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Time/Information Flow

[Information/Time Flow]

What makes time go forward? Or rather, what makes us go forward in time? Why can’t we remember the past? This seems a silly question for people but it really is a fundamental question at the center of physics (though it isn’t phrased so beautifully). Put simply, the laws of physics work equally well forward and backward in time. There is nothing preventing you from literally reversing the direction (and velocity) of every single little piece of that shattered wine glass and watch it reassemble. But we only ever observe rooms get messier or cream mix into our cups, never the other way around (unless we put in the work). This forward flow of time is frequently attributed to the second law of thermodynamics, and the principle that entropy is always increasing. In other words, things get more disordered.

Side note: Microsoft’s Project Tuva is a highly recommended set of lectures delivered by Richard Feynman (my favorite thinker ever) to a general audience about generally awesome stuff in physics. Again, its meant for a general audience and so is very approachable. Amongst these awesome talks is Lecture 5: The Distinction of Past and Future where Feynman does what he does best, and take you on a journey through some of physics deepest and most beautiful concepts with astounding clarity. I can’t recommend the entire series of lectures anymore!

And finally, onto the Quanta article: “Times Arrow Traced to Quantum Source”. The article explains recent work by quantum theorists linking “the tendency for systems to reach equilibrium” (aka the flow of time) to quantum entanglement - that thing Einstein famously called “spooky action at a distance”. Before diving into it, Ill give my One Sentence Summary (OSS): Systems reach equilibrium because their state becomes entangled with that of its surrounding system - the information about its state “diffuses” out and becomes part of the state of the system.

Whoa! So at this point, we need to clarify (or rather make sure the article does/did and we understand them):

  • What is entanglement? (explain to me like I’m not a theoretical physics PhD please)
  • Where does information come into play and how does it diffuse?

There is an interesting back story to this recent work worth mentioning. Yet another of my favorite scientists is Seth Lloyd. His PhD thesis was awesomely named “Black Holes, Demons and the Loss of Coherence: How complex systems get information and what they do with it”. I had come across this previously and added it to the reading list and haven’t gotten to it yet (PhD theses are long!). Turns out, that very same thesis was the first to conceptually think about the flow of time this way but the world wasn’t ready! It wasn’t well received and as Lloyd says “I was darn close to driving a taxicab”. I can only assume this is because quantum information theory wasn’t as studied or accepted, and even now the article says Lloyd uses an “obscure approach to quantum mechanics”. Either way the new work builds directly off of his much earlier work! Its so interesting (and reassuring) to find his thesis come back up again with such a splash!

Back to our questions: “What is entanglement?” The article does an ok job explaining it for a general audience needing to understand the article so lets start there: “An elementary particle lacks definite physical properties and is defined only by probabilities of being in various states. For example, at a particular moment, a particle might have a 50 percent chance of spinning clockwise and a 50 percent chance of spinning counterclockwise…When two particles interact, they can no longer even be described by their own, independently evolving probabilities, called “pure states”. Instead, they become entangled components of a more complicated probability distribution that describes both particles together… The system as a whole is in a pure state, but the state of each individual particle is “mixed” with that of its acquaintance.” Gross oversimplification, but hey thats how I communicate: science fast and dirty.

Before getting to the next question its worth saying something about the nature of probability and quantum mechanics. Let me first say that I can’t recommend E.T. Jaynes “Probability Theory: The Logic of Science” anymore! He puts forth the foundations of probability as an extension of logic. We use probability as a representation of our incomplete knowledge, and use its rules to logically make decisions despite this incomplete knowledge. This viewpoint is very different then the feel we all get for probability being some mechanical extension of “odds” that we learn in school. And yet here we were just presented with an explanation of entanglement where probability is not a reflection of our lack of information about the particles state. Instead, it is a fundamental limit of what we can know. Or rather, it isn’t that the particle is indeed in one state or another and we just use these probabilities to reason when we don’t know. Its that the particle is actually in a super position of those states and it doesn’t “make up its mind” until we actually perform a measurement! Whoa! This topic deserves a whole other post and will certainly get one! I just wanted to mark it down here so we have something to think about!

So what about information? Well we can use the quantum information theoretic language to represent the “state” of a cup of coffee. Imagine representing each atom by a collection of 1s and 0s, specifying its momentum, spin, location, etc. Then we can describe its evolution in time as a changing stream of 1s and 0s. Using this framework, Lloyd “found that as the particles became increasingly entangled with one another, the information that originally described them would shift to describe the system of entangled particles as a whole. It was as though the particles gradually lost their individual autonomy and became pawns of the collective state. Eventually, the correlations contained all the information, and the individual particles contained none. At that point, Lloyd discovered, particles arrived at a state of equilibrium, and their states stopped changing, like coffee that has cooled to room temperature.” As one system becomes entangled with another, the information about its state leaks out and smears into the rest of the environment. We call this equilibrium!

Researchers will continue to expand on this viewpoint and many more interesting developments await! Until then, I leave you with his even better OSS: “The arrow of time is an arrow of increasing correlations.” - Lloyd

Further Resources

Note: This post (and most of the ones to follow) is a combination of paraphrasing, copy/pasting, and my own thoughts/questions.

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