What Gravity Is

[Reality Check]

Can you describe to me fundamentally what F is without using equations?

I am telling you it's the direction matter will tend to move to. Do you agree or disagree with this statement?

In all physics text books F is a force. A force is an action between 2 objects. It changes the momentum of an object. An example of a contace force is two pool balls on a frictionless table. Replace the pool balls with magnets and you have a contactless force.
The change in momentum is in the same direction as the force (no "tend" about it). See Newton's laws of motion.

Newtons second law: The net force on an object is equal to the mass of the object multiplied by its acceleration.

A force is a vector and so has a direction which is the direction of the change of momentum. It does not have the units of a direction. It has the units of a force. The SI units are Newtons.

From your OP:

The Gravity Field - here is how to think of ‘empty’ space:
Imagine a 3D Grid and at each line intersection consider a particle
Each particle repels the other equally - think of an imaginary spring between each adjacent particle which can contract and expand caused by the particles repelling each other.
Anything that has mass is too big to fit between the gaps (where the imaginary springs are) so has to push the particles out of the way. Anything small enough can move between the particles and hence has no mass.
The denser the particles the higher the gravitational force – it’s harder for the atoms, for example, to push past.

You cannot use Newton's law of gravity in a model that is trying to derive a law of gravity. So whereve you have mentioned Newton's law of gravity in your posts (the D = 3 case) the model is wrong.

 

[Reality Check]

Primes are the transformations using the Zeta function which result in zero's on the imaginary landscape. You can think of the imaginary landscape as time. When time increases (the volume of the grid expands) another zero on the line is added - another prime number is ‘created’.

I assumed you knew the definition I am telling you where they come from.

The imaginary landscape is the complex numbers. There is no time involved. You may be confused by "Thus the non-trivial zeros should lie on the so-called critical line, ½ + it, where t is a real number and i is the imaginary unit". t is a real number not time.

 

[nathan]

Yet more problems with this model:

The spring model only has pairwise forces between adjacent grid particles. It has zero direct force between, say, particles diagonally opposite a unit cube. Is that because the inter-particle force is only active over a tightly constrained range of distances? If that were so, distortions in the grid caused by matter would seem to destroy the grid's integrity though.

You claim the grid particles have a cubic packing, and that is their stable arrangement, in the absence of matter. For that to be true, the pairwise force between grid particles must follow something like the same function as atoms in a crystal. If they didn't the cubic packing would not be stable.

Now the thing about crystals is that they are robust in the face of defects. If an alien atom is incorporated into the matrix, its influence is localized. It doesn't disturb the lattice beyond a few atoms away. So there is no action at a distance here.

 

[martu]

Yet more problems with this model:

The spring model only has pairwise forces between adjacent grid particles. It has zero direct force between, say, particles diagonally opposite a unit cube. Is that because the inter-particle force is only active over a tightly constrained range of distances? If that were so, distortions in the grid caused by matter would seem to destroy the grid's integrity though.

You can calculate the diagonal effect by working out the shape of the Grid after a particle has moved. If you have a Grid of squares (2D) which is bounded and you modify the size or shape of one of the squares what happens to all the other squares? They are changed slightly right? Squares adjacent to the original square (that has changed it’s parameters) will change more than those further away – action at a distance proportional to the distance.

Picture it in 2D – consider a slice of time as a point moving from one square to another. The point doesn’t influence the Grid therefore there is no effect on the Grid therefore the structure of the Grid is maintained. The point will tend follow a path towards the largest square in the Grid.

Picture it in 3D – to think of what happens when an atom moves from one cube to another imagine a ball falling into a cube. The point where the ball hits the edge of the cube it’s moving into defines how the Grid is going to change shape, how the Grid is going to get distorted.

The Grid’s integrity will be broken when the sides of the cube equal c, where c is the length of the sides of the largest cube. This is what a Black Hole is – any particle in an adjacent cube to a cube where it’s sides are c will tend to move towards that largest cube.

You claim the grid particles have a cubic packing, and that is their stable arrangement, in the absence of matter. For that to be true, the pairwise force between grid particles must follow something like the same function as atoms in a crystal. If they didn't the cubic packing would not be stable.

