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  1. Solar eclipse & Einstein's theory of relativity

    In late 1915, Einstein finalized his general theory of relativity using Riemannian geometry, predicting Mercury's perihelion precession and gravitational lensing. Arthur Eddington verified these predictions four years later during the 1919 solar eclipse.

    en.wikipedia.org/wiki/Eddingto

    Books by Eddington at PG:
    gutenberg.org/ebooks/author/34

    #books #relativity #astronomy #solareclipse

  2. Solar eclipse & Einstein's theory of relativity

    In late 1915, Einstein finalized his general theory of relativity using Riemannian geometry, predicting Mercury's perihelion precession and gravitational lensing. Arthur Eddington verified these predictions four years later during the 1919 solar eclipse.

    en.wikipedia.org/wiki/Eddingto

    Books by Eddington at PG:
    gutenberg.org/ebooks/author/34

    #books #relativity #astronomy #solareclipse

  3. `The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.`

    en.wikipedia.org/wiki/Kerr_met

    #physics #relativity #generalRelativity #cosmology

  4. `The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.`

    en.wikipedia.org/wiki/Kerr_met

    #physics #relativity #generalRelativity #cosmology

  5. @argv_minus_one
    #Mastodon for the way at the start...

    #Jitsi Meet realtime audio chat after checking people's'profile more deeply and their direction.

    Finding the #art of #talking while accepting some #relativity in / #motivation to do more / #sharing your likes / talents to #test and increment #trust.

    Going for the win in #humanity "slowly but surely".

    Perhaps not all-in but half-in (?) for those with time to #improve #logic.

    #Mastodon + #Jitsi WebRTC
    =
    #Human AND #Software #Development

  6. @argv_minus_one
    #Mastodon for the way at the start...

    #Jitsi Meet realtime audio chat after checking people's'profile more deeply and their direction.

    Finding the #art of #talking while accepting some #relativity in / #motivation to do more / #sharing your likes / talents to #test and increment #trust.

    Going for the win in #humanity "slowly but surely".

    Perhaps not all-in but half-in (?) for those with time to #improve #logic.

    #Mastodon + #Jitsi WebRTC
    =
    #Human AND #Software #Development

  7. Perhaps some day you will realize your "troubles " are really not so...
    #Relativity

  8. Perhaps some day you will realize your "troubles " are really not so...
    #Relativity

  9. You can't ride alongside a beam of light, and the reason why opens a door onto the strangest parts of relativity. A tour of rest frames, why a photon has no point of view, and how your speed reshapes… #science #relativity #spacetime

    universetoday.com/articles/wha

    Posted into FLIPBOARD EXCHANGE FEED 🗞️ @flipboard-exchange-feed-Econopass

  10. A quotation from Montaigne

    Things are neither so grievous nor so difficult in themselves, but our weakness and cowardice make them so.
     
    [Les choses ne sont pas si douloureuses, ny difficiles d’elles mesmes: mais nostre foiblesse & lascheté les fait telles.]

    Michel de Montaigne (1533-1592) French essayist
    Essays, Book 1, ch. 14 (1.14), “The Taste of Good and Bad Things Depends Mostly on the Opinion We Have of Them [Que le goust des biens et des maux despend en bonne partie de l’opinion que nous en avons]” (1572) [tr. Ives (1925)]

    More about (and translations of) this quote: wist.info/montaigne-michel-de/…

    #quote #quotes #quotation #qotd #montaigne #micheldemontaigne #cowardice #difficulty #fear #pain #perspective #relativity #subjectivity #weakness #nerves #selfcontempt #selfdoubt #selfsabotage #

  11. Long unsolved problems in (place favorite discipline here) are always going to evolve camps that believe some other camp has screwed up big time. The #StandardModel has problems. #QuantumMechanics has problems. #Cosmology has issues. #Relativity has...okay you do you.
    At the boundary of our abilities things always get a bit wonky,. For #QuantumMechanics things get pretty weird almost immediately.
    Our theory and knowledge have limits. We push them and then complain incessantly.
    Onward march

  12. @level98 wrote (Jul 06, 2026, 21:46 UTC):

    > In SR we are NOT suggesting one clock runs slower than one other clock.

