well ... I believe that "your expression" $$\omega = \omega_0~(1 - v)~\gamma$$ is not perfectly correct even for uniform motion, even with $$ (\Delta \mathbf r \cdot \mathbf v)^2 = (\Delta \mathbf r)^2~(\mathbf v)^2 ;$$ but even then only if "$\Delta \mathbf r \cdot \mathbf v$ doesn't invert its sign between wavefronts". (It's of course a separate "technician's problem" to decide what to consider still "probably ok" in some circumstance, or the other.)
Jul
9
comment Doppler shift for a uniformly accelerating observer
Rob Jeffries: "The doppler shift can be written as: $$\omega = \omega_0~(1 - v)~\gamma.$$ Do you claim that this relation holds exactly, even if $$a \gg c~\omega_0$$? Otherwise, please discuss the approximation you're using; or (even better) use an exact expression for "_the doppler shift_" (in terms of $\omega_0$, $v$ and $a$).
Jul
9
answered How do I sum up speed though space and time to obtain c (in terms of units)?
Jul
9
revised Two apparent contradictions in SR involving time dilation and length contraction
(v3.1415: more copy-editing)
Jul
9
revised Two apparent contradictions in SR involving time dilation and length contraction
(v3.141: corrected/inverted duration ratio; and some copy-editing)
Jul
9
answered Two apparent contradictions in SR involving time dilation and length contraction
Jul
4
comment Simple Harmonic Motion in Special Relativity
Prish Chakraborty: "Thanks for your contribution." -- You're welcome. "Please read the edit!" -- I did; and added some additional evaluations to my answer.
Jul
4
revised Simple Harmonic Motion in Special Relativity
(v3.141592: mistaken minus-sign removed.)
Jul
4
answered Simple Harmonic Motion in Special Relativity
Jul
3
comment Two apparent contradictions in SR involving time dilation and length contraction
Madde Anerson: "Yes, we are comparing rates here." -- Good. (For the record: That is proper rates, of some specific clocks being considered; I presume.) "[...] a fancy way to say that time ticks at a slower rate than "my time."" -- But the topic (as far as I am capable of addressing it) is not "time ticking", but specific clocks ticking. Therefore, you should mean to say that "one specific clock ticked at a slower rate than ..." what, exactly?? (p.s. I hope that I'll get around to submitting an answer to your question by Monday; and the "second part" is interesting, too.)
Jul
3
revised Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?
Expressed the Uncertainty Principle (also) as **in**equality; and corrected spelling the surname of M. Planck.
Jul
3
revised Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?
corrected an omission (exponent) and minor spelling