Does the 4D Vortex have anything to do with 3D gravitation

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Does the 4D Vortex have anything to do with 3D gravitation

Postby Sphericality » Thu Jun 08, 2017 11:46 am

How is it that we are held by the curvature of spacetime around the mass of the Earth ?
In how many dimensions does gravity curve spacetime?

I understand that there is more than one equivalent of the torus in 4D.
I am wondering is whether there is also more than one equivalent of the spiral vortex that appears in such 3D forms as whirlpools and tornadoes?
Of course a vortex is a temporal spin dynamic rather than a static geometry.
The way I see it though,circular movement is just a spiral form in a higher dimension being scanned temporally.

I suspect another way to ask the question is what is the equivalent 4D form to the 3D electromagnetic toroidal field ?
Or what would the geometry of a 4D electromagnetic field be if a 3D field is a cycling torus contracting and expanding vortex ?
I presume a 4D vortex would spin around a plane rather than around an axis line.
Im thinking that as 3D vortex pulls nearby items into it primarily from a circular perimeter on the plane surrounding the top of the vortex
a 4D vortex would pull in items from a spherical perimeter in the surrounding 3D space near the entry to the vortex.

So - does the 4D Vortex geometry have anything to do with 3D gravitation and black holes ?
If so ... how would you describe it ?
If not - how would you describe the geometric dynamics in a more accurate way ?

Here are what I consider to be two inadequate attempts by someone to illustrate what is happening in the General Relativity description of Gravity

Image - - - Image
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby wendy » Wed Jun 14, 2017 10:58 am

The theory of general relativity, supposes that gravity does not exist, but instead a geometric effect. Although it supposes space curvature, this does not mean that space is curved in any higher dimension. The problem is made worse by students etc, feeding out these diagrams, and simply quoting Einstein's Hamiltonians with little to no connection to things like Newton's law.

We will now discuss the diagrams.

The first diagram shows the earth casuing a cubic grid to dra under it. The cubes are elongated towards the planet. It's wildly out of scale, since the distortion of space around the earth is no more than 4.43 mm over 6000 km. You would not see that level. It's a passing attempt at something like a neutron star or the like.

The second picture shows a satelite orbiting the earth, over a giant dimple. This is a potential diagram, in that the gravitational potential is height, and you have two dimensions of space. Because ordinary gravity at the surface of the earth converts height to potential, you can use this as a billiard table, where the speed of the ball and its trajectory would follow something that happens in space. But since space does not have a potential-dimension, this is also not a representation of gravity.

Curvature.

The trick with curvature, is that it is not so much space buckled into a higher dimension, but rather that the length of an arc can vary with angle. That is, a degree is longer than a millimetre in one direction, and shorter in another. We then suppose that space is in tension, and that the slight variance of long degrees over short degrees is what causes gravity.

A fairly simple model of curvature can be made with a cloth, a ball and a ring. The ring should pass over the ball. You put the ball on the table, cover the ball with cloth, and then put the ring over the ball. The effect is that every circumference of circles around the ball is increased by some constant K, which will cause the cloth to ruffle (like a curtain), in diminishing intensity. From this we derive GM/R², which causes any smaller mass m to accelerate towards the larger mass M.
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby Teragon » Thu Jun 22, 2017 7:01 am

You'd need about 46 dimensions to reproduce all aspects of curvature that general relativity can describe. So no, we shouldn't think of the universe as curved in extra dimensions.
What is deep in our world is superficial in higher dimensions.
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby Sphericality » Tue Jul 18, 2017 12:20 pm

Do I understand correctly then that you are both saying that what is referred to as curvature is more like a compression and expansion of 3D space that does not require any extra dimensions?
I think I can understand that from a 2D model where the space is pinched in around the mass, (similar to illustration 2 but no dimple).


Teragon wrote:You'd need about 46 dimensions to reproduce all aspects of curvature that general relativity can describe. So no, we shouldn't think of the universe as curved in extra dimensions.

