• Re: Challenge for Paul; Probe that with Mercury ds^2>0 and the solution

    From Richard Hachel@21:1/5 to All on Wed Feb 12 22:55:48 2025
    Le 12/02/2025 à 23:27, [email protected] (rhertz) a écrit :
    To get you out of boredom, I have this problem:

    Given the metric ds^2 = (ct)^2-x^2+-y^2-z^2 > 0 for Mercury's perihelion analysis, prove that S gives the additional 43"/cy.

    Also explain why this problem is treated as spacelike and not as
    timelike.


    Enjoy!

    The advance of the perihelion of Mercury can probably be given by simple
    RR.
    I think I did it a long time ago, and found an exact result.
    We must first consider one thing, there is a contraction of the
    circumference as a function of the speed, and therefore of the orbit of Mercury.
    The effects of the contraction are not enormous, but over a century, we
    can easily observe them.
    Just as there is a contraction of the circumference (the orbit), there is
    an equal contraction of the radius (pi is an invariant in Hachel).

    I think that if someone were to stick to it, they could easily find the
    exact advance of the perihelion of Mercury (Personally, I get tired).

    I give the equations relating to transformations in rotating media here.

    <http://nemoweb.net/jntp?bSU98M6KIUBzLsrpIgbePkDLQD8@jntp/Data.Media:1>

    C'=C.sqrt(1-v²/c²) Circonférence

    R'=R.sqrt(1-v²/c²) Rayon

    R.H.

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  • From Paul B. Andersen@21:1/5 to All on Sun Feb 16 19:26:01 2025
    Den 12.02.2025 23:27, skrev rhertz:
    To get you out of boredom, I have this problem:

    Given the metric ds^2 = (ct)^2-x^2+-y^2-z^2 > 0 for Mercury's perihelion analysis, prove that S gives the additional 43"/cy.

    Also explain why this problem is treated as spacelike and not as
    timelike.


    Enjoy!

    ROFL

    You have yet again made a giant fool of yourself, Richard.

    Now you can wonder why! :-D

    --
    Paul

    https://paulba.no/

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  • From Paul B. Andersen@21:1/5 to All on Tue Feb 18 21:59:50 2025
    Den 17.02.2025 22:29, skrev rhertz:
    Line element ds in the Schwarzschild metric(describing spacetime around
    a massive object like the Sun):

    ds² = -(1 - 2GM/c² r) c² dt² + 1/(1 - 2GM/c² r) dr² + r² dɸ²


    So you have realised that it was a blunder to think you could
    use the metric for flat spacetime in an environment where geodesics
    are ellipses.

    ----------------------

    It is very obvious that you don't know what a metric is, so
    I will give a short lesson about the most elementary concepts
    in spacetime geometry:

    In physics, an "event" is a point in space at a time,
    or a point in spacetime.

    The metric can be used to find the spacetime interval between
    two events, or the spacetime interval along a path between two events.

    It is quite common to use s² as the interval, but it is more 'natural'
    to call the interval s, so that's what I will do.

    's' consists of two components, a temporal and a spatial.
    If we call the temporal component cT and the spatial component D,
    we have: s² = −c²T² + D²

    If D > cT then S is spacelike (s² > 0) D/T > c
    If D = cT then S is lightlike (s² = 0) D/T = c
    If D < cT then S is timelike (s² < 0) D/T < c

    Two events on the worldline of a massive object will always be
    separated by a timelike interval, because the object's speed D/T
    is always less than c, and D < cT.

    In the latter case it is common to set s = -cτ, and
    the Schwarzschild metric becomes:

    c²dτ² = (1 - 2GM/c²r)c²dt² - 1/(1 - 2GM/c²r)dr² - r² dɸ²

    You can see this metric applied on satellites here: https://paulba.no/pdf/Clock_rate.pdf

    (I know I am an idiot who bother to try to teach you
    what you never will learn.)


    Why, to approximate a solution, dt=0 (spacelike event)?

    This sure makes ds² > 0.

    These cryptic statement comes from your OP.
    Which, if we exchange the wrong metric for the right one,
    becomes:
    "Given the metric
    ds² = -(1 - 2GM/c² r)c²dt² + 1/(1 - 2GM/c²r)dr² + r²dɸ² > 0
    for Mercury's perihelion analysis, prove that S gives
    the additional 43"/cy."

    This is still a meaningless statement of several reasons:
    #1:
    ds² > 0 is meaningless in calculus.
    Given: dy/dx = ax
    Please explain what dy = ax⋅dx > 0 means.

    The point is that you can't assign specific values to
    dy and dx, it is only the ratio dy/dx that is defined.

