Fractals, entropy and probabilities.

[TheRedshiftRider]

Hello everyone,

I was reading some articles about time and entropy and there were some things I was thinking about and I still cant find the right answers. So I will try to explain the problems and I hope some of you can helpl me to solve them and maybe give me some other ideas.



The first thing I was thinking about is this:

I read an article about entropy it explained how entropy works and how the universe could have been created and also how another one could be created out of another. According to the second law of thermodynamics entropy increases after time continues. So the chaos increases and also the number of possible combinations. So every universe or something else like a cup of tea with milk in it starts with a state without chaos. After some time  most of the particles move a bit and the number of combinations changes.

So we still dont know how the universe is created. There is a theory about that a new universe can be created out of another but: if a universe has to be created the same way, it has to start in the same state of entropy. And we still dont know how that should happen.


I thought about this and I realized that fractals work allmost the same as the whole system of entropy:

It starts with a simple shape (This can be compared with the stat of the start of the universe). After calculating the formula several time the shape of the fractal becomes more complex (the same way entropy increases over time). And after repeating this a number of times a smaller version is created out of the fractal, that smaller version also starts with a simple shape and becomes more complex after more iterations (think about multiversus). So I think that could actually be a solution to the problem.

And the same as every particle in the cup of tea, every calculation of a pixel in a fractal is following a path through the fractal.



The second things I was thinking about was this:


We all learned at school about fractional numbers. They are very simple:

1/2

-The first number of a fration is the number of observations of a certain thing in a thing that contains more than one of those things.

-The second number is the number of the maximum time you can find those things in one thing.


If the first number is as big as the other it means that all things are found in the the whole thing.
If the first number is bigger than the second number it mostly means that there are more than on parts than the maximum so there are more than one parts with smaller parts in it, for example:


1/2 only on half of the thing is found.

3/2 This isnt possible so we need to make it possible by creating a whole new thing: 2/2+1/2



But I was thinking about the way this system works if infinity is used in it:

I heard some people say that infinity can be bigger than itself. So if you use infinity in fractions you will get a few problems:

First you will never find all results.


And the second problem:

If infinity can be bigger than itself you can get a fraction like this:

∞(bigger version)/∞(smaller version)

This is an impossible fraction.

And because infinity isnt a thing we can see completely it is possible in things that repeat eternally. So could this be a problem?




I hope I was able to explain my theories. And I hope some people can help me with these problems.



Toof
  __

[kram1032]

You have a bit of a wrong notion of Entropy there. - Most people have.

First of all, Entropy is a statistical effect. As such, systems of only few particles pretty much do not obey it.
Thus, if the universe started "infinitely compressed", it would have been pretty much like a single particle and, as such, wouldn't really have been affected by entropy at all. Instead, it would have been subject to quantum fluctuations which, at the tiny scale everything once was, would have been incredibly high. These fluctuations likely are what started the expansion.

Second, take two cups of milk that have the same number of particles in them, the same volume, the same shape and stand in the same room with equal temperature everywhere.
Those two cups of milk do not see any increase in entropy. The number of combination is equal in them.
Now, if you cool one of them down, you constrain the movement of individual milk molecules. Eventually, it'll freeze, e.g. build solid crystals. These solid structures are very limited in the way they can move. They are lower entropy than the other glass of milk. There are only so many ways in which crystals can be formed.
If you, instead, heat the milk up, it will eventually start to boil. This gas is a new state which adds possible configurations. Things suddenly can be more apart while, before, they had to be tightly packed together. In liquids, there are weak bonds between neighbouring molecules. They can easily be moved around but there is a small force preventing them to split up (surface tension) which reduces the possible configurations. In a gas, basically everything is possible, as long as the individual atoms are kept intact. In a plasma you go up a step. Here, electrons are no longer bound to atomic cores, so they move freely. There no longer are molecules. Way more ways in which electrons and atomic cores can be arranged are now available. And if you go even further, eventually even the cores break apart and you get a quark-gluon-plasma, where individual quarks are no longer bound to each other. Even more possible configurations now exist.

