Chimp

Is gravity a statistical probability distribution?

Yes, the force called gravity is actually geometry, non-Euclidean geometry, where spacetime becomes anisotropic and inhomogeneous in the presence of mass-energy.

Then the question becomes "what is space?" "What is time?"

Space is relational. Time is a process.

Heisenberg Uncertainty:

DxDp >= hbar/2

The relation becomes totally "chaotic" below the Planck length. So, space could be described as a self similar relation which is generated by the quantum foam, and forms Penrose's "spin networks".

The curvature of spacetime could be represented as a Gaussian distribution? If mathematics only is an approximation of reality, then the mathematics of probability corresponds "exactly" with reality.

The Riemann tensor explains how a tangent vector, parallel translated around a tiny parallellogram is changed. So, to say that spacetime is "curved" means how much a tangent vector changes during parallel transport around a loop. Parallel transport is the translation of an infinitesimal tangent vector along a geodesic.

The probability distribution should agree exactly with the Riemann tensor of Einstein's relativity.

Is the universe a closed system? The million dollar question

Russell E. Rierson
analog57@yahoo.com

paul30

I have always thought space was relational.

It is not just an emptiness in which things act or sit.

As to time being a process, I think time is also a relation--that is, time is our way of describing change, and that involves the change of relations.

Chimp

Interesting...


The Planck length, 10^(-35) meters, sqrt(G*hbar/c^3) and below, is postulated to become a boiling sea of chaos called "quantum foam". These are vacuum fluctuations, where the geometry and topology of space becomes probabilistic.

John Wheeler derived the "quantum foam" concept in 1955.

http://www.usd.edu/phys/courses/phys...k/wheeler.html


Spin foam concept:

http://faculty.washington.edu/smcohe...ainySpace.html


http://math.ucr.edu/home/baez/foam/

Friar Bellows

Back in the 1960's Andrei Sakharov came up with an interesting interpretation of gravity (fully compatible with general relativity) as an "elasticity" of space that arises from some complicated particle physics. In this view, the relationship of gravitation to particle physics is analogous to the relationship of elasticity to chemical physics ... in other words, gravity, like elasticity, is nothing but a statistical measure of residual energies (in the former case, the energy due to the curvature of space; in the latter case, the energy due to the deformation of molecular bonds). See the book: Gravitation (Meisner, Thorne, Wheeler, pp 426-428).

Chimp

Thank you for the book reference Friar Bellows.

Very interesting!

A geodesic is the shortest distance between two points on a curved surface. An object in free fall traces out a geodesic. Parallel translation with tangent vectors along a curved manifold is an abstraction of course. It is difficult to imagine actual "infinitesimal tangent vectors" following imaginary paths on spacelike hypersurfaces.

Infinitesimals are mathematical objects, less than finite but greater than zero. It seems to me that symmetry groups resolve the infinitesimals paradox quite nicely!

Worldlines seem much more "realistic" than imaginary paths and tangent vectors. The coordinate independence of GR, is very appealing.

Richard Feynman's sum over histories-path integral, gives a particle's four dimensional worldline, from point A to point B. The principle of least action applies and energy is conserved. It appears that the universe has laws to maximize efficiency.

Thought experiment:

An object in "free fall" is basically equivalent to an inertial reference frame, if the object is relatively small. Two clocks are synchronized at the top of a tower. Also, there are more clocks affixed along regular intervals from the bottom, to the top OF the tower.

When the clock is dropped from the tower, it will be accelerated at 9.8 meters/sec^2. Yet, since it is in free fall it will be equivalent to a rest frame. As its velocity continues to increase in its fall, it will have a relativistic time dilation, t1:

t1/sqrt[1-(v/c)^2]

Where "v" is the instantaneous velocity at any one "instant", approximately

The clocks affixed to the tower will have the approximate gravitational time dilation, t2:

t2/sqrt[1-2GM/((c^2)*r)]

G is Newton's universal gravitational constant. M is mass of the perfectly spherical planet(Earth?) that the tower is standing on. r is the radius of the perfectly spherical planet and c is the speed of light in vacuum.

As the clock falls next to the tower, at each instant that the falling clock passes a clock affixed to the tower, a third observer would observe the two clocks to be ticking at the same rate.

The clock at the bottom of the tower will be the slowest, since it is in the stronger part of the gravitational field. When the falling clock reaches this bottom level, the two clocks should have the "same" time dilation, if the falling clock was dropped from rest, with no additional accelerating forces.

Energy is conserved.

t1/sqrt[1-(v/c)^2] = t2/sqrt[1-2GM/((c^2)*r)] ???

goat37

Maybe I am mistaken but...

I thought time moved slower the further away you were from the gravitational force, not the other way around.

So if you were at the top of Mt. Everest, your clock would actually run slower than one in Death Valley, CA (not really a noticible difference, but a difference)

?

Jesse

No, it's the opposite. For example, as you cross the event horizon of a black hole you'll see the entire infinite future history of the universe pass by in a finite time; if you just go near the event horizon but then rocket away, you may find yourself in the distant future.

goat37

ack.. sorry, you are correct. I had the last half of the equation right, but had the first half backwards.

Time runs slower nearer the center of the gravitational force.

I read it like it is, but for some reason my brain put it in my head backwards. Thanks for the clarification.