Does time's arrow define time?
And discussion about the nano magnet brownian motion order from disorder entropy paradox
Consider a bunch of nano magnets held together in a clump. A small asteroid hits the clump of magnets and breaks them
apart (high entropy). Over time, the nano magnets vibrate due to brownian motion and when they randomly come near each
other they clump together again (low entropy). Random brownian motion of nano magnets can cause them to go into their
clump once again, even though they were broken apart into a high entropy state.
Or instead of the asteroid let's just consider vigorously stirring the nano magnets or blenderizing them to create a
high entropy suspension of nano magnets in a somewhat viscous fluid. If the fluid is not too viscous there will be
enough brownian motion that the high entropy nano magnets will eventually clump back together over time...
A classic example books use to describe entropy is an egg breaking apart and not coming back together
again. The egg shell peices get scattered when it breaks. Consider if egg shells had nano magnets embedded in them, so
that when you break apart an egg shell it sticks back together again if it comes near another egg shell peice. The wind blows an empty hollow egg off the table and it
breaks apart the shell. The wind blows the broken pieces around randomly, and voila - over time, the broken egg shells
clump together again in a low entropy state if they randomly blow in the wind and come near each other. However, once
they clump together again, they don't necessarily end up in the exact same configuration as the original egg shell -
they may just end up as a clump of shells piled together, without forming a oval egg. However the pile of magnetic
egg shells may form some kind of beautiful artistic piece or something that looks like one of the alphabets, or a
Clumped together egg shell peices are low entropy compared to scattered ones. Did we reverse time? No we
just had egg shells form a low entropy clump without going back to their original low entropy oval shape. Just
because the eggs clump together not in a perfect oval doesn't mean it isn't low entropy: it's just a different
configuration of information, and still low entropy.
Hence why I don't think the second law is as much tied to time as people think. More importantly information configuration
is deeply related to time. Even if the second law weren't true in many situations, time would still exist since low entropy
states can be reconfigured to be a different state than before (different configuration of information). You can still go
back to a low entropy state without it being the same low entropy state as before! The information configuration is simply
different. Consider the word jumble "dog" which becomes "god". Which is more ordered, the word dog, or god? Dog and god words
are both about the same low entropy, they are just reconfigurations of the information (forgive me for using this example, as
this website is not intended to promote the belief in your dog - I am non religious).
Another strange issue with information
is that entropy could be partly subjective: a non english speaking person may not even know what a dog is, and therefore the
information to them is high entropy as it is just scrambled symbols (consider an alien reading a web page, who doesn't even
use the same letters as humans - the internet information to an alien would be high entropy scrambled jibber jabber, although
he may detect some ordered patterns even if he can't understand what the symbols mean. Even if he sees some order, it is not
as ordered to the alien as it is to a human - is information/entropy subjective, or ultimately objective?).
I think the arrow of time is tied to Information configuration, not entropy in general. Information is related to entropy, but
it's an important distinction. If the second law were violated (hypothetical) you can lower the entropy of the entire universe
to the same low entropy as the big bang state, but have a different configuration of the particles in different locations than
before (but still a low entropy state just as low as before, but a different order or configuration of the items or information).
With the blenderized nano magnets becoming ordered again due to brownian motion (not energy input, brownian motion is free) this
is a paradox because brownian motion should randomize everything, not clump things together. One could argue that you had to
add energy to the system in order to blenderize/randomize the nano magnets first. But this is like arguing that if you
blenderized sugar or salt particles, you are adding energy to make them higher entropy, therefore they should clump together
again when you dump them in water? The only way salt or sugar would clump together if you added energy once again to the system,
to evaporate the water and let the sugar/salt crystallize once again. Whereas with the nano magnets you don't need to add energy
again for them to clump back together, the random brownian motion does the work for you and the magnets clump together
automatically over time without energy input. The nano magnets would not all instantly clump back together, as random
brownian motion does take a lot of time in order to do anything specific with nano magnets.
Another paradox is it takes energy to make things high entropy (not just low entropy). Consider rolling dice: this takes
quite a bit of energy to shuffle and throw the dice. Compare this to brownian motion, which randomizes things for free (but
it doesn't maximally randomize things as much as it could, see my other articles on "container information theory"). If
brownian motion creates a free random number generator, is this not a machine? In computer programs it takes energy (cpu
outputs heat) to create a random number generator. In brownian motion, the machine is created for you at no expense of energy).
Although this is interesting (since the second law doesn't allow one to make machines at no cost) it's not as interesting
as thinking about the blenderized nano magnet paradox where random brownian motion creates ordered clumps, at no cost of
energy (order from chaos?).
Macroscopic magnets will also clump together but they are a bit different since when they collide with each other, heat is
given off. In the case of nano scopic magnets, if any heat is given off when nano magnets collide, this heat recycles back
into the system perfectly to cause more brownian motion, clumping more magnets together (the heat isn't lost, it recycles back
into more brownian motion causing more chance that the magnets will come near each other and become ordered, since more brownian
motion increases the probability that two nano magnets will come near each other). Therefore the microscopic world is quite
different than the macroscopic world, and more paradoxes occur mesoscopically or nanoscopically.
You can see a video I made with my microscope of
nano magnets clumping together into a low entropy state due to random
vibrations of brownian motion. If random motion can create ordered clumps, is this a paradox to the second law? Over time,
nano magnets should tend to go toward maximum disorder or highest entropy. But when nano magnets collide from random brownian
motion, they go into low entropy clumps, not high entropy ones. In order for the magnets to be in this low entropy state,
did the universe spend way more energy at some other point in time (during the big bang) to create the magnetism in the first
place? But magnets can be reused... over and over, so if an asteroid kept hitting a clump of nano magnets and putting it
into high entropy state, the magnets would clump back together over time due to brownian motion (assuming the magnets
were in a container close enough together). Or instead of the asteroid analogy, think about blenderizing nano magnets
utterly randomly. After time, brownian motion causes them to go into a low entropy clump if you let the fluid rest at
room temperature, as long as the nano magnets were in a container (related: container information theory). It would be like
dice always rolling six no matter how much you try to make the dice roll random numbers by shuffling the dice.
Related also is the milk demon potential second law violating device which uses
gravity and randomness to extract energy from directed motion. Are magnetism and gravity (forces) a key to putting structure
into randomness (order into disorder) without expending energy? But what about
viscosity, not just magnetism, and what about