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The following questions (in no particular order) which I had submitted have been "removed from PSE for reasons of moderation":

  1. Which geometric relations obtain between two distinct rest systems?

Consider, as a thought experiment, a set of participants who measure throughout the experiment having been at rest to each other; among them explicitly participants ${\mathbf A}$, ${\mathbf B}$ and ${\mathbf F}$ who determine the ratios of their (chronogeometric) distances between each other as real number values $\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}$, $\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}$, and $\frac{{\mathbf A}{\mathbf B}}{{\mathbf B}{\mathbf F}} = \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} / \frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}$.

Further let there be another set of participants (of which neither ${\mathbf A}$, nor ${\mathbf B}$, nor ${\mathbf F}$ are a member) who measure throughout the experiment having been at rest to each other as well; among them ${\mathbf J}$, ${\mathbf K}$ and ${\mathbf Q}$, who determine the ratios of their (chronogeometric) distances between each other as real number values $\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}$, $\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}$, and $\frac{{\mathbf J}{\mathbf K}}{{\mathbf K}{\mathbf Q}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} / \frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}$,

such that

  • ${\mathbf J}$ passed ${\mathbf A}$, then passed ${\mathbf B}$,

  • ${\mathbf A}$ passed ${\mathbf J}$, then passed ${\mathbf K}$,

  • ${\mathbf Q}$ passed ${\mathbf F}$, in coincidence with ${\mathbf Q}$ and ${\mathbf F}$ observing ${\mathbf J}$ and ${\mathbf A}$ having passed each other,

  • ${\mathbf B}$ and ${\mathbf F}$ determined that ${\mathbf B}$'s indication of the passage of ${\mathbf J}$ was simultaneous to ${\mathbf F}$'s indication of the passage of ${\mathbf Q}$, and

  • ${\mathbf K}$ and ${\mathbf Q}$ determined that ${\mathbf K}$'s indication of the passage of ${\mathbf A}$ was simultaneous to ${\mathbf Q}$'s indication of the passage of ${\mathbf F}$.

Question:
Is thereby guaranteed that for these distance ratios obtains

(1)
$\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}$ ?,

and (moreover)

(2)
$\left( \left(\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}\right)^2 + 1 - \left(\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}\right)^2 \right) \left( \left(\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}\right)^2 + 1 - \left(\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}\right)^2 \right) = 4 \left( 1 - \left( \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} \right) \left( \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} \right) \right)$ ?

Or otherwise:
What could be concluded if (1) and/or (2) were not found satisfied?


4h
awarded  Yearling
6h
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
(v3.1: corrected question title.)
6h
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
(v3: named the quantity "s^2"; and some formatting.)
6h
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
rolled back to a previous revision
6h
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
(v3: naming the quantity
7h
asked Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
8h
comment How does the number of events per bunch collision scale (as function of energy, luminosity …)
DarioP: "However he [B. Richter, 1409.1196] gets the result multiplying by 7 both $N_1$ and $N_2$ while the total inelastic cross section $\sigma$ stays constant." -- That was my understanding, too. "the specific cross section of a resonance interesting to study. Those tends to scale with $E^{-2}$, [PDG Fig.] 49.5" -- Also matching PDG eqs. (47.1) - (47.12). "[...] The total inelastic cross section, $\sigma$, is assumed constant." -- Is there some justification for this difference? (Secondary processes?? ...) "$\sigma_{x,y}=$ [...]" -- Is there perhaps a derivation at PhysSE already?
Sep
12
comment In QFT, why do fermions have to anticommute in order to insure causality?
Andrew McAddams: "From the causality principle we must have [... eq.] $(5)$." -- Can you please give more detailed justification of that? (Or is there perhaps already some PhysSE-Q&A treatment of this particular point as rigorous as your answer to the OP question seems otherwise?)
Sep
12
revised How to define a convex surface in case of refraction?
(v3.1415: corrected my off-the-seat-of-my-pants spelling of "off the seat of my pants".)
Sep
12
comment How to define a convex surface in case of refraction?
Saurabh Raje: "can we fix our observation point as the source of light?" -- Regarding optical imaging there's surely a practical, conventional "optician's view": "along the ray(s)", from object to image. In the case of your example, that's just the reverse of the (practical, conventional) "lensmaker's view": from the outside of the (dense) material. My point: The corresponding surface has a particular intrinsic geometry. Now: it may be said (concisely) that the surface to be considered in your exam must have been "bulging away from the material". But how exactly should we draw that??
Sep
11
revised Why are alpha particles such a prominent form of radiation and not other types of nucleon arrangement?
consistent spelling the name of G. Gamow; cmp. http://en.wikipedia.org/wiki/Gamow_factor
Sep
11
suggested suggested edit on Why are alpha particles such a prominent form of radiation and not other types of nucleon arrangement?
Sep
11
revised Why can interactions be neglected for the Integer Quantum Hall effect?
corrected spelling the name of C.-A. de Coulomb; cmp. http://en.wikipedia.org/wiki/Coulomb_interaction
Sep
11
revised Radioactive decay - What mechanism decides when an unstable nucleus decays?
(v3.1415: corrected spelling the name of G. Gamow; as had been linked already)
Sep
11
suggested suggested edit on Why can interactions be neglected for the Integer Quantum Hall effect?
Sep
11
revised Greenhouse gases
corrected formatting, and spelling the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_spectrum
Sep
11
revised Naturalness and experiments
corrected spelling; such as the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_scale
Sep
11
revised ${1 \over T} e^{-i/T}$ for Boltzmann-Gibbs distribution
corrected spelling the names of L. Boltzmann (cmp. http://en.wikipedia.org/wiki/Boltzmann_distribution) and of M. Planck (cmp. http://en.wikipedia.org/wiki/Black-body_radiation#Planck.27s_law_of_black-body_radiation)
Sep
10
suggested suggested edit on Greenhouse gases
Sep
10
suggested suggested edit on Naturalness and experiments