Does Mass Curve Spacetime or it just feels like it does...:)
Always or most of the time, I show the double cross-sections of my lightspeed expanding hyperspherical shockwave Universe topology.
The right panel contains the spacetime Einstein and many other relativistic scientists learned to love...:)
You might be puzzled that this picture is quite smooth...:) I don't leave any doubt about what is the curvature of the spacetime. The curvature is exactly the same on both cross-sections.
Einstein made it so shameful to conjure up anything absolute that nobody dared to embed the spacetime (proper time plus three spatial coordinates) into a higher dimensionality or in my case, equal dimensionality space.
That was a horrendous handicap and since I am not shy with respect to ideas, I wasn't drag down by Relativismism...
The are more than one way to skin a cat...:)
I see science going crazy with different approaches to keep the Einstein paradigm (explaning motion through geodesics). This is an aesthetics motivation, the beauty of the form as opposed to the expression of the Truth...:)
I believe that this is one of the cardinal sins: The Vanity of Keeping a Beautiful Paradigm.
Einstein had a bed sheet as a paradim for space. If you place a bowling ball on a bed, the bowling ball will depress the region where it is located. If you are daring enough to consider the perpendicular to the surface at any given point of that bed sheet as the proper time, then you will understand that any trajectory in a depressed region contains accelerations not found in the undisturbed bed sheet. Closed geodesics around the bowling ball are the orbits of the stars, comeths, asteroids, moons and Earth..:)
That is a nice and neat paradigm. Neat might not be the correct description if you consider that Einstein never made his bed...:) Spacetime is crumpled all over the place...:) nobody knows exactly where time is pointing to... It should be called instead of Relativistic Spacetime, Einstein's Bachelor's Bed...:)
It is a fake paradigm in the sense that the elements of the metric of space (how the metric is affected by mass) are "discovered" by comparison with classical mechanics.
One could easily wrap that bed sheet on a light speed expanding soccer ball...:) and derive the corresponding metric...
I could be shy and just say that my universe is like that expanding soccer ball wrapped with a bed sheet...:) and let the soccer ball to be deformed by mass distribution, thus conserving the paradigm of mass deformation of space by mass distribution...
I would have a problem explaining why a concentration of dilators would travel slower than the rest of the shockwave..:)
I don't think pleasing Einstein Relativists, Cartan Geometrists is worth the trouble.
The spacetime mass induced deformation exists because Einstein didn't have the concept of dilator nor the concept of a Shockwave Universe. It doesn't make any sense to talk about deformation of spacetime or torsion in spacetime in this model.
Dilators are quite well behaved creatures, always traveling at the speed of light and always in phase with the rest of the Universe. If any event in our Universe were to make them lose phase-matching, they would disappear from sight and never come back..:)
So, how do I explain the "curvature" of spacetime by mass....:) I certainly used Lorentz transforms to derive how moving dilators interacts (Biot-Savart Law).
I've never bothered to describe Black Holes for a few reasons...:) One of them has to do with the Fabric of Space energy...:) Everyone knows how to transform a small fraction of our elements into energy...:) but nobody knows how to transform the whole chimichanga in energy...:)
Let's go back to the Einstein's Paradigm. In my theory, dilators are coherences between 4D stationary states of deformation, that is, around a dilator (particle), space is modulated. What we observe in our Stroboscopic Univers is always the two phases of a state corresponding to a single side of the 4D Spinning Double Potential Well.
As the dilator shape shifts, it creates a metric wave (dilaton). Due to the Quantum Lagrangian Principle, all dilators always dilate in phase thus adding coherently their little amplitudes.
This is the reason why people can speak of a Field and the why there is such a thing as Quantum Field Theory. People talk about that if its was a great thing..:) Like a Gauge change were the greatest invention since sliced bread...
