A Question for Curved Spacetime.

[MigL]

If you click on the hyperlinks embedded in the partial quotes I provided from the two Wiki articles, it will take you to a further description.

For example, in the quote from the Big Bang article the embedded hyperlink "universe expanded" will take you to another aricle describing how the intrinsic, metric expansion of the universe differs from an explosion originating at a central point.

I think we on this forum, sometimes forget that we are not here just to boost our egos.
We are here to learn, and pass on what knowledge we have, or gain, onto others.

[J.Merrill]

7 hours ago, zapatos said:

Again, NO. That is incorrect.

I guess I figured that after you "REFUSED" to discuss conflicting ideas with me you weren't really interested.

LOL! You're killing me Smalls!

This was an intentional wrong claim. 

Like the others  here on this forum.

I know what dark matter is and what dark energy is.

This was a personal experiment set in place to trigger the same response I have been getting from the beginning to help prove my point in my last post here.

I'm doing a social experiment for school!

Some peoples social skills are really poor  in My Honest opinion.

Again rather than explain I had a small mix up between the two constructs A (Dark Matter) and B(Dark Energy)

You are instead resorting to just saying wrong and then reverted to name calling once more.

ad hominem!

A reaction directed against a person rather than the position they are maintaining.

Rather than attack the user, attack the topic and be helpful!

I really hope none of you are teachers because I wonder if you have ever considered how other feel when you intentionally insult one asking questions and comparing what they know to what they don't understand. 

I really enjoyed this social experiment. And it helps Me with my assignment so thank you all for being who you really are!!!!

I can only wander though.  If results might have changed if anyone here knew it was for a social experiment. 

What you do and how you act when you think no one is looking, determines the type of person you are.

This is my last post here, and I have enough to right my paper!

 

 

[zapatos]

4 minutes ago, J.Merrill said:

This is my last post here

Don't let the door hit you on the way out.

[Bufofrog]

25 minutes ago, J.Merrill said:

If results might have changed if anyone here knew it was for a social experiment.

It seems like your experiment was to act like an anti-science troll and see if you are treated like an anti-science troll.  The outcome was easily predictable IMO.

[Phi for All]

7 minutes ago, Bufofrog said:

It seems like your experiment was to act like an anti-science troll and see if you are treated like an anti-science troll.  The outcome was easily predictable IMO.

Hopefully the teacher will require evidence, and the transcripts of their posts will be reviewed. They clearly aren't the victim of insult and ridicule.

[Moontanman]

He knows what dark matter and dark energy is?  

[mistermack]

9 hours ago, J.Merrill said:

This is my last post here, and I have enough to right my paper!

Today I right my paper. Tomorrow I right the world!

I'm write with you, go for it !!

[geordief]

Would I be right to say the the curvature of spacetime is an entirely local effect and it  would be wrong to make  a global picture of spacetime which would hold all the sources of energy-momentum at all the different "events" in the global set?

Does one have  to calculate the curvature at each event and  somehow knit them together in an approximative  fashion in order to draw a picture of the spacetime curvature of a system as a whole?

[joigus]

19 hours ago, Moontanman said:

Can you give a link to that idea? I'd like to study it a bit. 

At several points on his lectures, Lenny Susskind makes a very emphatic case for that. I'm guessing it's in his book, The Theoretical Minimum? Any introductory book that explains to you that the most relevant thing about GR is equating geometry to energy-momentum, will do the job. Mass is not a central concept of GR, to put it mildly. 

I'm sorry I don't remember in what particular lecture he delves into that a little bit more, due to a question from the audience. But you should be alright if you follow his lectures on GR.

 

[studiot]

1 hour ago, geordief said:

Would I be right to say the the curvature of spacetime is an entirely local effect and it  would be wrong to make  a global picture of spacetime which would hold all the sources of energy-momentum at all the different "events" in the global set?

Does one have  to calculate the curvature at each event and  somehow knit them together in an approximative  fashion in order to draw a picture of the spacetime curvature of a system as a whole?

No it would not be wrong to create a global picture, but you would have to do it as you describe in your second paragraph because GR functions are pointwise functions.
You could create a standard net and calculate deviations from it, as opposed to calculate absolute (ie direct coordinate) values but you would still have to do this point by point.

There is an analagous pair of approaches in fluid mechanics, respectively called Eulerian and Lagrangian.

[geordief]

47 minutes ago, studiot said:

No it would not be wrong to create a global picture, but you would have to do it as you describe in your second paragraph because GR functions are pointwise functions.
You could create a standard net and calculate deviations from it, as opposed to calculate absolute (ie direct coordinate) values but you would still have to do this point by point.

