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

On Tue, 18 Feb 2025 21:04:00 +0000, Maciej Wozniak wrote:

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".

Imbecile Paul. You're lucky that your post didn't show up in
news.novabbs.com, and that only realized that you wrote that shitty
answer BECAUSE Maciej replied to you. What happened? Did you delete your
post after you realized the STUPIDITY that you wrote?
To make things clear, read these specific points:
1) I don't give a fuck about relativity, either SR or GR. I only limit
myself
   to use the math of relativity to bait idiots like you. Right or
wrong, I use
   SR/GR math instead of words, to shove results down into your throat.
It's a
   two-edged sword: You use that shit to promote relativity and I use
the same
   to demote relativity, as far as I can.
   Therefore, ASSHOLE, there is nothing that you can teach to me. And
even when
   you "try", you SUCK AT IT. You scramble different theories
(Minkowski,
   Schartzschild) and write concepts that let you as a pretentious self
entitled
   ignorant ASSHOLE/IDIOT.
2) I think that relativity is just a crappy pseudoscience. It can be a
display
   of mathematical fireworks, but without the slightest physical
meaning. Only
   generations of retarded people (like you) have been milking the new
field
   opened with the dark mathematics of GR and the fallacious SR to get a
job
   as a fucking desktop physicist (like many here, either amateur or
   professionals). It's though to get a job in REAL PHYSICS, then
parasite.
3) Even for an amateur with more than 30 years on this shit, grooming
your
   narcissism plagiarizing papers on your OWN website (how possibly a
SANE
   PERSON could need to do that?), your post SUCKS: Full of errors,
confusion
   and mixed theories (Minkowski flat ST, Schwarzschild curved ST).
   In your stupid (and deleted) post, you start with Minkowski BUT with
your
   own terminology. What kind of imbecile are you?
   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.
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:
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 = -(c dt)² + dr²
In this FLAT metric, ds²>0 doesn't mean FTL events. 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.
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
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)
Since 1/(1-2GM/c²r) > 0 outside the event horizon (c²rv>v2GM), ds²>0,
and the events are spacelike separated.
2.Two Events at the Same Radius but Different Times (conflicting views):
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
Since (1-2GM/c²r) > 0 outside the event horizon, ds² < 0, and the events
are timelike separated. 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:
ds² = r²(Δθ² + sin² θ Δϕ²) r
If the angular separation is large enough, ds²>0, and the events are
SPACELIKE separated.
MORE EXAMPLES
3.Events on Opposite Sides of the Event Horizon
4.Events at Large Spatial Separation
Spacelike separation in the Schwarzschild metric typically arises when
events are separated by a large spatial distance or when they occur at
the same time but at different locations. The key feature is that the
spacetime interval ds² is positive, ensuring no causal connection
between the events.
I could follow with examples extracted from major books and papers, like
simultaneous events at two opposite side of the Sun (Mercury case), but
the
above is enough to show you as a CHARLATAN that invent things and
pretend to pass as a knowledgeable person, Paul.
You fucked it up with your stupid  s² = −c²T² + D².  WHY?
You are not an expert on relativity. Just an educated PARROT.
Why do you pretend?
Do you need so desperately to pass as a connoisseur of relativity? But
if you
are only a lame EE, who taught about PICs 25 years ago. Problems with
ego?
I may or may not continue with this shit. I'm not happy with this post.
So I'll see how it goes.