What would represent a a universe with almost the most entropy possible? Would it be uniformly spread matter, like an ink drop in a bathtub?
There is a name for the theoretical maximum amount of entropy that a given
volume of space may contain. It is called the Beckenstein Bound, and is defined
as S<=2πER, where S=entropy, E=energy contained in a given region, and R=the radius
of the region. It also happens that the Beckenstein Bound also corresponds to the radius of
a black hole event horizon. This may seem surprising at first, but after some though it makes
sense that a black hole represents a region which contains the maximum amount of entropy
possible for a given unit of space.
What is truly surprising to physicists is that this relation implies that the maximum entropy
that a region can contain is proportional to the surface area of the space, not its volume!
There is still much controversy about what this really means, but it is quite an interesting topic.
What would this look like? It actually depends on the density of the matter and energy contained
in the given volume. A small area of space containing maximal entropy would have all particles
contained within it traveling at the speed of light, this level of kinetic energy known as the
Planck energy. This much energy contained in a small volume automatically curves space
to the point of generating a
black hole, so of course we cannot see inside it. A sort of ‘cosmic censorship’.
A sufficiently large area of space, however, with lower energy density could look completely different. As you surmise, the matter within it would simply need to be evenly distributed. If it
has maximum energy, then everything would still be traveling at c, but if separated by enough
space we could observe that it is randomly distributed everywhere. There may be random
agglomerations of material that are fleeting, but no long lasting large accumulations would be
allowed. The fundamental forces,( gravity, electromagnetism, etc.), would have no observable
effects because maximal entropy and energy would overcome the ability of any force to organize
matter.
Interesting stuff to think about~
There is a name for the theoretical maximum amount of entropy that a given
volume of space may contain. It is called the Beckenstein Bound, and is defined
as S<=2πER, where S=entropy, E=energy contained in a given region, and R=the radius
of the region. It also happens that the Beckenstein Bound also corresponds to the radius of
a black hole event horizon. This may seem surprising at first, but after some though it makes
sense that a black hole represents a region which contains the maximum amount of entropy
possible for a given unit of space.
What is truly surprising to physicists is that this relation implies that the maximum entropy
that a region can contain is proportional to the surface area of the space, not its volume!
There is still much controversy about what this really means, but it is quite an interesting topic.
What would this look like? It actually depends on the density of the matter and energy contained
in the given volume. A small area of space containing maximal entropy would have all particles
contained within it traveling at the speed of light, this level of kinetic energy known as the
Planck energy. This much energy contained in a small volume automatically curves space
to the point of generating a
black hole, so of course we cannot see inside it. A sort of ‘cosmic censorship’.
A sufficiently large area of space, however, with lower energy density could look completely different. As you surmise, the matter within it would simply need to be evenly distributed. If it
has maximum energy, then everything would still be traveling at c, but if separated by enough
space we could observe that it is randomly distributed everywhere. There may be random
agglomerations of material that are fleeting, but no long lasting large accumulations would be
allowed. The fundamental forces,( gravity, electromagnetism, etc.), would have no observable
effects because maximal entropy and energy would overcome the ability of any force to organize
matter.
Interesting stuff to think about~
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