There is an analagous pair of approaches in fluid mechanics, respectively called Eulerian and Lagrangian.

Would it be possible to make a spacetime model of the complete (ish) Solar system?(say from 2000 to 2010)

 

Would it be visible in the round  or would it be in mathematical form only?

[NTuft]

On 6/19/2022 at 3:00 PM, J.Merrill said:

Gravity is not a force, all though the term Force follows gravity around through miss understanding. 

I am insinuating that Mass Causes a gradient in time. And this Curvature of time is Gravity.

We are describing a force that acts on certain lines. 

What Einstein proposed was that being under a uniform acceleration would be indistinguishable from being in a gravity field where inertial masses = gravitational masses, and, that by appearances, for descriptive purposes, we can conceive of a flat space being bent in time by displacement from masses. 

If a charged mass extends to matter, moves, it induces a magnetic field. There could be acceleration in the rest frame. Field equations jibe with spherical, elliptical, hyperbolic curvature.

You say, "this Curvature of time is Gravity." Is you time continuous (i.e. are you trying to trace back to the start), or is it discrete, quantized? I think maybe yes once mass is moving over a "gradient" -- level curves of field lines, like form electrostatics but with electric field lines stretching out, not ending, and going through a dimensional wormhole -- of time evolution, it is then translating through the emergent force field. Perhaps not a gravity field. And I'd say more like the force of gravity can be equated with a diminished force multiple, like the third term of the kinetic energy series:

but, since we're in an accelerating frame, this is kinetic energy ("gravity") instead of potential energy as currently described (with time poorly defined).

[MigL]

5 hours ago, geordief said:

Would I be right to say the the curvature of spacetime is an entirely local effect and it  would be wrong to make  a global picture of spacetime which would hold all the sources of energy-momentum at all the different "events" in the global set?

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.

 

53 minutes ago, NTuft said:

You say, "this Curvature of time is Gravity." Is you time continuous (i.e. are you trying to trace back to the start), or is it discrete, quantized? I think maybe yes once mass is moving over a "gradient" -- level curves of field lines, like form electrostatics but with electric field lines stretching out, not ending, and going through a dimensional wormhole -- of time evolution, it is then translating through the emergent force field. Perhaps not a gravity field. And I'd say more like the force of gravity can be equated with a diminished force multiple, like the third term of the kinetic energy series:

but, since we're in an accelerating frame, this is kinetic energy ("gravity") instead of potential energy as currently described (with time poorly

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.

Edited June 23, 2022 by MigL

[NTuft]

12 minutes ago, MigL said:

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.

What all can we explain with motion off the geodesics?

"Adding to Markus' point, if you consider space-time geometry as the 'field' in GR, then the analogy would be the effect on the EM field that you get when moving charges around ( minus the self interaction ).
The field, space-time geometry, changes with changes in the energy-momentum distribution."

 

The change can be explained equivalently with stress-energy-momentum tensor accounting for mass charge distribution effects, with a repulsion/anti-gravity and gravitic attraction, which I don't think are equatable, but I put a paper on it in my speculations thread.

Edited June 23, 2022 by NTuft

[MigL]

Geodesics determine trajectories.
( for massive and massless particles )
Unless other forces are in play.

[NTuft]

  

39 minutes ago, MigL said:

other forces are in play.

 

Yea. So, if we have an emergent curved geometry from charge seperation(see edited comment above, quoting you on such), setting level curves or gradients that then do have those self (and other force) interactions, we can account for foreful motion off the.. curved geodesics. They could be locally flat in various configurations if I understand it.

On 6/21/2022 at 6:24 AM, J.Merrill said:

(I.E) The mathematical construct of numbers would not be a thing if humans did not occur.

... conceptualist. No wonder you can't actually do any math.

Edited June 23, 2022 by NTuft

[geordief]

54 minutes ago, 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

Trying to flesh out/ fill in  gaps in my understanding (using you guys to help me in that)

So ,would you have any examples of a "local"Cauchy surface ,defined by causal  boundaries  and structures that would model a real life system of objects?

Could it  be a snapshot(time-slice of the 4d manifold) of the Solar system ?

 

Or is that too big a system to be "local"?

 

I am not  sure I understood  exactly  what you were describing  by "local surfaces".Did you mean local as in " simultaneous"?

 

(it feels to me that a slice of the manifold  where t=constant could be described  as "local"  in the same way as a unique location in  space  ,but moving in time  would also be "local")

 

Hope my question was coherent. 

[studiot]

5 hours ago, geordief said:

Would it be possible to make a spacetime model of the complete (ish) Solar system?(say from 2000 to 2010)

 

Would it be visible in the round  or would it be in mathematical form only?

