“Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way…” – Henry Poincare
In Part I of “All About Entropy” we’ve delved some into the standard thermodynamics definition of entropy. Part II shall was about a different yet similar in many ways type of entropy introduced by information theory founder Claude Shannon.
Although it had the feeling of somewhat disconnected from the previous part, it was shoen that “All About Entropy…” connects the dots perfectly through a silk thread.
Again, I am not in any way a renowned expert on the subject (far from it…😉 ), so no post will by no means be all encompassing (you can get that from very in-depth academic resources…), nor it is intended to be such…
I therefore have no thought that this blog might be a benefit to all others, I wrote it only to sustain my understanding.
I hope for the essence to be captured, and even more so communicated…✨✨✨
It would be very incomprehensible (at least for the most if we could be born old and be able to shift our lifes back and forth into our childhood, our adolescents, throw our self to actual days where we felt fully in love, or simply live our best experience over and over without walking into a place we all know as the future. It is somewhat a day dream or narrative that we all took upon ourselves at one point or time: “what if I had done that, and keep playing a movie of a parallel existence”, or “what if I had said and acted the right words, followed by the correct actions” and try to re-live the happy ever after till death do us part in our imaginary, yet beautiful thoughts…
There is an obvious reason why reversing the relative arrow of time is such an effecting and comforting tool of our imagination: in the actual, non imaginary world it never happens.
There is the arrow I’ve hinted for, and this arrow is that of time pointing from the past to the future, and reluctantly, or maybe luckily it points to the same direction for all of us.
Some Obvious Examples for The Functioning of The arrow of Tine
Lets say that we are watching a movie (most of us love a good movie every now and then. The choice of the janer is up for grabs 😊). If by any case we were to decide to decide to run the movie in reverse it owuld be most clear that the physical reality being watched is advancing very peculiar, and noticeable to all watchers that it is running in an “unccaptable” way. Yet a different example is at a dinner table, when a glass filled with red wine is pushed gently from the table and to the wooden flor, its wine soaking in a rare and beautiful carpet and the thin glass of wine breaks into tiny little pieces of glass. Now if by which the wine is re-soaked by a sudden realization we would happen to see the aromatic wine extracts gently the luxury carpet, the pieces of the glass simply attach while at the immediate following short moment the aromatic wine was to exactly fill the the gentle glass cup while jumping back to its former place on the table before gently pushed. I would have find myself amazed if all of us were convincing that what happened could even be deemed as remarkable…
The Essence of The Arrow of Time and Irreversible Processes
It turns out that most all events we come across in our daily life always happen in a characterized same order. The pain seem to come before the slap, yet not the other way around, we pour and mix milk in our coffee, yet never seem to collect it to back to the milk carton post mixing… Physics has came to a word for such sequences described: Irreversible Processes.
It is not that we can not use our extraordinary imagination, shut unwantedly some of the parts of brain and perform magic (we do, It’s bee proven in fMRI imaging), but as far as our not imaginary collective comprehension of physics as we became to know it quite good, events happened in some sequence, and Irreversible processes are in the core of the arrow of time. Events shall happen in some in some sequences, and (almost – and this is important), and not in others.
Moreover, this line of sequence of events is not secluded to gentle wine glasses and backwards forwarding movies, but to the entire universe (biggggg place… 😎). Even if we you shall find a planet occupied by advanced intelligent green (we like the to be green… 😉), we would not expect them to separate their green milk stirred in their green cup coffee right back to their green milk carton with some additive swirling of their green spoon… And why is that not surprising? The universe is incomprehensively huge. Why would not a distinct far may own a very different form of sequencing? gee well, they just don’t. As far as certain kinds of processes are concerned, complicated forms and actions, with lots of individual lego parts – there is ascertain allowed of fabricated order inherent to our worlds. It might be somewhat puzzling, but for certain types of processes – the kind which involve complicated actions with lots of individual metaphorical “lego parts” – there seem to be an allowed order built into the fabric of our realization. There is no denial (and actually, maybe besides some unimportant fringe) The answer lies in the concept of entropy. Like energy or temperature, entropy tells us something about the particular state of a physical system; specifically, it measures how disorderly the system is. A collection of deck of a neatly set of cards stacked neatly on top of one another has a low entropy; the same collection, scattered haphazardly on a desktop, has a high entropy. And about that regular or green entropy of a cup of coffee along with a separate teaspoon of milk is low, because there is a particular orderly segregation of the molecules into “milk” and “coffee”. while the entropy of the two mixed together (whether our earthly one or that one from our green found planet) is comparatively large.
