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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
27
comment Is momentum an invariant?
@dmckee: "This is in no way related to the meaning of the word "invariant" used by relativists." -- Please note the Edit of the answer: "invariant, i.e. unchanged by any and all coordinate transformations, such as Lorentz transformations"; referring specificly to the meaning of the word "invariant" used by relativists.
Jul
27
revised Is momentum an invariant?
(v3.1: referring specificly to the sense of the word "invariant" as used in the theory of relativity.)
Jul
27
answered Is momentum an invariant?
Jul
27
revised Is momentum an invariant?
(v3.14159: capitalization still matters!)
Jul
27
comment Is momentum an invariant?
@Kyle Kanos: "$p^a$ [...] what everyone else uses" -- This notation seems to obscure the two arguments required for defining and evaluating "momentum"; namely "of whom" the value is to be obtained (e.g. the specific $\Lambda^0$ baryon), and "by whom and with respect to whom" the value is obtained (e.g. the specific constituents of the beam pipe wall etc.) So, yes, I'm primarily questioning this notation which "everyone else uses" (as far as you seem to know).
Jul
27
comment Is momentum an invariant?
@Jerry Schirmer: Please consider expanding your extremely terse comments into an answer. Don't omit to make explicit the coordinate dependence of the momentum value (e.g. of the specific $\Lambda^0$ baryon wrt. specific suitable constituents of the beam pipe wall), if you believe that such a dependence exists.
Jul
27
comment Is momentum an invariant?
@Jerry Schirmer: "how invariant do you expect it to be?" -- Perfectly independent of any coordinates whatsoever; hence perfectly invariant. If you believe that a momentum value such as the momentum of a specific $\lambda^0$ baryon with respect to (suitable) constituents of a specific lab is not invariant, then please state its specific dependence on coordinates.
Jul
27
comment Is momentum an invariant?
@dmckee: "[...] whether you mean the 3-vector, the 4-vector, the magnitude of the 3-vector or the magnitude of the 4-vector." -- Vectors ?? ...
Jul
27
comment Is momentum an invariant?
@Kyle Kanos: "you have not defined what $\beta_{\text{lab}}[~\lambda^0~]$ is" -- The definition of this quantity, for the purpose of my question, is implicit in the OP question statement; namely as a (the?) real number value such that the expression $$m[~\lambda^0~] ~ c ~ \frac{\beta_{\text{lab}}[~\lambda^0~]}{\sqrt{1 - (\beta_{\text{lab}}[~\lambda^0~])^2}} ~ \mathbf e_{\text{lab}}[~\lambda^0~] $$ is equal to the momentum value $\mathbf p_{\text{lab}}[~\lambda^0~]$; where all remaining symbols ($m$, $c$, $\mathbf e$) have been named in the OP, too. (Additional definitions may have existed.)
Jul
27
asked Is momentum an invariant?
Jul
24
revised Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
suggested an expansion of the title to make it more descriptive and specific. Also: some gentle copy-editing
Jul
24
revised Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
(v3.14159265: a bit neater, still ...)
Jul
24
suggested approved edit on Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
Jul
24
comment How do neutrons escape nuclei?
mathdummy: "there are repulsive components to the strong force as well. It's hard to trivially describe it [...]" -- Is it at all appropriate to think of the neutron together with the (heavier) "remainder" of the excited nucleus being (temporarily) bound together within the confines of a "potential barricade", which has a maximum as a function of separation between neutron and "remainder"; so the neutron could be said to "slide off the outside slope after having tunnelled"? (That's at least the narrative/model when considering $\alpha$ decay, due to long-range em repulsion ...)
Jul
23
revised Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
(v3.1415926: matching squares, instead of square root)
Jul
23
revised Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
(v3.141592: replaced incorrect dot multiplication by plain scalar multiplication; rearranging terms suitably. Also some additional formatting.)
Jul
23
revised Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
(v3.14159: copy-editing.)
Jul
23
answered Angle between two momenta in particle physics (principal axis of a two-body decay vs. center-of-mass motion in the lab)
Jul
23
revised How to achieve vertical lift using magnets
title modified; copy editing
Jul
23
suggested approved edit on How to achieve vertical lift using magnets