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Newtonian laws of motion in time-space

Note: terminology updated June 2017. See glossary above.

Isaac Newton’s three laws of motion and law of gravity apply to space-time, the 3D space and 1D time of classical physics. What do these laws look like in time-space, with 3D time and 1D space?

Newton’s laws of motion in space-time state:

Law I: Every body continues in a state of rest or uniform motion (i.e., constant
velocity without change of direction) unless acted on by a force.

Law II: The acceleration (i.e., change in velocity per change in time) of a body is proportional to the applied force divided by the mass of the body (i.e., a = F/m).

Law III: To every action, there is an equal and opposite reaction, i.e. forces are mutual.

The corresponding laws of motion in time-space are as follows:

Law I: Every body continues in a state of rest or uniform motion (i.e., constant
celerity without change of direction) unless acted on by a gorce.

Law II: The prestination (i.e., change in celerity per change in distance) of a body is proportional to the applied gorce times the mass of the body (i.e., b = Γm) or gorce divided by the vass of the body (i.e., b = Γ/n).

Law III: To every action, there is an equal and opposite reaction, i.e. gorces are mutual.

Newton’s law of gravity in space-time states:

1. Every mass attracts every other mass.

2. The force of gravity is directly proportional to the product of their masses.

3. The force of gravity is inversely proportional to the square of the distance between their centers of mass.

4. The force of gravity is directed radially toward the larger mass.

Thus Fg = G m1m2/ with space-time gravitational constant G.

The corresponding law of levity in time-space states:

1. Every vass attracts every other vass.

2. The gorce of levity is inversely proportional to the product of their masses; i.e., directly proportional to the product of their vasses.

3. The gorce of levity is inversely proportional to the square root of the distance between their centers of mass.

4. The gorce of levity is directed radially toward the larger vass, or smaller mass.

Thus Γh = H / (m1m2√d) with time-space levitational constant H.

While this was presented in 1D space and 1D time, for time-space it may be generalized to 3D time and 1D space. In particular, the time, celerity, prestination, and gorce are 3D vectors in time, or 4D vectors in time-space.

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