    A meaningful statement would be s² > 0, s is spacelike.

    #2:
    "Given s² > 0 for Mercury's perihelion analysis"
    is still a meaningless statement.
    If you mean that perihelion is an event on Mercury's
    worldline, and that s is the spacetime interval between
    two consecutive perihelia (the "length" of Mercury's path
    between the perihelia) then s is timelike and s² < 0.


    Have any answer, amateur expert relativist?

    If you mean an answer to your challenge in the subject line:
    "Probe that with Mercury ds^2>0 and the solution is spacelike"
    the answer is that this is meaningless babble so no sensible
    answer exists.

    If the challenge is:
    Show that the Schwarzschild metric can be used to calculate
    that GR predicts that if no other planets than Mercury existed,
    then its perihelion advance would be 43"/century.

    Then my answer is: no, I am neither a physicist nor a mathematician
    so I am not qualified to do that particular calculation.
    But many physicists are and have done it.

    Ray d'Inverno does it in his book "Introducing Einstein's Relativity"

    The general equation for perihelion advance is:
    ε = 3m²/h² in natural units.

    I am however capable of understanding d'Inverno's calculations,
    and I take it from there and find the equation in SI units.

    See chapter 3 in:
    https://paulba.no/pdf/GRPerihelionAdvance.pdf

    See also:
    https://paulba.no/PerihelionAdvance.html


    I'm waiting for your display of wisdom, Paul.


    --
    Paul

    https://paulba.no/

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  • From Maciej Wozniak@21:1/5 to All on Tue Feb 18 22:04:00 2025
    W dniu 18.02.2025 o 21:59, Paul B. Andersen pisze:
    Den 17.02.2025 22:29, skrev rhertz:
    Line element ds in the Schwarzschild metric(describing spacetime around
    a massive object like the Sun):

    ds² = -(1 - 2GM/c² r) c² dt² + 1/(1 - 2GM/c² r) dr² + r² dɸ²


    So you have realised that it was a blunder to think you could
    use the metric for flat spacetime in an environment where geodesics
    are ellipses.

    ----------------------

    It is very obvious that you don't know what a metric is, so
    I will give a short lesson about the most elementary concepts
    in spacetime geometry:

    In physics, an "event" is a point in space at a time,
    or a point in spacetime.

    The metric can be used to find the spacetime interval between
    two events, or the spacetime interval along a path between two events.

    It is quite common to use s² as the interval, but it is more 'natural'
    to call the interval s, so that's what I will do.

    's' consists of two components, a temporal and a spatial.
    If we call the temporal component cT and the spatial component D,
    we have: s² = −c²T² + D²

    If D > cT then S is spacelike  (s² > 0)  D/T > c
    If D = cT then S is lightlike  (s² = 0)  D/T = c
    If D < cT then S is timelike   (s² < 0)  D/T < c

    Two events on the worldline of a massive object will always be
    separated by a timelike interval, because the object's speed D/T
    is always less than c, and D < cT.

    In the latter case it is common to set s = -cτ, and
    the Schwarzschild metric becomes:

    c²dτ² = (1 - 2GM/c²r)c²dt² - 1/(1 - 2GM/c²r)dr² - r² dɸ²

    You can see this metric applied on satellites here: https://paulba.no/pdf/Clock_rate.pdf

    (I know I am an idiot who bother to try to teach you
     what you never will learn.)

    Nope. You're just an idiot desperately
    wanting to impress someone with your
    "knowledge".

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  • From Paul B. Andersen@21:1/5 to All on Tue Feb 18 22:08:36 2025
    Den 13.02.2025 18:26, skrev rhertz:
    Can you derive, for GPS satellites, the alleged shift in frequency:

    Δf/f ≈ GM/c²  [1/r_E − 1/(r_E + h)]− GM/[2 c² (r_E + h)]

    https://paulba.no/pdf/Clock_rate.pdf

    --
    Paul

    https://paulba.no/

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  • From J. J. Lodder@21:1/5 to Paul B. Andersen on Wed Feb 19 12:53:54 2025
    Paul B. Andersen <[email protected]> wrote:

    Den 13.02.2025 18:26, skrev rhertz:
    Can you derive, for GPS satellites, the alleged shift in frequency:

    ?f/f ≈ GM/c? [1/r_E ? 1/(r_E + h)]? GM/[2 c? (r_E + h)]

    https://paulba.no/pdf/Clock_rate.pdf

    If you ever are in the mood, you could add a section
    on non-circular GPS orbits.
    (they all are a little, no point in wasting precious fuel in keeping
    orbits exactly circular)

    When the orbit is elliptical the clock correction varies over the orbit.
    Only the average is corrected for in the constant clock offset.
    Relativistic corrections for this have to be applied in the receivers.
    (based on the almanac date that the sat also transmits in the full
    message)

    And yes, it does matter if you want the best possible accuracy.
    It will for example decrease the CEP of GPS-guided munitions
    from perhaps 10m to a few meter.
    This may make the difference between a shell landing in a trench
    rather than next to it.

