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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?


Nov
4
comment How can we measure time?
Qmechanic: "By repeating the synchronization procedure many times, we can test SR. Any inconsistency (that can't be explained by faulty equipment etc)" -- This parenthetical remark has profound implications: we always only test hypotheses concerning our models/expectations/prejudices about the "equipment etc" involved having been and remained "not faulty"; we cannot experimentally test our definitions of what we mean by "inconsistent" or "faulty" in the first place. Any theory serving this purpose, such as (S)RT, must be selected beforehand, and stuck to, based on comprehension alone
Nov
4
asked Is there a rigorous, explicitly geometric, general characterization for whether a given clock had been “good”, or not?
Nov
3
comment How to determine “timelike”-ness without using a coordinate system?
Incnis Mrsi:"Strictly speaking, two endpoints of a time-like interval are not necessarily causally related" -- Alright; causal relations, as considered in geometry are not quite the same as causation, e.g. due to some "material trace propagating". "[...] situations 2 and 3 are not possible in Special Relativity." -- But they certainly are (read the descriptions carefully again ...)
Oct
28
comment How to determine “timelike”-ness without using a coordinate system?
[... continued] Or 3: if there exists at least one "material trace" who to part in distinct events $\mathcal{A, B, P}$ (in that order) where $\mathcal{A, Q}$ as well as $\mathcal{B, Q}$ are lightlike?
Oct
28
comment How to determine “timelike”-ness without using a coordinate system?
Incnis Mrsi: "[...] reflected or scattered light, or by their material traces" -- So, applying this terminology to what I asked specificly at the end of my question text: Do you agree that two events ($\mathcal{P, Q}$) are related by a timelike interval 1: if there exists at least one "material trace" which took part in both of these events; Or 2: if there exists at least one "material trace" who to part in distinct events $\mathcal{A, B, Q}$ (in that order) where $\mathcal{A, P}$ as well as $\mathcal{B, P}$ are lightlike; [... to be continued]
Oct
28
comment Which nucleus is the most resilient against gamma-induced fission?
@Ben Crowell: "Generally we don't call it fission unless both of the products are heavier than alpha particles." -- Note, however, the "neutron-induced fission of Uranium-235", for example ...
Oct
28
comment Which nucleus is the most resilient against gamma-induced fission?
@Ben Crowell: "[...] would include processes that I don't think any nuclear physicist would call fission, such as knocking out a single neutron." -- It'd be helpful to learn how nuclear physicists, if any, who wouldn't call the (gamma-induced) knocking out of a single neutron a "(gamma-induced) fission" might call such a process instead. Speaking perhaps of "(gamma-induced) nuclear disintegration" is not (at present) viable either, since Wikipedia (presently) claims that's synonymous to "(gamma-induced) nuclear decay chain".
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
24
revised When has the speed of light been measured, recently?
(v3.1415926: tiny typos corrected.)
Sep
23
answered When has the speed of light been measured, recently?
Sep
15
awarded  Yearling
Sep
15
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
(v3.1: corrected question title.)
Sep
15
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.)
Sep
15
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
rolled back to a previous revision
Sep
15
revised Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
(v3: naming the quantity
Sep
15
asked Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?
Sep
15
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".)