All of the irreversible processes that reflect time’s arrow – we can turn eggs and ingredients by preparing a Shaksuka dish but not our Shaksuka to its separated ingredients. ice cubes in water melt but
glasses of warm water don’t spontaneously form ice cubes. All of them share a common feature entropy increases throughout, as the system progresses from order to disorder. When-
ever we disturb the universe, we tend to increase its entropy.
Nature’s most reliable law
“If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation…” – Sir Arthur Eddington
The principle underlying irreversible processes is summed up in the second law of thermodynamics: the entropy of an isolated system either remains constant or increases with time. The second law is arguably the most dependable law in all of physics. If you were asked to predict what currently accepted principles of physics would still be considered inviolate a thousand years from now, the second law would be a good bet.
Our modern understanding of entropy was developed in 1877 by Ludwig Boltzmann, who was one of the few physicists at the time who believed in the existence of atoms. Boltzmann realized that when we look at some macroscopic system, we cerainly don’t keep track of the exact properties of every single atom.
it is interesting to note that no atom was to be found by a microscopic research or any way otherwise by then (read post: All About Entropy… – Part I – Beginnings). A purified example to to illustrate that would be by example:
If we have a glass of water in front of us, and someone takes the secret initiative switche some of the water molecules around without changing the overall temperature and density and so on, we would never notice. There are many different arrangements of particular atoms that are indistinguishable from our macroscopic perspective (my best illustration in a fully rounded post, is to regard the concept of emergent properties: Some Fundamental Thoughts About Emergent Theories…).
And then Boltzmann noticed that low-entropy objects are more delicate with respect to such rearrangements. If you have an egg, and start exchanging bits of the yolk with bits of the egg white, pretty soon you will notice. The situations that we characterize as “low entropy” seem to be
easily disturbed by rearranging the atoms within them, while “high-entropy” ones are able to keep evolving.
Boltzmann took the concept of entropy, which had previously been defined by a rough grained, albeit quite correct measure of the uselessness of an object’s energy content, and redefined it in terms of a : entropy is a measure of the number of particular microscopic arrangements of atoms that appear indistinguishable from a macroscopic perspective, relying somewhat unknowingly (but who am I to judge… 🦝).
It would be difficult to underestimate the importance of Boltzmann insight. Before Boltzmann, entropy was a phenomenological thermodynamic concept, which followed the second law of thermodynamics. After Boltzmann, the behavior of entropy could be derived from deeper underlying lower level principles. Suddenly it made perfect sense why entropy tends to increase in an isolated system and its because there are more ways to be high entropy than to be low entropy.
This line of thinking becomes larger than life in its revelation. Just imagine this Physicals theoretical description and its strong reliance on entropy in accordance with Boltzmann’s line of thought:
If we start with a system that has a high entropy, we’ll be in equilibrium—no reason for anything to happen. It seems that the asymmetry in time, is manifested by privileging earlier times over later ones. This Boltzmann based line of reasoning takes us all the way back to the very low entropy that had to be around aמ establishing occurrence such as that of the initialization of our universe such as the maitiest “Big Bang”. For whatever reason, of the many ways we could arrange the premortial building blocks of the universe, at early times as if they they were in a very special, low-entropy configuration. Absolutely mind boggling!!
Living with entropy
All of the above is indeed very mind boggling and very fascinating for the field of theoretical physics, but as it seems, this octopus named entropy impacts us in more than many ways. Far beyond steam engines and cups of coffee (also those drank by green people… 😉), The arrow of time is an is a very capable octopus which touches simultaneously many aspects indirent to our lifes: bodies change as we get older, we remember the past but never the future, effects always follow causes. It is simply remarkable that all of these phenomena are strongly related to the second law of thermodynamocs, i.e., Entropy.
second law. Entropy,
The major source of energy for life on earth is by all means the light from the sun. One consequence of the second law is that heat naturally flows from a hot object (the sun) to a cooler object (Earth, and some other cooler planets around us, but it’s for no matter right now).