Think of a uniform volume of particles that are all repelling each other equally, there is nothing else that exists. This would form a cube arrangement wouldn’t it?

Now the thing about crystals is that they are robust in the face of defects. If an alien atom is incorporated into the matrix, its influence is localized. It doesn't disturb the lattice beyond a few atoms away. So there is no action at a distance here.

How about if the vertices of the crystal could move? You could have action at a distance then right? Move one vertex and the rest will move somehow to accommodate it.

 

[nathan]

You can calculate the diagonal effect by working out the shape of the Grid after a particle has moved. If you have a Grid of squares (2D) which is bounded and you modify the size or shape of one of the squares what happens to all the other squares? They are changed slightly right? Squares adjacent to the original square (that has changed it’s parameters) will change more than those further away – action at a distance proportional to the distance.

Here you seem to be confirming that there is no direct force between particles that are not manhattan-adjacent ... see below

Picture it in 2D – consider a slice of time as a point moving from one square to another. The point doesn’t influence the Grid therefore there is no effect on the Grid therefore the structure of the Grid is maintained. The point will tend follow a path towards the largest square in the Grid.

Now time is a particle? this just gets weirder.

The Grid’s integrity will be broken when the sides of the cube equal c, where c is the length of the sides of the largest cube. This is what a Black Hole is – any particle in an adjacent cube to a cube where it’s sides are c will tend to move towards that largest cube.

'c' is usually reserved for the speed of light in a vacuum. You've been using 'c' in your 'maths'. Are you now redefining that symbol, or did you always use it with a non-standard meaning?

Think of a uniform volume of particles that are all repelling each other equally, there is nothing else that exists.

... but here you seem to be saying the force pairwise between any pair of particles, and independent of distance. Please be precise in what you say.

This would form a cube arrangement wouldn’t it?

I very much doubt it. If the force is indeed constant, it will have no stable arrangement. I suspect the initial conditions would be crucial in determining the configuration at any later time.

Oh, I think the onus is on you to prove it would be a cubic arrangement.

How about if the vertices of the crystal could move? You could have action at a distance then right? Move one vertex and the rest will move somehow to accommodate it.

You're missing my point. You could move one vertex -- you could even yank it out of the crystal. The point is such deformations would be local. I can't remember precisely how localized such a distortion might be, but I think it'd be around a few tens of atoms.

 

[Paul]

Think of a uniform volume of particles that are all repelling each other equally, there is nothing else that exists. This would form a cube arrangement wouldn’t it?

How many particles? What volume? What is the size of the repulsive force? What is the relationship of the force to particle distance? What is limiting the volume? Does anything influence movement other than the repulsion of other particles?

 

[Almo]

It's really time to get out a college freshman physics book and read the chapters on Newtonian Mechanics. It will save you loads of time.

I have the same "I want to do it myself" attitude with video games, so I can understand your motivation. But this model is really not working; not even a little bit.

 

[martu]

Here you seem to be confirming that there is no direct force between particles that are not manhattan-adjacent ... see below

Now time is a particle? this just gets weirder.

No the expansion of the Grid is time – what are the consequences of working out what F and E are when D = 4? Why is it m³ and r³? Because we’re now talking about an increase in volume, the expansion of the Grid. We experience time as linear as everything expands at the same rate which is defined by the expansion of the Grid.

A snapshot in time is basically stopping the grid from expanding. You can consider this collapsing the waveform. At this point of time you know where all the particles in the Grid are. Let the Grid expand again– all the particles move so now you know where they are going.

'c' is usually reserved for the speed of light in a vacuum. You've been using 'c' in your 'maths'. Are you now redefining that symbol, or did you always use it with a non-standard meaning?

I am defining what c is. c is the maximum speed anything can move in the Grid and this relates to the size of the Grid, the maximum length of one of the sides. The maximum length of a side is defined by the size of the Grid.

... Oh, I think the onus is on you to prove it would be a cubic arrangement.

Ok. A gravity particle is a particle that repels all other gravity particles, this defines the shape of the Grid. Consider this repulsion equal for all the particles. Again we’ll think about it in 2D so these particles can only exists in a plane. If 4 particles exist in what arrangement will they be? A square. Why is it a square? Because the equations for F and E suggest it’s a square.

