#inertialframe — Public Fediverse posts

My comment (10.04.2024) on https://scirate.com/arxiv/2302.12209

A. V. Nenashev, S. D. Baranovskii

"How to detect the spacetime curvature without rulers and clocks"

(1) Nenashev and Baranovskii introduce an innovative and relevant notion; they even give it a unique name : "#WellStitchedness" of (conformally flat) #Spacetime.
It would be suitable and helpful to advertise this important new notion already in the abstract of the article.

(2) Problematic but easy to correct is their frequent referral to individual participants ("Alice", or "Bob", etc.) having seen several distinct signal indications "simultaneously", although they mean that the participant under consider had seen those signals "together", a.k.a. "in coincidence", or "in the same moment". (The characterization as "simultaneous" has very specific different meaning, especially in the context of the theory of #Relativity, of course.)

(3) The specific set of 16 #CausalRelations (being fulfilled) between 8 (suitable #Events), as it appears in the definition of a well-stitched spacetime, in the particular variant sketched in Fig. 1d, also appears (multiple times) in the elementary cell of "#TetrahedralOctahedral #PingCoincidenceLattices" (and therefore also in the elementary cell of "#OctetTruss #PCLs"); in the projection to 3D Euclidean space (namely; in tetrahedral-octahedral honeycombs, or in octet truss space frames) recognizable as regular octahedra.

The main result ("A 4-dimensional spacetime is conformally flat if and only if it is well-stitched.") is therefore also and especially relevant for defining, exclusively in terms of causal relations, notions of "#InertialFrame" and "#Ruler" and "#Clock" in conformally flat spacetime regions.

Heads-up! to https://arxiv.org/abs/2302.12209
"How to detect the spacetime curvature without rulers and #Clocks"
(A. V. Nenashev, S. D. Baranovskii)

-- which investigates the question (p. 2)
"Is it possible to figure out that a spacetime [region] is curved [instead conformally flat] by testing #CausalRelations only ?"

-- and provides proof of a positive answer through a criterion in terms of causal relations among any set of eight #events (#StitchConfiguration).

Closely related is the question
"Is it possible to figure out whether two (or more) participants are sitting still wrt. each other in a flat region (or whatever is equivalent in a conformally flat region) by testing causal relations only ?",

(referring to the notion of #InertialFrame in the sense of W. Rindler as "set of point particles sitting still wrt. each other"; cmp. http://www.scholarpedia.org/article/Special_relativity:_kinematics),

-- which is presumably solved by #tetrahedral-octahedral #PingCoincidenceLattices, closely related to #OctetTruss #PingCoincidenceLattices; see e.g. https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb and https://www.google.com/search?q=%22octet+truss%22&tbm=isch&prmd=ivnbz

-- and where, notably, eight events in one particular variant of the #StitchConfiguration do indeed occur as integral part of those mentioned #PingCoincidenceLattices (namely, not surprisingly, depicted as #Octahedra in the familiar drawings of the corresponding "plain 3D" lattices).

#Relativity #Spacetime

@ocfnash
http://olivernash.org/2018/07/08/poring-over-poncelet/index.html

Awesome!
I'd love to find out about #Poncelet generalizations or related results in 3+1 dimensional flat #MinkowskiSpace, with

- all relevant edges along light cones (Are those "singular" and perhaps problematic, even in 3+1 D ?), and

- the \(n\)-sided polygon generalized to a #PingCoincidenceLattice (cmp. my sketch https://mathstodon.xyz/@MisterRelativity/109435130217990848 )

#SpaceTime #InertialFrame #geometry #relativity

@ocfnash
http://olivernash.org/2018/07/08/poring-over-poncelet/index.html

Awesome!
I'd love to find out about #Poncelet generalizations or related results in 3+1 dimensional flat #MinkowskiSpace, with

- all relevant edges along light cones (Are those "singular" and perhaps problematic, even in 3+1 D ?), and

