Irreversibility

Irreversibility is a fact of life. A hot cup of coffee sitting on the counter of your kitchen gets cold. The opposite never happens spontaneously. A gas released in vacuum quickly expands to fill the whole volume. But this simple fact of irreversiblity is actually a conceptually messy thing in physics. The following is my attempt to explain this rather obtuse concept in a non-mathematical and jargon free form.

In order to motivate what I want to say in this post, I ask you to try and do the following Gedanken experiment (German for thought experiment) in your heads. Imagine that I have turned off gravity for the moment. Imagine a big box in which I put two balls with some kinetic energy. What would they do? They would move with constant velocity in the direction of their velocity. Further I assume that if they hit one of the walls of the box or each other, they will rebound elastically (i.e., will not loose any of their energy). So, if I watch these balls for a while, they are just going to rattle around for ever. Now, I make a movie of this experiment and then show it to somebody else. But, I play the movie backwards in the rewind mode. Will they be able to tell that I am playing the movie backwards? The answer is no.

The system we used in the above experiment can be thought as a minimal model for a gas in a container, albeit a gas with only two molecules. Now, note two things about the above model system. The total amount of energy in the system is the same at all times, this is called “conservation of energy”. Next, note the claim that I cannot distinguish between the movie of the above experiment played forward in time and backward in time. This is called “time reversal invariance”. These two properties are fundamental properties of real physical interactions between molecules. All of microscopic physics has time reversal invariance [1].

Now, let us do another experiment. Again, I have turned off gravity. I take a big room, I seal it off and then vacuum it, in that I remove all the air from the room. In the middle of this room I have a little nozzle that when I start this experiment, releases a small amount of a pink gas. Now, if I wait a while, what will happen? The pink gas will expand and fill the whole room. And hence if I make a movie of this experiment and show it to somebody in the rewind mode, they will be able to tell immediately that I am showing them the movie backwards for a gas that fills the whole room will appear to spontaneously go back to a small volume in the middle of the room. And everybody knows that that cannot happen. Yes?

Next, let us reformulate the second experiment in terms of the model for a gas we used in the first experiment. So what am I doing? I am releasing a large number (about 10000 billion say [2]) of pink balls, each with some kinetic energy into a big box and watching them for a while. The microscopic physics for this system is the same as in the first experiment, i.e., it has “time reversal invariance”. But, when I look at a system with a large number of balls, I “know” the direction of time. So, what is wrong? What did I miss?

The first thing you might ask is “Did you do the calculation for the 10000 billion balls to see that the theory predicts that the system still has time reversal invariance?” The answer to this question is that nobody and no computer can do this calculation. Then you say “Ah! Then you don’t know what your theory says so the whole point is moot!” Well, you would be right but for the fact that the mathematician Poincare proved that if you take a finite system (i.e., a system in a box say) with finite energy, then it will always come back to where it started from [3]. In the case of our experiment, Poincare’s theorem says that the gas that fills the room will eventually all come back and sit in the middle of the room again. But we know this does not happen. So, ask again, what is wrong? The catch here is that you have to ask how long does it take for the system to come back to where it started from. The answer to this question, for the case of the billions and billions of balls that is our gas is a time greater than the age of the universe! So, no matter how long you watch it, it is never going to come and sit in the middle of the room because you can never watch long enough! So, the message here is that the irreversibility that we ubiquitously observe in the world around us is an accident of the time scales over which we conduct the said observations.

Ok, we explained the paradox. But so what? Physics is supposed to be a mathematical model for observed phenomena. And the observed phenomenon here is that the spontaneous expansion of a gas is irreversible on the time scales that are relevant to life on earth. Poincare Recurrence might be a fact of life, but is irrelevant for anything we observe. So, what physics should give me is a rule of thumb that some things will happen (eg., a gas released in vacuum will expand to fill all available space, or a hot cup of coffee placed in a cold room will get cooler) and some things won’t (eg., gas in a room will not all spontaneously go and sit in one corner of the room, or coffee will not get hotter by taking energy from the cold room and hence making it even colder). This rule of thumb is called the Second Law of Thermodynamics that we all learnt in high school.

In the form we learnt in high school, this law is usually stated as “Heat always flows from a body at a higher temperature to a body at a lower temperature”. But a more general statement of this law would be that any system evolves so as to maximize its randomness. It is easy to see that this law explains why a gas will expand to fill the whole room. A given number of molecules occupying a small volume is less random than the same number of molecules occupying a larger volume right? It is rather more obscure to see how the two forms of the law (the first one more naturally explains the coffee scenario while the latter more naturally explains our Gedanken experiments) are equivalent, but it can be shown that they indeed are. But the point to note is that as I said earlier, this law, as is all of thermodynamics, is a rule of thumb to explain observed reality on length scales and time scales relevant to us. Deriving this from fundamental theory is a major mathematical headache addressed by all manners of scientists, mathematicians studying dynamical systems, physicists studying statistical mechanics and so on, with various degrees of success [4]. But clearly, it works and works very well! So we use it anyway.

