Einstein’s General Relativity Becomes Elementary in 2024
We are talking about changing Newton’s gravitational formula
F = — G×M×m/R²
to
F = — G×M×m/(R²×D²), explained in Universal Inverse-Square Laws without Singularities!
with time dilation factor D — time slowing down around an attractor at a rate D (explained more in [1]). For example, near the Sun time slows down at the rate D=1.000002 (for 1 second near the Sun, 1.000002 seconds pass on the Earth). Sounds like not a big difference, but all the gravity comes from the time difference alone: no difference in time flow = no gravity! The simplest way to understand the cause of gravity (which was a mystery to Newton himself) is through so-called Potential — function that shows the origin of force. Derivative of Potential gives acceleration produced by the force (acceleration caused by gravity is denoted by g = F/m):
- — Potential'(R) = F(R)/m (apostrophe stands for derivative).
For Newton’s gravity F = — G×M×m/R² , Potential(R) = – G×M/R, and this potential does not explain what causes gravity (that is why Newton was confused). But for the second formula F = — G×M×m/(R²×D²), we have
- Potential = 0.5×c²/D²,
where c is the speed of light, which is constant, thus, gravity solely depends on time dilation D (explained more in [2] or [3]). Having such a simple formula, can we understand why time dilation rate D near the Sun is 1.000002? Yes, and it is in the realm of elementary physics now! Let’s derive formula for D from what we already know:
- — Potential'(R) = F(R)/m = — G×M/(R²×D²)
- (0.5×c²/D²)' = G×M/(R²×D²)
- 0.5×c²×(D⁻²)' = G×M/(R²×D²)
- 0.5×c²×(–2D'×D⁻³) = G×M/(R²×D²)
- – c²×(D'/D) = G×M/R²
- – c²×(ln(D))' = G×M×(–1/R)'
- c²×ln(D) = G×M×(1/R)
- ln(D) = G×M/(R×c²)
- D = exp[G×M/(R×c²)], where exp(x)=eˣ.
Now, it is easy to find time dilation D near the Sun, replacing letters in the last formula for D with numbers:
- G = 6.674×10⁻¹¹, M= 2×10³⁰, R= 7×10⁸, c=3×10⁸
- D ≈ exp[6.674×10⁻¹¹×2×10³⁰/(7×10⁸×3²×10¹⁶)] ≈ exp(2.12×10⁻⁶) ≈ 1.000002.
And you can calculate the time dilation near the Earth for M=5.97×10²⁴ kg and R=6.37×10⁶ m, using Wolfram calculator:
Formula D = exp[G×M/(R×c²)] debunks Black Holes, because it shows that there is no so-called “Event Horizon” where time stops — where time dilation D becomes infinite. Time can slow down by a finite factor D, but it never stops anywhere: D≠∞!
References:
[1] Universal Inverse-Square Laws without Singularities!
[2] Time Energy Potential = 0.5 c²/D²
[3] Simpler Derivation of Gravitational Potential = 0.5×c²/D²
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