That sounds like you are saying that curvature in 46 dimensions CAN correctly model relativity 8)
If so ... isn't that a useful thing?
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby gonegahgah » Fri Jul 21, 2017 10:05 am

I tend to regard dimensions as just mathematical constructs rather than physical objects.
To me if a mathematical formula can describe reality then every factor that is in the equation is a dimension of that mathematical formula.
I tend to regard that anything that affects the reality is a dimension. But, that's just me...
So if you can create a formula that closely represents what happens with 46 different necessary effecting factors then go for it!!!
Personally I think that gravity does effect things in the real world and is an affecting factor in formulas so really is a mathematical dimension of reality...

I also am of the belief that things like field theory and space-time are just new variations on æther theories.
There is an imperative need of science for things to be somehow touching each other. The acceptance of effect without physical connection seems to be abhorrent to many.
So we can shuffle science around and decide that the cart is pushing the horse; unless it is somehow right if it somehow is...
Particles then become the realisation of fields rather than the other way around.

The inherit problem of this approach is how do these fields and things exist over each other within each other's space.
And this is where I believe the need for proposing higher numbers of dimensions spills out from.
Things need to go somewhere so extra dimensions will provide plenty of space for that...

I do like it because it is certainly imaginative and creative and makes for great story matter - which I do think we need.
However, I will be curious to know whether any of these touching theories actually bare any resemblance to reality in the long run!
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby Sphericality » Thu Jul 27, 2017 12:53 am

Thanks @gonegahgah , I agree with much of what you said.
In particular, that every parameter is a dimension, which is certainly how I understand the mathematical definition of dimensions.
I think of each parameter in a 3D fractal as being a dimension, and the displayed image as being a cross section of the higher dimensional fractal that contains all possible settings.

However, I believe that as our 3 spacial dimensions are 'a useful concept that may or may not represent 'reality'
so too is the idea of higher spacial dimensions.
A 2D universe is just as imaginary as a 4D universe. So why should a 3D universe be somehow 'real' and they be unreal?

You would probably like the amplituhedron here
https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/

But to come back to the question of a 4D vortex ...
from the perspective of a non mathematically trained but hopefully somewhat intelligent observer :mrgreen: ...

A vortex in our 3D universe is one section of a toroidal flow of particles.
It sucks in from one side and spews out from the other side of the torus creating convection cells or a toroidal standing wave.
I realise that there are a few 4D equivalents of the torus, so Im wondering if there is an equivalent energetic cycling dynamic
and how many of them would suck in spherically and spew out spherically ?
If so, they begin to sound a lot like an often described cosmological black hole / white hole.
To totally overstate my hypothesis... if this is also a valid description, then gravity seems to be a 4D vortex of some kind.

I came across a novel description of the gravity black hole dynamic recently.
I heard Leonard Susskind say in a video, that the reason light cant get out of a black hole is that
inside a black hole space is collapsing faster than the speed of light.
It surprised me to hear a respected physicist describe it that way. :o_o:
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby Sphericality » Wed Mar 13, 2019 3:23 am

I would like to re-open this discussion and focus on the question of what the 4D equivalent(s) of the 3D vortex are.
Do they relate to the varioud types of 4D torus? Does each type of torus potentially have its own type of vortex ?
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Re: Does the 4D Vortex have anything to do with 3D gravitati

Postby PatrickPowers » Sun Mar 17, 2019 2:11 pm

Sphericality wrote:I would like to re-open this discussion and focus on the question of what the 4D equivalent(s) of the 3D vortex are.
Do they relate to the varioud types of 4D torus? Does each type of torus potentially have its own type of vortex ?


I've considered this, but never really got anywhere. Vortices are basically rotations, so they are essentially 2D. My best guess is that in a 4D world they would usually be similar to what we see here. Fancier vortices seem possible, but I'm not sure they occur very often. It seemed to me that there wasn't any answer simple enough to be within my reach with a reasonable amount of effort.

Here in 3D a ring vortex is possible. Would they be more stable in 4D? I don't know, but I would think yes. In 4D a ring can have a rigid rotation.
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