## Simple Curvature of space

17th - 20th July 2016

Private & Confidential Copyright © Mr A Pépés

Simple Curvature of space.

It is only simple when you know what you are curving.

I hear and read that we can't visualise more than 3 dimensions, so people give up trying and resort to only abstract mathematics to explain the Universe.

This I whole heartedly believe is wrong. We can and do experience many more dimensions than we are lead to believe.

Although many people find it hard to even visualise objects in 3 dimensions in their head, they can easily see and experience real things in 3D. What they don't realise is that they can and do experience many more dimensions.

To understand what I mean you have to imagine that you are a child that is blind that has not been taught about dimensions and at the same time imagine yourself looking at this child with your current thinking.

Every time you ask the child to do something, you ask them what they experience and compare it to what they experienced before.

The child is still, and you tell them that they are standing at a point in space and you ask the child what they experience. They say nothing much, so you say this means there are no dimensions at a point. You then ask them to move several steps forward one step at a time then backwards, and say that what they experience is moving in 1 dimension and at each step there is a point.

So as not to confuse the child with infinities (because you believe there are an infinite number of points between each step) you say for each step, they can make 10 mini steps, which will end at the same point as one big step. Therefore you tell them there are 10 mini points between each of the previous points (big steps).

Now you tell them to move left and right in steps as before, then tell them what they experience is the 2nd dimension. It feels the same, so moving in 2 dimensions is just a change of direction (it happens to be at 90⁰, right angles to the 1st dimension). Now because they can't simply step up and down in space you take them to the edge of a pool (which is empty) that has a ladder, and you use the same logic to make them move up and down. This you tell them is the 3rd dimension. So if they go to the bottom of the pool they can take steps forward just like outside the pool. You tell them this is all there is, just these 3 dimensions.

So far so good, on another day they decide to investigate these new found dimensions. As they start to go into the pool this time they experience something different (it has water in it, not too deep).

They ask "why is this dimension of up and down different today"? And when they walk along the bottom, the forward and backwards dimension also feels different to the forwards and backwards higher up outside the pool.

They say it is harder to move, they have to take mini steps to make it easier, is this another dimension? You tell them it's because of the water that is denser, it is still 3D space.

They reply I get it, it is denser space (the points are closer together).

You don't want to confuse them so you just say there is something there, but the space is still there and if you were really tiny you could move between the space (avoiding the molecules of water, everything is made of atoms), and it would feel the same as without the water.

Then as they move more forward they bump into the wall.

"What's happened to my 3D world, why can't I move forwards in my 3D world? they ask.

It's a wall you reply. You can't move forwards because it is too dense, but the space is there.

The child replies if I become really tiny, would I be able to move through the spaces like the water?

You explain that they could, but they would have to be even smaller than before to avoid the atoms, otherwise the atoms would be like mini walls that would stop them. The child then says "if the atoms are like mini walls, could I not go even smaller and move through the spaces of the atoms?

You should realise by now that these "real" things that we experience (as matter) are not just things in 3D abstract space, but are also spaces in themselves, that are different to the abstract 3D space, but are superimposed on our abstract 3D space.

How can this be an additional dimension in space?

You have to go back to the drawing board as the saying goes.

A Point = no dimension, no units. (It is only a reference to something that maybe at that point in space). (Has No Units).

A Line = 1 dimension, plus ∞ at one end and minus ∞ at the other end. Units - lengths of the line.

A Plane = 2 dimensions, 2 plus ∞ at two ends and 2 minus ∞ at the other ends. Units - areas on the plane (surface).

Before we go any further and spoil things we need to get 'real' and eliminate infinities (∞) in space.

This is easily done by imagining we are GOD and we can always go to one dimension higher.

All we need to do is bend the 1D line in a higher dimension and join the 2 opposite ∞ together to form a circle (loop). [My Tea Break Book 'Bending Dimensions to eliminate infinities'].

Now anything on the line is unaware of the 2nd dimension higher up (where we are), so the line stays 1 dimensional and is curved. As far as anything on the line is concerned the empty space inside and outside the the circle does not exist.

[Everything existing in this 1 dimensional world (Universe) is also 1 dimensional].

