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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?


Apr
4
accepted Are signal fronts in a beam not at rest to each other?
Apr
4
comment The scissor paradox: can we pass the information faster than light?
user43796: "Point A and photon travel for a same distance, the photon gets there later." -- ok, let me try again to catch that in my own words: There's a thread placed between/across the still open scissor blades ("close to the start"); the scissors close --> the thread is cut (that's widely visible!). So when (or rather: how) will the scissor tips first learn about that cut event? Well: not necessecarily just because the tips touched each other (i.e. point $A$ had gotten there). Rather: they first learned it when they said they learned it.
Apr
4
comment The scissor paradox: can we pass the information faster than light?
user43796: "[...] Wherever A is, the light will be blocked" -- Allright, I think I got that setup: just e.g. a series (or "bank") of cameras with the scissor blades making a shutter. They're watching some movie. The shutter will close. (According to your setup, i.e. "sequentially rapidly progressing"; or, just as another consideration: the shutter might instead close in front of individual cameras in some arbitrary order.) Now: Is there information being passed from one camera to the other?? How should one camera know what "the final scene" was, that some other camera saw before being shut?
Apr
4
revised The scissor paradox: can we pass the information faster than light?
(v3.14159265: better description of motion in response to signal; which is not perfectly rigid ...)
Apr
4
comment The scissor paradox: can we pass the information faster than light?
user43796: "Point A could exceed the speed of light since it's a geometric object" -- Yes; similar to a "(wave) phase". Therefore its speed is phase speed. Another example is the "(virtual) motion" of a laser pointer dot over a screen. "but then what if I place a detector close enough to where A starts to move?" -- Yes, $A$ can and will arrive at (and pass by) detectors. But: thereby there's no information/signal being passed from fulcrum $O$ to any of those detectors (or likewise from one detector to another).
Apr
4
revised The scissor paradox: can we pass the information faster than light?
(v3.1415926: having proof-read to sloppily ...)
Apr
4
answered The scissor paradox: can we pass the information faster than light?
Apr
4
comment Query into the cumulative velocity of mounted platforms
@DumpsterDoofus: "A railgun with 100,000 stages as drawn would probably end up the size of the solar system, so I think the possibility can be ruled out in the near future, given the current state of space research funding :)" -- Well, projecting the generally expected rate of proposal maturation h_t_a might instead take steps through the long tail of thermal distributions and make his scheme fit snugly in the solar core. p.s. Just noticed jazzwhiz's contribution So: your turn?
Apr
4
comment Query into the cumulative velocity of mounted platforms
@DumpsterDoofus DumpsterDoofus: "That fails once you get to relativistic speeds, but typical rail-gun velocities are between 10000 and 100000 times slower than light, so you can safely ignore relativity" -- Then let's consider the conservative "$\beta_i := 10^{(-5)}$"; or, as hello_there_andy might put it: "v_i := 3000 ms-1". So: What exactly do we tell him about "Russian Dolls" with 100000 or even more such stages ?!? @hello_there_andy -- I remember that drawing (or sth similar?), too. You might find it helpful for now to get rid of any energy considerations and focus on kinematics.
Apr
3
comment Query into the cumulative velocity of mounted platforms
hello_there_andy: "[...] Now throw that stone whilst running at [speed] Ums-1. It seems in the latter scenario the total [speed] of the stone is [(V + U)][ms-1]." -- Not really. From the detailed definitions of how to determine (compare, "add") "velocity" values (which involves detailed definitions of how to determine geometric relations between "starting gate" and "finish line") it follows, that in the indicated scenario the total speed of the stone (wrt. the "race track") "seems" (V + U)ms-1 only as far as the number "V * U / 300000000^2" is considered negligible.
Apr
3
comment What is charge actually? How to define it?
+1 -- After all, this answer provides an avenue towards understanding what's meant by "field (strength)" and "coupling" in the first place; and that "electromagnetic" charges and fields may be (systematically, reliably) distinguished from certain other kinds of charges and corresponding fields.
Apr
3
answered Can we think of gravity as space itself moving?
Apr
3
answered Are signal fronts in a beam not at rest to each other?
Apr
3
comment Is the universe flat?
Christoph: First I have to correct: The relations $AB = JK$ and $AJ = AK = BJ = BK$ are of course also satisfied by those four points being "corners of a square" (with "diagonals" $AB$ and $JK$) which is of course plane since precisely $AB = JK = \sqrt{2} \, AJ$. My point was then that on a torus surface (or even on a cylinder) four points can be easily found such that $AB = JK$ and $AJ = AK = BJ = BK$ and $AB < AJ$. "en.wikipedia.org/wiki/Torus#Flat_torus" -- Indeed, one more reason to be extremely wary to use coordinates in cosmology, or in physics overall.
Apr
3
comment How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?
George G: "you could hypothetically find a lower limit, but no experiment has ever been able to do so" -- Well, the point I've been trying to express in my answer here was that, No: such an hypothesis is outright inconsistent. "The results listed there are from many different experiments using different methods, so I don't think you would find a systematic error across all of them" -- In order to deal with syst. uncert.ies they should all have had a (thought-experimentally) definite notion how to get the "true value" of the quantity they sought
Apr
2
comment Is the universe flat?
Christoph: "eg a torus can be equipped with a flat connection" -- On any usual torus surface e.g. there are easily 4 points, $A$, $B$, $J$, $K$ such that $AB = JK$ and $AJ = AK = BJ = BK$. (In the sketch e.g. $A$ and $B$ on the red ring symmetrically above and below the outer black circumference; together with $J$, $K$ on the inner black ring left and right of the red ring.) Those are explicitly not plane to each other: their Cayley-Menger determinant doesn't vanish. (So: the universe is flat?? ...)
Apr
2
comment Orthogonality of summed wave functions
@PoetryInMotion: The underlying assumption is that the symbols "plus ($+$)" and "minus ($-$)" that you used to express $\Psi_3$ and $\Psi_4$ in terms of the "orthonormal basis" states $\Psi_1$ and $\Psi_2$ do in fact represent the corresponding arithmetic operations between the complex number values of inner products. Consequently: $\langle \Psi_1 - \Psi_2 | \Psi_1 + \Psi_2 \rangle \text{=(means the same as)=} \langle \Psi_1 | \Psi_1 \rangle + \langle \Psi_1 | \Psi_2 \rangle - \langle \Psi_2 | \Psi_1 \rangle - \langle \Psi_2 | \Psi_2 \rangle$ which can be readily evaluated further (being $0$)
Apr
2
comment How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?
George G: "There is no way to be 100% sure" -- If there were no way to be 100 % sure, at least in principle, could there be "systematic uncertainteis" evaluated for the quoted "experimental limits"; and eventually the values "$\text{CL%}$ in pdg.lbl.gov/2013/listings/rpp2013-list-photon.pdf ? "but we can put upper limits on the mass." -- Can we also put lower limits on the photon mass; at least in principle and/or experimentally?
Apr
2
answered How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?
Apr
1
comment Are signal fronts in a beam not at rest to each other?
Jim: "being separately represented by time-like four-vectors is [...] a necessary condition [for being qualified as having been] at rest wrt. each other" -- I'd consider any answer more valuable which derives/proves this assertion, than any answer which makes this assertion as an axiomatic claim. (The desired proof should be based on the (or a suitable) operational definition of how to measure whether or not given somethings were "at rest wrt. each other". The hint again: google.com/#q=%22chronogeometry%22 )