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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]
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.
Nov
25
comment Angular velocity from orientational displacement
@Floris: "I'm not convinced there is a unique solution for any combination of $a$ and $b$. Is there?" -- If the vector differences $\vec a - \vec a_0$ and $\vec b - \vec b_0$ are parallel to each other then the direction of the angular velocity $\vec \omega$ is not uniquely determined. (This seems obvious in "my approach", and should therefore apply to "your approach", too.) Also, there's an ambiguity in the magnitude; related to the periodicity/multiplicity of $\text{ArcCos}$. But (... obviously ... &) trials may be restricted so that $\| \vec a - \vec a_0 \|$ only increased.
Nov
25
comment Angular velocity from orientational displacement
@Floris: "This may turn out to be simpler than my approach..." -- Yeah. At least, by "some algebra", I find that our answers agree in determining the direction of $\vec \omega$. If "my approach" should be not immediately obvious, I could add that, obviously, $\vec a$'s "component along" $\vec \omega$ should remain constant; thus $$\frac{\vec \omega~(\vec a \cdot \vec \omega)}{(\| \vec \omega \|)^2} = \frac{\vec\omega~(\vec a_0 \cdot \vec \omega)}{(\| \vec\omega \|)^2}. $$ So $$(\vec a \cdot\vec\omega) = (\vec a_0 \cdot\vec\omega)$$ and immediately $$((\vec a - \vec a_0)\cdot\vec\omega)=0.$$
Nov
24
comment Is there a principal difference in acceleration from an impulse and the free fall of a body in the orbit around a gravitational mass?
HolgerFiedler: +1 for having asked a question admitting an answer that's expressed in terms of spacetime intervals (or suitable generalizations) and which therefore points in turn to the more fundamental and pressing problem of how exactly spacetime intervals (or suitable generalizations) ought to be determined strictly from "determination of space-time coincidences {such as} encounters between two or more {...} material points" in the first place.
Nov
12
comment Is presuming that any linear uniform motion is transformed into another one sufficient to assume that Lorentz transformation must be linear?
failtrolol: "[...] uniform motion must be a uniform motion in any reference frame." -- Perhaps "any reference frame" is here meant to be understood as "any inertial reference frame". (Otherwise, "uniform motion in a non-inertial frame" seems a paradoxial notion. Though it can be said in any case that "mutual rest of participants being described" is a intrinsic, proper notion.) If so, yes: the (pairwise) motions of members of distinct inertial systems is mutually uniform, and moreover with mutually equal speed. But all that's independent of coordinate assignments, or transformations.
Nov
12
comment Is it appropriate to attribute an entangled state description to only one trial?
Timaeus: "The word measurement is just a (rather silly) name for certain kinds of interactions." -- No (that'd be silly), but moreover: to record and to evaluate relevant interactions (or their absence); noting "with whom" and "in which sequence (or in coincidence)", and applying subsequent measurement/evaluation operators. "[Is it possible to quantify ...] No." -- Well, there seem to be some attempts after all, such as this (though admittedly I haven't figured out yet how this particular approach might be applied to my specific question).
Nov
12
comment Is it appropriate to attribute an entangled state description to only one trial?
Timaeus: "Edited. [...] common to have decay products be in an entangled state." -- Sure. Does this impede distinguishing the state attributed to the products of just one decay from the state atttributed to products of an ensemble of decays? "there is simply no empirical evidence that [...]" -- Claims of "evidence" (or lack thereof) can only be convincing if it's already agreed what constitutes (and how to gather) "evidence".
Oct
29
comment Is it appropriate to attribute an entangled state description to only one trial?
Timaeus: Thanks for your detailed and notably rapid answer; +1. "The way you tell it" ... "It": the (suitably numerous) ensemble ... "was in the [entangled] state [...] by considering lots of potential different types of measurements." -- Right (not least, to determine ratios between coefficients). Thus: just one trial is not enough for this characterization. "Being entangled is about the state prior to measurement." -- That's unacceptable. Even "preparing" an ensemble is about first measuring, and then discarding trials (as "invalid") which didn't match the prep. prescription.
Oct
29
comment What is the dilation relation of the distance to a moving point (in special relativity)?
aayyachi: "frame $F_a$ is being translated with a speed $v$ according to another frame F_b$" -- These frames are thus two inertial systems; where (mutually) the members of one determine the speed of each member of the other as the same value $v$. "point $A$ is attached to $F_a$. $B$ is attached to $F_b$" -- Alright. (Instead of "is attached to" I'd say "was and remained a member of"). "$D_a$ is the distance $AB$ [...]" -- No: distance values are attributed to pairs of members of the same IS. The relation between $A$ and $B$ is characterized not by some distance, but by speed $v$.
Oct
29
comment Quantum entanglement and Compton Effect
Timaeus: "Entangled just means not factorizable. [...] you have a definite correlation [...] there are lots of entanglements and degrees of entanglement [...] we do need the energies to be different to be entangled." -- These are fair, crisp descriptions; +1. I'd like your answer even more if you could address how this relates to calling only one pair "entangled" (cmp. OP: "Suppose we generate 2 entangled photons [...]"). p.s. If you decide to edit your answer there are also some typos to correct.
Oct
29
comment Quantum entanglement and Compton Effect
Timaeus: "One way to entangle photons is to have a state like $$\frac{1}{\sqrt 2}\left|\nu_{i,1}+\right\rangle_1\otimes\left|\nu_{i,1}+\right\rangle_2+\frac{1}‌​{\sqrt 2}\left|\nu_{i,2}+\right\rangle_1\otimes\left|\nu_{i,2}+\right\rangle_2$$ [...]" -- Not to argue about style and taste, but your expression is even wrong by confusing indices which are distinct. Better write: $$\frac{1}{\sqrt 2}\left|\nu_{i,\text{low}} +\right\rangle_A\otimes\left|\nu_{i,\text{low}} +\right\rangle_B+\frac{1}{\sqrt 2}\left|\nu_{i,\text{high}} +\right\rangle_A\otimes\left|\nu_{i,\text{high}}+\right\rangle_B$$.
Oct
28
comment Difference between Distance and Space
@Hep: "So what you're saying is that we can measure their separation [...]" -- If A and B found (separately) constant and (mutually) equal ping durations of 2.000.000 years each then they're attributed a value of their mutual separation: 1.000.000 light years. "but [we can] not [measure] their distance from one another" -- If A and B found their ping durations as described, and are accordingly being attributed a mutual separation of 1.000.000 light years, but if the region containing them was not flat (due to whatever), then we don't call this result a "distance" value.
Oct
27
comment Delayed Choice Quantum Eraser: Am I missing something here?
Related: "Kim delayed choice experiment" (PSE/q/214040).