`` As if - the explanation of Emergence

Gravity - a 4D Hypersphere Visualization


A picture paints a thousand words -


What it shows: A simplified 2D slice of 4D space - real axis (x) vs imaginary axis (iw).


  • Alice and Bob as dots on a semicircle (hypersphere cross-section).

  • George is the centre of gravity of Alice and Bob. George is no more there than is Dave, but eventually only George is there.

  • Dave is the imaginary center.

  • Increase Radius to simulate massless Alice and Bob - no boost > no gravity. Alice and Bob follow straight lines of radius from Dave, and so drift apart.

  • Increase Boost to simulate massive Alice and Bob - boost increase - equivalent to increased momentum. Alice and Bob follow curved lines of radius from Dave, and so converge on George. In taking up new positions relative to Dave, Alice and Bob are persuaded by paradox to increase their imaginary rotation, i.e. their boost, which is the same thing as accelerating under gravity, and momentum increases just 'as if' they had both been plastered with photons.

    • Adjust the radius and boost to see how Alice and Bob move on the hypersphere.




    Not to scale.


    Why paradox drives gravity

    Why is gravity paradoxical? It is not that gravity is paradoxical per se. Gravity is just the apparent consequence of change elsewhere. That change causes Dave to move slightly, which is exactly equivalent to everything else moving slightly, and so adopting new positions. Any object with energy will be forced to rotate into a mathematically imaginary dimension in order to avoid the paradox of having external relationships that place it one distance from another object, while at the same time having internal relationships that place it at a smaller distance. When two such objects are in proximity, their response to Dave moving is to adopt new positions that are closer to one another. This is due to their already being partially boosted, and after the change in Dave their boost has to increase to accommodate their partially imaginary direction. Boost is imaginary rotation, boost is both the consequence and cause of things appearing smaller, slower and more massive than they are at rest, and appearing smaller makes things appear closer, and move closer together when other things change. Effectively, the imaginary hypersurface, centred on Dave, is smaller than the entirely real hypersurface would be, and the more rotated to the imaginary, the smaller the surface, and that is why the straight lines from Dave, and to two rotated [boosted] objects, point [lead] to those two objects moving closer and becoming more rotated whenever anything anywhere changes. That translates to added momentum because it is equivalent to adding photons, except that the changes are far too small to accommodate the quantum nature of photons, so it cannnot properly be called the same cause.


    Why there is a paradox

    The paradox that drives this, and all other forces that act on spatial objects to make them attract, or repel, comes about because 3D space is naturally Euclidean, flat and uniform, and would remain so had not the points that cause it to exist got their own internal mass. But according to Virtualism the internal properties of massive particles, usually quarks and gluons, have a greater number of dimensions than do the external properties. One consequence being that while photons have two dimensionality, quarks have three dimensionality - the RGB of colour charge. This is what create the paradox that rotates rest mass into the imaginary, and as we have seen from Albert Einstein and General Relativity, the presence of objects with mass unflattens space. That is, mass causes dilation, and dilation shortens the radius around a point by adding imaginary rotation, making the outer smaller than the inner, as if it where some kind of Tardis. And that is more than somewhat paradoxical.


    Why more dimensions are paradoxical - and internal

    Virtualism is a theory that, like Pythagoras, claims that fundamentally all things that exist are composed of numbers, but it goes further in saying all things emerge from numbers, which demands that number objects must combine for some reason, to cause more complex objects to emerge. This means that any compound object could have numeric properties that give it three dimensions - Euclidean properties, but also othe numeric properties that give it higher dimensions - non-Euclidean properties.


    One fact we know about objects with higher dimensionality is that, above 5D and 7D, properties such as area and volume curtail dramatically. One consequance of this is that the higher dimensions of any object with such properties, would necessarily be contained within those objects, creating the paradox of rest mass, where the emergent space is one thing, and paradoxically another thing.


    So in the vizualisation shown above, George, being the sum of Alice and Bob, emerges 'as if' there, existing as a centre of gravity that itself is imaginary, has that rotation, and not much else that could be called its own; except George does have Alice and Bob. It is almost 'as if' Alice and Bob are constrained by the presence of George, and George rotating more and more, as Alice and Bob get closer together. I mean, we can see why Alice, Bob and George are all rotated, boosted, but why are Alice and Bob boosted in such a way that they move closer together, if not for George?


    The answer to that question is that the non-Euclidean boost of Alice and Bob, is precisely the same thing as the shape of space in General Relativity, and boosted space is smaller than unboosted space. So, in the absence of countering forces, Alice and Bob must move closer, because the space between them, the space that they more than anything actually cause to be, that space becomes smaller - George shrinks - but the paradox of mass means that Alice and Bob must rotate more.


    It should always be remembered that behind Alice and Bob moving is the more prosaic fact of Alice and Bob demerging from what and where they used to be, and emerging where they are in the Here and Now, leaving behind the faint trace of the facts of where they used to be.



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