(For my few regular readers, don’t worry, this post is an anomaly, not the new norm!)

Caveats for experts

[1] CP violating weak forces are not in my picture, I am living in a QED+classical gravity world of macroscopic physicists.

[2] Actually, an Avogadro number of molecules.

[3] I know that Poincare Recurrence theorem talks about approach within an arbitrarily small neighborhood of the initial condition and is stated in terms of bounded orbits, but I did not know how else to say this in plain English.

[4] The basis of thermodynamics in Statistical Mechanics is well established and there is a well developed theory of Hamiltonian dynamics that lets you ask such things as ergodicity and mixing in the trajectory space to substantiate domain of validity of the postulates of Stat Mech, but all this is rather esoteric stuff is n’t it? Or can we state it in plain English in an accessible way?

Love in the BlogSphere

I have been around in the Desi Blogsphere for about 4 months now, since my new year’s resolution to pick up a leisure activity that can keep me from getting crazy when research is not going so well (Ok, I started doing this in November, but what is a couple of months in a life time?). Much to my surprise, it has been exactly like the “real world” in many ways. And the surprise is largely because I did not know what to expect, but found out that it was something very familiar in the end.

Just like when you step into a new community (say, people doing theoretical physics research) in the real world, you don’t know anybody. First you acquire the knowledge of who the famous people are, for example Ed Witten if you are talking about theoretical particle physics or Amit Varma if you are talking about the blogsphere. Then, you try to make acquaintances with the people that are already in the community, in the case at hand by reading what they have to say and commenting on their thoughts. Some acquaintances stick, either because you keep going back for more and/or they reciprocate by evincing an interest in what you have to say. And others don’t. And as in the real world, the probability that an acquaintance sticks is directly proportional to how much of your life experience is the same as theirs and how much you respect the person’s thoughts and how well the respect is reciprocated.

I am finding many similarities between my experiences in the Blogsphere to my experiences when I was starting out as a grad student in theoretical physics. I am a novice here just like I was a novice in physics. I don’t know what tags are and am unable to figure out the Technorati thing. I don’t know about RSS and Atom feeds and still read blogs the old fashioned way, by actually going to people’s pages. Most of Web 2.0 befuddles me. For heaven’s sake, I am not even able to embed a video in my blog that I uploaded into youtube several weeks ago! I like to write and read and that is the only thing that brought me here, just like I like thinking about, formulating mathematically and solving physics problems and that is the only thing that brought me to physics. But in physics I had an advisor who helped me a little with some of the other technical things and the rest kind of worked out on its own. And this blogsphere thing being a hobby and me being the extremely lazy bum that I am, I am just hoping that things work out here on their own as well.

I could go on and on about similarities, the Indibloggies being the Oliver Buckley prize in physics (that makes Falstaff and Greatbong this year’s Steve Girvin and Allan MacDonald) and the Bloggies being the Nobel (and that makes PostSecret the guys behind COBE) and so on and so forth. But, let me get back to what I was saying earlier and to the choice of title for this post. As in my real world, I have not made that many acquaintances. And all of them are in the “I know them but I don’t think they know me” stage. And 4 months is too short a time for me to able to see if any of them are going to stick. But the reason I started writing this little note is that I felt a new (for me, the novice) “emotion” in the blogsphere yesterday. The real world analogue of this is called “Love at first sight”. The object of this “emotion” was PrimalSoup. But this is rather inevitable in this case. How could I not fall in love with someone whose domain name is that of Rhett Butler’s darling daughter, whose screen name is PrimalSoup (I wonder if she was thinking about the carbon-sulfur dominated pre life era of the earth that Carl Sagan tried to reproduce in his lab in Cornell or the quarks-leptons mixture that was our early Universe? In either case, I loved it), who is a Madrasi living in the Madras I want to go back to? And the clincher here was that she chose the phrase “Kafka meets Johnny Depp” to describe her dream guy! Is this just an infatuation or will it last? Well, only time will tell.

Well...

So much for my conspiracy theory...foot firmly in my mouth...now time for national mourning.

Conspiracy theory – India vs Bangladesh

Right after we lost to the young Bangladeshi side in the Group B match of the world cup, I saw this post on DP linking to various people ranting and raving about the dismal performance of Team India. I watched this match and was as upset as the other ranters. But I had a theory. I did not want to voice my theory ahead of the other league matches so as not to jinx them, in a manner of speaking. But I cannot hold my tongue (or my fingers on my keyboard) any longer.

I have come to think of the World Cup as a commercial carnival. Let me give you a for-instance from a different world to tell you how I came to this point of view. Why do you think Sushmitha Sen and Aishwarya Rai and Lara Dutta and what-is-her-name Chopra get crowned in the beauty contests in consecutive years? Because the cosmetic industry realized that Indian women now had the buying power for their products and hence the time was ripe to tap this virgin market. And why did n’t the assorted ladies in subsequent years win the same beauty contests? Because the market was established by then and the industry turned its attention to other sectors. Do you think the above argument is reasonable (from a cynic's point of view that is)?