    Russian soldiers must hate relativity,

    Jan

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  • From Maciej Wozniak@21:1/5 to All on Wed Feb 19 13:45:21 2025
    W dniu 19.02.2025 o 12:53, J. J. Lodder pisze:
    Paul B. Andersen <[email protected]> wrote:

    Den 13.02.2025 18:26, skrev rhertz:
    Can you derive, for GPS satellites, the alleged shift in frequency:

    ?f/f ≈ GM/c? [1/r_E ? 1/(r_E + h)]? GM/[2 c? (r_E + h)]

    https://paulba.no/pdf/Clock_rate.pdf

    If you ever are in the mood, you could add a section
    on non-circular GPS orbits.
    (they all are a little, no point in wasting precious fuel in keeping
    orbits exactly circular)

    When the orbit is elliptical the clock correction varies over the orbit.
    Only the average is corrected for in the constant clock offset.
    Relativistic corrections for this have to be applied in the receivers.

    A lie, of course - there are no relativistic
    corrections, according to your insane guru
    the clocks should be left alone and desynchronize.

    Of course, GPS wouldn't work, but what a beautiful
    symmetry we would have instead.

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  • From Paul B. Andersen@21:1/5 to All on Thu Feb 20 19:29:49 2025
    Den 19.02.2025 12:53, skrev J. J. Lodder:
    Paul B. Andersen <[email protected]> wrote:


    https://paulba.no/pdf/Clock_rate.pdf

    If you ever are in the mood, you could add a section
    on non-circular GPS orbits.
    (they all are a little, no point in wasting precious fuel in keeping
    orbits exactly circular)

    When the orbit is elliptical the clock correction varies over the orbit.
    Only the average is corrected for in the constant clock offset.
    Relativistic corrections for this have to be applied in the receivers.
    (based on the almanac date that the sat also transmits in the full
    message)

    Yes, I know. This correction is part of the correction polynomial.

    I have written a few words about it: https://paulba.no/div/GPS_clock_correction.pdf

    taken from:
    20.3.3.3.3.1 "User Algorithm for SV Clock Correction"
    page 98 in the Interface Specification Document https://www.gps.gov/technical/icwg/IS-GPS-200N.pdf

    It was an "ad hoc" article when the correction was discussed.


    My article: "The rate of clocks in circular orbit
    compared to clocks on the geoid" isn't about the GPS,
    the correction isn't mentioned at all. It was about
    what is meant by "rate". You can't literally "compare
    clocks in orbit to clocks on the geoid.
    But you can compare it to UTC (or GPS-time) if you have many
    monitoring stations to help you in the process.

    The "as it appears to an observer on the ground" in 3.3.1.1
    of the GPS Interface Specification Document is bordering to meaningless.

    But never mind, all who need to understand what is meant, will.


    And yes, it does matter if you want the best possible accuracy.
    It will for example decrease the CEP of GPS-guided munitions
    from perhaps 10m to a few meter.
    This may make the difference between a shell landing in a trench
    rather than next to it.

    Russian soldiers must hate relativity,

    Jan





    --
    Paul

    https://paulba.no/

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  • From Paul B. Andersen@21:1/5 to All on Fri Feb 21 20:48:16 2025
    Den 21.02.2025 02:45, skrev rhertz:

    18.02.2025 o 21:59, Paul B. Andersen wrote:

    In physics, an "event" is a point in space at a time,
    or a point in spacetime.

    The metric can be used to find the spacetime interval between
    two events, or the spacetime interval along a path between two events.

    It is quite common to use s² as the interval, but it is more 'natural'
    to call the interval s, so that's what I will do.

    's' consists of two components, a temporal and a spatial.
    If we call the temporal component cT and the spatial component D,
    we have: s² = −c²T² + D²

    If D > cT then S is spacelike  (s² > 0)  D/T > c
    If D = cT then S is lightlike  (s² = 0)  D/T = c
    If D < cT then S is timelike   (s² < 0)  D/T < c

    Two events on the worldline of a massive object will always be
    separated by a timelike interval, because the object's speed D/T
    is always less than c, and D < cT.