- the \(n\)-sided polygon generalized to a #PingCoincidenceLattice (cmp. my sketch https://mathstodon.xyz/@MisterRelativity/109435130217990848 )

#SpaceTime #InertialFrame #geometry #relativity

@ocfnash
http://olivernash.org/2018/07/08/poring-over-poncelet/index.html

Awesome!
I'd love to find out about #Poncelet generalizations or related results in 3+1 dimensional flat #MinkowskiSpace, with

- all relevant edges along light cones (Are those "singular" and perhaps problematic, even in 3+1 D ?), and

- the \(n\)-sided polygon generalized to a #PingCoincidenceLattice (cmp. my sketch https://mathstodon.xyz/@MisterRelativity/109435130217990848 )

#SpaceTime #InertialFrame #geometry #relativity

@heafnerj
Joe Heafner wrote:
> <em> [...] concept of #InertialFrame in [... the ST] of #relativity https://arxiv.org/abs/2103.15570 </em>

So ... author Boris Čulina, who

- doesn't even acknowledge a distinction of "good #clock" vs. "bad #clock" (cmp. MTW, Fig. 1.9),

- much less #HowTo define + measure such a distinction by [#CoincidenceDeterminations](http://einsteinpapers.press.princeton.edu/vol6-trans/165?highlightText=coincidences),

is nevertheless https://arxiv.org/auth/show-endorsers/2103.15570 ?!? ...

Well, therefore, we have #mastodon

@heafnerj
Joe Heafner wrote:
> <em> [...] concept of #InertialFrame in [... the ST] of #relativity https://arxiv.org/abs/2103.15570 </em>

So ... author Boris Čulina, who

- doesn't even acknowledge a distinction of "good #clock" vs. "bad #clock" (cmp. MTW, Fig. 1.9),

- much less #HowTo define + measure such a distinction by [#CoincidenceDeterminations](http://einsteinpapers.press.princeton.edu/vol6-trans/165?highlightText=coincidences),

is nevertheless https://arxiv.org/auth/show-endorsers/2103.15570 ?!? ...

Well, therefore, we have #mastodon

@heafnerj
Joe Heafner wrote:
> <em> [...] concept of #InertialFrame in [... the ST] of #relativity https://arxiv.org/abs/2103.15570 </em>

So ... author Boris Čulina, who

- doesn't even acknowledge a distinction of "good #clock" vs. "bad #clock" (cmp. MTW, Fig. 1.9),

- much less #HowTo define + measure such a distinction by [#CoincidenceDeterminations](http://einsteinpapers.press.princeton.edu/vol6-trans/165?highlightText=coincidences),

is nevertheless https://arxiv.org/auth/show-endorsers/2103.15570 ?!? ...

Well, therefore, we have #mastodon

@heafnerj
Joe Heafner wrote:
> <em> [...] concept of #InertialFrame in [... the ST] of #relativity https://arxiv.org/abs/2103.15570 </em>

So ... author Boris Čulina, who

- doesn't even acknowledge a distinction of "good #clock" vs. "bad #clock" (cmp. MTW, Fig. 1.9),

- much less #HowTo define + measure such a distinction by [#CoincidenceDeterminations](http://einsteinpapers.press.princeton.edu/vol6-trans/165?highlightText=coincidences),

is nevertheless https://arxiv.org/auth/show-endorsers/2103.15570 ?!? ...

Well, therefore, we have #mastodon

#HyperbolicMotion of participant \(A\) in a "flat #spacetime region", in terms of Minkowski coordinates \((t, x)\) (which are of course adapted to the geometric relations between members of an #InertialFrame \(\mathcal F\)):

\(x_{\mathcal F}[ \, A \, ] = (c^2/a) \, \left(\sqrt{1+(a/c\, t_{\mathcal F}[ \, A \, ])^2}-1\right) \)

which can be re-arranged to "the canonical form" of an [hyperbola equation](https://en.wikipedia.org/wiki/Hyperbola#Equation) (wrt. Cartesian coordinates).

(2/7) #Relativity #TeachRelativity