You do the same for the 2D plane, imagine the higher 3rd dimension, now bend both dimensions of the 2D plane by joining the opposite infinities together. Now anything in the 2D plane is unaware of the 3rd dimension higher up (where we are), so the plane stays 2 dimensional and is curved. As far as anything on the 2D plane is concerned all the empty space inside and outside the plane does not exist. I.e. Above and below the plane.

[Everything existing in this 2 dimensional world (Universe) is also 2 dimensional].

A big note. I intentionally did not say what this shape was, that lives in this higher 3rd dimensional space, but the shape is not a sphere (I will explain fully later).

Now as this shape lives in 3D but is a 2 dimensional (surface), all we need do is to image we are one dimension higher 4th dimension (where we would be) and make this solid, truly 3D and join the opposing infinities together.

I will skip time for the moment, to make things easier to imagine.

You should note that anything, when viewed from a (Godlike) higher dimension is finite. I.e. The 1D line does not go to ∞. (It is a circle in the higher 2nd dimension). The 2D plane is an area the shape of ... in the higher 3rd dimension. The 3D object is a volume in the 4th dimension [the dimension of time I believe is in fact 4 or more dimensions explained in an other Tea Break Book]. As far as anything inside these volumes (dimensions) are concerned anything outside their space does not exist. This is the image that your God would see.

Note: - in the higher 2nd dimension you can have many 1D lines (bent as circles) next to each other, I.e. Many circles next to each other, that can form a new line of unit (Universal) circles in 2 dimensions! In other words the unit lines in 2D are quantised and can be considered (are) areas, because you can have many (Universal) 1D lines that are finite in 2D space (from this Godlike perspective of one dimension higher).

[When you measure a length in one of the dimensions in this higher state, you are measuring the number of diameters of the quantised (Universal) circles (spaces) that create that length in the higher dimension].

If you can imagine a 3D object of space, all we have to do is imagine one dimension higher as before and join the 3 plus infinities to the opposing 3 minus infinities.

You can only do this if you realise that you already live in this higher dimension, and that these 3D (Universal) spaces are the 'real' spaces already bent in the 4th dimension. In other words each little bit of space is the real 3D spaces (that are quantised like the circles in the 2nd dimension), you can have many 3D spaces (volumes) next to each other that create what we normally say is one, two and three dimensional, the infinities have already been bent and joined together (in each of these quantised bits of 3D spaces).

[This is also how time is inextricably linked to space and never independent].

[You are now looking at the Universe from the 5th dimension, but this is explained further in another Tea Break Book, in which the 5th dimension is further bent to eliminate ∞].

This can then be a sphere (a ball).

To clarify, the abstract sphere (ball) is solid through and through.

Any 'real' sphere (ball) is not totally solid and consists of (Universal) 3D volumes of space (and time) [dynamic quanta 'APE's] in a higher dimension.

So if you imagine that your God makes 'you' in 'his image', you will see what your God sees in this higher dimension, 'you' in(side) 'this Universe'.

Once you realise this, then going one dimension higher still and bending these 3D spaces (as a whole) and joining their infinities becomes easier (adding the missing dimensions as you go).

Before we do that let me explain why the sphere is not the true bending of space (2D plane) to eliminate infinities.

I explain this in another Tea Break Book. To understand this you must be methodical and bend each dimension separately so that the plus ∞ joins the minus ∞. (No matter how many dimensions you are bending). When bending a line, there is no problem, because there is only one positive and one negative ∞, therefore you have no choice but to join them together to form a circle.

But when you come to the unbent 2D plane you have 2 positive ∞ and 2 negative ∞ (these 2 positive and 2 negative ∞ are in fact multiple positive and multiple negative parallel lines, therefore you can have 2 ways to join them, all positives ∞ to all negatives ∞ (twice, once for each dimension), the correct way, or you can join one set of positives to one set of negatives, then join the remaining positives together and then the remaining negatives together, this is the wrong way to do it, because by doing it this way you end up getting a sphere!

In other words if you where to travel along just one line on the original unbent 2D plane the correct way you will go to positive ∞ and end up at negative ∞ and back to your starting point.