    In the latter case it is common to set s = -cτ, and
    the Schwarzschild metric becomes:

    c²dτ² = (1 - 2GM/c²r)c²dt² - 1/(1 - 2GM/c²r)dr² - r² dɸ²

    You can see this metric applied on satellites here:
    https://paulba.no/pdf/Clock_rate.pdf

    (I know I am an idiot who bother to try to teach you
      what you never will learn.)


      Watch what you asserted. A string of idiocies, scrambling everything
    and
      introducing your own terminology (arrogant asshole): :

    *************************************************************************
    It is quite common to use s² as the interval, but it is more 'natural'
    to call the interval s, so that's what I will do.

    's' consists of two components, a temporal and a spatial.
    If we call the temporal component cT and the spatial component D,
    we have: s² = −c²T² + D²

    If D > cT then S is spacelike  (s² > 0)  D/T > c
    If D = cT then S is lightlike  (s² = 0)  D/T = c
    If D < cT then S is timelike   (s² < 0)  D/T < c

    Two events on the worldline of a massive object will always be
    separated by a timelike interval, because the object's speed D/T
    is always less than c, and D < cT. *************************************************************************

    Pretentious asshole: Using s instead of ds? You are a mental case.

    ROFL

    You are yet again making a fool of yourself.



    Instead of your ignorant expression: s² = −c²T² + D²

    Minkowski's metric for spacetime is universally represented as:

    ds² = c² dτ²  =  -(c dx⁰)² + (dx¹)² + (dx²)² + (dx³)²
    or
    ds² = c² dτ²  =  -(c dt)² + dx² + dy² + dz² = -(c dt)² + dr²

    ds² = - c²dτ²


    ds² = -(c dt)² + dr²

    In this FLAT metric, ds²>0 doesn't mean FTL events.

    You are right about that, because ds²>0 is meaningless nonsense.

    It only takes two
    events
    to be SIMULTANEOUS in the same worldline to define dt=0.

    But in a curved spacetime defined by Schwarzschild's metric (around a
    massive body), the line element is much more complex and subtle.
    Spacelike events don't require FTL occurrence. It's just mathematical
    common sense.

    "Spacelike events don't require FTL occurrence."

    :-D


    Being


    ds² = -(1-2GM/c²r) c²dt² + 1/(1-2GM/c²r) dr² + r²(dθ² + sin² θ dϕ²)

    For events around a single massive object (what was Schwarzschild's
    metric
    conceived for), the equation for different examples, being ds²>0 are:


    1.Two Events at the Same Time but Different Radial Coordinates

    So let's specify the events:
    E(t,r,θ,ϕ) E₁ = (0,r₁,0,0) E₂ = (0,r₂,0,0)


    Consider two events occurring at the same coordinate time t but at
    different radial coordinates r1 and r2. The spacetime interval between
    these events is:

    ds²  = dr²/(1-2GM/c²r) + r²(dθ² + sin² θ dϕ²)

    If the angular separation is zero (dθ = dϕ = 0), the interval simplifies to:

    ds² = dr²/(1-2GM/c²r)

    OK

    ds = (1/√(1-2GM/c²r))dr

    r₂
    s = ∫(1/√(1-2GM/c²r))dr = D, a distance
    r₁

    s² = D²>0 the interval is spacelike , D/T = ∞ > c

    Obviously! Same time and separate position => space like.


    Since 1/(1-2GM/c²r) > 0 outside the event horizon (c²rv>v2GM), ds²>0,
    and the events are spacelike separated.

    Your blunder again. ds can't be assigned a value.
    Basic calculus error!



    2.Two Events at the Same Radius but Different Times (conflicting views):

    E(t,r,θ,ϕ) E₁ = (t₁,r,0,0) E₂ = (t₂,r,0,0)

    Note that the events are at the same spatial position.



    Two events occurring at the same radial coordinate r but at different
    times t1 and t2. The spacetime interval between these events is:

    ds² = −(1-2GM/c²r) dt²

    ds² = −(1-2GM/c²r)c²dt²

    t₂
    s = √(-(1-2GM/c²r))c∫dt = √(-(1-2GM/c²r))c(t₂-t₁) an imaginary number
    t₁

    s² = -(1-2GM/c²r)c²(t₂-t₁) < 0, the interval is timelike

    In this case it would be better to use the metric:

    c²dτ² = (1-2GM/c²r)c²dt²

    t₂
    τ = √(1-2GM/c²r)∫dt = (1-2GM/c²r))(t₂-t₁) = T, a time interval
    t₁

    s² = - c²τ² = - c²T² < 0, the interval is timelike, D/T = 0 < c

    Obviously! Same position and separate time => timelike.


