A Question for Curved Spacetime.

[NTuft]

On 6/23/2022 at 8:12 PM, Markus Hanke said:

That’s not true - a Euclidean spacetime would have the same sign for the space and time parts of the metric; for Minkowski spacetime these are opposite. In Euclidean spacetime there wouldn’t be any relativistic effects, since the speed of light can’t be invariant. You need the hyperbolic geometry of Minkowski for that.

Au contraire, what is juxtaposed is an imaginary component for the time-dimension, which throws that sign before the multiplication (which should be quantized), thus making it opposite sign from the spatial dimensions. Minkowski space is 1-D: taken as a Pseudo-Euclidian (slightly bent) map of spacetime, no? It is not quite yet hyperbolic, but more like elliptic -- you're not presuming it's a flat rectangle, are you??

Elliptic I'd call positive cosmological constant, equatable to Gaussian curvature >0. Towards spherical or de Sitter at 1. Reflecting through the origin to generate a hyperbolic -1 Gaussian curvature with an elliptic asymptote we have hyperbolic geometry, a la Lobachevsky-Bolyai.

21 hours ago, studiot said:

To the best of my knowledge Minkowski didn't write any books, only papers and died prematurely.

Dieing early, sounds like W.K. Clifford and N.H. Abel, etc. We on Fire¹.

¹Pascal

20 hours ago, Sensei said:

especially solar wind

3,4,5 ray spallation. Tear the roof off this mo**erf**ker².

²Banks

Edited June 25, 2022 by NTuft
emphasis on rectangle. also, it's not a fluid so stop modelling that. it's a gas or plasma PV=nRT.

[Markus Hanke]

25 minutes ago, NTuft said:

Minkowski space is 1-D: taken as a Pseudo-Euclidian (slightly bent) map of spacetime, no?

No. Minkowski spacetime is (3+1)D, and it is perfectly flat.

[NTuft]

7 minutes ago, Markus Hanke said:

No. Minkowski spacetime is (3+1)D, and it is perfectly flat.

As a graph.

Any masses, extension, self re-inforcing electromagnetics?

Edited June 25, 2022 by NTuft
dented map vs. constant acceleration

[studiot]

18 hours ago, geordief said:

Yes,that is the sort of thing(I was looking for the way the   different gravity wells joined up)

It wouldn't be a problem to add the 3rd spatial dimension (and use  3d glasses) and to run a series of those still frames  too  get the time dimension, would  it?

The point of spacetime is that the timelike and spacelike dimensions have a quadratic relationship, not a linear one so you can't separate them.

2 hours ago, NTuft said:

Minkowski space is 1-D: taken as a Pseudo-Euclidian (slightly bent) map of spacetime, no? It is not quite yet hyperbolic, but more like elliptic -- you're not presuming it's a flat rectangle, are you??

1-D space has no curvature. Space has to be at least 2 -D to have curvature.

Please go back a few posts and read (the translation of) what Minkowski actually said. At the top of page 88 in my attachment.

Euclidian space is the name given to space with the usual or standard metric distance function

[math]dis\tan ce = \sqrt {x_1^2 + x_2^2 + x_3^2 + ......x_n^2} [/math]

for n dimensions. The space can be physical or abstract.

Edited June 25, 2022 by studiot

[Ni Mimi.]

Hi all.

In response to Merril's question, we were to look at the passage of time as a straight line which in essence espouses a break-down process, analogically, can't curved space-time be describing a differential process?

[Markus Hanke]

21 hours ago, NTuft said:

Any masses, extension, self re-inforcing electromagnetics?

Minkowski spacetime does not contain any sources of gravitation. If you add such sources, you will get spacetime geometries other than Minkowski. 

[studiot]

4 hours ago, Markus Hanke said:

Minkowski spacetime does not contain any sources of gravitation. If you add such sources, you will get spacetime geometries other than Minkowski. 

Short and sweet again. +1

 

Lack of Gravitation was the reason Einstein moved on from SR to GR.

[NTuft]

On 6/25/2022 at 11:47 AM, Ni Mimi. said:

Hi all.

In response to Merril's question, we were to look at the passage of time as a straight line which in essence espouses a break-down process, analogically, can't curved space-time be describing a differential process?

I read @J.Merrill's "question" to be a declarative statement, and something about the syntax and formulation were so offensive to my thinking I don't think I even registered a question. I may re-read the original question. The "graph", with pictures, of time vs. mass or whatever it was was there, too.

And apparently the presentation of this was a school project. As to your proposition, I'm uncertain about the arrow of time or what breakdown process you're describing. I do think we are able to describe spacetime mathematically and are doing the mathematical operation you mention to interpret measurements of spacetime.

Thanks to all for the discussion here.

[swansont]

10 minutes ago, NTuft said:

I read @J.Merrill's "question" to be a declarative statement, and something about the syntax and formulation were so offensive to my thinking I don't think I even registered a question. I may re-read the original question. The "graph", with pictures, of time vs. mass or whatever it was was there, too.

 “what causes the "Curved Fabric of Space"  return to its previous state, into its unbent position?” is pretty clearly a question, albeit based on a physically unrealistic scenario

[NTuft]

On 6/23/2022 at 1:21 PM, MigL said:

Not sure what you are after with this ?
I know it is impossible to have a global Cauchy surface to describe all of space-time, but local surfaces are allowed.
A Cauchy surface is a submanifold of the Lorentzian manifold defined by GR, and is usually interpreted as a time-slice of the 4Dimensional manifold, and is 'local' because it is defined by causal boundries and structures.

 

I don't know what any of this means, and unless you explain it better, it reads as word salad.
In GR, the geometry is the field.
Each point of he field has associated infnformaion describing the deviation from flat, at that point. These deviations define the local 'curvaure', and geodesics, we call gravity.
So, no, in GR graviy is not a force.

Foundations of the Quaternion Quantum Mechanics https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7766457/

Quote

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of 

the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.

Keywords: relativistic quaternion quantum mechanics, Cauchy-elastic solid, Schrödinger and Poisson equations, quaternions, Klein–Gordon equation

 

[Ni Mimi.]

NTuft, in our pursuit of answers for those aspects we know nothing of; even do not comprehend, do we start from the known to the unknown. Because if we knew, then we wouldn’t be asking questions.

Let us not try to be emotional; that’ll tend to limit the free pursuit of thought.

Objectivity and being open-minded ought to be the baton by which we interact.