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Mar
25
comment For flat space-time as axiomatized by John W. Schutz can the notion of “betweenness” be defined through “paths” and “events”?
@CuriousOne: "no idea what "betweenness" is supposed to mean." -- From Schutz's monograph, or at least (via OP link) this intro you'd have some idea how it appears in relevant axioms. "I don't have a "betweenness" detector [...]" -- But I've suggested one in my OP. ""Paths" go out the window [...]" -- as soon as it has sunk in that here they don't correspond to trajectories of just any and all "material points" intended by Einstein, but only to some undefined few (called "in uniform motion", or "free"). EPS were just as ... lacking.
Mar
25
comment For flat space-time as axiomatized by John W. Schutz can the notion of “betweenness” be defined through “paths” and “events”?
@CuriousOne: "I don't see a physics question here." -- To emphasize what's already explained in the OP: By Einstein's assertion, All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more material points; therefore they do not amount to determinations of "betweenness" of such coincidences or encounters. Consequently, my asking how to define (or get rid of) "betweenness" is a (mathematical-)physics question
Mar
25
comment For flat space-time as axiomatized by John W. Schutz can the notion of “betweenness” be defined through “paths” and “events”?
@Kyle Kanos: "<sub></sub> and <sup></sup> work just fine." -- As far as rendering plain text in small size suitable for footnotes; but they seem to fail to accomplish this for MathJax symbols. (That doesn't mean I'm entirely happy with what I've written using MathJax either, because the \href command doesn't seem to work, so I haven't been able to put links in the footnotes.) Also: the issue of text size didn't seem to be mentioned on page physics.stackexchange.com/editing-help at all; but yes, the tags you mentioned happen to be included on another page which is linked there
Mar
25
revised For flat space-time as axiomatized by John W. Schutz can the notion of “betweenness” be defined through “paths” and “events”?
(v3.1415: more minor formatting)
Mar
25
asked For flat space-time as axiomatized by John W. Schutz can the notion of “betweenness” be defined through “paths” and “events”?
Jan
4
comment Comparing durations for two simply described motions in Schwarzschild geometry
John Rennie: "[...] watching from afar (which makes you a Schwarzschild observer)" ... surely there's an appropriate more specific (and coordinate-free) description of what you mean by "Schwarzschild observer (wrt. object $M$)" ... "if you start your stopwatch when [you saw that] $A$ passe[d] $B$ then the next time [you saw that] $A$ passe[d] $B$ your stopwatch will show a time $t$. The equations for the time measured by $A$'s clock and $B$'s clock are given [as ...]" -- No, no, no! Instead: If these "t" values of these three clocks were related as stated then they ran equally.
Jan
4
comment Comparing durations for two simply described motions in Schwarzschild geometry
John Rennie: "An object is following a geodesic if it is falling freely. [...]" Alright, thanks. Sorry for responding so late; partly due to the holiday break, partly because my question is quite shallow and rather an expression of my surprise about ... the remarkable inequality of durations arising in such a seemingly simple setting. I'll rather reward (and/or question) your more detailed derivation elsewhere. Here's just a general objection: [continued]
Jan
2
awarded  Popular Question
Dec
22
asked Comparing durations for two simply described motions in Schwarzschild geometry
Dec
4
answered Is it possible to learn about an event that occurred outside of your observable universe?
Dec
4
reviewed Approve Guess the wave function in a given potential
Dec
3
revised Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)
(v3.14159: reference corrected)
Dec
3
revised Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)
(v3.1415: formatting)
Dec
3
asked Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)
Nov
27
comment Angular velocity from orientational displacement
@Markus Fjellheim: "I found a solution where" -- Thanks for letting me know. I plan to look and possibly comment or vote on your answer later today. Without having done so, for now just some thoughts: "the difference vectors can be [...] zero" -- Interesting idea. If only one difference vector is zero, but not the other, then I suppose/believe that the constant vector gives the rotation axis. If both difference vectors are zero then angular speed seems ambiguous by some multiple of $2~\pi / \tau$, and the direction of rotation is completely undetermined.
Nov
26
comment Is max speed of causality (light) proven experimentally?
@Benito Ciaro: "signaling mechanism [...] Why stop there, just because we don't yet [...]?" -- We're considering thought experiments where each participant is supposed to be able to judge whether some signal had been observed (first) regardless of whatever "mechanism"; as a prerequisit for even being able to define various "mechanisms" and (possibly) attributing the signal front to one particular such "signaling mechanism". The remaining difficult practical questions: How sensitive is some actual detector to some definite "sig. mechanism"?, and: What's its actual index of refraction?
Nov
26
comment Is max speed of causality (light) proven experimentally?
Benito Ciaro: "if $c_0$ were speed of sound or the speed of carrier pigeons." -- $c_0$ is signal front speed (cmp. the link given in the answer). In the hypothetical case that a carrier pigeon has landed on your shoulder and that only on this occasion you're learning for the very first time that it had taken off from "somewhere else" at all, then the speed of this carrier pigeon (wrt. yourself and the suitable "starting pad") is correctly evaluated as $c_0$. (More typically you can see a pigeon already as it approached you, thus learning that it had started before it lands on you.)
Nov
26
comment Is max speed of causality (light) proven experimentally?
@Benito Ciaro: "your argument says nothing about a maximum." -- I wrote already: "the signal front speed $c_0$ constitutes a maximum: any signals having been exchanged, as far as a speed value can be attributed at all, had at most the speed of the corresponding signal front." I can add: the symbol $c_0$ is not "infinity" either, because a finite ping duration should define a finite distance value; and zero ping duration should define zero distance. "only talks about the speed of communication between participants." -- Sure. What else? [continued]
Nov
26
comment Angular velocity from orientational displacement
@Floris: "presumably in OP's case the vectors are "real life" and therefore have some relationship" -- The OP is specificly asking to consider an applicable case ("a,b") ("A 3-D object is rotating around an unknown 3-D axis [...]"); rather than asking "How do we determine whether two vector pairs arose from a rotation, or not?". If answers to the actual OP question may serve to characterize inapplicable cases ("p,q") as well, that's just a bonus. "Add measurement error [...]" -- IMHO that's deserving of a separate question. (Which I'd find interesting and might get around asking.)
Nov
25
comment Angular velocity from orientational displacement
@Floris: "But [...]" -- As far as I (am beginning to) understand what you meant by "the problem being overconstrained", I agree: there are examples of two vector pairs, say $\vec p_0,\vec p$, and $\vec q_0,\vec q$, with non-parallel vector differences and even with $$\|\vec p\|=\|\vec p_0\|,\qquad\|\vec q\|=\|\vec q_0\|,$$ which are not related by the same one rotation (described though angular velocity $\vec\omega$, and duration $\tau$). They fail to have equal "corresponding expressions" for determining a consistent value of angular speed; in contrast to the case considered in my answer.