    Since (1-2GM/c²r) > 0 outside the event horizon, ds² < 0, and the events are timelike separated.

    Your blunder yet again.


    HOWEVER, if the events occur at the same radius
    but are separated by a large angular distance (e.g., Δϕ or Δθ), the interval becomes:

    Another one with same time and separate position is too boring.

    Let's have separate position and separate times.
    A more interesting case.

    I choose to let ϕ = 0

    E(t,r,θ,ϕ) E₁ = (t₁,r,θ₁,0) E₂ = (t₂,r,θ₂,0)

    ds² = -(1-2GM/c²r)c²dt² + r²dθ²

    ds² = ds₁² + ds₂²

    ds₁² = -(1-2GM/c²r)c²dt² or τ² = (1-2GM/c²r)dt²

    t₂
    τ = √(1-2GM/c²r)∫dt = (1-2GM/c²r))(t₂-t₁) = T, a proper time interval
    t₁
    s₁² = −c²T²

    ds₂² = r²dθ²

    θ₂
    s₂ = r∫dθ = r(θ₂-θ₁) = D, a distance, the length of an arc
    θ₁

    s² = s₁² + s₂² = −c²T² + D²

    Why did you think that this equation meant that spacetime was flat?

    If cT > D or (1-2GM/c²r))(ct₂-ct₁) > r(θ₂-θ₁), the interval is timelike

    If cT < D or (1-2GM/c²r))(ct₂-ct₁) < r(θ₂-θ₁), the interval is spacelike

    If cT = D or (1-2GM/c²r))(ct₂-ct₁) = r(θ₂-θ₁), the interval is lightlike



    ds² = r²(Δθ² + sin² θ Δϕ²) r

    If the angular separation is large enough, ds²>0, and the events are SPACELIKE separated.

    In this case you have same time and separate positions and
    the interval is _always_ spacelike irrespective of what the distance
    between the positions might be.

    But for the umpteenth time: you can't assign a specific value to ds,
    and if you could ds² would always be positive and according to you,
    all intervals should be spacelike. This is nonsense!

    Why are you so ignorant of basic calculus?

    We stop here.


    --
    Paul, ignorant ASSHOLE/IDIOT, arrogant asshole and Pretentious asshole

    https://paulba.no/

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  • From Paul B. Andersen@21:1/5 to Richard Hertz on Sat Feb 22 22:04:53 2025
    Den 22.02.2025 01:59, skrev rhertz:


    I'm bored with your stupid replies.

    I can understand why you don't like being caught in
    doing the same blunders over an over.


    Spacelike events using Schwarzschild metric are seriously analyzed and
    used by relativists in several fields.

    There is no such thing as "Spacelike events".

    Snap your fingers!
    Was the event "Richard snapped his fingers" spacelike or timelike?

    intervals (distance and time) between events can be
    spacelike or timelike.


    Before I post a wall of words with examples, I want to clarify your
    stupid comment "ds can't be assigned a value" and having the stoneface
    to attribute to me such interpretation. This is far from true, norwegian wood.

    Richard Hertz wrote:
    | ds² = dr²/(1-2GM/c²r)
    |
    | Since 1/(1-2GM/c²r) > 0 outside the event horizon (c²rv>v2GM), ds²>0,
    | and the events are spacelike separated.

    This is crystal clear, you claim:
    ds² = 1/(1-2GM/c²r)⋅dr² implies ds² = 1/(1-2GM/c²r)

    Don't you understand how ridiculous this is?

    Neither ds² nor dr² can be assigned a specific value,
    only the ratio is defined, (ds/dr)² = 1/(1-2GM/c²r)

    You are doing this blunder over and over, and I have
    pointed it out over and over, but you seem to
    be unable to learn.

    I find your ignorance of basic calculus astonishing.


    Now, EAT THIS EXTRACT ABOUT USE OF SPACELIKE EVENTS IN CURRENT PHYSICS
    (Hint: It doesn't imply AT ALL FTL events).

    "FTL events" can only mean that something is moving faster
    than light, which is impossible, so what is your point?

    And why do you have problems with understanding the concept
    "spacelike interval" and "timelike interval"? It has nothing
    specific do do with SR or GR, it is simple common sense.

    If two events can be causally connected, the interval
    between them is timelike.
    If they can not be causally connected, the interval
    between them is spacelike.

    Example:
    The events are that I snap my fingers, and you snap your fingers.
    We have a two way video link, so we can see each other all the time.

    If you snap your fingers at 12:00 UTC today, and I do the same,
    then there is no way you snapped your fingers because you saw
    I did it, or vice versa. Causal connection is impossible,
    the interval between our finger snaps is spacelike.