    This can be claimed MORE SINCERELY by you and me (who reject and avoid the *terrible* phrase) than by anyone using it uncritically.

    p.s.
    Other than this agreement (the main point) I continue to disapprove of your terminology; e.g.: What do you mean by a "location" ?

    Note W. Rindler's description
    _»An inertial frame is simply an infinite set of point particles sitting still in space relative to each other.«_

    (The #relativity problem of first of all finding out whether any abstract-hypothetical reference frame is an inertial system, or not, you may delegate to Nenashev, Baranovskii arxiv.org/abs/2302.12209
    and Your's truly.)

    Rindler's description see at scholarpedia.org/article/Speci

    #relativity

  13. @level98 wrote (Jul 06, 2026, 21:46 UTC):

    > In SR we are NOT suggesting one clock runs slower than one other clock.

    This can be claimed MORE SINCERELY by you and me (who reject and avoid the *terrible* phrase) than by anyone using it uncritically.

    p.s.
    Other than this agreement (the main point) I continue to disapprove of your terminology; e.g.: What do you mean by a "location" ?

    Note W. Rindler's description
    _»An inertial frame is simply an infinite set of point particles sitting still in space relative to each other.«_

    (The #relativity problem of first of all finding out whether any abstract-hypothetical reference frame is an inertial system, or not, you may delegate to Nenashev, Baranovskii arxiv.org/abs/2302.12209
    and Your's truly.)

    Rindler's description see at scholarpedia.org/article/Speci

    #relativity

  14. @level98

    > [_» ... that there is no fact of the matter about who is moving and if I think you are moving then you think I am moving.«_ ]

    > Given that was the whole point of the OP [...]

    By "the OP" surely you mean what Level 98 wrote (22. Juni 2026, 02:45): mastodon.social/@level98/11679

    >>> the words "moving clocks run slow" is a *terrible* phrase to use in talking about relativity. [...]

    In my reading, quoting and responding to that/your OP, the sophomorics about "Who's moving?" were far from making up its *whole point*.

    > The OP was not about what *you're* bothered with.

    Out of an abundance of caution I repeat here what bothers me mainly about the *terrible* OP phrase: it refers to comparison of *rates* instead of comparison of *durations*.

    If your OP was not about this concern *at all* then I hereby stand corrected.
    (Please note my question at the end, though ...)

    > [...] It's odd you commented [at all].

    At the very least I commented to express my whole-hearted agreement with calling the phrase "moving clocks run slow" *terrible* for teaching #relativity.
    (Thanks to mathstodon for enabling me to do so, publicly and archived.)

    > i.e. what people in general struggle with in learning SR

    I certainly don't mean to defend referring to _»the inertial system "at rest"«_
    vs. _»the inertial system "in motion"«_;
    such terminology surely contributes to the OP phrase being *terible*.

    But any imaginable confusion due to this didactic blunder from 1905 vanishes, in my experience, as soon as the lectures turn to _»the platform system«_ vs.
    _»the train system«_, for instance;
    both (close enough to) being inertial systems, moving *wrt. each other*, mutually, interchangeably --
    resulting in [contd.]

  15. @level98

    > [_» ... that there is no fact of the matter about who is moving and if I think you are moving then you think I am moving.«_ ]

    > Given that was the whole point of the OP [...]

    By "the OP" surely you mean what Level 98 wrote (22. Juni 2026, 02:45): mastodon.social/@level98/11679

    >>> the words "moving clocks run slow" is a *terrible* phrase to use in talking about relativity. [...]

    In my reading, quoting and responding to that/your OP, the sophomorics about "Who's moving?" were far from making up its *whole point*.

    > The OP was not about what *you're* bothered with.

    Out of an abundance of caution I repeat here what bothers me mainly about the *terrible* OP phrase: it refers to comparison of *rates* instead of comparison of *durations*.

    If your OP was not about this concern *at all* then I hereby stand corrected.
    (Please note my question at the end, though ...)

    > [...] It's odd you commented [at all].

    At the very least I commented to express my whole-hearted agreement with calling the phrase "moving clocks run slow" *terrible* for teaching #relativity.
    (Thanks to mathstodon for enabling me to do so, publicly and archived.)

