Re: Are There Unresolver Foundational Issues With GR

On Apr 28, 9:17 pm, JanPB <film...@xxxxxxxxx> wrote:
On Apr 28, 8:51 pm, Koobee Wublee <koobee.wub...@xxxxxxxxx> wrote:

This question remains the most stupid as I have seriously
encountered. It is not that I refuse to answer that question. I am
still appalled by your lack of understanding in the very fundamental
algebra. Sometimes, I am even debating with myself if I should
continue with this pointless discussion with you on the most basic of
the mathematics involved.

You are now gradually changing the topics of our discussion. Obviously
if one has two different "metrics" as you call them (meaning, two
different matrices of g_ij's) written wrt one and the same coordinate
system, then they represent different geometries.

Yes, 2 different metrics using the same coordinate system represent 2
different geometries. <shrug>

This was never under the discussion.

Bullsh*t! This is exactly what I have been talking about. This is so
obvious, and I am so surprise that you have so much trouble to
understand this.

What we are debating is your claim that there are infinitely many
solutions to EFE in the spherically symmetric vacuum case. You gave
several examples of different line elements claiming they were
physically different solutions. These line elements differed by a
coordinate change - so what you said above does not apply. Nobody here
ever claimed than in a _fixed coordinate system_ different line
elements yielded the same geometry.

You have been speaking with a forked tongue here. These very
different and thus independent line elements share the same coordinate
system. They are not coordinate transform of the other. What you
call coordinate transformation is merely a mathematical tool and trick
but certainly no matheMagic that allows one to find other solutions if
one is found.

Here is the problem. Since you keep insisting on existence of
different solutions besides Schwarzschild's I'm simply asking (for the
third time) HOW are they different? IOW, what can an observer
physically do to tell these "infinitely many" solutions of yours
apart?

For the third time, I am answering that they are very different just
as the mathematics that represent them is very different.

You've agreed that geometry is determined by an assignment of lengths
and angles to tangent vectors. So obviously there must be something
ELSE in your mind besides lengths and angles that is physically
detectable and is implied by the EFE. WHAT IS IT? Is this some kind of
a secret?

The geometry cannot be determined, shaped, modified, or annihilated.
It can only be observed and interpreted. So, I have no clues as to
what you are claiming of my agreement with whatever.

So I'm asking a simple question: HOW can a person - some observer in
space or whatever - tell the difference?

Your question has no relevance to our discussion.

Just answer it, please. (Of course I think it's not only relevant,
it's the crux of the matter, that's why I'm asking it.)

Through the metric.

I am not claiming
two different expressions for the same geometry. I am claiming two
different metrics using the same coordinate system must each
represents a different geometry. <shrug>

Of course. But that was never under the discussion.

Again, this is exactly what my point is. It is pitiful that you just
start to understand what I have been saying.

That is not what Crothers claims.

I have never said that was what Mr. Crothers was claiming. He had his
own agenda. He wanted to promote his metric out of the infinite
numbers of them. My point is that no one can say the metric he
discovers after solving the field equations represents the actual
geometry of our universe. The hypothesis known as GR is totally BS.

What you and Crothers have been saying was that there
was more than one solution to the EFE in the spherically symmetric
vacuum case.

No, I have been saying that there are more than one independent
solution to the field equations regardless of it being spherically
symmetric or not.

Each such solution is a function assigning lengths and angles to
vectors. So you and Crothers claim that there is more than one such
function satisfying EFE.

Yes.

And yet ALL examples he and you produced so
far were of the following form: ONE AND THE SAME FUNCTION assigning
lengths and angles to vectors, ONLY WRITTEN IN DIFFERENT COORDINATES.

Back to the solutions to that quadratic equation, (x = 2) is merely a
coordinate transformation from (x = 1). That does not make (x = 1)
and (x = 2) identical.

Same function assigning lengths and angles to vectors. Same solution.

Your logic is very faulty. You don't understand the basics of
algebra. <shrug>

Given a quadratic equation of the following,

x^2 - 3 x + 2 = 0

The solutions are (x = 2) or (x = 1).

What make all solutions equivalent? What makes (x = 1 = 2)?

This is of course irrelevant. Here you have an equation for points in
the parameter space R^1 - not a manifold. Einstein's equation OTOH is
an equation for an unknown function between two manifolds.

This is very relevant. Your question is like asking the above.

It's not. I've explained why.

You are in denial. <shrug>

Or
better yet let's throw in the units. Given the following,

x^2 - 3 dollars * x + 2 dollars^2 = 0

What are the solutions?

Your stupid question is like asking how (x = 1 dollar) and (x = 2
dollars) can be in co-existence at the same time. In your twisted
logic, you somehow conjured up another unit say 'gollar' where (1
gollar = 0.50 dollar). Therefore, continuing with your fouled
mathematics, you are claiming (x = 1 dollar) and (x = 2 gollars).
Since (x = 1 dollar = 2 gollars), therefore the above quadratic
equation really has only one solution. This is called matheMagic.

You really need to go back to the basics of algebra. I cannot help
you on this one.

Nonsense.

It is up to you to go back to understand the basics of algebra. I
cannot make you. You need to make that initiative yourself. Good
night, Mr. Bielawski!

.

Relevant Pages

  • Re: PROOF: Schwarzschild Radius r=2*G*M/c^2 is wrong
    ... spherically symmetric but not necessarily asymptotically flat. ... I am not changing the geometry. ... coordinate system must be fixed at this point. ... Again, this is mathematics. ...
    (sci.physics.relativity)
  • Re: Are There Unresolver Foundational Issues With GR
    ... "Spacetime and Geometry" - S. Carroll ... You still have to know what coordinate system your metric is abided ... metrics must be the same regardless the coordinate system. ...
    (sci.physics.relativity)
  • Re: Are There Unresolver Foundational Issues With GR
    ... metrics") are to be treated as physically different. ... two different expressions for the same geometry. ... Then show us two different metrics using the same coordinate system ...
    (sci.physics.relativity)
  • Re: Are There Unresolver Foundational Issues With GR
    ... "Differential Geometry of Curves and Surfaces" - M. Do Camro ... You still have to know what coordinate system your metric is abided ... metrics must be the same regardless the coordinate system. ...
    (sci.physics.relativity)
  • Re: mulling metrics
    ... | three dimensional block with an embedded cartesian coordinate system. ... Use that if you want to argue metrics. ... The law in mathematics is that you be consistent, ... As long as he sees a distance of 2, the distortion can be pulled ...
    (sci.physics)