On the other hand. The wrong way, where you have the sphere, you go to positive ∞ join to the other positive ∞ then return to your starting point, you do not go to negative ∞ unless you keep traveling to negative ∞ join to the other negative ∞ then back to the starting point again!

You can look at it in another way, in the correct bending of dimensions you can keep travelling forever without changing directions. It becomes clearer if there are 2 of you traveling along (you have to keep track of how many dimension you are). In the line example you can go forwards with the other person and they can never overtake you (because you are both 1 dimensional) and you will never see them coming towards you in the opposite direction. In the correct bending of the plane you can both go forwards in a straight line (parallel to each other) and they can overtake you, but you will still never see them coming towards you in the opposite direction (I.e. Never travelling backwards towards you). But on the sphere if the other person is going faster than you, you will see them returning in the opposite direction to your travel. (I.e. They would reach their positive ∞ and start returning from your positive ∞).

Back to the curvature of space. Once you realise that space is quantised as little volumes in a higher dimension, you can then simplify them back to points, like the little steps the child took, there are a finite number between points (real points are finite, not infinite as in the abstract space).

The closer the real points, the greater the density of space. These 'real' points (I call min {minimal}points or 'poynts', which are really volumes) can have momentum, various spins etc. All the notions of imaginary higher dimensions and things appearing from nothing, vacuum energy and the like are just real manifestations of these quantised bits of 3D spaces in this higher dimension that we already live in.

In simple terms curvature of space is curvature of the overall space that these 3D volumes live in. When you add time and momentum to them plus ... in another Tea Break Book you get quantised multidimensional spaces that I call 'APE's. Generally the more dense these 'APE' are, the greater the curvature. It is like the mini steps, the closer the points the more dense the space is, forces are concentrated the greater the curvature, (each point has a certain amount of energy that generates a force around it), when these points are closer is the reason why gravity increases with mass, because these spaces are more curved and compacted therefore concentrate their forces).

28th May 2019

Private & Confidential Copyright © Mr A Pépés

The same goes for the other forces, so for eg. the strong force is the most curved and most dense at the centre of the protons and neutrons.

Morph your mind with Morphological at

apepes.com

Private & Confidential Copyright © Mr A Pépés

Simple Curvature of space.

It is only simple when you know what you are curving.

I hear and read that we can't visualise more than 3 dimensions, so people give up trying and resort to only abstract mathematics to explain the Universe.

This I whole heartedly believe is wrong. We can and do experience many more dimensions than we are lead to believe.

Although many people find it hard to even visualise objects in 3 dimensions in their head, they can easily see and experience real things in 3D. What they don't realise is that they can and do experience many more dimensions.

To understand what I mean you have to imagine that you are a child that is blind that has not been taught about dimensions and at the same time imagine yourself looking at this child with your current thinking.

Every time you ask the child to do something, you ask them what they experience and compare it to what they experienced before.

The child is still, and you tell them that they are standing at a point in space and you ask the child what they experience. They say nothing much, so you say this means there are no dimensions at a point. You then ask them to move several steps forward one step at a time then backwards, and say that what they experience is moving in 1 dimension and at each step there is a point.

So as not to confuse the child with infinities (because you believe there are an infinite number of points between each step) you say for each step, they can make 10 mini steps, which will end at the same point as one big step. Therefore you tell them there are 10 mini points between each of the previous points (big steps).

Now you tell them to move left and right in steps as before, then tell them what they experience is the 2nd dimension. It feels the same, so moving in 2 dimensions is just a change of direction (it happens to be at 90⁰, right angles to the 1st dimension). Now because they can't simply step up and down in space you take them to the edge of a pool (which is empty) that has a ladder, and you use the same logic to make them move up and down. This you tell them is the 3rd dimension. So if they go to the bottom of the pool they can take steps forward just like outside the pool. You tell them this is all there is, just these 3 dimensions.

So far so good, on another day they decide to investigate these new found dimensions. As they start to go into the pool this time they experience something different (it has water in it, not too deep).

They ask "why is this dimension of up and down different today"? And when they walk along the bottom, the forward and backwards dimension also feels different to the forwards and backwards higher up outside the pool.