I have a horrible feeling this is sort of circular as I have explained it. But fundamentally the structure of the Grid is defining reality – it is defining what the relationships between F, E, G, m and r are.

... You're missing my point. You could move one vertex -- you could even yank it out of the crystal. The point is such deformations would be local. I can't remember precisely how localized such a distortion might be, but I think it'd be around a few tens of atoms.

Here is how to picture it.

Consider a crystal with a cubic structure, all the cubes are equal. These cubes are defining the space a particle could reside in and the possible directions of movement which is moving from one cube to the next. Now we add a particle in the crystal at the centre – you can consider this particle as residing in one of the cubes. Gravity (or the effect of it) can be considered as the most probable direction a particle will travel in the crystal if the structure of the Grid is distorted. While the crystal is a uniform Grid of cubes the particle will probably go nowhere, every direction is as likely as another.

Now let’s expand one of the cubes adjacent to the cube the particle is in. The expansion in this cube will expand all the adjacent cubes – it is defining the area of one side of all the adjacent cubes. So our particle will now be more likely to go towards the expanded cube, this is the effect of Gravity.

Why does this work at a distance? Let’s start again with the particle in the uniform Grid. Instead of expanding a cube adjacent to our particle let’s expand a cube two cubes in one direction, so not next to our particle cube but the one next to that. When this cube expands it distorts all the cubes next to it – including the cube adjacent to our cube that contains the particle. So again the cube next to our particle’s cube has expanded therefore that is the likely direction.

So the effect of Gravity is the area of the square the particle is likely to move to, calculated by m1 * m2 where m1 and m2 are the lengths of the sides of the largest square (direction of movement), proportional to the distance squared as we are talking about differences in area.

 

[martu]

The imaginary landscape is the complex numbers. There is no time involved. You may be confused by "Thus the non-trivial zeros should lie on the so-called critical line, ½ + it, where t is a real number and i is the imaginary unit". t is a real number not time.

Think of the imaginary landscape in 3D as the expansion of the Grid.

If you are in 2D the imaginary landscape is the 3D cube. In 3D the imaginary landscape is the hypevolume as defined by making D = 4 which is effectively the expansion on the Grid.

The Grid expands in steps - every step the Grid expands can be considered a unit of time. Each time the Grid expands the volume increases, time moves on. The march of time is defined by the march of the primes, the building blocks of the numbers.

 

[LordoftheLeftHand]

Don’t think about force just think about what direction all the atoms in the balls tend towards. On the surface of the Earth the grid is most distorted by the Earth itself therefore the direction of the atoms will be towards the centre of the Earth*, the centre of the Earth is where the largest distortion of the Grid is. So if all the atoms of the balls are tending towards the centre of the Earth the objects will be stationary on the table. Unless you give them a push.

Show your work! (I want to see some numbers)

LLH

 

[Lothian]

Ok. A gravity particle is a particle that repels all other gravity particles, this defines the shape of t/he Grid. Consider this repulsion equal for all the particles. Again we’ll think about it in 2D so these particles can only exists in a plane. If 4 particles exist in what arrangement will they be?

A diamond ? I think that they would try to form two equilateral triangles.

My turn

A gravity particle is a particle that repels all other gravity particles, this defines the shape of the Grid. Consider this repulsion equal for all the particles. Again we’ll think about it in 2D so these particles can only exists in a plane. If 5 particles exist in what arrangement will they be?

 

[X]

A gravity particle is a particle that repels all other gravity particles, this defines the shape of the Grid. Consider this repulsion equal for all the particles. Again we’ll think about it in 2D so these particles can only exists in a plane. If 4 particles exist in what arrangement will they be? A square. Why is it a square? Because the equations for F and E suggest it’s a square.

Consider the part I've bolded.
If this is the situation for adjacent particles, iy will not be a cubic grid.

The diagonal distances will not be the same as the direct distances.
Thus, the repulsive forces will not be equal.

In order for alll adjacent particles to be equally repelled, they would have to be equidistant from each other.

You would find an array of equilateral triangles.