    > i.e. what people in general struggle with in learning SR

    I certainly don't mean to defend referring to _»the inertial system "at rest"«_
    vs. _»the inertial system "in motion"«_;
    such terminology surely contributes to the OP phrase being *terible*.

    But any imaginable confusion due to this didactic blunder from 1905 vanishes, in my experience, as soon as the lectures turn to _»the platform system«_ vs.
    _»the train system«_, for instance;
    both (close enough to) being inertial systems, moving *wrt. each other*, mutually, interchangeably --
    resulting in [contd.]

  16. @level98
    You wrote (Jul 05 2026, 2:34 AM):
    > The intro's nice. Particularly [...]

    I.e. concerning the recent arxiv article by D. Garfinkle, on which I commented via SciRate a few days ago.
    (I rather raise interest in arxiv.org/abs/2302.12209 -- hoping for help on projects which exemplify _"well-stitchedness"_.)

    > _»Time dilation is 'fast clocks run slow' while length contraction is 'fast rulers get short.' [...]«_

    Cmp. p. 4 of arxiv.org/abs/2605.21660
    In the very next paragraph he suggests

    _»Thus there may be room for improvement in the way that special #relativity is often presented [...]«_

    I strongly agree and I solve thus:

    - Time dilation is: 'the arc-length of a straight/inertial timelike worldline section is shorter, by γ, than the arc-length of any straight/inertial timelike worldline section on which the former is (invertably) (Einstein-) projected'.

    and

    - length contraction is: 'a train is longer, by factor γ, than the platform on which the constituents of the train are (simultaneously) (Einstein-) projected'.

    Curiously, Garfinkle doesn't arrive there ...

    > _»On the other hand we are told that there is no fact of the matter about who is moving and if I think you are moving then you think I am moving.«_

    I didn't even bother with such sophomorics; they're not involed in expressing what time dilation is, and what length contraction is.

    What may be measured is:

    - whether any one timelike worldline is straight (inertial),

    - whether any two participants find constant ping durations wrt. each other.

    p.s.
    > You're trying to teach your grandma how to suck eggs.

    Physicists do indeed make their points by considering grandmas, based on R.P. Feynman's appreciation.

  17. @level98
    You wrote (Jul 05 2026, 2:34 AM):
    > The intro's nice. Particularly [...]

    I.e. concerning the recent arxiv article by D. Garfinkle, on which I commented via SciRate a few days ago.
    (I rather raise interest in arxiv.org/abs/2302.12209 -- hoping for help on projects which exemplify _"well-stitchedness"_.)

    > _»Time dilation is 'fast clocks run slow' while length contraction is 'fast rulers get short.' [...]«_

    Cmp. p. 4 of arxiv.org/abs/2605.21660
    In the very next paragraph he suggests

    _»Thus there may be room for improvement in the way that special #relativity is often presented [...]«_

    I strongly agree and I solve thus:

    - Time dilation is: 'the arc-length of a straight/inertial timelike worldline section is shorter, by γ, than the arc-length of any straight/inertial timelike worldline section on which the former is (invertably) (Einstein-) projected'.

    and

    - length contraction is: 'a train is longer, by factor γ, than the platform on which the constituents of the train are (simultaneously) (Einstein-) projected'.

    Curiously, Garfinkle doesn't arrive there ...

    > _»On the other hand we are told that there is no fact of the matter about who is moving and if I think you are moving then you think I am moving.«_

    I didn't even bother with such sophomorics; they're not involed in expressing what time dilation is, and what length contraction is.

    What may be measured is:

    - whether any one timelike worldline is straight (inertial),

    - whether any two participants find constant ping durations wrt. each other.

    p.s.
    > You're trying to teach your grandma how to suck eggs.

    Physicists do indeed make their points by considering grandmas, based on R.P. Feynman's appreciation.

  18. @level98

    > [...] "time" vs "duration" [...] makes no difference. Except...

    > t [...]

    ... i.e. individually: "a timestamp" also: "a reading"; (either way some real number value),
    and collectively typically (thought of as) parametrizing a time-like worldline.

    > [ vs. ] Δt

    ... i.e. individually (certainly "on first sight"):
    "a numerical difference (of two timestamps)".

