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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?


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
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
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
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
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
revised How do the energy eigenvalues of rotational degrees of freedom in statistical mechanics come about?
corrected spelling; such as the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_constant
Sep
10
revised What is information?
corrected spelling, such as the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_area
Sep
10
revised Why is the absolute zero a rational number in Celcius?
corrected spelling the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_constant
Sep
10
revised Could strings be geons?
corrected spelling the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_length
Sep
10
revised Is string length in string theory quantized?
corrected spelling the name of M. Planck; cmp. http://en.wikipedia.org/wiki/Planck_length
Sep
10
revised How to define a convex surface in case of refraction?
(v3.141: Added a note explaining the relation to standard/Wikipedia terminology.)
Sep
9
revised How does the number of events per bunch collision scale (as function of energy, luminosity …)
(v3.1: added the "minus"-sign in the quoted expression. (It's a bit difficult to recognize in the original document, and it might not even be considered essential for correctly understanding the assertion about the cross section dropping.))
Sep
8
revised Lightspeed (invariance) measurement methods
corrected spelling the name of A. A. Michelson; cmp. https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment
Aug
31
revised Why is the cross product between two vectors calculated by the determinant of a matrix
(v3.1415926535: Correction of mistake pointed out in comment by firtree.)