    But if you snapped your fingers yesterday at 12:00 UTC, and I
    did it today at 12:00 UTC, then it is possible that I snapped my
    fingers because I saw you did it. Causal connection is possible,
    the interval is timelike.

    Mathematically this can be expressed thus: s² = −c²T² + D²
    where D is the distance between our positions when we
    snapped our fingers, and T is the time between our finger snaps.

    If s² > 0 then D > cT and D/T > c so no signal from you
    could have reached me before I snapped my fingers, and no signal
    from me could have reached you before you snapped your fingers.
    Causal connection is impossible, the interval between us is spacelike.

    If s² < 0 then D < cT and D/T < c so a signal from you
    could have reached me before I snapped my fingers.
    Causal connection is possible, the interval between us is timelike.

    There is no way you can fail to understand this.

    "Timelike" and "spacelike" is used in relativity,
    but that the equation s² = −c²T² + D² and
    s² > 0 means Causal connection is impossible and
    s² < 0 means Causal connection is possible
    is simple common sense.

    But your response to s² = −c²T² + D² was:

    Richard Hertz wrote:
    | Pretentious asshole: Using s instead of ds?
    | You are a mental case.
    | Also, this is a resemblance of Minkowski's metric (no gravity).
    | But then you switch to Schwarzschild?
    | It's painful to read your shit.
    |
    | Instead of your ignorant expression: s² = −c²T² + D²
    | Minkowski's metric for spacetime is universally represented as:
    | etc.

    :-D


    THIS EXTRACT SHOWS HOW FUCKED UP RELATIVISTIC PHYSICS IS, TRYING TO
    EXPLAIN
    THE WEIRDEST THINGS ACCOMODATING GENERAL RELATIVITY AT EVERY CORNER.

    AND THAT'S WHY MODERN SCIENCE BASED ON RELATIVITY IS SO FUCKED UP.

    AS I SAID, YOU CAN EAT WHAT FOLLOWS, EXTRACTED FROM THE CORE OF GR
    MODERN
    APPLICATIONS. IT'S PURE SHIT. A PSEUDOSCIENCE.

    BUT, AS YOU LIKE IT, GO AHEAD AND EAT IT.

    I, MEANWHILE, LAUGH AND DISPISE ALL THIS CRAPPY SHIT.

    ENJOY.

    Does this whining mean that you have given up your claim
    that ds² > 0 means that the interval between two events is spacelike?



    *************************************************************************

    Spacelike events do have real use in science, especially in the context
    of theoretical physics and general relativity. While spacelike events themselves aren't directly observable (since they can’t be connected causally through any physical signal, like light or matter), they are
    crucial in understanding the structure of spacetime and the behavior of
    the universe.

    Whenever you write "spacelike event" I will read "spacelike interval"

    "Spacelike intervals do have real use in science" :-D
    Word salad, with no real content.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?


    Some ways spacelike events are relevant:

    1. Defining Causality and Spacetime Structure
    Spacelike events help establish the causal structure of spacetime. Understanding which events can influence each other and which cannot
    (based on whether they are timelike, lightlike, or spacelike separated)
    is essential in general relativity. It allows physicists to:

    • Determine the behavior of particles and light in curved spacetime.
    • Define the boundaries of possible information flow in the universe.
    • Make predictions about the future evolution of systems (like stars,
    black holes, or cosmological models).

    In general relativity, the concept of spacelike separation plays an
    important role in causal diagrams and spacetime diagrams, which are
    used to visually understand the structure of events in spacetime.
    In these diagrams, spacelike events are those that lie outside of
    the light cones of each other and cannot be causally connected.

    Isn't light cones common sense?

    Events outside of light cones:
    D > cT, causal connection impossible.
    Events inside future light cone:
    D < cT, casual connection to future events possible.
    Events inside past light cone:
    D < cT, casual connection to past events possible.

    The visible universe is on the past light cone.
    The interval between the event "light source emits light" and
    the event "observer sees the light" is lightlike, D = cT.

    Obvious common sense, isn't it?

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?




    2. Relativity and the Speed of Light
    The speed of light acts as a strict upper limit on the speed at which information can travel through spacetime. Spacelike separation
    represents situations where the distance between events is so large that
    no signal,
    even light, could travel from one to the other within any reasonable
    time frame.

    Obvious trivialities, isn't it?

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?


    3. Quantum Field Theory and Entanglement
    In the realm of quantum mechanics, spacelike separation also plays a
    role,
    especially in the context of quantum entanglement. Although two
    particles
    may be spacelike-separated (meaning no signal could travel between
    them),
    they can still exhibit correlated behavior due to their quantum
    entanglement.

