Newton

 

Good Advice

Sir Isaac Newton came around to my house one day
His face was all sunburned and red
He said he didn't want to sleep in the shade of a tree,
Because an apple might fall on his head
I said, "Sir Isaac, you dumbbell, take my advice
Go right back there and sleep beneath that tree
And if you let that rotten apple fall down on your head,
Why you'll discover gravity"

Maybe Newton only APPEARED to discover gravity!

Newton’s Laws of Motion are:

Law 1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

These laws describe the motion in a flat, Euclidean, spacetime.  If the universe is hyperbolic, and Einstein’s General Relativity is considered, it should be :

Law 1. A body remains at rest, or in motion at a constant speed in a straight line along a geodesic in spacetime, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.  If a body moves along a geodesic to decrease its energy, it may appear in a Euclidean frame of reference that a force has changed that body's momentum.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

This has an implication on the Lorentz Factor that governs time dilation, T=T₀*γ; length contraction, L=L₀/ γ ; and rest mass, M=M₀*γ.  The Lorentz Factor is typically given as

γ=1/sqrt(1-(v/c)² ).

where 

sqrt    = the square root operation;

v        = velocity, and

c        = the speed of light.   

This has the problem that there is a discontinuity, it is undefined, at a v/c of 1.

In hyperbolic spacetime, this factor would be

γ=1_ln(cosh(v/c)±sinh(v/c))

where 

ln    = the natural logarithm function, a logarithm with  a base of e

This does not have a discontinuity of 1 at a v/c of 1.  At a v/c of 1, the factor is zero. 

It also means that Gravity is NOT a force in hyperbolic spacetime.  It is an apparent force, unlike the other fundamental forces:

• The strong nuclear force: the force responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
• The electromagnetic force: the familiar force that acts on electrically charged particles. The photon is the exchange particle for this force.
• The weak nuclear force: a short-range force responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. The W and Z bosons are the exchange particles for this force.

The difficulty of including gravity in a unified field theory, and the inability to discover a graviton as the exchange particle, is proposed to be a consequence of the hyperbolic shape of the universe, spacetime.

Newton Law of Gravity, which is from a Euclidean frame of reference, states that the force of gravity is

F=G*(M₁*M₂)/(d₁₂ )²

where:

F             = The force of gravity,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between mass one and mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.

From a hyperbolic, non-Euclidean, frame of reference there is no force, and the movement of the two masses to a center of mass is a consequence of entropy maximization and the objects moving from their initial positions to their center of mass along a geodesic.

 

F'=G*M₁*M₂*exp (-1/2*d₁₂ )

where:

F’            = The apparent force of gravity,

exp         = the exponential function,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between Mass one and Mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.