    > I'd prefer Δ because it emphasises that it's a time

    ... time STAMP DIFFERENCE (btw., right ?) ...

    > between two Events,

    You're right in that, in order to specify and determine a duration, there are (typically) two arguments to be considered -- that is, besides considering exactly WHOSE worldline-section (duration) is to be determined (which can show up as third argument) -- namely the declarations BEGINNING FROM, and ENDING AT (a.k.a. UNTIL) to delimit the applicable worldline section.

    Now, if you recall Fig. 1 of your article, there were events shown which you (and/or co-author?) had distinctly labelled with different integers ("1", "2"), while in my preceding post I had referred to them by explicitly listing all (relevant) participants; viz. "e_RY" for the event in which the two participants "R" and "Y" had met each other (once, in passing), etc.

    So: just identifying an event (as the argument FROM) and another event (as UNTIL) wouldn't quite suffice to unambiguously declare WHOSE reading(s) are meant to be taken for calculating the sought difference, Δt.

    That's why I prefer and suggest to consider instead the distinctive "indications" of individual participants, in the sense of their distinctive individual shares of the relevant event in which they took part. [contd.]

    #Relativity

  19. @level98

    > [...] "time" vs "duration" [...] makes no difference. Except...

    > t [...]

    ... i.e. individually: "a timestamp" also: "a reading"; (either way some real number value),
    and collectively typically (thought of as) parametrizing a time-like worldline.

    > [ vs. ] Δt

    ... i.e. individually (certainly "on first sight"):
    "a numerical difference (of two timestamps)".

    > I'd prefer Δ because it emphasises that it's a time

    ... time STAMP DIFFERENCE (btw., right ?) ...

    > between two Events,

    You're right in that, in order to specify and determine a duration, there are (typically) two arguments to be considered -- that is, besides considering exactly WHOSE worldline-section (duration) is to be determined (which can show up as third argument) -- namely the declarations BEGINNING FROM, and ENDING AT (a.k.a. UNTIL) to delimit the applicable worldline section.

    Now, if you recall Fig. 1 of your article, there were events shown which you (and/or co-author?) had distinctly labelled with different integers ("1", "2"), while in my preceding post I had referred to them by explicitly listing all (relevant) participants; viz. "e_RY" for the event in which the two participants "R" and "Y" had met each other (once, in passing), etc.

    So: just identifying an event (as the argument FROM) and another event (as UNTIL) wouldn't quite suffice to unambiguously declare WHOSE reading(s) are meant to be taken for calculating the sought difference, Δt.

    That's why I prefer and suggest to consider instead the distinctive "indications" of individual participants, in the sense of their distinctive individual shares of the relevant event in which they took part. [contd.]

    #Relativity

  20. @level98

    2/2:

    > A key relationship to the basics of SR being that the two IRFs disagree on the synchronisation of the two clocks etc.

    Important of course; but **not basic**.

    "Synchronism" (Einstein, 1905) **presumes/requires** readings, i.e. t-values;

    but the analysis linked above, and Einstein's simultaneity definition of 1916/17 archive.org/details/in.ernet.d
    **do not**.

    Consequence: t-values are **derived** from more basic
    given observational circumstances:
    coincidence determinations, causal relations.

    #relativity

  21. @level98

    2/2:

    > A key relationship to the basics of SR being that the two IRFs disagree on the synchronisation of the two clocks etc.

    Important of course; but **not basic**.

    "Synchronism" (Einstein, 1905) **presumes/requires** readings, i.e. t-values;

    but the analysis linked above, and Einstein's simultaneity definition of 1916/17 archive.org/details/in.ernet.d
    **do not**.

    Consequence: t-values are **derived** from more basic
    given observational circumstances:
    coincidence determinations, causal relations.

    #relativity

  22. @level98

    1/2:

    > This simple scenario

    ... To be sure, that's Fig. 1 of your Austr. Phys. 56 (6), 2019,
    and as analyzed (to my ability & satsfaction) in section 2. of physics.stackexchange.com/a/68 ...

    > compares a measurement of time between the two Events where we're comparing a single clock along its (inertial) worldline, with that of two (synchronised) clocks in another inertial reference frame.

