1,314 reputation
121
bio website
location
age
visits member for 1 year, 10 months
seen 4 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?


2d
revised Double slit experiment and single particles. Is the wave function just a mathematical model?
spelling: Niels Bohr, etc.
2d
suggested suggested edit on Double slit experiment and single particles. Is the wave function just a mathematical model?
2d
suggested suggested edit on Gravitational Redshift between spacecraft
2d
suggested suggested edit on Can a super-extremal charged black hole be made out of electrons only?
2d
suggested suggested edit on Would an Object Near a Pre-Blackhole Star Experience the Same Gravity as Post-Blackhole?
2d
revised Energy-momentum tensor of Bosonic Ghost Action in String Theory
corrected spelling the name of H. Grassmann, cmp. http://en.wikipedia.org/wiki/Grassmann_variable; as well as the name of L. D. Faddeev
2d
suggested suggested edit on Energy-momentum tensor of Bosonic Ghost Action in String Theory
2d
suggested suggested edit on QED BRST Symmetry
2d
suggested suggested edit on Hilbert Space of (quantum) Gauge theory
2d
revised Stabilizer formalism for symmetric spin-states?
corrected spelling the name of W. Heisenberg; cmp. http://en.wikipedia.org/wiki/Heisenberg_picture
2d
suggested suggested edit on Stabilizer formalism for symmetric spin-states?
2d
revised Labelling representations using isospin and hypercharge
corrected spelling the name of P. Gordan; cmp. http://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients
2d
revised Triangle inequality Clebsch-Gordan coeffcients
corrected spelling the name of P. Gordan; cmp. http://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients
2d
revised Shouldn't the addition of angular momentum be commutative?
corrected spelling the name of P. Gordan; cmp. http://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients
2d
revised Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket?
corrected spelling the name of P. Gordan; cmp. http://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients
2d
suggested suggested edit on Shouldn't the addition of angular momentum be commutative?
2d
suggested suggested edit on Labelling representations using isospin and hypercharge
2d
suggested suggested edit on Triangle inequality Clebsch-Gordan coeffcients
2d
suggested suggested edit on Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket?
2d
answered Why Light and Observers have different laws of physics