But if that were the end of the story, at a certain time, the two objects would come into equilibrium with each other attain the same temperature. unknown to most, if the sun had indeed filled our entire sky, rather than describing disk disk about one degree across (that we love to stare at at sunrise…😊) that is exactly just what would have happen. I guess the result would be an unhappy world if an inhospitable one could be even called this way. Mind you, this is not just only because the temperature was to high, but also because it would be so stataic that no change shall allow a biosphere to be created.
As far as the universe as we know it is concerned, the reason our planet doesn’t heat up until it reaches the temperature of the sun is tiightly related to the fact that earth loses heat by radiating out into space. One of the only reasons it can do that is that space is much colder than Earth. And It is because the sun is a truly spot in a mostly cold sky that Earth doesn’t just heat up, but rather can absorb the sun’s energy, process it, and radiate it into space. Along the way, of course, entropy increases;
a fixed amount of energy in the form of solar radiation has a much lower entropy than
the same amount of energy in the form of Earth’s radiation into space.
The explained above also hints why Earth’s biosphere is not a static place. We receive energy from the sun, but it doesn’t just heat us up until we reach equilibrium (thankfully 🤗) it’s what weconsider a low-entropy radiation, so we can make use of it and then release it as high-entropy (as if we have another choice…) radiation. All of which is only possible because the universe as a whole, and the solar system in particular, has a relatively low entropy at the present time (and had an even lower entropy in the past).
But hey you guys, don’t cheer up too much. Nothing good lasts forever. Our universe is a lively place because there is plenty of room for entropy to increase before we hit equilibrium and everything grinds to a halt. Entropy might be able to simply grow forever, albeit this is not the most supported scenario (not that we shall be there to examine that in real-time… 😎),
But alternatively, entropy may reach a maximum value and stop. This scenario is known as the “heat death” 🥶 of the universe. It is a wonder it was alternatively, entropy may reach a maximum
value and stop. This scenario is known as the “heat death” of the universe, a,amidst all the exciting theoretical developments in thermodynamics.
Past Vs. Future and it relation to Entropy
The arrow of time is not only about theoretical cosmology and and other exotic things alike…
it’s a necessary feature of the existence of life itself. But it’s also responsible for a deep feature of
what it means to be a conscious person: the fact that we remember the past, but not the future. According to the fundamental laws of physics, the past and future are treated on an equal footing; but when it comes to how we perceive the world, they couldn’t be more different. We carry in our heads representations of the past, in the form of memories.
Yet we are accustomed to simulate the future non-stop, mostly relying on our memories from the past as initial (somewhat fabricated and confabulated). Sadly those predictions have nowhere near the reliability of our memories of the past. The dynamics and chaotic nature of system with an almost infinite degrees of freedom makes included by the fact that our brain tends to confabulate information as time passes in order to keep a coherent memory makes the future too hard for an open prediction.
Past Vs. Future II:
Concerning the future, we can make predictions, but those predictions have nowhere near the reliability of our memories of the past.
Ultimately, the reason we can form a reliable memory of the past is that the entropy was lower then. In a complicated system like the universe, there are many ways for the underlying the building boxes to arrange themselves into the form of what essentially is “you” with a certain memory of the past, plus the rest with an addition of the rest of the universe.
imagine all you know that you exist right now, with a memory of going skiing in the just in the midst of the snowing winter before seventh and eight grade, then you simply don’t have enough information to reliably conclude that you really did go skiing that winter. Weird as it might sound It turns out to be overwhelmingly more likely that your memory is just a random fluctuation, like the air in a room spontaneously congregating over on one side. Here lies the BIG issue: To make sense of your memories, you need to assume as well that the universe is ordered such that the entropy was lower in the past.
If we imagine we are walking down the street and notice a broken crystal like glass glass shuddered into pieces near the edge of the park. We certainly shall not find it probable that it will suddenly reconnect by itself into a beautiful cristal looking glass, albeit, strictly speaking, this is a possibility that should be taken into account.
