Re: [asa] big bang question ... and the start of matter...

I should probably clarify what I said below. In the simple model I described, in which 2 particles pop into existence in a state of zero energy, the speeds of the particles will decrease as their separation increases until they come to a stop & then fall back together. (There can be no orbital angular momentum if the particles are spinless.) This can be seen by solving the special relativity equation of motion with Newtonian gravity. In this sense the model corresponds to the closed universes of general relativity.

But in relativistic cosmology things are different. The Friedman equation for the scale factor of a uniform model universe has the mathematical form of the Newtonian - i.e., nonrelativistic - equation of motion of a particle. (This resuult seems surprising but there's a reason for it. In a uniform universe the scale factor of any small part is the same as that of an arbitrarily large part. & for a sufficiently small region containing a very small amount of matter, the equations of Einstein's theory approach those of Newton's.) What corresponds to the Newtonian energy is -kc^2/2 where k is the curvature which is +1 , -1 or 0. So zero "energy" corresponds to flat space, the borderline between spaces which will expand forever and those which will eventually collapse. k = 0 is like the case of a rocket sent away from the earth at exactly escape velocity - it would in the limit creep out to infinity at a speed approaching zero but would never fall back.

Both inflationary cosmology and present observations indicates that our universe is, on the average, spatially flat. But it's possible that it's a closed (spherical) space with an extremely large radius of curvature.

Shalom
George
http://web.raex.com/~gmurphy/
  ----- Original Message -----
  From: George Murphy
  To: Dehler, Bernie ; asa@calvin.edu
  Sent: Monday, May 05, 2008 6:04 PM
  Subject: Re: [asa] big bang question ... and the start of matter...

  Bernie -

  Briefly, matter could come into existence from a state of zero energy if its mc^2 energy plus any kinetic energy were exactly cancelled by its negative gravitational potential energy. In the simplest case of 2 particles of mass m at a distance r, 2mc^2 - Gm^2/r = 0. In a more general case of a homogeneous distribution of matter, this corresponds to the spatially closed universes of Einstein's theory. The transition from a state of no particles to one of 2 (or of N) particles would be discontinuous but quantum theory allows such "jumps." Thus you need a correct quantum theory of gravitation to make this work rigorously & whether we have that or not is a matter of debate.

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Received on Tue May 6 11:12:10 2008