    This phenomena, often discussed in terms of spooky action at a distance
    (a phrase coined by Einstein), raises intriguing questions about
    non-locality
    in quantum mechanics.

    While this doesn’t imply any physical causal connection in the classical sense, the concept of spacelike separation helps to clarify the limits
    of classical causality versus quantum entanglement, which is relevant in quantum field theory.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?



    4. Cosmology and the Early Universe
    In cosmology, spacelike events are sometimes used to describe the relationship between different points in the universe’s history or different regions of spacetime that are not causally connected. For
    example:

    • During the early universe, before the universe became transparent
    (before
    the cosmic microwave background formed), different regions were causally disconnected because they were separated by large distances, meaning
    they
    were spacelike-separated.

    Right.
    We are (loosely) inside of the expanding sphere from the big-bang,
    so we will see the MBR radiation from different parts of the sphere
    when the universe became transparent in different direction.
    Since the temperature of the MBR varies (very little) in different
    direction, the different parts of the sphere when the universe became transparent must have had different temperature, which means that
    the different parts of the sphere can't have been causally connected.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?


    • Events that happened in distant regions of the universe at the same
    time
    can be spacelike-separated if no signal could travel between them due to
    the
    finite speed of light and the expansion of the universe.

    Obvious trivialities, isn't it?

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?


    • Understanding spacelike separation in this context helps to understand cosmological models like the inflationary universe, where certain
    regions
    of space may have never interacted but are still part of the same
    overall
    structure.

    Now we are back to the interpretations of the variations in the MBR. Cosmological models like the inflationary universe is not part of GR.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?




    5. Black Hole Information Paradox
    In the context of black holes, the concept of spacelike-separated events becomes important when analyzing phenomena like the information paradox.

    When one part of the spacetime near a black hole’s event horizon might
    be
    spacelike-separated from another part inside the event horizon, and it's wanted to understand how information might be preserved or lost. This
    plays a role in understanding the fundamental principles behind quantum gravity and the interaction between quantum mechanics and general
    relativity.

    All testable predictions of GR are outside the event horizon,
    and we know that objects outside the event horizon behave
    as predicted by GR, but what happens inside it isn't observable.
    So GR's predictions for what happens inside are unfalsifiable.

    GR is a valid theory outside the event horizon,
    but no theory of physics is valid inside the event horizon.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?


    6. Relativity in High-Energy Physics
    In high-energy physics, such as in particle collisions or accelerator experiments, spacelike separation come into play when dealing with relativistic particles. For example:


    • High-energy collisions can produce spacelike-separated events if the particles created are far apart enough, and their separation exceeds
    what can be connected by the speed of light during the time of the experiment.


    • These kinds of interactions can be analyzed using tools like Feynman diagrams in quantum field theory, where spacelike-separated events might represent interactions that cannot influence one another directly but
    are part of a broader process.

    QED and other quantum theories can predict things which
    SR and GR can't, but that doesn't mean that QED shows that
    the predictions of SR and GR are wrong.

    How does this show that RELATIVISTIC PHYSICS IS FUCKED UP?



    Summary
    While spacelike events themselves are not "observable" in the
    traditional
    sense (since they cannot influence each other causally), they are an essential part of the theoretical understanding of spacetime, causality,
    and the limits of information transfer. They help to understand:


    • Causal structure in general relativity.
    • The limits of communication in spacetime.
    • Quantum phenomena like entanglement.
    • Cosmological models of the early universe and inflation.
    • High-energy particle interactions.

    What exactly do you mean with the following statement?


    Spacelike-separated events play a significant role in the
    theoretical framework that governs relativistic physics, helping to understand the universe at both large and small scales.

    "Spacelike-separated events help to understand the universe" :-D

    This is a word salad with no real content.

    You wrote:
    "THIS EXTRACT SHOWS HOW FUCKED UP RELATIVISTIC PHYSICS IS"

    Where is the "EXTRACT" that SHOWS HOW FUCKED UP RELATIVISTIC PHYSICS IS?

    --
    Paul

    https://paulba.no/

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Paul B. Andersen@21:1/5 to All on Mon Feb 24 22:21:16 2025
    Den 24.02.2025 01:37, skrev rhertz:
    Schwarzschild metric

    ds² = -(1-2GM/c²r) c²dt² + 1/(1-2GM/c²r) dr² + r²(dθ² + sin² θ dϕ²)

    A general solution is spacetime S = ∫ds

    S = ∫√[-(1-2GM/c²r) c²dt² + 1/(1-2GM/c²r) dr² + r²(dθ² + sin² θ dϕ²)]

    Now, genius, explain this stupid simplification that you wrote, enabling
    to wrote the general solution S, or its derivate ds, when you can't
    integrate a function with several differentials that is under a square
    root operation.

