There is a flat space, which can be used as a basis to show positive curvature. There is another space, where photons are allowed to go. The second space can be mapped on the first space, but have additional displacements from positive curvature generators that move where light can go. This is an ideal graph, and it should be noted that the physics of real life includes additional interactions that will often prevent following ideal geodesics; except in the extreme case that black holes represent.
See also: mathSphereDecay.md
Light emitted at a particular point is subject to being emitted at the frequency within that space. That is, if the emitter is deeper in gravity, the emitter occupies a certain physical space that is in flat space; while the photon space is has a non-rectangular mapping, the curvature in that space is wider and shorter than an emitter further away from a gravitational source; between that, and the reduced speed that clocks run, the frequency emitted is red shifted already, and when received by a higher speed clock, in a less dense space that is narrower and taller than the emitter measures red shift.
Conversely, emitted from a narrow, tall space, with a fast clock, with the same physical dimensions emits a blue shifted signal, which a slower clock, and wider, shorter space will see as blue shifted (compressed in space, across a shorter counted time).
In the above image, consider the spatial displacements (white circles) as the effective gravity of galaxies, and from the center a photon is emitted, which does not interact with anything, but follows its own geodesics. The average displacement of space increases as a emitted photon passes past galaxies from the center (relative to 0 in flat space), is greater and greater
(Only a certain portion of flat to curved space can really be considered... the further away from some relative origin or some relative point, the greater the effective displacement. This additional shove on the curvature of the space may seem cumulative and resemble dark energy; but the displacement does not shove other displacments (rather they are actually attracted to each other because of the gradient of spaces). It's more that from a relative perspective of emission, vs the displaced space that matters; the spatial displacement measured in the opposite direction will also be a net positive dispalcement from its relative flat space coordinates.)
One might call light photons corpuscular; running in little tubes that generally get stretched more and more; end up covering more effective flat space than they should, thereby making them red shifted.
If a path of light takes less time to cross a space, it is blue shifted; such as on the right side slightly below center, the photon is travelling between two gravitational gradients that cause it to blue shift while between them, but the net effect will be to red shift it once it passes those.
It's effectively the sum of the masses that are in a sphere behind a photon that controls how much the space is displaced.... and the further the photon goes, the more mass is behind it, effecitvely generating a constant progressive gradient.
I've been trying to come up with a demonstration of the general increase of spatial curvature for light geodesics. As light travels past additional massive bodies, the space is additionally longer for it the further it goes. The increased density is the average of all the galaxies within a expanding sphere (really move of a snow-cone, the entire arc of the sphere isn't so relavent, because the other side is really additional displacment in the other direction and it already had low effect when the photon was emitted, so would have even less effect now; It's probably more like the sphere between where is currently is, and where it was emitted from that has an effective additional displacment on the space light travels through.
The bottom row in the above picture, starting from top left and going across, then to the second row; shows if light were emitted somewhere on the left side, and travelled further and further, the total displacment of the space (the right green edge) is progressively longer and longer; which makes for a constant displacement of space that lengthens the wavelength of the photon as it goes on.
There is an issue, however; doing the calculation as the total sum of all the points, the effecitve displacment of the space offsets the space from the actual displacment source; but,
- it's possible that the space is NOT stretched (but then Eddington's experiment fails); 2) space itself would have automatically already 'flowed' (for lack of a better word) around the point appropriately to just be displaced... so I have to run some sort of relation over the graph ; though maybe more advanced math that considers all the peer displacments with the self displacment would work; sorting the points almost works to either draw the closest first (which still gets displaced by the later points), or drawing the closest last (which shoves all the outer ones away from their sources)... maybe it's the average of both sorts? (I could really wish I had any other brain to bounce this off of)
The last image in the sequence above is each point with a very small radius of displacment that shows where the actual locations are, since their net effect is small enough to not displace others very far; compared to the broadend and heightened displacments in the other images.
When I first did the mathSphereDecay plot, and realized that the curvature is a positive pressure in space, this lead me to consider the dark energy aspect of modern science; and that this displacment of space pushes stuff away from each other. When I started to dig into that as a method of implementing gravity force, everything move away from each other instead of towards each other, and I had anti-gravity; so the space displacement itself does not affect the thing displacing it. This is proven in the null experiment of Michelson-Morley. Mass is not affected by the curvature of space; that is the cause of the mass is not subject to the curvature; the bobbers in the water don't feel the water(?).
https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment shows red shift without doppler cause; the top of the building is not moving away from or towards the ground in any way; the gradient of gravity itself shifts the frequency.
The frequency component of light is generally along it's travel velocity, and is the wavelength forward/backward; while there is also an amplitude tangentially, which is also related to the wavelength. If light emitted at some frequency goes from a gravitational gradient further away, the linear component in the direction of gravity is less compressed further away, so approaching the gravitational source, the frequency compresses, and becomes blue shifted; Conversely, travelling away from a gravitational source the gradient of space is less compressed and the signal appears red shifted. This is only one aspect of the shift though, also the frequency generator deeper in the gravity well is running slower, what it emits as a frequency is slightly lower when received by a clock further out in the gradient, and again, emitted from outside, the clock is slightly faster than the low clocks, so the top to bottom is blue shifted from a time delay.
