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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?


Aug
5
revised How should two particles accelerate to have their separation Lorentz-contract?
(v3.14: some grammar fixed.)
Aug
5
answered Is time not a universal parameter, really, in special relativity?
Aug
5
answered How should two particles accelerate to have their separation Lorentz-contract?
Aug
5
comment A question about special relativity theory
Minimus Heximus: "by observes I mean exactly what you explained." -- Doubtful, because: How would you call what I meant above by "the given set of (raw) observational data"? "I do not understand the second part of your comment [...]" -- As far as I understand the (thought-)experimental setup described in your question, it requires that $$\frac{\text{distance between the two touchers of set No. 1}}{\text{distance between the two touchers of set No. 2}} =\frac{10~\text m}{10~\text m} = 1.$$ Is my understanding of your question correct? If so, you should understand my above comment in turn.
Aug
5
comment a thought experiment in special relativity theory
Minimus Heximus: "probably dmckee has deleted those comments to keep things tidy." -- Possibly so. Nevertheless: one user's "tidy" may be another's "outrageous". If user dmckee, or any other particular user, prefers not to see some selected comments (or all comments) I wish that each would be given the possibility of user:preference settings for this purpose; without infringing on the availability of those comments for other users who wish to read and quote them. There should even be a setting to adopt dmckee's settings (regarding comments, or otherwise) for those who'd prefer that.
Aug
5
comment A question about special relativity theory
Minimus Heximus: "observer on set No. 1 observes the distance between touchers in each set 10 meters." -- Distance values (or strictly: real values of distance ratios) are nothing to be "observed", but to be measured; i.e. by applying the corresponding measurement operator to a suitable given set of observational data, calculating its corresponding eigenvalue. "touchers in it [set No. 1] will be touched simultaneously." -- That's inconsistent with setup requirement $$\text{distance ratio "1/2"}=1,$$ but instead consistent with $$\text{distance ratio "1/2"}=\sqrt{1-\beta^2}.$$
Aug
5
comment a thought experiment in special relativity theory
Minimus Heximus: "your suggestion is the previous question linked. As the accepted answer there shows [...]" -- Alright, I'll have a look at the link and especially the accepted answer there (PSE/a/128527). (Sorry that I hadn't already before submitting my above comment. Also: I find it disturbing and inconsiderate that some comments at PSE are deleted without any trace, and possibly, as I've experienced myself, even without consent of the respective authors.) "By calculating I mean measuring." -- Sure. And physicists should care about that.
Aug
5
comment a thought experiment in special relativity theory
Minimus Heximus: "My question: Will set No. 2 slow down?" -- May I suggest that it was instead intended to ask: "Will set No. 2 light up?" ? (Also, considering that "the wiring" of set No. 1 might be thought of as having finite capacitance, the answer could be plainly: "Yes." .) "Note: the numbers in the picture is what an observer on set No. 1 calculates." -- What's that calculation explicitly? Does the value $$\sqrt{1 - \left(\frac{100000~\text{m/s}}{c}\right)^2} \lesssim 1$$ play a role in that calculation?
Aug
4
comment Relativity of simultaneity example in Resnick
Sean: "The two blue signal fonts indicate what would not actually occur" -- O.k. "the light reflected off the mirrors would not actually reach the green man located on the train simultaneously." -- It's incorrect to speak of "simultaneity" in this case. Instead: The light reflected off the mirrors would not actually reach the green man located on the train in coincidence. "Thus to him, the 2 reflected images of the lightning strike do not seem to be 1 in the same, but seem to be two separate events." -- Sure: two separate reflection events; in addition to the initial strike event.
Aug
4
revised Relativity of simultaneity example in Resnick
(v3.14159265: corrected order of comparison.)
Aug
4
revised Relativity of simultaneity example in Resnick
(some spelling corrected. Also: inserted one word in order to accumulate the required minimum of 6 changed characters.)
Aug
4
suggested suggested edit on Relativity of simultaneity example in Resnick
Aug
4
comment Relativity of simultaneity example in Resnick
Sean: "If one bolt of lightening struck the ground near the little red man, and the light expanded outward until eventually striking mirrors that are located at the ends of a train passing by [...] to those aboard the train, the light did not reach to opposite ends at the same time" -- Correct. (Details can be supplied. Note: there are several photons required.) "thus to them it seemed to be 2 separate lightening strikes." -- No; but two separate reflections of one signal (lightning strike). "Am I missing something ?" -- For one: the "blue signal fronts" seem unreal/unphysical.
Aug
4
answered Relativity of simultaneity example in Resnick
Aug
4
revised Relativity of simultaneity example in Resnick
(fixed grammar)
Aug
4
suggested suggested edit on Relativity of simultaneity example in Resnick
Jul
26
comment Relativity of simultaneity example in Resnick
Nevertheless: +1 for picking Resnick's pics which explicitly identify participant A' in distinction to participant A, and B' in distinction to B. Because: this allows (also in accordance with Einstein's definition) for instance to conclude and say that (A)'s indication of "being passed by (A')" was simultaneous to (B)'s indication of "being passed by (B')" as well as (A')'s indication of "being passed by (A)" was not simultaneous to (B')'s indication of "being passed by (B)". (I plan to elaborate this and submit as an answer, but I can get to that only in more than a week.)
Jul
26
comment Relativity of simultaneity example in Resnick
KartMan: "When the event happens at A, A' coincides with A, and when the event happens at B, B' coincides with B." -- Rather, the one event is the coincidence event of A and A' "meeting in passing" (consisting explicitly of of (A)'s indication of "being passed by (A')", and of (A')'s indication of "being passed by (A)"); and the other event is the coincidence event of B and B' "meeting in passing" (consisting explicitly of of (B)'s indication of "being passed by (B')", and of (B')'s indication of "being passed by (B)"). You notice that "primes" as part of names are inconvenient, btw.
Jul
25
revised metric-space wiki description
(still proof-reading ...)
Jul
25
suggested suggested edit on metric-space tag wiki