It is a field with a beautiful mathematical framework. People who master QFT are always vain...:) by definition. I have been told that I would have to study Cartan Geometry, just to have the right to have an opinion about Relativity..>:)
I think it is not necessary to speak a dead language to communicate with the living...:)
The reason why the bed sheet paradigm is dead (or should be) is because there is another model based upon dilators (not mass) that explains dilator motion (not mass) in a perfectly locally flat (wrapped tightly on a ligthspeed expanding soccer ball...:)
Of course, since we are talking Physics, there is got to be a paradigm explaining what happens to the hapless bed sheet...:)
As I mentioned each dilator creates dilatons. Many dilators creates a dilaton field that decreases with the number of wavelengths measured from their centers. Notice that I didn't say, with distance...:) Distance is irrelevant, since what really matters is how many waves from the origin you are...:)
As you can see, the Grand Unification Equation doesn't mention an Electromagnetic, Gravitational or otherwise field. It just express the dilaton intensity due to a single dilator or a Kilogram of it - Remember that when I reached out to our known physics to create its link between with my theory, I recasted all classical equations to be described in terms of 4D masses. The 4D mass of a proton is the same as the 4D mass of an electron. Their 4D mass is the same as the 3D mass of an Hydrogen Atom...:) Don't bother with units, the 4D Masses are only used to find out the number of dilators...
Notice that the decay description of the dilaton intensity is quantized and has no poles or infinities...I dare to say it makes more sense than Newton's Law of Gravitation... or Gauss Law of Electrostatics or Maxwel's Equations...:) Anything with a pole is a crime against common sense...
If you get to explain something in terms of the constructs of your model..:) you are just doing your obligation..:) For example... I don't need to know the trajectory of a baseball to tell you what is its vertical speed at any given ball's height (given that I know how to express potential energy as a function of height)... That is what Einstein used to describe Gravitational induced red-shifting...If one creates a more accurate picture (e.g. Torriceli equation) to describe the baseball's trajectory, that is great, but it doesn't make the initial description invalid...
Of course, if Gravitation creates red-shifting it will also affect the passage of time...thus the Mercury's perihelion precession correction...If one includes torsion into the model and adjust it to explain problem of precession, that is good... but that is just a model and not necessarily reality nor the best model....:)
They didn't bother with poles in the Electrostatics and Gravitational potentials because one could use them to explain mass..:) through the concept of self-energy...If you average something over a pole you might as well get anything your little hearth desires out of it...:)
I've never bothered to explain what is the equivalent paradigm to Einstein's paradigm of a depressed bed and its bed sheet...:)
The reason is that I didn't want to formalize the theory at this time.
By now, the correct paradigm should be clear and easy to guess. I will give you the answer.
The bed sheet tightly wrapped on a ligthspeed expanding soccer ball is the correct starting point.
Instead of having a depression on the hapless bed sheet, one has a shrinkage or expansion due to the presence of dilators. The bed sheet metric grid is just narrower or broader around a group of dilator than it is in regions far from any dilators.
This is an ugly paradigm. As you know, one can get similar shrinkage by curving or twisting the bedding...:) As much as I would like to take the easy way out, I have to denounce (like Obama) mass induced curvature or Cartan Torsion..:) They are just meaningless mathematical constructs - at least if my theory is correct. A curvature is easier to model than a just plain shrinkage...:)
Of course, a curvature of space is the most studied paradigm which might as well be used within the framework of the Hypergeometrical Universe Theory. Hence, you can continue deforming spacetime, as long as you don't talk crazy...:) Don't start believing in mass induced spacetime curvature...:)
One just have to remember that the bed sheet deformation outwards or inwards from the surface of the soccer ball is just a mathematical trick to replicate the effect of a bed sheet local shrinkage...:) and not a real deformation. The bed sheet is tightly wrapped around the lightspeed expanding hyperspherical shochwave universe (soccer ball)....:)
As you should know by now, there are many ways to skin a cat...:) even if that cat is Schrodinger's Cat...:)
Although that might not be the case. I know that nobody made any valiant effort to create a Shrinkage Metric Spacetime Model..:)
I think it would be worthwhile... It would provide more natural framework to describe the Hypergeometrical Universe Theory...
Now, you vain scientists, have a new target...:) Go for it...:)