1,889 reputation
326
bio website
location
age
visits member for 2 years, 9 months
seen 9 hours ago

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?


1d
revised Simple Harmonic Motion in Special Relativity
(v3.141592: mistaken minus-sign removed.)
2d
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.
2d
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
2
revised Accuracy and Error of Atomic Clocks
some corrections and copy-editing
Jun
30
revised Why are neutrino and antineutrino cross sections different?
Corrected spelling the surname of N. Cabibbo; together with some minor copy-editing to reach the required change of at least six characters.
Jun
29
revised Has anyone tried Michelson-Morley in an accelerated frame?
corrected spelling the last name of A. A. Michelson; cmp. https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment (NB: also consistent with the spelling used in R. A. Mould, "Basic Relativity".)
Jun
27
revised Does “$\mathbf r[~t~]$” correctly denote the trajectory of a point particle wrt. a reference system w/o having to decide on a particular origin?
(v3.14159265: minor edit)
Jun
27
revised Is magnitude of velocity same as speed?
(v3.14159: Note on the distinction between "speed before reaching the evaluation point" and "speed afterwards"; particularly in response to the example in yuggib's answer PSE/a/191299.)
Jun
19
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v1.61803: identification corrected. (The ping being considered were between separated participants; not the trivial coincidence of one participant with itself.))
Jun
10
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v3.14159265: Extraneous HTML source code removed. (Point kept.))
Jun
10
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v3.1415926: Edit in response to ... anonymous modifications. Added tag [tag:equivalence-principle].)
Jun
10
revised What is the heaviest stable element in the center of the sun due to Photodisintegration?
added tag "astrophysics"
Jun
8
revised Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?
(v3.141592: Added a note to empasize the notions of "pings"/"signal round trips" in the statement of my question; in notable distinction to the question statement of PSE/q/187917 and any answers there.)
May
30
revised Is there a name for the linear quantity corresponding to the (quadratic) “interval $\Delta s^2$”?
(v3.141592653: there had been an "end quote" mark missing in the question title.)
May
27
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
(v3.141: Removed in appropriate tag "[tag:time]"; restoration of the appropriate tag "[tag:duration]" is pending.)
May
27
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
(v3.14: Added two "Notes (p.s.)". Also: (trying to) restore the appropriate tag "[tag:duration]".)
May
21
revised Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?
(v3.1: Added excerpts of MTW Boxes 16.4 and 10.2; in response to comments.)
May
20
revised Lorentz Transformations and time of event
(v3.14159265: more minor copy-editing.)
May
12
revised Does the trial index of typical CHSH experiments constitute a “hidden variable”?
(v3.1415: expressions of separate constraints corrected.)
May
7
revised Time taken by a stone to reach the ground is independent of point of dropping
(v4: minor spelling correction.)