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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
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
comment How to define a convex surface in case of refraction?
Saurabh Raje: "can we fix our observation point as the source of light?" -- Regarding optical imaging there's surely a practical, conventional "optician's view": "along the ray(s)", from object to image. In the case of your example, that's just the reverse of the (practical, conventional) "lensmaker's view": from the outside of the (dense) material. My point: The corresponding surface has a particular intrinsic geometry. Now: it may be said (concisely) that the surface to be considered in your exam must have been "bulging away from the material". But how exactly should we draw that??
Sep
10
comment How to define a convex surface in case of refraction?
akrasia: "A convex surface is one that bulges out towards the person who is talking about it." -- You've got a (virtual! ;) point there: a cave is usually understood from the perspective of "being (wrapped) inside"; hence it's said to have a "concave surface". Then as the opposite (watching a cave from the outside): a "convex surface". But: Does a surface whose cross section is shaped like the capital letter "B" "bulge out towards" a person (looking at it from the right-hand side), for instance? "we do not live inside glass" -- But, typically: air. Some, part-time, even: water.
Sep
10
comment How to define a convex surface in case of refraction?
@akrasia: "talk about using a sledgehammer!" -- Talk about giving a forthright, self-respecting, defensible answer.
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
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
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
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
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
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]
Sep
5
comment As the universe expands, the wavelengths of photons are stretched, and energy is lost. What about electrons?
@dmckee: "The notion of "free propagation" here [...] Nothing mysterious at all." -- Well, as far as I understand there are profound questions (if not mysteries) being addressed in investigations such as "Characterizability of Free Motion in Special Relativity", U. Schelb, FP 30(6):867-892 (2000); and they seem even more difficult outside SR. "The changing of the scale factor is not a force in the conventional sense [...]" -- In order to prove this assertion you'd have to consider in detail the definitions of (how to measure) both these quantities.