Re: Relativity Derives Zero Deflection of Light By Gravity.

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:
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On 02/22/2025 01:30 PM, Paul B. Andersen wrote:

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This rather funny statement of yours reveals that the only
non-Euclidean geometry you know is Gaussian geometry.
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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.

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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.

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Yes it was written for you. Twice.
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Paul doesn't understand the difference between not understanding and
disagreeing. I disagree with him and you.

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You were obviously ignorant of the fact that there are
other non-Euclidean geometries than Gaussian geometry.
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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.
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Note that we must use three coordinates to describe a 2-dimentional
surface.
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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.
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The metric describes the length of a line element.
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The metric for a "flat 3D-space" (Euclidean space) is:
  ds² = dx² + dy² + dy²   (Pythagoras!)
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The metric for a 3D-sphere is:
  ds² = dr² + r²dθ² + r²sin²θ⋅dφ²
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Note that only three coordinates are needed to describe
the shape of a 3D space.
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It is not possible to disagree about this:
Riemannian geometry can describe curved 3D space.
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Fact!
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Paul is unable to learn.
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Very simply, manifolds are not literal spaces.

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A 3D manifold is literally a 3D space.
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They are only diagrams
representing non-spatial facts as if they were spatial.

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Read this again and try not to laugh! :-D
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What is a "non-spatial fact" ?
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Which "non-spatial facts" are represented as if they were spatial?
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What you are
speaking about are not surfaces.

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Indeed! I am speaking about 3d spaces
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Riemannian geometry is about representing non-spatial elements as
spatial diagrammatically. Taken literally, this is a reification
fallacy.

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A reification fallacy? :-D
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So Riemannian geometry is as treating abstract "non spatial entities"
as if they were real "spatial diagrammatically".
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Make sense, doesn't it? :-D
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Riemannian geometry is mathematics.
It is correct by definition. Like Euclidean geometry.
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And there is no such thing as "disagreeing" with
a mathematical definition.
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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.

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So let's talk about "spacetime".
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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".
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The only test of the validity of a mathematically consistent theory
is if its predictions are in accordance with measurements.
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"Spacetime" is an entity in GR, and spacetime geometry is mathematics,
so the following is correct by definition:
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In spacetime geometry there is a four dimensional manifold called
spacetime. The spacetime metric has four coordinates, one temporal
and three spatial.
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The metric for a static flat spacetime is:
  ds² = − (c⋅dt)²  + dx² + dy² + dz²
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or since ds² = - (c⋅dτ)²
  (c⋅dτ)² =  (c⋅dt)² − dx² − dy² − dz²
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If there is a mass present (Sun, Earth) spacetime will be curved.
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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)
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Note that there are four coordinates,  t, r, θ and ϕ
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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).
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You are however free to believe that the predictions of GR not
are in accordance with real measurements.
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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.
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Is that what you believe?  :-D
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Paul, you have not been able to explain how curved spacetime can curve
3D space when it has no surface because you can't. Relativity is
nonsense.