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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
9
comment Minkowski spacetime vs Euclidian space
@frodeborli: Well, since you comment above seems to lead significantly beyond your OP question (as far as I understand it at all), I won't respond to it here in any detail. But at least: it is my impression that you should be capable of continuing to ask about what's of interest to you and/or to benefit from the Q&As which have been submitted here at PSE already.
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
9
comment How does the number of events per bunch collision scale (as function of energy, luminosity …)
Burton Richter wrote: "[...] cross sections [$\sigma$] typically drop as $E^{-2}$." -- This seems to match formulas (47.1) - (47.12) of "The PDG Data Book", chap. 47: "Cross section formulae for specific processes", where $$\frac{1}{s}\simeq E^{-2}.$$ However, Figure 49.9 of chap. 49: "Plots of cross sections {...}" shows otherwise: $\sigma^{~p p}_{\text{tot}}$ rising with $\sqrt{s}$. This apparent discrepancy might be the root of my question...
Sep
8
asked How does the number of events per bunch collision scale (as function of energy, luminosity …)
Sep
8
answered Lightspeed (invariance) measurement methods
Sep
8
comment Minkowski spacetime vs Euclidian space
@frodeborli: "The magnitude is simply |v1 - v2|." -- By "v <index>" do you mean to denote a four-vector? Four-vectors are referring to pairs of events, e.g. pair "{event 1, origin event}", or pair "{event 2, origin event}". Yes, their difference is again a four-vector (referring to pair "{event 1, event 2}"), and its magnitude may be evaluated. But in your comment Sep 2 [2014] at 19:29 above you were discussing "objects"; as far as I understand, any "object" generally took part in several distinct events (which are timelike related to each other). So: which is it?
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
Sep
8
comment Lightspeed (invariance) measurement methods
Certainly a worthwhile question, +1. I'm especially curious whether there might be any answers forthcoming to claim that "measuring lightspeed" (in the sense of comparing quantitatively between different trials) were still, or had ever been, a reasonable proposition. (I plan to soon submit an answer to the contrary.)
Sep
8
suggested suggested edit on Lightspeed (invariance) measurement methods
Sep
8
comment Lightspeed (invariance) measurement methods
[Continued] Regarding notation: please provide a distinctive symbolic expression for the notion "round-trip length" which appears in your answer; ideally distinctive enough to be distinguishable from notation of "single-trip length(s)", and along with distinctive symbolic expressions for other relevant "round-trip quantities".
Sep
8
comment Lightspeed (invariance) measurement methods
David Hammen: "Everyone who knows the relevant metrological techniques knows that [...]" -- It seems unbecoming to the CGPM to (even give the impression to) rely on possibly obscure "relevant metrological techniques" in the definition of a so-called base unit. Also, it seems questionable whether any "relevant metrological techniques" could and have been expressed without referring to any particular values of "lengths" (or "distances") whatsoever, so they might indeed be unambiguosly known by any experimenter without having to insert ideosynchratic presumptions about such values.
Sep
7
comment Lightspeed (invariance) measurement methods
David Hammen: "[...] experiments to establish the length of a meter. (But it's still a round-trip length that is being measured.)" -- The "round trip" condition is however notably absent from the SI "metre" definition. (Absent there is also the condition that "two ends which are attibuted a length of one meter apart had to be at rest, or at least rigid, to each other". However, since my corresponding question has been "closed", it appears anathema to find that noteworthy at PSE, too.)
Sep
7
comment Minkowski spacetime vs Euclidian space
@frodeborli: "if you have absolute values for each of the four components of the world line, of both objects - a distance can easily be calculated." -- I'd like to see such a calculation in some detail. Are you perhaps considering to attribute a value of "distance" to a pair of object which are not at rest to each other ?? If so, that's (at best) called an "improper distance" between these two objects.
Sep
7
answered Special Relativity Question: Doppler shift
Sep
7
comment Is it possible for information to be transmitted faster than light by using a rigid pole?
user34793: "You then are aware that with this phenomena [...]" -- I've certainly noticed plenty Q&As specificly about that having been posted here already. "send data instantly, irrespective of the distance between the transmitter and the reciever" -- No, and that's the main point (about which you seem to be mistaken): two sets of transmitter/receiver/observer who communicate (referring to signal round trips) instantly among each other are thus measured having had zero separation (a.k.a. having been coincident).
Sep
6
comment Is it possible for information to be transmitted faster than light by using a rigid pole?
user34793: "Are you [user12262] aware of what quantum entanglement is?" -- Yes,and confidently enough to occasionally contribute answers here on that topic. However, the point is: That's not even relevant. We might as well talk about two black boxes whose "inner workings" are unknown to either of us; both equipped with screen and keyboard. Any signal which was transmitted from one keyboard to the other screen was either (at best) itself the signal front and consequently "just as fast as" the signal front, or it was/arrived even later than the signal front. By definition.
Sep
6
comment Is it possible for information to be transmitted faster than light by using a rigid pole?
user34793: "There is however a more pragmatic, effective solution, [...]" -- Not at all. Signals cannot be transmitted faster than the signal front, as a matter of principle.
Sep
6
comment Minkowski spacetime vs Euclidian space
@John Rennie: "[...] proper time. For a freely falling observer it's equal to the time shown on a clock carried by the observer" -- No, not in general. A clock does not necessarily show coordinate values $t$ whose differences are affine (proportional) to the duration (a.k.a. "proper time", or "magnitude of world line segment") of this clock (incl. the incidental observer "carrying it"). Only if it does it is called a "good clock".
Sep
6
comment Minkowski spacetime vs Euclidian space
[contd. ...] where $A$'s ping duration $\tau_A^{\text{ping to B and back}}$ is the (constant) magnitude of any segment of $A$'s world line from any signal event in which $A$ took part until the corresponding event at which $A$ observed that $B$ had observed this signal event, $B$'s ping duration $\tau_B^{\text{ping to A and back}}$ is the (constant) magnitude of any segment of $B$'s world line from any signal event in which $B$ took part until the event at which $B$ observed that $A$ had observed this signal event, factor $\frac{1}{2}$ is conventional, and letter $c$ is a distinctive symbol.
Sep
6
comment Minkowski spacetime vs Euclidian space
@frodeborli: "that a distance can be calculated in terms of "world line distance" between two objects." -- Not exactly. 1: Two objects, $A$ and $B$, are characterized by a "distance" between each other only if and while they were at rest to each other (a.k.a. both having been members of the same inertial frame). If so then 2: the value of the distance between objects $A$ and $B$ (at rest to each other) is $$\overline{AB} = \overline{BA} := \frac{c}{2} \tau_A^{\text{ping to B and back}} = \frac{c}{2} \tau_B^{\text{ping to A and back}}$$ where [... to be continued]