    If you think I have made an error in a derivation, you better
    quote my derivation and point out exactly what you think is wrong.


    Even if you work only with ds², who ILLUMINATED YOU to write that
    s² = −c²T² + D²?

    What is your problem?
    I explained this in my posting of 22.02.
    Read it again.


    This is another proof that you are a self-entitled pompous retarded.

    This was part of your post (quite common my ass): *************************************************************************
    It is quite common to use s² as the interval, but it is more 'natural'
    to call the interval s, so that's what I will do.

    's' consists of two components, a temporal and a spatial.
    If we call the temporal component cT and the spatial component D,
    we have: s² = −c²T² + D²

    If D > cT then S is spacelike  (s² > 0)  D/T > c
    If D = cT then S is lightlike  (s² = 0)  D/T = c
    If D < cT then S is timelike   (s² < 0)  D/T < c

    Two events on the worldline of a massive object will always be
    separated by a timelike interval, because the object's speed D/T
    is always less than c, and D < cT. *************************************************************************



    Dig this example of spacelike events in the surface of the Sun. No FTL
    here.

    "spacelike events" again! You never learn, do you?

    The following should be obvious even to you:

    The interval between two events at "the same time"
    is always spacelike because T = 0, so s² = D² > 0

    The interval between two events at "the same spatial point"
    is always timelike because D = 0, so s² = -(cT)² < 0


    /////////////////////////////////////////////////////////////////////

    Numerical example using the Schwarzschild metric to determine spacelike-separated events around a single star. To calculate whether
    two events that
    on the surface of the star (at different points) are
    spacelike-separated,
    it's assumed that the Schwarzschild metric applies to the spacetime
    around
    the star.

    The Schwarzschild metric is given by:

    ds² = -(1-2GM/c²r) c²dt² + 1/(1-2GM/c²r) dr² + r²(dθ² + sin² θ dϕ²)

    Focusing on two events that occur at different positions on the surface
    of the star, where both are located at the same radius r, but the
    spatial separation between them is along the ϕ-direction (longitude) on
    the surface.

    For two events to be spacelike-separated, the spacetime interval ds²
    between them must be positive. This means ds²>0

    Consider two events that happen at the same time t1=t2 but at different points on the surface of the star (θ=π/2 and different ϕ -coordinates).

    So the interval between them is spatial because because T = 0,
    so s² = D² > 0

    This is trivial, and no calculation is needed to know that
    the interval is spacelike.


    For events on the surface of the star, r is constant, and the only
    nonzero spatial separation is along the ϕ-direction.

    Therefore, the differential dr=0, dθ=0, and the only spatial
    component left is dϕ.

    The spacetime interval between these events reduces to:

    ds² = r²dϕ²

    No , it is ds² = -(1-2GM/c²r) c²dt² + dr²dϕ²)

    You can't skip the temporal part even if t1=t2,
    because the metric above will give cT = 0,
    while your metric will not give any value for cT.


    For these two events to be spacelike-separated, ds² must be greater than zero, which is trivially true since the spatial distance between them is nonzero.

    This is nonsense.
    The interval between the events is spacelikel because
    cT = 0, not because D > 0


    Numerical Example

    Assumptions:
    • The mass of the Sun M ≈ 1.989×10^30 kg.
    • The radius of the Sun r = 7×10^8m (about the radius of the Sun).
    • Gravitational constant G = 6.67430×10^−11 m^3 kg^−1 s^−2
    • The two events occur at angular separation Δϕ=0.1 radians (which corresponds to 5.7°).

    Using the formula ds² = r²dϕ², and substituting the values:

    ds² = (7×10^8m)² × (0.1 radians)² = 4.9×10^15m²

    L = 7×10^8m ϕ₁ = 0 ϕ₂ = 0.1 rad

    ds = L⋅dϕ

    ϕ₂ ϕ₂
    s = ∫L⋅dϕ = L⋅∫dϕ = L⋅0.1
    ϕ₁ ϕ₁

    T = 0 so s² = 0 + (L⋅0.1)² > 0


    ds = (7×10^8m) × (0.1 radians) = +70km

    Good grief!
    I can only repeat what I have said before:
    Your ignorance of elementary calculus is astonishing.

    And irreparable!

    This is too stupid. Goodbye.

    --
    Paul

    https://paulba.no/

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