expansion mechanisms - the inertia story
- From: "John McCrone" <johnmccrone@xxxxxxxxxxx>
- Date: Sat, 28 May 2005 09:12:16 +0000 (UTC)
What is the right way to think about the expansion of the Universe if
we take the old "inertial motion of mass" approach? The one that said
the Big Bang created kinetic energy and a gravity potential in equal
amounts so that the Universe would always expand, but asymptotically
coast towards a halt. Is the following toy model of how gravity and
inertia balance out anything like correct?
[Of course, we now need to include a dark energy or cosmological
constant angle in any complete story on expansion mechanisms. But as I
understand it, a gravity~inertia balancing act still does the heavy
work for the first few billion years after the Big Bang.]
Imagine two masses at a distance from each other. The first can be
considered at rest, the second has a momentum that is above the escape
velocity for an object at that distance. So we can say the second mass
is poised on the surface of the gravitational sphere produced by the
first mass. If the second mass was also at rest, then there would be
just an inwards pull of gravity dragging the two masses together. But
the second mass has a randomly oriented momentum derived from the Big
Bang. Any paths that happened to take the mass into the gravitational
sphere would hasten a gravitational collapse of the system. Equally,
any paths outwards and away from the surface of the gravitational
sphere would fight the pull and continue the expansion. Importantly,
the curved surface of the gravitational sphere means that on average
there will be more escaping than collapsing. More paths point out than
point in.
We have the interesting situation where there is one force - gravity
- which pulls in a single constant direction. Then we have gravity
being balanced by a random mechanism reminiscent of Boltzmann's story
on entropy. On average, a second mass is more likely to be heading out
of a gravitational sphere than into it and this produces a continuous
state of expansion. The actual rate of expansion would relate to the
degree of curvature of the sphere. For a small sphere, most paths would
lead away and so the average rate of expansion would be higher. For a
large sphere, the surface would look almost flat and so the odds would
be tilted only slightly towards expansion.
The real world is of course messier with many masses generating many
gravitational spheres. And so inertial flight away from one would be
also inertial flight towards another. But in any universe that was not
perfectly smooth there would be a clumping of mass to one side of our
inertial test object, and a relative scarcity to the other. So we can
imagine that there is an overall centre of gravity to any region of
slightly higher mass density that defines a sphere from which the test
object must be either escaping or heading into. And on average, due to
simple geometry (and assuming test objects with the necessary escape
velocity inertia), escape will be the rule.
This very simple Newtonian picture doesn't really explain the
expansion of space itself. The forces of gravity and the random
inertial flight of masses are happening "in" space rather than helping
to make an every increasing amount of it. But perhaps a relativistic
version might fix this? Gravity warps space to contract it, and random
inertial escape is a matching dewarping effect. It causes the paths of
spacetime to diverge slightly faster than they can converge.
This would be like the standard Boltzmann "gas in a box" model, but
with gravity making for a dynamic container. The box would grow at a
steady rate over time - approaching the equillibrium point where the
tendency of gas molecules to depart the space would be exactly matched
by their tendency to move back in.
Cheers - John McCrone
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