No matter what the nature of spacetime is, continuous or discrete, peaceful or fluctuating, we can assume that there does not need to be another "spacetime" behind spacetime.
According to the Einstein field equation of general relativity [1], Rµν - (1/2)gµνR = G*Tµν, at the macroscopic level spacetime is expressed in terms of dynamic curvature. "A general space can be intrinsically curved, defined not by embedding in a flat space, but by the arbitrary functions gµν(x) (the metric). "[2] If Space-Time can be bent, curvature must be a physical reality. Curvature, like spin, should not be masked by the term "intrinsic" (besides, spin is a fixed number, whereas curvature is continuously variable). Real bending should be a motion, at least locally. So we ask, since Space-Time can move, does it only bend and twist and not other motions, such as local translations, stretches, and oscillations?
We need to note that Einstein has not made any argument for Space-Time Curvature, even a simple explanation. In his search for a geometrical description, he emphasized that “This problem was unsolved until 1912, when I hit upon the idea that the surface theory of Karl Friedrich Gauss might be the key to this mystery. I found that Gauss' surface coordinates were very meaningful for understanding this problem.”[3] And, although many physicists do not understand what Space-Time Curvature is all about, everyone accepted this setup. This concept of `intrinsic curvature', which cannot be mapped to physical reality, is at least a suitable choice from a modeling point of view.
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Related Question:
* “Are Space-Time Curvature and Expansion Two Different Geometrical Mechanical Properties?” (2) 【NO.38】Doubts about General Relativity (3) - Are Space-Time Curvature and Expansion Two Different Geometrical Mechanical Properties? | ResearchGate
* “How the View of Space-Time is Unified (4) - Is Space-Time Expansion a Space-Time Creation? “ https://www.researchgate.net/post/NO18How_the_View_of_Space-Time_is_Unified_4-Is_Space-Time_Expansion_a_Space-Time_Creation
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References：
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
[2] Nastase, H. (2011). Introduction to supergravity. arXiv preprint arXiv:1112.3502.
[3] Einstein, A. (1982). How I created the theory of relativity(1922). Physics Today, 35(8), 45-47.
@@The nature of spacetime, whether continuous or discrete, peaceful or fluctuating, suggests that there does not need to be another "spacetime" underlying the one we perceive. According to the Einstein field equation of general relativity, \( R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = G T_{\mu\nu} \), spacetime is characterized by dynamic curvature at the macroscopic level. A general space can be intrinsically curved, defined not by embedding in a flat space, but by the arbitrary functions \( g_{\mu\nu}(x) \), or the metric .
If spacetime can be bent, then curvature must be a physical reality. Like spin, which is a fixed quantum number, curvature should not be obscured by being termed "intrinsic"; it is a continuously variable property. Real bending implies motion, at least on a local scale. Therefore, we must ask: If spacetime can move, does it only bend and twist, or can it also undergo other motions, such as local translations, stretches, and oscillations?
Einstein did not provide a simple explanation for spacetime curvature in his works. In his pursuit of a geometrical description, he noted, "This problem was unsolved until 1912, when I hit upon the idea that the surface theory of Karl Friedrich Gauss might be the key to this mystery. I found that Gauss' surface coordinates were very meaningful for understanding this problem" . Although many physicists might not fully grasp the concept of spacetime curvature, they have widely accepted it. The concept of 'intrinsic curvature', which may not be directly mapped to physical reality, remains a suitable choice from a modeling perspective.
the picture of gravity will be totally different in quantum gravity, which is still not existing.
There is an easy explanation. According to the divergence of the field, the energy density currents passing through the defining 4-local event points build the space-time structure through the rearrangement of the distribution. Thus, everywhere there is a consistently valid form of curvature to control the free fall as tidal stresses.
“…the picture of gravity will be totally different in quantum gravity, which is still not existing.….”
- the picture of gravity will be correct after instead of the GR that is based on postulate that gravitational objects/events/processes in gravitationally coupled systems of macro bodies are determined by interactions in systems “mass-spacetime-mass”, what is fundamentally wrong, as that is rigorously proven in the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, and Planck scale informational initial physical Gravity model:
- Matter’s spacetime is absolute, and fundamentally cannot be “contracted”, "dilated”, “curved” , “bend”, so on, while Gravity fundamentally is nothing else than some fundamental Nature force, which in a few traits is similar to Electric Force,
- really scientific theory of Gravity will be developed.
After this the “quantum gravity theory” will be developed, but that changes nothing principal in this case, as, say, “quantum Electric Force theory” in existent QM nothing changed principally in physics.
SS posts July 6, and recent one, in
https://www.researchgate.net/post/NO40Doubts_about_General_Relativity_5-Should_there_be_negative_gravity_in_General_Relativity
- are relevant to this thread discussion.
Cheers
The answer to this question is that there is actually no General Relativity, because there is no "spacetime". The Lorentz relations (light cone &c.) describe the offsets and corrections to the light rays -only-, such that space and time are left Absolute.
The reason why we know, for certain, that we have an Absolute character to space and time, is because the "Relativity of Simultaneity" has been demonstrated to be a logical impossibility. Confer above, tilting-mirror demonstration, and also the proof by Kılıç below :
Preprint Precis of the proof we have an Absolute character to time an...
Article The incompatibility of Einstein's relativity of simultaneity...
Dear @Preston Guynn
Thank you very much for your reply.
However, I think you have not understood the meaning of my question. My question is very direct and clear, ‘Doubts about General Relativity - Is Space-Time Bend a Motion?’This is questioning whether ‘Space-Time Curvature’ is a true physical curvature, or a mathematical intrinsic curvature. If curvature is a physical motion, then Space-Time Curvature must be able to manifest itself; if not, where does this intrinsic nature manifest itself in space-time？ If we have to resort to the concept of discrete spacetime to solve this problem, does it mean that spacetime curvature is not intrinsic and is still produced by motion? My point is clear, a mathematical expression that cannot be mapped to physics cannot be realistic, i.e. it cannot be the final concept. Either the concept of curvature or the structure of spacetime has to be changed.
You cite the concept of ‘gravitational lensing’ to justify the curvature of spacetime, but we should know that there is no curvature of index of refraction of a lens, whether n is uniform or non-uniform. We also know that the early hesitations about the concept of spacetime curvature were not limited to ordinary physicists, but included Dirac, Feynman, and even Einstein himself.
Researchgate is a free and open community for the exchange of views on scientific research. What do you think is the proper or correct motivation for a person to post a ‘Question’, ‘Discussion’ or ‘Doubt’? I would like to hear your opinion. My opinion is here:Preprint No Question, No Answer - Part Ⅰ
Confucius (551BC-479BC) said, "When I walk along with two others, they may serve me as my teachers. I will select their good qualities and follow them, their bad qualities and avoid them." Therefore, I learn from anyone, including from you, but Learning’not equal to 'accepting’, it won't be all of them.
Best Regards, Chian
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