Newton’s Third Law Is Violated: Action ≠ Reaction!
In Time Matters (also available on Google and Amazon; or in Medium stories about Mercury and Oumuamua) we discussed how uneven time flow, time dilation, causes celestial bodies to deviate from their classic (by Copernicus and Newton) trajectories:
Dr. Vivian Robinson recently derived the exact formula for the observed gravitational force as F = G×m×M/[R×(1+Z)]², where Z is the redshift value:
All we need to know is that redshift value Z is tied up with time dilation D, as D = 1+Z. Thus, Dr. Robinson’s formula looks even better as
F = G×m×M/(R²×D²).
D² is what makes this formula different to Newton’s inverse square law for the gravitational force F = G×m×M/R². Such correction makes perfect sense because any force is measured in kg×meter/sec², and D is just a factor exerted on sec.
Now, to the Newton’s Third Law, Action & Reaction:
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
It looked perfectly fine for Newton’s formula for gravitational force F = G×m×M/R². But not anymore, if time dilation is taken into account — let us take Mercury and the Sun interaction, for example:
Consider that gravitational time dilation that we observe near the Sun D1 is greater than time dilation D2 farther from the Sun (that includes infinitesimal contribution to time dilation caused by Mercury’s tiny mass).
D1 > D2 => F1 < F2 !!!
How should we correct Newton’s 3rd law now? Since F1×D1² = G×m×M/R² and F2×D2² = G×m×M/R², we have now: F2×D2² = F1×D1². That would be the new form of the 3rd law:
F×D² is the same for Action & Reaction.
And it is true for any type of force besides the gravitational, because any force is measured in kg×meter/sec², thus experiencing the same dependency on time dilation D.
P.S. The same result will be for an observer on the Sun and for an observer on Mercury: force exerted by the Sun on Mercury is greater than the force exerted by Mercury on the Sun. “Observer” is about D-value only: How much time flow is slower at the point that he observes than at the point where he is. Regardless of the observer’s position, time near the Sun runs slower than near Mercury. Thus, D² near the Sun is greater than D² near Mercury, and since F×D² is the same, F on the Sun is smaller than F on Mercury. Like Newton’s “inverse square law” F~1/R² for gravity is easy to remember, Newton’s 3rd law becomes “inverse square law” easy to remember: F1/F2=(D2/D1)². Although D1 and D2 values depend on an observer’s location (on the Earth, Mercury, or the Sun), D2/D1 ratio remains the same irrespective of the observer’s position.
