I was wondering... gravity seems to work over immense distances, nobody knows how.
Suppose you could create something suddenly out of nowhere, maybe pop out of a worm hole or something.
How would gravity know you were there?
How fast would it find out?
Suppose you are out past Pluto somewhere, and suddenly popped into existence there. Would you feel the suns gravity immediately?
How long would it take?
This is a good question.
Force of gravity is an inverse square law.
F = (Gm1m2)(
r/r^3),
where G is a constant, m1 is a test mass, and m2 is a mass at radius
r. In the above equation, r = |
r|. Most people will say gravity does not have speed, but force can also be written in terms of momentum (mass times velocity):
F =d
p/dt
where
p = m
v. In quantum mechanics,
p is a differential operator, operating on quantum state functions (which are most times sinusoidal.) For example, in the
x coordinate,
p = -(
ih/2pi)(d/dx), where
i is the square root of -1, and h/2pi is the reduced Plank Constant. Quantum mechanics will then state that instead of linear momentum that depends on velocity, quantum momentum of particles move as wave packets. These wave packets usually have a packet speed equal to
c, the speed of light.
Just like a moving car has a force of impact and a velocity, gravity waves propagate at a speed, and exert a force. The thing is, the strength of the force-field is reduced by the square of the distance. So, the effects of gravity are short-ranged: the closer the mass is to the test mass, the higher the force exerted on the test mass. For example, the earth's center of mass is the core. In reality, nothing could ever drill through the core to China because you would oscillate between the core forever.
To answer your questions:
Gravity is a short-term force. The only way gravity can affect long range is if the wave packets have compressed enough to form very dense wave-lengths with very low frequencies (i.e. matter.) You must collapse the gravity waves into a dense packet in order for it to exert a cumulatively detectable physical force. Suns, planets and celestial bodies are examples of this. In the quantum world, where frequencies are high and densities are low, matter is rarely affected on a classical level. If the test particle is smaller than the mass object
AND the test particle is very far from the mass object (relative to the radius of the test particle,) then there is very little physical effect on the test particle. Very minute.
If you popped out of a worm hole, which itself is a gravitational distortion of space-time, gravity would know you were there because the matter in the space you enter would act like test masses, and your entry into that part of space time would exert a force on the test masses (1) from the worm-hole, and (2) from your entry. The universe most definitely notices gravitational distortions of specs of dust, so a mega gravitational distortion would be noticed very far.
The speed of a wave packet depends on the medium you are in. For example, the Cherenkov Phenomenon is an event in which neutrinos move faster than the speed of light
in heavy water, causing photonic sonic booms: the water radiates blue light. In a medium like space, where the temperature is only 2.5 K, the neutrino goes slower than a photon (light particle) because a neutrino has more collapsed wave packets/mass than light. So, if you enter into the vacuum of space, and we assume you move through the wormhole at the speed of light, quantum gravity would know you arrive instantaneously. Classical gravity, or even a mix, would know much later (comparatively speaking). A sun may be affected by the wormhole and entry 0.00000000000000000000000000000001 seconds
after it is quantum mechanically visible.
Because it is theorized that collapsed gravitational wave packets (matter) may exist as infinitesimally massive particle called a graviton, you would feel the affect of the sun immediately (as you do the sum of affects of all things in the universe,) but the force of the sun is so diminished at that distance for a test-mass like a human. Pluto would have more gravitational effect on you than the sun, though you would immediately feel its quantum mechanical effects.