Note I wrote this earlier but obviously never got round to posting it.  Sorry.
I seem to be having all sorts of trouble with postings here and elsewhere just lately.

 

Just think. We can't calculate the weather on our own planet over 10 days.

I tell you what.

When I win all the lotteries in the world at once I will buy lots of supercomputers from @Sensei and help you.

How does that sound ?

🙂

 

 

[geordief]

@studiot Don't want to derail the thread but we can calculate the weather on our planet over any period if we don't mind inaccurate results.

 

As an aside I was actually  kind of amazed to hear on a BBC science documentary  recently  ,(forgotten  the title) that  a particular theory  could be plugged into BB and give an accurate representation of the universe we are living in

That was some forecast!

Edited June 23, 2022 by geordief

[studiot]

7 minutes ago, geordief said:

inaccurate results.

Inaccurate  ?

Damn perhaps that's why I never win those lotteries.

[geordief]

12 minutes ago, studiot said:

Inaccurate  ?

Damn perhaps that's why I never win those lotteries.

Apparently it was  Voltaire  who first said

"Dans ses écrits, un sage Italien
Dit que le mieux est l'ennemi du bien"

Edited June 23, 2022 by geordief

[NTuft]

2 hours ago, geordief said:

Trying to flesh out/ fill in  gaps in my understanding (using you guys to help me in that)

So ,would you have any examples of a "local"Cauchy surface ,defined by causal  boundaries  and structures that would model a real life system of objects?

Could it  be a snapshot(time-slice of the 4d manifold) of the Solar system ?

 

Or is that too big a system to be "local"?

Quote

Manifolds of constant curvature are most familiar in the case of two dimensions, where the surface of a sphere is a surface of constant positive curvature, a flat (Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature.

Einstein's general theory of relativity places space and time on equal footing, so that one considers the geometry of a unified spacetime instead of considering space and time separately. The cases of spacetime of constant curvature are de Sitter space (positive), Minkowski space (zero), and anti-de Sitter space (negative). As such, they are exact solutions of Einstein's field equations for an empty universe with a positive, zero, or negative cosmological constant, respectively.

As I understand it, a local area on a Riemannian manifold is a section we can take to be flat. Or we are asking to be flat. By observation, it apperas the whole dang universe is flat... So yes, I think what we are doing often is taking time-slices (i.e. at time=specific value) effectively reducing the snapshot to 3-D.

So taking flat Euclidean space + time is known as Minkowski space (most common in S.R. but also in G.R., and really pseudo-Euclidean in G.R. I think). I highly doubt I know as much about it as MigL.

Quote

In differential geometry, a differentiable manifold is a space which is locally similar to a Euclidean space. In an n-dimensional Euclidean space any point can be specified by n real numbers. These are called the coordinates of the point.

 

In differential geometry, a pseudo-Riemannian manifold,^[1][2] also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed.

Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space.

A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike.


...how de Sitter space describes a distinct variant of the ordinary spacetime of general relativity (called Minkowski space) related to the cosmological constant, and how anti-de Sitter space differs from de Sitter space. It also explains that Minkowski space, de Sitter space and anti-de Sitter space, as applied to general relativity, can all be thought of as being embedded in a flat five-dimensional spacetime.
 

 

[Markus Hanke]

2 hours ago, NTuft said:

So taking flat Euclidean space + time is known as Minkowski space

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.

[studiot]

4 hours ago, 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.

Yes indeed, +1.

However, as ever,  life is more complicated than that.

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

Here is an extract from one of his papers on the subject.

The first 13 pages of this paper are as Markus implies but doesn't say explicitly.

They are couched in terms of the real numbers.
That is all variables are are measured in real numbers.

Minkowsk then introduced imaginary numbers (note not complex numbers) to the mix, near the end of the paper.

 

I am not sure if the reference at the bottom of the left hand page to Schutz acknowledges that Schutz did this first.

Some later authors formalised this by starting with the inclusion of i.

 

The use of the 'mystic'  formula from natural units is also interesting.

[math]3x{10^8}kilometres = \sqrt { - 1} \sec onds[/math]

 

 

 

 

 

 

 

[Sensei]

16 hours ago, geordief said:

Would it be possible to make a spacetime model of the complete (ish) Solar system?(say from 2000 to 2010)

Complete, with micro-scale asteroids? They are made every day, every second.. new free particles in cosmic space, especially solar wind are emitted by Sun, planets, etc. so complete data is not possible due to never enough amount of data..

..but to some level of accuracy, based on sizes of cosmic objects, it's not a big problem..