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From: clzb93ynxj@att.net (LaurenceClarkCrossen)
Newsgroups: sci.physics.relativity
Subject: Re: Relativity Derives Zero Deflection of Light By Gravity.
Date: Sun, 23 Feb 2025 21:46:09 +0000
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On Sun, 23 Feb 2025 13:17:32 +0000, Paul.B.Andersen wrote:

> Den 23.02.2025 05:50, skrev LaurenceClarkCrossen:
>> On Sun, 23 Feb 2025 0:05:29 +0000, Ross Finlayson wrote:
>>
>>> On 02/22/2025 01:30 PM, Paul B. Andersen wrote:
>>>>
>>>> This rather funny statement of yours reveals that the only
>>>> non-Euclidean geometry you know is Gaussian geometry.
>>>>
>>>
>>> Mostly those are all piece-wise and broken one way or the
>>> other with regards to invariance and symmetry, these
>>> "non-Euclidean" geometries, with regards to something
>>> like "Poincare completion", which in the theory of continuous
>>> manifolds, has that it's a continuous manifold.
>
>> Thank you for conveying Paul's comment to me. But wait. That doesn't
>> seem to be anything he said to me. I don't find it in the search
>> function. I don't recall noticing it, and I do not have a lot of time
>> for this forum.
>
> Yes it was written for you. Twice.
>
>>
>> Paul doesn't understand the difference between not understanding and
>> disagreeing. I disagree with him and you.
>
> You were obviously ignorant of the fact that there are
> other non-Euclidean geometries than Gaussian geometry.
>
> Loosely explained, Gaussian geometry is about surfaces in 3-dimentinal
> Euclidean space. The shape of the surface is defined by a function
> f(x,y,z) where x,y,z are Cartesian coordinates.
>
> Note that we must use three coordinates to describe a 2-dimentional
> surface.
>
> Riemannian geometry is more general.
> Loosely explained,  Riemannian geometry is about manifolds (spaces)
> of any dimensions. The "shape" of the manifold is described by
> the metric.
>
> The metric describes the length of a line element.
>
> The metric for a "flat 3D-space" (Euclidean space) is:
>   ds² = dx² + dy² + dy²   (Pythagoras!)
>
> The metric for a 3D-sphere is:
>   ds² = dr² + r²dθ² + r²sin²θ⋅dφ²
>
> Note that only three coordinates are needed to describe
> the shape of a 3D space.
>
> It is not possible to disagree about this:
> Riemannian geometry can describe curved 3D space.
>
> Fact!
>
>>
>> Paul is unable to learn.
>>
>> Very simply, manifolds are not literal spaces.
>
> A 3D manifold is literally a 3D space.
>
>> They are only diagrams
>> representing non-spatial facts as if they were spatial.
>
> Read this again and try not to laugh! :-D
>
> What is a "non-spatial fact" ?
>
> Which "non-spatial facts" are represented as if they were spatial?
>
>> What you are
>> speaking about are not surfaces.
>
> Indeed! I am speaking about 3d spaces
>
>> Riemannian geometry is about representing non-spatial elements as
>> spatial diagrammatically. Taken literally, this is a reification
>> fallacy.
>
> A reification fallacy? :-D
>
> So Riemannian geometry is as treating abstract "non spatial entities"
> as if they were real "spatial diagrammatically".
>
> Make sense, doesn't it? :-D
>
> Riemannian geometry is mathematics.
> It is correct by definition. Like Euclidean geometry.
>
> And there is no such thing as "disagreeing" with
> a mathematical definition.
>
>>
>> Curves in manifolds are not curves in spaces. Non-Euclidean geometry
>> cannot bend space or even describe bent space. There is no such thing
>> because space is not a surface. Space-time fabric is not space.
>
> So let's talk about "spacetime".
>
> First:
> Theories of physics such as Newtonian Mechanics [NM], The Special
> Theory of Relativity [SR] and The General Theory of Relativity [GR]
> are mathematical models of Nature (or the reality or whatever)
> they are not  Nature. It is meaningless to ask if the entities
> in the theory "really exist".
>
> The only test of the validity of a mathematically consistent theory
> is if its predictions are in accordance with measurements.
>
> "Spacetime" is an entity in GR, and spacetime geometry is mathematics,
> so the following is correct by definition:
>
> In spacetime geometry there is a four dimensional manifold called
> spacetime. The spacetime metric has four coordinates, one temporal
> and three spatial.
>
> The metric for a static flat spacetime is:
>   ds² = − (c⋅dt)²  + dx² + dy² + dz²
>
> or since ds² = - (c⋅dτ)²
>   (c⋅dτ)² =  (c⋅dt)² − dx² − dy² − dz²
>
> If there is a mass present (Sun, Earth) spacetime will be curved.
>
> The metric for spacetime in the vicinity of a spherical mass is:
> ds² = -(1-2GM/c²r)c²dt² + (1/(1-2GM/c²r))dr² + r²(dθ² + sin²θ⋅dϕ²)
>   or:
> (c⋅dτ)² = (1-2GM/c²r)c²dt² - (1/(1-2GM/c²r))dr² - r²(dθ² + sin²θ⋅dϕ²)
>
> Note that there are four coordinates,  t, r, θ and ϕ
>
> Bottom line:
> It is a fact that the entity spacetime in the mathematical model GR
> will be curved if there is a mass present (Sun, Earth).
>
> You are however free to believe that the predictions of GR not
> are in accordance with real measurements.
>
> But then you must also believe that all the physicists involved
> in all the experiments that have confirmed GR, don't know what
> they are doing or are frauds.
>
> Is that what you believe?  :-D
>
I disagree with it, as do thousands of excellent scientists. Riemannian
geometry can't describe curved 3D space without a surface. What it
describes does not exist. To think it does involves you in reification
fallacy. The GR interpretation of gravity relies on making this facile
error.

You are unaware that any non-Euclidean geometry claiming to describe
curved space is making the reification error. Curved space has to
involve surfaces. A 4D manifold is not a literal space.  It is a
diagrammatic illustration representing things (like time) that are not
spatial as if they were spatial. A 3D manifold cannot describe curved
space because it cannot curve without a surface. Such a description is
only of an imaginary surface.

Time is a non-spatial fact.

Treating non-spatial realities as spatial is a reification fallacy.

Riemannian geometry is correct when applied to actual spatial surfaces.
Otherwise, it is a reification fallacy.

There are incorrect mathematical definitions, and those should be
disagreed with.

Nothing is correct by definition.

If geometry is correct, then parallel lines don't meet on plane
surfaces.

If it is meaningless to ask if the entities exist, that theory is math
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