Now, also, the tangential component of light will spread with distance in a gravitational source. The light would have to be described by a line and a cylinder around it, and any line on the cylinder will diverge tangentially from the center when leaving a gravitational source, which causes a red shift; any gravitational displacements of space that happen tangnetial to the light will not have any effect on making the light converge or diverge more; except in the region that is closest, if a probe was in that spot, it might see a blue shifted signal when between two other massive objects. But, then as I was following along in the Einstein Field Equations, which are built from the results of various other math, the Ricci tensor and scalar are just describing the transformation of space, and time really isn't even a factor.
So... there wasn't a big bang? Nothing's moving away from each other? The Hubble Constant is just the general mass of objects - and how much space is displaced by gravitational sources? The gravitational sources do not push each other away by displacing the space (they're generally attracted to each other) which does push more space to the outside of themselves. The least dense space is near a massive object (and technically IN the massive object, since that's where the negative curvature actually happens; I mean if there's a positive side to the curve, there must be a negative; and as demonstrated in images below, the negative curvature is NOT on the outside).
As far as I can tell, the Big Bang Theory isn't so much of a theory as a creation myth.
A lot of science is being based on assigning some meaning of this big bang that has led to a lot of misconceptions...
When building the spatial displacement https://www.geogebra.org/3d/sadtqz3x math from
It's almost like noone has actually plotted out the math to see it; so it's some abstract concept math people have in their heads
that is unsharable with the rest of the world. Keeping it a secret art burying it in for() loop iterator symbols (christoffel symbols) and mis-projecting rotations as 2D when they're actually 3D (though you can omit one, it's best not to)
The sort of rotation and curvature I was developing with Dual lnQuats ( https://github.com/d3x0r/STFRPhysics/blob/master/MATH.md https://github.com/d3x0r/STFRPhysics/blob/master/whitepaper.md ) is not the sort of curvature that happens to space. Rotation of space would look more like a twist, which we don't see.
Gravitational Lensing isn't convex lense lensing; it's gravitational lensing.
Light follow straight lines; from a far enough away source the light rays are nearly all parallel... but really they come from a point source, and have a small angle/spread to them...
This graph highlights straight light geodesics which appear to reach the other side of the gravity source (seeing around the corner)
This is the same graph as above, but compared with negative curvature and the same light geodesic emitter.
It's pretty clear to me that the negative curvature that is commonly shown in modern animations is just wrong; except maybe in the case of matter, and considering the curvature as what happens to massive objects, which constantly change velocity and are not on light geodesics. (Well they may be, but they are free to change geodesics where light isn't).
This demo needs refinement and documentation....
https://d3x0r.github.io/STFRPhysics/3d/indexSphereMap2.html
This is a tool observing the curavture behavior, (One of the Ricci Scalar values) is just the Y offset getting back to start after going out along a curvature; (Other Ricci curvature values are better represented on this demo https://d3x0r.github.io/STFRPhysics/3d/indexSphereMap.html (Turn off "Use Polar Map", and increase the size to see curvature applied to rectangular geodesics). It's sort of hard to have a single value for this, unless the value is only considered radially, which then only shows up in hyperbolic spatial displacement... ( https://d3x0r.github.io/STFRPhysics/math/mathSphereDecay, https://d3x0r.github.io/STFRPhysics/math/gravityFields.html' , https://d3x0r.github.io/STFRPhysics/3d/index-gravity-field.html ). It's the time axis that's negative coordinates, space is still positive... and the displacement we see across time in space is also positive.
The X/Y Sliders control the segments of the square stepping formation; X column sliders control how far each leg is, Y column sliders control the angle turned before stepping along the new geodesic.
The Z (Size) slider controls the curvature of a surface. The greater the curvature, the more angle is covered for a unit step of arc-length.
Under the Z column, the bottom most slider controls the angular step taken at each step; instead of taking many steps like the square, this path turns at every forward step.
This is a partial list of resources that at least partially influenced the understanding of curvature.
These are good with pictures, and don't do anything specificially but keeps all the relationships abstract, to not get confused with real space.
https://www.youtube.com/watch?v=xodtfM1r9FA The Maths of General Relativity (1/8) - Spacetime and Worldlines
https://www.youtube.com/watch?v=hhhYzfozon0 Ricci Tensor & Scalar (eigenchris)
https://www.youtube.com/watch?v=3LBitCErlBE Geodesic Curves
https://www.youtube.com/watch?v=km7WTO_6K5s Relativity 104e: Special Relativity - Spacetime Interval and Minkowski Metric ( eigenchris)
More Modern (after this phase of the project) https://www.youtube.com/watch?v=fvqXshyuvOg Chapter 1-4: Rethinking General Relativity as 5 Dimensions of Physics - A Unifying Theory of Gravity (Chris "The Brain")
https://www.youtube.com/watch?v=qDaoV5S9oTE Quantum Spin (2) - Pauli Matrices
https://www.youtube.com/watch?v=10qvMocHFZg Quantum Spin (3) - The Bloch Sphere (quntum spin)