(And I can't remember the name for the 3d shape where all sides are equilateral triangles. It's not a pyramid.)

 

[Hellbound]

*sigh*

I posted links a couple pages ago to the shape you'd get: either a cubic close packing or a hexagonal close packing. Both are arrays of equilateral triangles, though.

[X]: It's a tetrahedron.

 

[martu]

Consider the part I've bolded.
If this is the situation for adjacent particles, iy will not be a cubic grid.

The diagonal distances will not be the same as the direct distances.
Thus, the repulsive forces will not be equal.

In order for alll adjacent particles to be equally repelled, they would have to be equidistant from each other.

You would find an array of equilateral triangles.

(And I can't remember the name for the 3d shape where all sides are equilateral triangles. It's not a pyramid.)

Bugger. This is true, gravity partciles equally repelling each other can't explain the Grid. Well at least the maths worked for the relationships of E and F depending on D.

Thank you.

 

[X]

Bugger. This is true, gravity partciles equally repelling each other can't explain the Grid. Well at least the maths worked for the relationships of E and F depending on D.

Thank you.

And congratulations on admitting error.
Far too many never reach that step.

 

[nathan]

No the expansion of the Grid is time

What? Expansion is change in position over time. expansion is time makes no sense at all. You need to clarify what you mean here.

A snapshot in time is basically stopping the grid from expanding.

This is calculating the instantaneous configuration.

You can consider this collapsing the waveform.

What waveform? So far you've just describe particle with some solidarity -- your description of matter pushing past the grid particles and distorting it are a classical model.

At this point of time you know where all the particles in the Grid are. Let the Grid expand again– all the particles move so now you know where they are going.

Only if you know the forces, and your description of that has been inconsistent. You've variously described it as springs between adjacent grid particles, and as felt equally by all particles. You may have described it in other ways too, I'm not sure.

Oh, if the force is independent of distance, then in an unbounded grid, each particle will remain stationary, as it will have an infinite number of equal and opposing forces operating on it.

I am defining what c is. c is the maximum speed anything can move in the Grid and this relates to the size of the Grid, the maximum length of one of the sides. The maximum length of a side is defined by the size of the Grid.

No, you don't get to define 'c'. You can show how it relates to some constant(s) from your system. But you can't redefine 'c'. Again, you're getting dimensions wrong. c is a velocity, the distance between grid particles is a length.

I gave up trying to follow the remainder, because, to be honest, it's nonsense.

 

[martu]

Time to confess, this is a description of the computer program that would describe the Matrix. Each constant is a class. If the Matrix was real you would have to define 0, 1, a unit of time and infinity limited by the hardware. 0D is just the OS running. 1D is adding a class E. 2D is adding a class F, a class m, a class r, a class c and a relationship between them. 3D is adding a class m, a class r, a class c and a class G.

 

[Reality Check]

Think of the imaginary landscape in 3D as the expansion of the Grid.

If you are in 2D the imaginary landscape is the 3D cube. In 3D the imaginary landscape is the hypevolume as defined by making D = 4 which is effectively the expansion on the Grid.

The Grid expands in steps - every step the Grid expands can be considered a unit of time. Each time the Grid expands the volume increases, time moves on. The march of time is defined by the march of the primes, the building blocks of the numbers.

There is no imaginary landscape in 3D. Complex numbers exist in a 2D plane only. Time does not exists in a complex plane.

 

[Reality Check]

Bugger. This is true, gravity partciles equally repelling each other can't explain the Grid. Well at least the maths worked for the relationships of E and F depending on D.

Thank you.

Actually it did not except for the case of D = 3 where you used the mass/energy equivalence and Newtons law of gravity.

 

[Reality Check]

Time to confess, this is a description of the computer program that would describe the Matrix. Each constant is a class. If the Matrix was real you would have to define 0, 1, a unit of time and infinity limited by the hardware. 0D is just the OS running. 1D is adding a class E. 2D is adding a class F, a class m, a class r, a class c and a relationship between them. 3D is adding a class m, a class r, a class c and a class G.

Now we have a Grid and a Matrix. Is Keanu Reeves going to pop up next?

But: A constant is not a class. The rest of the post is just weird.