?If black holes are the result of the density of matter, wouldn't that
mean that the big bang theory and black holes are mutually exclusive??
That depends upon what you mean by ?exclusive?. A theory typically
will be relevant only within some constrained domain of conditions.
That is to say, there are no good theories in hand which are expected
to be perfectly reliable under all conceivable conditions. Theories
are inspired by questions asked of specific circumstances. It?s true
that the best theories are useful over as large a spectrum of
conditions as possible, but there are none which cover all conditions.
Such a theory would be the proverbial theory of everything, which no
one has.
So, there are some very useful theories which are also, in
principle, incompatible with each other. The most notorious example is
that of general relativity with quantum mechanics. Thus far, if one
attempts to extend one too far into the other?s definitive territory,
the results tend to be very suspicious. One (or both) of these
theories is incomplete. But, by sticking to the domain of a theory,
very valid & reliable results can be had. So, even though GR & QM are
?mutually? exclusive (sometimes), they?re still spectacularly good
theories, validated experimentally to high precision.
So suppose that big bang theory & black hole theory are
incompatible. (They aren?t, but let?s suppose so for the sake of
argument.) It wouldn?t necessarily mean that neither theory is good.
It could mean that there are limits to their respective domains, the
breadth of circumstances within which they yield meaningful results.
Indeed, all that big bang theory amounts to is ?The body of evidence
indicates that the observable universe is undergoing an approximately
uniform expansion.? All that black hole theory amounts to is ?If you
pack a mass within a boundary at which said mass?s escape velocity
exceeds the speed of light, then it?ll be trapped within that boundary
by the non-exceedability of the speed of light.? Each of these is
internally consistent. If it were indisputably demonstrated that one
contradicts the other, it?s more likely that this would just place
constraints upon the domain of one or the other. (In fact, big bang
cosmology already does have constraints on it, emplaced by the fact
that no theories in hand give meaningful results for the universe
before about t = 10^-42 second.)
?Also, if the density of matter that causes black holes is so high, how
can we possibly know how much gravity is required to cause black holes
to form at the centers of galaxies??
The density required is a straightforward calculation. Useful
insight can be gotten by way of Newtonian theory. Newton?s generic
force law is
F = ma
m = mass
F = the force upon m
a = the acceleration (change in velocity) of m, due to F.
Newton?s gravity is given by
F = GMm/r^2
M = mass 1
M = mass 2
F = the force between M & m
R = the radius (distance) between the mass-centers of M & m
G = the gravitational constant, which simply calibrates the magnitude
of force in relation to the units used.
So, as I stand here, both Earth & I are being pressed together by
our mutual gravitational force. We are accelerated toward each other.
The magnitude of that acceleration is due to the values of M & m, and
the distance between our individual mass-centers. My mass-center is
perhaps somewhere in my gut, and Earth?s is roughly 4,000 miles away
from mine, between me & Australia. If I were to climb to the top of a
skyscraper, r would be even greater, F would be smaller, and my
acceleration downward would also be smaller. But for whatever value of
r, there?s a value for escape velocity, the initial velocity required
which will carry me away from Earth, on a free-fall trajectory, never
to return. If, for a given combination of plugged-in values for the
variables, the escape velocity at Earth?s surface is less than the
speed of light, then it?ll be possible in principle to escape from
Earth, as is the case now for the real Earth. Suppose however that I
squash Earth, compressing it to some arbitrarily small radius. I might
then reduce the planet?s radius to the point at which, for the given
values of M & m, r will imply a force so great as to require an escape
velocity in excess of the speed of light. That value of r is directly
calculable, and from it the volume of Earth under this condition is
easily computed from the formula for the volume of a sphere, V =
4r^3pi/3. Mass-density is then just M/V.
?Have particle accelerators given
us enough knowledge about the makeup of particles in order to figure
that out? If we've never built a particle accelerator capable of
creating a black hole, how can we know enough about matter at that
level to make predictions about black hole formation?
If the density of mass of a tiny black hole is a deformation in
spacetime then wouldn't that mean that we're still talking about
gravity? I didn't think we knew much about quantum-scale gravity.?
Gravity on extremely small scales isn?t yet known experimentally.
This takes us back to the inherent limits of a theory. Black hole
theory is currently a direct offshoot of GR, and GR is a theory of a
continuum, which is ultimately a classical approximation. |