Date: Tue, 18 Feb 2025 22:04:00 +0100
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Subject: Re: Challenge for Paul; Probe that with Mercury ds^2>0 and the solution is spacelike
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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".