Final Reality Check: Space Curvature vs. Time Dilation
On multiple occasions we discussed space bending illusion vs. time dilation effects. The most known test for Einstein’s theory of relativity is about some stars, which are obscured from us by the Sun, are still visible. That was confirmed by astronomers during Sun eclipses (when observation is not blinded by Sun radiation):
The last Einstein’s test for his theory was Mercury’s orbit precession:
attributed to space curvature caused by time slowing down around massive objects:
Now, coming closer to the truth. In “Time Matters” (free eBook, also available on Google and Amazon) I derived Snell’s law for light refraction caused by time dilation (time slowing down):
Such refraction explains visibility of stars obscured by the Sun, because slower time around the Sun causes light refraction, and not space bending. Then later in “Time Matters” I explained Mercury’s orbit precession by time dilation:
Since we do not have everyday experience of time dilation (except for its effect — gravity, caused by time/second being dilated by a nanosecond near the Earth), it is not easy to distinguish what is real and what is illusion, like we can do in this everyday case:
Most physicists lean to space bending reality. Recently Dr. Vivian Robinson published exact correction to the Newton’s inverse square law for gravity (which Einstein corrected as well, but approximately):
Exact formula for gravitational force is: F = G×m×M/[R×(1+Z)]², where (1+Z) is correction to the curved distance between objects in terms of so-called redshift Z:
Now, coming even closer to the truth. Dr. Robinson’s formula is 100% right, but its interpretation by distance increase due to space curvature is 100% wrong, let’s prove that. If by-distance interpretation was true, then both distances from the Sun to Mercury and from Mercury to the Sun would have changed the same way, thus, force exerted by the Sun on Mercury and force exerted by Mercury on the Sun would have the same value (inverse to the square of the corrected distance). That matches Action = Reaction Newton’s 3rd law, right? Wrong!
We can rewrite Dr. Robinson correction in terms of time dilation D, thanks to well-known tie between redshift and time dilation D=Z+1 (which means, for example, Z=0 — no redshift is the same as D=1 — no time dilation factor; and Z=1 corresponds to D=2 — time slowing down twice):
F = G×m×M / (R²×D²),
or F1/F2 = — (D2/D1)² with minus sign denoting the opposite direction. Time slows down near massive objects (genius Einstein’s discovery), the more massive, the slower time flows. Thus, time dilation D1 near the Sun is greater than time dilation D2 near Mercury:
That results in force F2 exerted by the Sun on Mercury being greater than force F1 exerted by Mercury on the Sun. The difference is well expressed by this ratio:
F1/F2=(D2/D1)².
And in this ratio D2/D1 does not depend on the observer: this ratio is the same for observers on the Earth, Mercury, the Sun, wherever — it expresses objective difference in time flow between two places: near Mercury and near the Sun. Now we clearly see that with the by-time-dilation explanation of gravity, Newton’s 3rd law is violated, unless D2/D1=1 when time flow is the same. Thus, by-space-curvature explanation differs completely from the by-time-dilation explanation in respect to Newton’s 3rd law. Forces change not because of inverse to squared distance, where distance changes, but because forces are measured in kg×meter/sec², and second changes. The main difference:
Time flow/dilation/speed is local, but distance is not.
Physically, why the change of force is not due to the distance increase from R to R+? Because it is about force / potential distribution over sphere area of 4πR² and not over 4π(R+)² area:
R becomes R+ (which is R×(1+Z) or R×D) not because of actual space bending (which is illusion only), but because of the lensing effect caused by refraction, by Snell’s law for time dilation. Einstein / Minkowski spacetime curvature is a mathematical illusion, no better than this illusion:
More 👉 Why Einstein / Minkowski Space Bending Is Not Real?
……..👉 Violation of Momentum Conservation Principle.