They say it is harder to move, they have to take mini steps to make it easier, is this another dimension? You tell them it's because of the water that is denser, it is still 3D space.

They reply I get it, it is denser space (the points are closer together).

You don't want to confuse them so you just say there is something there, but the space is still there and if you were really tiny you could move between the space (avoiding the molecules of water, everything is made of atoms), and it would feel the same as without the water.

Then as they move more forward they bump into the wall.

"What's happened to my 3D world, why can't I move forwards in my 3D world? they ask.

It's a wall you reply. You can't move forwards because it is too dense, but the space is there.

The child replies if I become really tiny, would I be able to move through the spaces like the water?

You explain that they could, but they would have to be even smaller than before to avoid the atoms, otherwise the atoms would be like mini walls that would stop them. The child then says "if the atoms are like mini walls, could I not go even smaller and move through the spaces of the atoms?

You should realise by now that these "real" things that we experience (as matter) are not just things in 3D abstract space, but are also spaces in themselves, that are different to the abstract 3D space, but are superimposed on our abstract 3D space.

How can this be an additional dimension in space?

You have to go back to the drawing board as the saying goes.

A Point = no dimension, no units. (It is only a reference to something that maybe at that point in space). (Has No Units).

A Line = 1 dimension, plus ∞ at one end and minus ∞ at the other end. Units - lengths of the line.

A Plane = 2 dimensions, 2 plus ∞ at two ends and 2 minus ∞ at the other ends. Units - areas on the plane (surface).

Before we go any further and spoil things we need to get 'real' and eliminate infinities (∞) in space.

This is easily done by imagining we are GOD and we can always go to one dimension higher.

All we need to do is bend the 1D line in a higher dimension and join the 2 opposite ∞ together to form a circle (loop). [My Tea Break Book 'Bending Dimensions to eliminate infinities'].

Now anything on the line is unaware of the 2nd dimension higher up (where we are), so the line stays 1 dimensional and is curved. As far as anything on the line is concerned the empty space inside and outside the the circle does not exist.

[Everything existing in this 1 dimensional world (Universe) is also 1 dimensional].

You do the same for the 2D plane, imagine the higher 3rd dimension, now bend both dimensions of the 2D plane by joining the opposite infinities together. Now anything in the 2D plane is unaware of the 3rd dimension higher up (where we are), so the plane stays 2 dimensional and is curved. As far as anything on the 2D plane is concerned all the empty space inside and outside the plane does not exist. I.e. Above and below the plane.

[Everything existing in this 2 dimensional world (Universe) is also 2 dimensional].

A big note. I intentionally did not say what this shape was, that lives in this higher 3rd dimensional space, but the shape is not a sphere (I will explain fully later).

Now as this shape lives in 3D but is a 2 dimensional (surface), all we need do is to image we are one dimension higher 4th dimension (where we would be) and make this solid, truly 3D and join the opposing infinities together.

I will skip time for the moment, to make things easier to imagine.

You should note that anything, when viewed from a (Godlike) higher dimension is finite. I.e. The 1D line does not go to ∞. (It is a circle in the higher 2nd dimension). The 2D plane is an area the shape of ... in the higher 3rd dimension. The 3D object is a volume in the 4th dimension [the dimension of time I believe is in fact 4 or more dimensions explained in an other Tea Break Book]. As far as anything inside these volumes (dimensions) are concerned anything outside their space does not exist. This is the image that your God would see.

Note: - in the higher 2nd dimension you can have many 1D lines (bent as circles) next to each other, I.e. Many circles next to each other, that can form a new line of unit (Universal) circles in 2 dimensions! In other words the unit lines in 2D are quantised and can be considered (are) areas, because you can have many (Universal) 1D lines that are finite in 2D space (from this Godlike perspective of one dimension higher).

[When you measure a length in one of the dimensions in this higher state, you are measuring the number of diameters of the quantised (Universal) circles (spaces) that create that length in the higher dimension].

If you can imagine a 3D object of space, all we have to do is imagine one dimension higher as before and join the 3 plus infinities to the opposing 3 minus infinities.