That shuddered crystal like glass is a perfect analogy to our brain in the sense that it’s a record of a prior event, but only if we assume a low-entropy boundary condition in the past. Our expectation for a low entropy past leaves us to believe with an extremely high degree of confidence that not long ago there must have been a crystal glass which someone dropped. nonetheless, as far as the future is concerned, we have no reason to suspect that entropy will decrease, there’s not much we can say about the future of the crystal glass shuddered on the edge of the park with its pieces close together. Why? simply because there are too many possibilities that could happen. Maybe it will stay there and grow dirty, maybe someone will clean it up, maybe a stormy wind will come by and spread the shatters of the crystal glass through the entire park… That crystal glass is somewhat like the memory in our head. A record of a prior event, but only if we inherently assume a state of low entropy condition in the past.
Another way to distinguish between past from future eveand simply spread the nts is cause and effect. causes comes first, and the effect follows. We wouldn’t expect to jump in the water and expect a splash before touching it. Nevertheless, according to the microscopic laws of physics, as reminded to us by Ludwig Boltzmann, it is certainly a possibility to arrange the water molecules and the air in the water such that we shall precisely be ejected from the pool and the air molecules to be set so orderly without us even leaving the pedestal to jump. As far as probability for such an event to occur it is such a very much negligible occurrence but by all means it is not unphysical.
Putting it in different yet to some of us outrages or at the very least mind boggling: The distinction between the fixedness of the past and the malleability of the future is nowhere to be found in the known laws of physics.
The deep microscopic rules dictates that nature run forward and backward in time from any given situation of nature to run forward or backward in time from any given situation quite equally.
If we knew the exact state of the universe combined with a fully understanding of all the laws of physics, then the future and the past were determined on an equal ground well above Lord John Calvin dreams of predestination and the end of what shall be ever needed to further know physically.
know the exact state of the universe, and all of the laws of physics, the future as well as the past is rigidly determined beyond John Calvin’s wildest dreams of predestination.
The way to reconcile these beliefs, is to act as (and it is…) the past is once and-for-all fixed, while the future can be changed, but the fundamental laws of physics are ultimately reversible, which tied in a Gordian knot to entropy.
Because we live in a universe with an intuitive sense of the arrow of time, we treat the past and future not just as different from a practical perspective, yet they are certainly are. The past has already happened, while the future is still up for as much possibilities as ine nay imgine. in some sense—we can sketch out alternative possibilities, but we don’t know which one is real. when it comes to the past, we have a weird connection to memories and records of what happened. Our records may have varying degrees of
reliability, but they fix the actuality of the past in a way that isn’t available when we imagine a prices future.
If we knew the precise state of every particle in the universe, we could deduce the future as well as the
past. But we don’t; we know something about the universe’s macroscopic characteristics, plus a few bits of what would be described as not so organized data. With that information, we can predict some certain broad-scale phenomena (like the fact that there an extremely high probability that the sun just might
rise tomorrow), but our knowledge seems also to be compatible with a wide spectrum of specific future occurrences. When it comes to the past, however, we actually hold in the palm of our hands knowledge of the current macroscopic state of the universe, plus the fact that the early universe began in a low-entropy state (this is actually an assumption, yet a good one at that).
I would have to finish with this scientific yet one that might sting some of you readers whilist without changing the words or diving into their deepest meaning it will elevate others to the highest levels of hope (or none of the above 😉)
ENTROPY AND FREE WILL
This one concerns what in my last sentence I’ve hinted for, but which is formally called “The Past Hypothessis”. That one extra bit of information, gives us enormous self confidence when it comes to reconstructing the past from the present. Actually, our notion of free will – the ability to change the future by making choices in a way that is not available to us as far as the past is concerned, is only possible because the past has a low entropy and the future has a high entropy.
The future seems open to us, while the past doors seemed to be locked forever, even though the laws of
physics actually treat them on an equal footing.
The major lesson to e undertaken about this specific Part about entropy and the arrow of time should be clear:
the existence of the arrow of time is both a profound feature of the physical universe, and a pervasive ingredient of our everyday lives. the existence of the arrow of time is both a profound feature of the physical universe, and a pervasive ingredient of our everyday lives. Should be attributed to Ludwig Boltzmann.
The major lesson of this overview of entropy and the arrow of time should be clear:
the existence of the arrow of time is both a profound feature of the physical universe, and non separable ingredient of our everyday lives. It’s a bit of a bumper, that with all of the progress made by modern physics and cosmology, we are still far from a final conclusive answer for why our universe and the physics describing it seem to present such an asymmetry in time. Entropy seems to be a part of the core in many aspects of life. It just seems like a worthwhile line of research to try and crack just a little more…