    I recognize this terminology from your article; there are reasons the terminology I use instead. Briefly:

    - The very old word "time" has very many (more or less related but) different meanings.
    Use "duration", i.e. the **measure of** temporal sepratation, when we **mean duration**. Last but not least, see the word/notion "duration" used here: bipm.org/en/si-base-units/seco

    - "between two (not necessarily distinct) events", say e_{RY} and e_(LY) of your Fig. 1 are

    (1) in generality: "Lorentzian distance" ℓ[ e_{RY}, e_(LY) ], cmp en.wikipedia.org/wiki/Globally also "Beem-Ehrlich-Easley",

    (2) "under certain circumstances": Synge's world function ℓ[ e_{RY}, e_(LY) ] , en.wikipedia.org/wiki/Synge%27

    (3) and (surely only) in flat spacetime regions: the interval s^2[ e_{RY}, e_(LY) ]

    > comparing a single clock along its (inertial) worldline

    That's in fact pretty much the duration (1).

    > with that of two (synchronised) clocks in another inertial reference frame.

    And to repeat, that is (in Fig. 1):

    "The duration of R, from having met/passed Y
    until R's indication simultaneous to L's indication of having met/passed Y."

    which (by definition) is equal to

    "The duration of L, from L's indication simultaneous to R's indication of having met/passed Y, until L having met/passed Y."

    #Relativity

  23. @level98

    1/2:

    > This simple scenario

    ... To be sure, that's Fig. 1 of your Austr. Phys. 56 (6), 2019,
    and as analyzed (to my ability & satsfaction) in section 2. of physics.stackexchange.com/a/68 ...

    > compares a measurement of time between the two Events where we're comparing a single clock along its (inertial) worldline, with that of two (synchronised) clocks in another inertial reference frame.

    I recognize this terminology from your article; there are reasons the terminology I use instead. Briefly:

    - The very old word "time" has very many (more or less related but) different meanings.
    Use "duration", i.e. the **measure of** temporal sepratation, when we **mean duration**. Last but not least, see the word/notion "duration" used here: bipm.org/en/si-base-units/seco

    - "between two (not necessarily distinct) events", say e_{RY} and e_(LY) of your Fig. 1 are

    (1) in generality: "Lorentzian distance" ℓ[ e_{RY}, e_(LY) ], cmp en.wikipedia.org/wiki/Globally also "Beem-Ehrlich-Easley",

    (2) "under certain circumstances": Synge's world function ℓ[ e_{RY}, e_(LY) ] , en.wikipedia.org/wiki/Synge%27

    (3) and (surely only) in flat spacetime regions: the interval s^2[ e_{RY}, e_(LY) ]

    > comparing a single clock along its (inertial) worldline

    That's in fact pretty much the duration (1).

    > with that of two (synchronised) clocks in another inertial reference frame.

    And to repeat, that is (in Fig. 1):

    "The duration of R, from having met/passed Y
    until R's indication simultaneous to L's indication of having met/passed Y."

    which (by definition) is equal to

    "The duration of L, from L's indication simultaneous to R's indication of having met/passed Y, until L having met/passed Y."

    #Relativity

  24. @level98

    Hi Theo,

    thanks for your replies.
    First of all, however, I'd like you to know that I managed to get a copy of your Austr. Phys. 56 (6), 2019, thanks to your website and the excellent archive of the AIP.

    Interesting article! While your repeated attempts to "save [parts of] that oft-used [abominable] phrase" didn't succeed, I was very glad that you -- almost in passing -- struck upon **the** **appropriate** phrase:

    > _»We know that it is you [circled Y in Fig. 1] who measures the proper time, and hence the shorter time interval.«_

    So the key/solution is: to refer to **duration**, certain clocks running **longer** (or **shorter**) than certain other clocks;
    instead of referring to clock rate (frequency), i.e. certain clocks running faster (or slower) than certain others.

    This holds for #GeneralRelativity just as well.

    All that inappropriate referring to clock rate has been nothing but a "red hering" from the outset (Einstein Ann. Phys. 17, 891 (1905))!