You can only do this if you realise that you already live in this higher dimension, and that these 3D (Universal) spaces are the 'real' spaces already bent in the 4th dimension. In other words each little bit of space is the real 3D spaces (that are quantised like the circles in the 2nd dimension), you can have many 3D spaces (volumes) next to each other that create what we normally say is one, two and three dimensional, the infinities have already been bent and joined together (in each of these quantised bits of 3D spaces).

[This is also how time is inextricably linked to space and never independent].

[You are now looking at the Universe from the 5th dimension, but this is explained further in another Tea Break Book, in which the 5th dimension is further bent to eliminate ∞].

This can then be a sphere (a ball).

To clarify, the abstract sphere (ball) is solid through and through.

Any 'real' sphere (ball) is not totally solid and consists of (Universal) 3D volumes of space (and time) [dynamic quanta 'APE's] in a higher dimension.

So if you imagine that your God makes 'you' in 'his image', you will see what your God sees in this higher dimension, 'you' in(side) 'this Universe'.

Once you realise this, then going one dimension higher still and bending these 3D spaces (as a whole) and joining their infinities becomes easier (adding the missing dimensions as you go).

Before we do that let me explain why the sphere is not the true bending of space (2D plane) to eliminate infinities.

I explain this in another Tea Break Book. To understand this you must be methodical and bend each dimension separately so that the plus ∞ joins the minus ∞. (No matter how many dimensions you are bending). When bending a line, there is no problem, because there is only one positive and one negative ∞, therefore you have no choice but to join them together to form a circle.

But when you come to the unbent 2D plane you have 2 positive ∞ and 2 negative ∞ (these 2 positive and 2 negative ∞ are in fact multiple positive and multiple negative parallel lines, therefore you can have 2 ways to join them, all positives ∞ to all negatives ∞ (twice, once for each dimension), the correct way, or you can join one set of positives to one set of negatives, then join the remaining positives together and then the remaining negatives together, this is the wrong way to do it, because by doing it this way you end up getting a sphere!

In other words if you where to travel along just one line on the original unbent 2D plane the correct way you will go to positive ∞ and end up at negative ∞ and back to your starting point.

On the other hand. The wrong way, where you have the sphere, you go to positive ∞ join to the other positive ∞ then return to your starting point, you do not go to negative ∞ unless you keep traveling to negative ∞ join to the other negative ∞ then back to the starting point again!

You can look at it in another way, in the correct bending of dimensions you can keep travelling forever without changing directions. It becomes clearer if there are 2 of you traveling along (you have to keep track of how many dimension you are). In the line example you can go forwards with the other person and they can never overtake you (because you are both 1 dimensional) and you will never see them coming towards you in the opposite direction. In the correct bending of the plane you can both go forwards in a straight line (parallel to each other) and they can overtake you, but you will still never see them coming towards you in the opposite direction (I.e. Never travelling backwards towards you). But on the sphere if the other person is going faster than you, you will see them returning in the opposite direction to your travel. (I.e. They would reach their positive ∞ and start returning from your positive ∞).

Back to the curvature of space. Once you realise that space is quantised as little volumes in a higher dimension, you can then simplify them back to points, like the little steps the child took, there are a finite number between points (real points are finite, not infinite as in the abstract space).

The closer the real points, the greater the density of space. These 'real' points (I call min {minimal}points or 'poynts', which are really volumes) can have momentum, various spins etc. All the notions of imaginary higher dimensions and things appearing from nothing, vacuum energy and the like are just real manifestations of these quantised bits of 3D spaces in this higher dimension that we already live in.

In simple terms curvature of space is curvature of the overall space that these 3D volumes live in. When you add time and momentum to them plus ... in another Tea Break Book you get quantised multidimensional spaces that I call 'APE's. Generally the more dense these 'APE' are, the greater the curvature. It is like the mini steps, the closer the points the more dense the space is, forces are concentrated the greater the curvature, (each point has a certain amount of energy that generates a force around it), when these points are closer is the reason why gravity increases with mass, because these spaces are more curved and compacted therefore concentrate their forces).

28th May 2019

Private & Confidential Copyright © Mr A Pépés

The same goes for the other forces, so for eg. the strong force is the most curved and most dense at the centre of the protons and neutrons.

Morph your mind with Morphological at

apepes.com