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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
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
Jul
3
comment Two apparent contradictions in SR involving time dilation and length contraction
Madde Anerson: "What if we'd look from an inertial frame with the mean velocity of v(a) and v(b)?" -- O.k. But you still need to decide: Do we compare the rates of these two clocks (which each regularly ticking "good" clock has by itself, properly) to each other? (If so, it won't matter "from" which inertial frame "we look" in particular for accomplishing this comparison.) Or what (else) do you mean by "running more slowly"?? (And: calling two distinct clocks "identical" surely doesn't spare specifying how to compare their rates, especially while they were separated.)
Jul
3
comment Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?
WetSavannaAnimal aka Rod Vance: Comparing the first and last equation of your answer I wonder whether your notation is consistent, i.e. in terms of the index which only appears in the latter eq. Otherwise +1. (Also, I've done a bit of copy-editing; still struggling hard to plug my assorted reputation leaks ... &)
Jul
3
suggested approved edit on Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?
Jul
3
suggested approved edit on Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?
Jul
2
comment Why is the momentum of a particle $\gamma mv$?
@0celo7: "This is a deterministic classical system, not a probabilistic quantum one." -- As far as I understand the OP question it is concerned with attributing and measuring momentum values, e.g. of objects (such as $A$) wrt. to suitable systems (such as $\mathcal S$). There doesn't seem to be any requirement or exclusion being made concerning some categorizazion as "classical or quantum"; whatever you might mean by that. "doesn't $\hbar =0$ [...]?" -- Perhaps you mean cases or limits in which $$\frac{m_A~c^2~\Delta \tau_A}{\hbar} \gg 1 $$ ? ...
Jul
2
revised Accuracy and Error of Atomic Clocks
some corrections and copy-editing
Jul
2
comment Two apparent contradictions in SR involving time dilation and length contraction
@Madde Anerson: "We wish to know which clock runs more slowly." -- If this request is understood as asking which one (of two "ticking" clocks) was ticking at a lower frequency (itself, properly), then that's a perfectly sensible and legitimate request, and SR is perfectly suited to address it consistently. (While other interpretations may lead to inconsistency.) "[...] is experiencing time dilation -- Time dilation refers to a ratio, comparing frequencies (or, foremost, durations) between participants who are not at rest to each other. It's not for only one individually "to experience".
Jul
1
comment Why is the momentum of a particle $\gamma mv$?
@0celo7: $\Delta\tau_A$ -- the duration of object $A$ throughout the trial (as spelled out in the answer). $\Delta\tau_{\mathcal S}$ -- the duration of system $\mathcal S$ throughout the trial (I may add that to my answer ...); $\Delta\mathbf r_{\mathcal S}$ -- the (spatial) separation between the member of system $\mathcal S$ who met/passed object $A$ at the beginning of the trial, and the member of system $\mathcal S$ who met/passed object $A$ at the end of the trial (I may add that, too.) "If this actually pans out, fantastic work!" -- Hmm ... What'ya mean by "panning out"??
Jul
1
comment Why is the momentum of a particle $\gamma mv$?
@0celo7: "where the phases and the $\hbar$ go" -- The "phases" can go into the description of states (see my above comment); and if so, the $\hbar$ goes both into the denominator of the "angle", and into the numerator of the applicable operator; so the $\hbar$ cancels (see my first comment) upon application of the operator to the state description. (So why bother inserting the $\hbar$ symbol at all? ...) "you saying special relativity follows from quantum mechanics?" -- I'd consider QM the general framework for "measurement", and GR/SR specifying particular geometric/kinematic operators.
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??