Calibrating general relativity
v. 5 n. 22
A persistent fundamental concern in general relativity is a stable point on which to calibrate "acceleration." It is this inconsistent foundational point on which general relativity is often criticized, even by its founder. [1]
The founding tenet of this theory is the equivalence of gravity and acceleration. For practical purposes acceleration is commonly treated as an absolute; in the fundamental sense it is not an absolute, because the Universe is observed to be accelerating. For example, any measured acceleration, as in an automobile is only with respect to the road the vehicle is on. But since the Universe itself is accelerating, the measured value in this case cannot be considered absolute, rather, with respect to the acceleration of the Universe as well as with respect to the road, i.e., even though the car is stationary on the road it is accelerating along with the Universe.
And not only that but also the road on the Earth is accelerating with respect to the Sun since Earth is rotating and revolving relative to the Sun. Similarly, for all the other twists and turns at higher scales before reaching deep space among galactic superclusters, where pure acceleration of the Universe is occurring, because the Universe is not observed to be rotating to date; [2] only the expansion appears to be accelerating.
The expansion value has been calculated at about 10^-14 m/s^2. [3] This is the value that acceleration and gravity should perhaps be calibrated to. Since at this level there does not appear to be any higher level, acceleration might be considered identical to gravity here. If this is the case the mystery of the origin of gravity might be settled in that the axiom of general relativity is that acceleration is only equivalent to gravity, implying conditionality; identities are unconditional, and different terms for the same entity. Gravity might be identical to the acceleration (of the Universe), and only apparently attractive at the smaller scales. [4] through [8]
The equivalence axiom of general relativity was from an observation at the surface of the Earth, where the acceleration of the Universe was not taken into account at the outset.
Common practice in general relativity is to employ the cosmological constant (capital Greek letter lambda, Λ) -- within the second term from the left in the cover equation. This term was added subsequently to the theory after the observation of the accelerating Universe and is not native to the theory as originally conceived with pure mathematical logic. This term might be considered a stand-in for the acceleration of the Universe; there is no actual value for this acceleration in common practice. Lambda is colloquially referred to as the unknown "dark energy." General relativity does not account for this energy, but only made to conform to it with lambda.
Recognizing this need for calibrating general relativity in a foundational or physically consistent sense suggests rederiving the theory considering the acceleration of the Universe from the outset so that the cosmological constant may be implicit, i.e., disappear into the remaining terms, instead of a physical correction to a mathematical theory. That is, the founding tenet might be the identity of acceleration and gravity with due consideration to the observed acceleration of the Universe as possibly gravity itself.
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Cover image less calibration schematic overlay: https://vis.sciencemag.org/generalrelativity/
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7 个月Sounds like a deep dive into foundational physics! Addressing acceleration in general relativity could be key.
Understand Time, our spatial orthogonal dimension, is physical and dilates our relative time.
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7 个月Your insights shed light on a critical aspect of general relativity!
Independent Researcher at Karma Barter
7 个月It doesn't help that there is no such thing as a point except as a mathematical abstraction. Satisfactory resolution necessitates a foundational shift in math itself because canonical geometry carries that that dang non-existent point into everything as if it were real and reference it as a touchstone as if such were reliable. It is not so hard to imagine the reasons this must be true. For something to exist, it must exist in 3 spatial dimensions at once, plus time if it is to exist long enough to be observed. There is no building up from fewer dimensions, so when we take derivatives and gradients, we are taking something that is complete and natural in its simplest 4 dimensional form and dissecting it into what must be abstract, non viable, non-extant forms with multiple-valued solutions, none of which are actually solutions. The original simplest form was the solution. The problem to solve is inventing a math system that embodies that solution from the outset. But all have dug their own rabbit hole, certain they'll be the one to strike gold. That the answer is to work together to climb out of the big rabbit hole we have all been in all along is scary to contemplate, much less imagine, because - just one more foot to the gold!