    In terminology I prefer, I teach the Fig.1-applicable appropriate #SpecialRelativity phrase as

    "The duration of Y, from having met/passed R until having met/passed L,
    is shorter, by factor √{ 1 - β^2 }, than
    the duration of R, from having met/passed Y
    until R's indication simultaneous to L's indication of having met/passed Y."

    p.s. For your kind consideration, here's "putting my money where my mouth is": scirate.com/arxiv/2605.21660

    p.p.s. The notion #Duration may have been depreciated in #Relativity due to nonsense by the French philosopher H. Bergson. Instead, "duration" plainly is in the SI-second-def

    p.p.p.s. I can mostly recommend tooting (!) by mathstodon: 1729 chars. + \(\LaTeX\) -- only "Markdown" still doesn't work!

  25. @level98

    Hi Theo,

    thanks for your replies.
    First of all, however, I'd like you to know that I managed to get a copy of your Austr. Phys. 56 (6), 2019, thanks to your website and the excellent archive of the AIP.

    Interesting article! While your repeated attempts to "save [parts of] that oft-used [abominable] phrase" didn't succeed, I was very glad that you -- almost in passing -- struck upon **the** **appropriate** phrase:

    > _»We know that it is you [circled Y in Fig. 1] who measures the proper time, and hence the shorter time interval.«_

    So the key/solution is: to refer to **duration**, certain clocks running **longer** (or **shorter**) than certain other clocks;
    instead of referring to clock rate (frequency), i.e. certain clocks running faster (or slower) than certain others.

    This holds for #GeneralRelativity just as well.

    All that inappropriate referring to clock rate has been nothing but a "red hering" from the outset (Einstein Ann. Phys. 17, 891 (1905))!

    In terminology I prefer, I teach the Fig.1-applicable appropriate #SpecialRelativity phrase as

    "The duration of Y, from having met/passed R until having met/passed L,
    is shorter, by factor √{ 1 - β^2 }, than
    the duration of R, from having met/passed Y
    until R's indication simultaneous to L's indication of having met/passed Y."

    p.s. For your kind consideration, here's "putting my money where my mouth is": scirate.com/arxiv/2605.21660

    p.p.s. The notion #Duration may have been depreciated in #Relativity due to nonsense by the French philosopher H. Bergson. Instead, "duration" plainly is in the SI-second-def

    p.p.p.s. I can mostly recommend tooting (!) by mathstodon: 1729 chars. + \(\LaTeX\) -- only "Markdown" still doesn't work!

  26. mastodon.social/@level98/11679

    @level98

    Level 98 wrote (22. Juni 2026, 02:45):
    > the words "moving clocks run slow" is a *terrible* phrase talking about #relativity.

    Agreed.

    Who would ever distort into such an abomination a perfectly legitimate standard phrase such as, say

    "clock \(A\) has run _slower_, i.e. at lower clock rate \(\nu_A\), on average, on its (time-like) worldline segment starting from event \(\varepsilon_{ABJ}\) and ending with event \(\varepsilon_{ABK}\)
    than
    \(\nu_B\), the rate clock \(B\) has run, on average, on _its_ (time-like) worldline segment starting (likewise) from event \(\varepsilon_{ABJ}\) and ending (likewise) with event \(\varepsilon_{ABK}\)"
    ?

    > The reality of SR is far cooler and (according to a teacher I was helping) easier to understand, if one doesn't use such pop sci phrases.

    How else could you even begin to communicate (e.g. to students) that, accordingly, a comparison is to be made between

    - the ratio \(\nu_A := \frac{(t_A[ ~ \text{_BK} ~ ] - t_A[ ~ \text{_BJ} ~ ] )}{ \tau A[ ~ \text{_BK}, \text{_BJ} ~ ]}\)

    and

    - the ratio \(\nu_B := \frac{(t_B[ ~ \text{_AK} ~ ] - t_B[ ~ \text{_AJ} ~ ] )}{ \tau B[ ~ \text{_AK}, \text{_AJ} ~ ]}\)

    ?

    p.s.
    Did you (or that fine teacher you mentioned) come up with a more efficient notation for identifying

    - distinctive events (by the names of their distinguishable coincident participants),

    - distinctive indications of any one participant (by the names of all other distinguishable participants coincident in the resp. event),

    - the (not necessarily distinct) readings "t" assigned to indications,

    - the durations (a.k.a. arc-lenghts) \("\tau"\) of specific worldline segments
    ?

