Lumpiness & Disorder: A Physics Comparison

[andresordonez]

Hi, first of all I have to say that I know practically nothing about cosmology, though I know some basic physics.

The reason for this post is that while reading "A brief history of time" by S. Hawking, he mentions in some parts of the book that a lumpy universe corresponds to a disordered state, and a smooth universe correspond to an ordered state.

"But it could equally well have started out in a very lumpy and disordered state. In that case, the universe would already be in a state of complete disorder, so disorder could not increase with time."

"The universe would have started in a smooth and ordered state, and would become lumpy and disordered as time went on."

I think this is wrong, using the same analogy of the cup of water in a table that is used in the book

"Imagine a cup of water falling off a table and breaking into pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or backward. If you run it backward you will see the pieces suddenly gather themselves together off the floor and jump back to form a whole cup on the table."

it's easy to see that the cup of water on the table corresponds to an ordered state and the broken cup corresponds to a disordered state. Now, as I see it, the cup on the table is lumpier than the the broken cup, so the ordered state corresponds to the lumpy state, and the disordered state corresponds to the not so lumpy (smooth) state, and not vice-versa.

I think this would be a significant conceptual error, and it seems to me that he draws some conclusions about this. I just want to know if my reasoning is correct, and if I'm right, how much does this affect the ideas developed in the book.

PS: I know a lot has changed since this book was written and I should not consider this book as a very serious reference in cosmology.
If you see anything wrong with my English, please let me know.

 

[bcrowell]

The correlation between lumpiness and entropy depends on the type of force. For a box full of gas molecules, which interact with one another repulsively, the maximum-entropy state is smooth. For an attractive interaction like Newtonian gravity, the maximum-entropy state is one in which all the mass is clumped at one point.

The correct definition and interpretation of entropy in general relativity is not completely well understood. A maximum-entropy cosmological state would probably be dominated by gravitational waves, not by matter.

 

[andresordonez]

"The correlation between lumpiness and entropy depends on the type of force"

Thanks for your answer. That pretty much changes everything. Very interesting fact by the way.