This post suggests an overall toroidal topology for the universe and tries to introduce a most important idea which is that the physical measure of distance is dependent upon (gravitational) field strength (Boscovich, Meyl) and is therefore a function of whereabouts the measurement is made in the universe.
The overall topology considered is that of a torus (below) and the behaviour is that of a continually flowing electromagnetic field as described by Konstantin Meyl. The flow is according to the laws of electromagnetism and itself takes the form of a dynamic vortex structure.
Electromagnetic field movement is continuous and therefore takes on the form of a torus as being the only structure capable of sustaining such a flow. Any other attempt at a continuous flowing vector field ends up having a discontinuity somewhere; see the Hairy Ball Theorem of topology: Wikipedia
The universe consists solely of a flowing electromagnetic field which determines the topology and since the field naturally forms a torus, the depiction of the universe as a torus is justified from this consideration alone.
There is only the Field
There is a strong temptation to imagine an electromagnetic field taking on a toroidal shape embedded within a Cartesian grid system which determines distance and angles, but the task here is to consider that it is the field itself that determines both topology and metric.
The field is not embedded in anything at all; there is no distance metric as separate from that which is physically measured, there is no such thing as ‘space’ that is separate from the field and no such thing as ’empty’ space.
All that is measurable is an electromagnetic field and anything that is not part of such a field is not part of the measurable universe and therefore cannot be said to ‘exist’ in any meaningful way.
The idea of a separate ‘ideal’ universe with nice tidy geometry is just a fantasy.
The electromagnetic field is the entirety of the universe and takes on a toroidal form and therefore the universe is toroidal in overall topology, i.e. the shape of the universe is determined by its contents and is not independent of them.
Physical ‘distance’
If we are not embedded in a Cartesian grid system then how is distance defined?
There is surely only one option; we define it from the physical matter of the universe as this is all that is available to us.
Construct some sort of yardstick and declare it to be one Cosmic Unit (CU) long. Imagine it to be the width of one of the grid squares in the above image and try to think what happens as it is moved around the universe.
Field strength is inversely proportional to the size of the square, with smaller squares having greater field strength. Length is determined by field strength with a stronger field compressing distance accordingly and as a natural consequence, ‘shrinking’ the yardstick to maintain proportion with the grid squares.
As our measurement instrument is moved towards the centre of the torus, the atoms are compressed and the stick physically shrinks, whereas if it moves outwards towards the periphery, then it and all the surrounding physical matter will expand.
To reiterate: all we have as a measurement tool is our physical-matter yardstick. This is our fundamental reference and any idea that it is somehow measuring something else more absolute called ‘length’ is just a hallucination.
All we have available in physics is our observations of physical events, and any relation to an underlying geometric model is mere inference. The theory of physics should start with observations and not with an assumed Cartesian framework with an already existing metric and 3-d geometry.
Is the universe expanding?
Now we are an observer within a toroidal universe and are looking around trying to make sense of things. Some parts of the universe seem to be expanding relative to us and even moving away from us whilst others appear to be contracting or spiralling inwards.
However, if we move to the periphery, where things seem to be expanding, then we will ourselves, expand with the toroidal geometry and find that our home planet is now shrinking relative to us even though we thought it to be constant in size when we were living there.
Moreover, in our expanded state, we find ourselves spiralling inwards much to our surprise and realise that the apparent expansion of the universe as seen from Earth was merely an illusion owing to the fact that our Earthly system is now seemingly shrinking and moving away from the outer reaches of space. This made it seem to us at the time that the universe was actually expanding away from us.
Parts of the universe are therefore expanding relative to us and others are shrinking, but the inhabitants of those parts are unaware of this and presumably imagine themselves to be somewhere near the centre and in an absolute frame of reference.
So is the universe expanding?
Relative to what? There is no absolute measure of distance apart from a yardstick which adapts its size to local conditions and within the universe itself, no perceivable ‘edge’ or defined outer boundary and so the question really doesn’t make much sense.