Entropy only has to increase for a whole system. Locally, it can decrease. - that happened in the frozen milk. To cool down something, you need to warm up something else. Air Conditioning works that way: It "pumps" heat out of one system, into another. That's why the stream of air that typically goes outside is actually rather hot. It increases the entropy in the world while cooling a room, reducing its entropy.

The often-mentioned analogy of sheep initially starting in a corner of a field and then spreading out is a bit flawed.

This would only be correct, if the sheep first are fenced off to only have a tiny space. They can't move around easily, they need to squeeze past each other.
Then, if the fence is removed, they can spread over a far wider area, they stand in more different configurations.

If, instead, you never have a fence, and the sheep happen to stand close to each other, that's just one of the possible configurations.

Decreasing Volume, increasing particle count or decreasing average particle speed all reduce entropy. (More, slower sheep in a smaller volume can't find as many possible ways to stand) The opposite things increase entropy.

Changing none of those variables keeps entropy on the same level. The glass of milk doesn't suddenly have an increase in entropy while it sits in that room at equilibrium.

[jehovajah]

There are a lot of misconceptions about entropy so I pretty much think it is not a very useful idea! I prefer the total Enthalpy of a system. This does not disconnect a system from its ignored surroundings. Especially if the surroundings are infinite in relation to the focus system, that is  it is unbounded!

To scale up a focus system to describe an unbounded universe is clearly not meaningful, but to consider a focus system in relation to its surroundings is, because the boundary then mediates the behaviours within the focus system.

Now if we distribute these kinds of systems fractally, and define that distribution as space, we get a complex structure which we can only know locally, but can make analogies of that knowledge at different scales.

What we leave out is often more important than what we keep in a system!

[Tglad]

It really is a very useful idea... it is of great importance across many fields of physics, and other sciences... plus used in mathematics and information theory. In fact a type of fractal dimension (called the information dimension) measures scaling of the entropy of an object, so it is useful in fractal theory too.

Toofgib, I like your first thought. If you imagine iterations as time then the 'universe' is created simple and gets more complex and spawns little baby universes (black holes?) that also start off simple.

Your second thought hard to comprehend... but there are millions of posts on forums about people who try to do algebra with infinities and get unlikely results. The fact is you can't just treat infinity as a number and expect normal results from algebraic expressions.

[jehovajah]

Granted Tglad!

However to clarify my point: it is not a very useful idea in the description of heat exchange where it was originally employed.

The specific heat concept on which it is based is a very useful material property and can help identify a material. In this regard it's entropic behaviour may be a useful distinguisher, but to derive a law from it is in my mind a false step. Entropy goes backwards as is well known, thus to maintain the law the external system has to be included. In which case it merely indicates that the original specification was not sufficient to uphold the "law". This is precisely where the Enthalpy of a system takes over, making you wonder why you wasted your time calculating the entropy!

If, now I recast entropy as a change in the specific heat per general surrounding energy transfer ( whether rate or some pressure/ density measure) then it falls in line with the general enthalpic description of a system making any reference to " order" unnecessary.

The analogy to the combinatorial or permutational freedom in a information message has more to do with the Gauss Boltzmann Maxwell distribution or the binomial distribution than with any "disorder" notion of entropy in my opinion.

[youhn]

@Toofgib
Many see entropy as a measure for the amount of order/chaos. Though this is vastly oversimplified, it can be of some use. You state that in order for two universes to be the samen, they should start with the same entropy. The other way around might not be true. I can image two baby universes with the same amount of order, but still different shapes. These universes would be very similar, if looked from a distance (read: sum up and average all local values). Differences will be visible when zooming in to the local scale. The "roughness" would be the same, but the shapes aint.

Infinite is not a thing, but a concept. I wonder if it is correct to state there can be a smaller and bigger version of infinity. Of couse, you can always add 1 to it ...  but the concept stay exactly the same. I think per definition ∞/∞ = 1.

@jehovajah
I see you're busy with laws. What would be your definition of a law. Do you think a physical law and a statistical law are basically the same?

[TheRedshiftRider]

Ok, thanks for your replies, I actually only thought about the way particles can move, if i think about all other things it gets a little bit more complex.

[youhn]

Up, down, left and right. Or did you mean spin ... ?

 

$%#@ ... of course forget the most obvious forwards and backwards ...