I wrote some weeks ago about the basic concepts behind
entropy and the arrow of time. It also conveniently served as test of
MathJax. If you have a blog or website where you want to show some equations, you can apply MathJax with a short string of html code, and voila, nice clean LaTeX typesetting becomes available!
Okay, enough advertising and let's get on with it. The two main reasons I wrote about entropy last time, is because 1. it is one of the most fascinating concepts in all of physics and 2. there are some fairly recent studies I wish to write about, and one needs to understand some basics before I go deeper into those.
There was this one study that was circulated widely in popular science channels, which got hyped into the form: "scientists reversed the arrow of time!" Spoiler alert, no they didn't.
I'm not saying that what the group did wasn't seriously cool and a great advancement, it's just that they didn't do what it said in the headlines.
Let's start from what they did do in the study. The group prepared two particles that had a correlated initial state. Then, they observed what happens when one of the particles is hotter than the other. The incredible finding was that, when the two particles have some specific initial correlations, the hot one gets hotter and the cold one gets colder (just like theory predicts).
What should you expect when two bodies exchange heat? Every schoolkid knows, that the hotter one gets cooler and the cold one gets warmer, which maximizes entropy (as I wrote
here).
And if the arrow of time always points toward larger entropy, then that direction is obviously reversed when heat flows from cold to hot, right? Well, not exactly.
The important part here is that the team prepared the two particles in a correlated state, so that they affect each other. For example, one can have a type of correlation that when particle A has spin up (\( \uparrow \)), then particle B always has spin down (\( \downarrow \)), and vice versa. This is called a perfectly anticorrelated state.
But do you remember what was one of the important assumptions we made in deriving the mathematical formula for entropy? It was that all microstates have equal probability to occur. So if you have two uncorrelated particles, then we have four equally probable microstates: (\( \uparrow \uparrow \)), (\( \downarrow \uparrow \)), (\( \uparrow \downarrow \)), (\( \downarrow \downarrow \)), meaning that there are three possible macrostates when the particles are indistinguishable.
But what about perfectly anticorrelated particles? They have only one possible macrostate, descibed by the two possible microstates (\( \downarrow \uparrow \)) and (\( \uparrow \downarrow \)). I dunno about you, but if I had particles like these, I would expect to find them from that one allowed macrostate. That state is the one with the highest entropy (obviously), and thus the arrow of time points towards it.
This effect was hypothesized decades ago, and said to lead to an apparent reduction in entropy and the reversal of the arrow of time. But this is only apparent, since the system still marches towards the highest entropy state.
Once the initial correlation has some time to decohere, the two particles are no longer dependent on each other and it is business as usual. Heat will flow towards colder bodies and the apparent disturbance in the second law of thermodynamics goes away. Though it was never actually disturbed, the state of highest entropy just changed.
A better headline would have been "scientists shifted the state of highest entropy to create an apparent reversal of the arrow of time!" A real reversal of the arrow of time would be to somehow make it point towards the state with the lowest entropy. And I highly doubt that will ever be possible.
Of course, having quantum systems with initial correlations between the particles that exchange heat is a highly abnormal situation and seriously cool. But if someone says that such systems reverse the direction of the arrow of time, well, then they are just wrong.
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