But .. geometry?
In the diagram below, the triangle on the left has equal sides and equal angles.
The sides are each 3 Cosmic Units long as measured with one CU rulers (shown).
The triangle on the right has its base in an area of increased (gravitational) field strength (maybe from a local sun) and so the metre rulers have shrunk. This means that it still measures 3x3x3 CU, but the angles have changed.
Local distances are determined by field strength which leads to a modified geometry. So geometry itself is determined by field conditions and is no longer ‘absolute’.
This is important when calculating the distance to other stars and galaxies. Cosmologists assume some an invariant Euclidean geometry to the universe but this doesn’t hold here and the stars may be much ‘nearer’ than we think.
As a spaceship exits our solar system, the field strength diminishes and the ship expands accordingly to a great degree. Vast ‘distances’ are covered in a very small time.
Platonic forms
Anyone wants to argue that metre rulers are always a metre long needs to think how to prove this. What is your control? What do you measure a metre against if not some other local physical object or waveform?
The whole idea of an abstract and invariant metric is unprovable. Distances are determined by the size of physical objects and these vary according to field strength .
Field strength varies slightly everywhere and as a consequence there is no such thing as a perfect circle or square anywhere in the universe, no such thing as a Platonic form in actual reality or even the expression of such.
Constants such as Pi exist only in an imaginary realm of perfect geometry.
Physical (real) geometry is determined by the laws of field physics and if something looks a bit like a cube it is because of the local laws of physics and not because of the laws of mathematics. The (approximate) cube is a perfect expression of the field equations and not an imperfect expression of a Platonic form.
Black holes
Take a look again at the overall topology and consider that within this structure lie smaller more local structures which are interpreted as stars, galaxies and black holes.
Now depending where you are on the torus you may see half the galaxy heading towards the central singularity and infer a great force emanating from the core and sucking everything in, or you may see a great outrush of matter pouring from an assumed ‘white hole’.
None of these assumptions are any good here and all that is happening is that matter is moving in an inevitable path as determined by the dynamic topology. Matter does not ‘collapse’ in a black hole but merely shrinks accordingly and will expand again when out comes out the other side.
Gravity
Such behaviour near a planet or star gives rise to the phenomenon known as gravity, which again is assumed to somehow ’emanate’ from the star and suck things towards it. Nobody has seen gravity emanate however and so it is permissible to think of it as an inward spiralling of the field geometry.
This isn’t too outrageous a statement and is comparable to Einstein’s bendy space idea except here we have no need for a separation between space and matter and all is a pleasing unity.
Einstein’s spacetime
“Spacetime tells matter how to move; matter tells spacetime how to curve.” – John Archibald Wheeler
Here we have a superfluity of ‘stuffs’ that is common in mainstream physics. How do spacetime and matter communicate with each other in such a fashion and where are the laws governing such an interaction? How is it proved that spacetime and matter are really separate entities? What are the innate properties of ‘spacetime’ that allow it to be manipulated in such a way and how does it ‘move’ matter?
More pertinently we can ask: “What does it mean that space is ‘curved’ and with respect to what exactly?” The whole idea of ‘curvature’ seems to assume the existence of some sort of Cartesian reference grid as separate from the curved space.
Progress has not been made and all that has happened is that the conceptually difficult part has been moved from one place to another in the hope that nobody will notice.
If matter and geometry are so closely linked, we can consider that they are really both manifestations of some other underlying phenomenon and that such a phenomenon is now seen to be an electromagnetic vortex field.
Gravitational lensing
The phenomenon of light bending its way past a massive body now needs almost no explanation.
The gravitational field of a star is no longer to be regarded as a force or even a distortion in spacetime but simply the centre of a field vortex.
The field strength closer to a star will be greater than the strength slightly further away and so lengths ‘increase’ further away from the star. A photon is a finite size in vortex physics and so contracts nearer the star and expands further away. Translation: it follows a curved path.
Space is not bent as there is no such thing as space to be bent, only a toroidal field creating a toroidal geometry.