    For #SpecialRelativity and in general.

  27. mastodon.social/@level98/11679

    @level98

    Level 98 wrote (22. Juni 2026, 02:45):
    > the words "moving clocks run slow" is a *terrible* phrase talking about #relativity.

    Agreed.

    Who would ever distort into such an abomination a perfectly legitimate standard phrase such as, say

    "clock \(A\) has run _slower_, i.e. at lower clock rate \(\nu_A\), on average, on its (time-like) worldline segment starting from event \(\varepsilon_{ABJ}\) and ending with event \(\varepsilon_{ABK}\)
    than
    \(\nu_B\), the rate clock \(B\) has run, on average, on _its_ (time-like) worldline segment starting (likewise) from event \(\varepsilon_{ABJ}\) and ending (likewise) with event \(\varepsilon_{ABK}\)"
    ?

    > The reality of SR is far cooler and (according to a teacher I was helping) easier to understand, if one doesn't use such pop sci phrases.

    How else could you even begin to communicate (e.g. to students) that, accordingly, a comparison is to be made between

    - the ratio \(\nu_A := \frac{(t_A[ ~ \text{_BK} ~ ] - t_A[ ~ \text{_BJ} ~ ] )}{ \tau A[ ~ \text{_BK}, \text{_BJ} ~ ]}\)

    and

    - the ratio \(\nu_B := \frac{(t_B[ ~ \text{_AK} ~ ] - t_B[ ~ \text{_AJ} ~ ] )}{ \tau B[ ~ \text{_AK}, \text{_AJ} ~ ]}\)

    ?

    p.s.
    Did you (or that fine teacher you mentioned) come up with a more efficient notation for identifying

    - distinctive events (by the names of their distinguishable coincident participants),

    - distinctive indications of any one participant (by the names of all other distinguishable participants coincident in the resp. event),

    - the (not necessarily distinct) readings "t" assigned to indications,

    - the durations (a.k.a. arc-lenghts) \("\tau"\) of specific worldline segments
    ?

    For #SpecialRelativity and in general.

  28. The brand-new 360-or-so-page book "Testing Einstein: One Hundred Years of Experimental #Relativity" is completely open access as a series of PDF files at direct.mit.edu/books/oa-edited (and talking about OA science & tech books: at nasa.gov/history/history-publi NASA has countless more).

  29. The brand-new 360-or-so-page book "Testing Einstein: One Hundred Years of Experimental #Relativity" is completely open access as a series of PDF files at direct.mit.edu/books/oa-edited (and talking about OA science & tech books: at nasa.gov/history/history-publi NASA has countless more).

  30. Under these circumstances, there is a "correct" use of the hypercomputer. While a civilization could use it to compute some strategy in a war, upload themselves into it for a form of immortality, or create a new world by instructing it to run some kind of Game of Life (en.wikipedia.org/wiki/Conway%2) program, a more practical use would be to compute the first few thousand digits of Chaitin's constant for a programming language. This is possible because we can finitely describe "attempt to run every possible source code and record if the result halts", we just need an infinite amount of time in order to finish the task. Importantly, although we can't know the exact value of \(\Omega\), the first few thousand digits are about just as good for mortal purposes.

    I always imagined that, in the story, one civilization would be unsubtle and look down on the other, which would only want to use the hypercomputer for the "academic" purpose of knowing \(\Omega\) approximately, only to realize that this knowledge is possibly the most practical use of the machine.

    (3/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  31. Under these circumstances, there is a "correct" use of the hypercomputer. While a civilization could use it to compute some strategy in a war, upload themselves into it for a form of immortality, or create a new world by instructing it to run some kind of Game of Life (en.wikipedia.org/wiki/Conway%2) program, a more practical use would be to compute the first few thousand digits of Chaitin's constant for a programming language. This is possible because we can finitely describe "attempt to run every possible source code and record if the result halts", we just need an infinite amount of time in order to finish the task. Importantly, although we can't know the exact value of \(\Omega\), the first few thousand digits are about just as good for mortal purposes.