Earth-sun orbital anomaly
The Earth is said to orbit the sun but the position of the sun is not fixed, being displaced by a distance of over a million kilometres by the gravitational fields of the Earth and other planets. Despite this, the gravitational pull on the Earth from the sun seems to be always towards the sun at the present and never where it was a few minutes ago. (Van Flandern)
Some have interpreted this as the gravitational field from the sun travelling at many time the speed of light in order to reach the Earth in time but nobody has seen a gravitational field ‘travel’ or ‘radiate’ from the sun and in any case better explanations are now available.
There is no unlimited gravity that emanates from the sun but instead the sun and planets move in a coordinated fashion according to an ever changing vortex geometry and as such it cannot be considered that the sun is ‘causal’ in moving the planets or that Saturn is ‘causal’ in moving the sun.
The sun is positioned at the centre of the most powerful vortex and it is this vortex that has the most influence on the solar system as a whole, thereby creating many correlations between the movements of the planets and the position of the sun. However, this in no way implies that the sun itself is the origin of such movements.
The whole arrangement moves as a whole and according to the laws of vortex physics. The sun is moved by the vortex as is Saturn and the Earth itself and any perceived influence of one body directly upon another is merely an illusion.
In addition to this mechanism, we now should concede that photons are travelling from the sun within a geometric vortex and will move accordingly. The idea that light always travels in a straight line through space is now meaningless as there is no such thing as Euclidean space and therefore no such thing as a straight line.
Instead, we have photons moving through a vortex system and whatever location of origin, will impact the Earth in a direction determined by the vagaries of their whole path taken from the sun through the intervening vortex field.
If you want to try and guess their origin from the direction they approach Earth, then .. “Good luck!”. This is like trying to locate the source of a river by standing at the estuary.
The mechanism
How does all ‘matter’ shrink in a strong gravitational field?
In Meyl’s vortex physics, all matter is made from an agglomeration of electrons and an electron is just a stable field vortex with electrical spin and a magnetic dipole. Put such a thing inside a magneto-gravitational field and the radius of the spin reduces so the radius of the electron reduces and all matter then shrinks.
Evidence?
Tamarack mines experiment A long piece of wire was dropped down a mine shaft and it was found to be shrunk by a significant amount, the implication being that it is the increase in strength of the magnetic component of the Earth’s gravitational field that is responsible.
Hafele – Keating experiment Clocks in aeroplanes run at different rates depending upon whether they are travelling East to West or West to East.
The origins
This scheme makes the idea of a Big Bang radiating all the energy and matter in the universe both unlikely and unnecessary.
We don’t know how things ‘started’ or even if there was a ‘start’, but if the general movement is from periphery to centre, opposite to conventional thinking, then it would make sense to think about the origins in a similar manner.
Field ‘energy’ originates as a vortex somehow and immediately starts to spiral inwards. The energy density increases and smaller vortices arise near the centre which will form smaller and smaller vortices in a fractal pattern.
These smaller vortices form galaxies, stars and single atoms that order, with the smaller structures arising from the larger and not the other way around.
The smallest vortices stabilise around the size of an electron and matter has materialised from a pure electromagnetic field. The creation of matter continues throughout the lifespan of the universe an there is no upper limit on the total mass.
It may seem that the universe needs to be exceedingly large at the outset in order to contain enough energy to materialise such matter and that the sheer volume required is enough to counter the argument. This is not the case, however, as there is no objective ‘size’ to the universe at all and all subsequent ‘expansion’ can as easily thought of as being inward expansion as outward.
There is no real expansion, creation or loss, but instead an increasing complexity of vortex structure arising from the inward concentration of field movement.
A Theory of Objectivity
How on earth do we do any science when distances keep changing and we have not even a consistent way of measuring the passage of time?
Meyl has the answer which he calls his Theory of Objectivity. A transformation is made from local coordinates to global, calculation is made in this new objective framework and the answer is transformed back into local coordinates.
Excellent.