    I always imagined that, in the story, one civilization would be unsubtle and look down on the other, which would only want to use the hypercomputer for the "academic" purpose of knowing \(\Omega\) approximately, only to realize that this knowledge is possibly the most practical use of the machine.

    (3/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  32. When I learned about this as an undergraduate I started telling people the following story: Suppose that, simultaneously, two space-faring civilizations discover a naturally-occurring closed timelike curve (en.wikipedia.org/wiki/Closed_t) around a nearby black hole. Suppose further that these civilizations both know that this structure can be used to build a hypercomputer (en.wikipedia.org/wiki/Hypercom), a machine that can perform an infinite number of classical computational steps in a finite amount of time. In order to make our story more realistic, we add the following constraints:

    (1) The hypercomputer can correctly perform an infinite calculation, but it must be described by a finite program.
    (2) The hypercomputer can access an arbitrarily large amount of memory during calculation, but there is a fixed finite size for its output after the infinite calculation is over.
    (3) A massive amount of resources are needed for each use of the hypercomputer. Perhaps it breaks after each use.

    (2/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  33. When I learned about this as an undergraduate I started telling people the following story: Suppose that, simultaneously, two space-faring civilizations discover a naturally-occurring closed timelike curve (en.wikipedia.org/wiki/Closed_t) around a nearby black hole. Suppose further that these civilizations both know that this structure can be used to build a hypercomputer (en.wikipedia.org/wiki/Hypercom), a machine that can perform an infinite number of classical computational steps in a finite amount of time. In order to make our story more realistic, we add the following constraints:

    (1) The hypercomputer can correctly perform an infinite calculation, but it must be described by a finite program.
    (2) The hypercomputer can access an arbitrarily large amount of memory during calculation, but there is a fixed finite size for its output after the infinite calculation is over.
    (3) A massive amount of resources are needed for each use of the hypercomputer. Perhaps it breaks after each use.

    (2/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  34. While organizing some files today I came across my copy of Charles H. Bennett's "On Random and Hard-to-Describe Numbers" from 1979 (worldscientific.com/doi/abs/10). It discusses Chaitin's constant (en.wikipedia.org/wiki/Chaitin%) for a programming language, which is the probability \(\Omega\) that a randomly-chosen program will compile. This is a real number between 0 and 1 which is definable but not computable.

    Bennett goes on to discuss the "Cabalistic" properties of \(\Omega\). Knowing the first few thousand digits of \(\Omega\) would allow one to decide practically all finitely refutable mathematical conjectures. Basically, \(\Omega\) is a very compact encoding of the Halting Problem (en.wikipedia.org/wiki/Halting_), so knowing its first \(n\) bits is enough to determine whether any program up to \(n\) bits in length would eventually halt. While there are some exceptions, many open problems in mathematics can be phrased in terms of the halting of some computer program of reasonably short length.

    (1/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  35. While organizing some files today I came across my copy of Charles H. Bennett's "On Random and Hard-to-Describe Numbers" from 1979 (worldscientific.com/doi/abs/10). It discusses Chaitin's constant (en.wikipedia.org/wiki/Chaitin%) for a programming language, which is the probability \(\Omega\) that a randomly-chosen program will compile. This is a real number between 0 and 1 which is definable but not computable.

    Bennett goes on to discuss the "Cabalistic" properties of \(\Omega\). Knowing the first few thousand digits of \(\Omega\) would allow one to decide practically all finitely refutable mathematical conjectures. Basically, \(\Omega\) is a very compact encoding of the Halting Problem (en.wikipedia.org/wiki/Halting_), so knowing its first \(n\) bits is enough to determine whether any program up to \(n\) bits in length would eventually halt. While there are some exceptions, many open problems in mathematics can be phrased in terms of the halting of some computer program of reasonably short length.

    (1/3)

    #math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability

  36. This one has serious SciFiScience and worldbuilding vibes about the formation of the dark-energy-cored, amazingly named gravestars. One read of this model is sort of like a bubbled big bang within the Schwarzschild limit.

    Link: journals.aps.org/prd/abstract/

    #SciFiScience #Worldbuilding #Astrophysics #Relativity