Now, in the same spirit, the main source of income to the cricket carnival that is the world cup are the billion avid cricket fans in India. So I cannot believe that they can afford to have India leave the tournament before the Super eights. Now, what is my conspiracy theory then? I want to claim that the match against Bangladesh we lost so that there is guaranteed viewer ship for the subsequent league matches featuring India. We would all have watched the opener anyway just because of the fact that it was the opener, but how many of us would have watched the Bermuda match on a week night/day, depending on the time zone you are in? And how many people ended up watching it, me (at the office, while pretending to work) and my dad (at night at home at the cost of being late to work the next day) included?

Well? Do you buy it?

Back Home

I am back home after a week long trip to the west. The official purpose was to attend the big meeting of the American Physical Society and present my current research in the form of three talks. The unofficial purpose was to network with the prominent people of the community and catch up with old friends. All of this happened with gusto. The high point was seeing all my grad school colleagues that are post-doc-ing all over the country (and finding out that they are in comparable amounts of misery as me :)). I also got to meet college friends from India that I have not seen for ever. That was good too.

Usually, when you see somebody you have not seen in a while, you use them as a reference to see how you have changed since the last time you have been with them. That is one of the primary purposes that catching up with old friends serves. But somehow I did not do that this time. It could mean several things. The simplest thing could be that I was so distracted by all the physics that filled this week that in the brief time that I was actually in a social mode, I did not tune out of it enough to think of the “gauging the change in me” thing. Another rather Freudian thing could be that I am either really secure (unlikely) or extremely insecure (possible) with where I am now that I was subconsciously avoiding any comparison. I am not sure which of the above scenarios is the truth. In any case, all of this sounds like over-analyzing some rather simple thing and I have to get back to work.

Also, I have been out of the Blogsphere for a week now. Wonder what I missed here?

Rubbing me the wrong way

Blogged as part of the BLANK NOISE PROJECT BLOGATHON-2007.

I grew up in the big and crowded city of Madras. But, relatively speaking, I led a sheltered life with respect to this whole phenomenon of eve teasing due to the following reasons. I went to school by the school bus and stayed on campus in the hostel when I was in college. My home in Madras is near a train station and trains in Madras have a ladies compartment where the worst thing that can happen to you is that you might be yelled at by some lady with a heavy basket for moving too slowly! In spite of these facts, I have had five or six experiences involving “groping” of some form that happened when I rode the city buses in Madras. That should give you a feeling for how frequent an occurrence this must be! I am usually non confrontational (“Dhushtanai kandaal doora vilagu” philosophy) and even perhaps forgiving. I am narrating below the only one of these times when I lost my temper and actually hit back at the guy in question, literally.

This is a little less than a decade ago. But, it disgusted me enough that I still remember. It was summer, the month of May. I was waiting in the fifth main road bus stand in Nanganallur for the bus numbered 18C to go to Thousand Lights on Mount Road in order to go to the British Consulate library. Those who know Madras will realize that this is a 45 minute stint on the bus, made worse at the time as they were constructing the Pazhavanthangal subway and the buses were taking a round about route into the city, enough time for the drama narrated here to unfold. It is 8:45 in the morning on a week day. I am dressed in what I have come to think of as my Madras street clothes as I now wear them only when I am on the streets of Madras, which these days is very rare. Modest cotton Salwar Kameez that covers everything and a big cotton Dupatta on top for extra measure. 18C comes. It is already pretty crowded. I get in. We are on our way. Now, for those who don’t know, nobody gets off the bus on this route until Guindy about 40 minutes away from now. But people keep getting in.

Fifteen uneventful minutes pass by and the bus gets progressively packed. There is hardly enough room to breath, let alone move. The drama starts. I feel something on my butt. I move what little I can to avoid what I think of as accidental contact. Then I feel it again. This time, I recognize definite and deliberate rubbing. I try to turn around to see who it is. I am only able to turn my head and shoulders. Contact withdraws. I only find innocent looking commuters. Five minutes pass. Contact again, definite deliberate rubbing of what I have by now recognized as somebody’s boner. Eee…w! I try to squirm away. No room. I try to turn around and contact withdraws and I can’t recognize the culprit. This goes on for another ten minutes and I am getting madder and more disgusted with every passing second. The bus comes to a halt at the race course bus stop. Some commotion ensues with the conductor yelling at some guy for not getting off fast enough or something. In this distraction, I lean into a girl standing next to me and tell her to watch my back and tell me which guy leans into me when the bus gets going. We wait for the commotion to subside and be on our way again. I am half hoping that this whole thing is finished with and I can ride the rest of the way in peace, but at the same time hoping he does try it again so I can confront him.

We are on our way. Five minutes pass, and nothing. So I am beginning to think it is over when…again, rubbing, slow, deliberate. I stay still for a minute then turn towards the girl, my ally. She nods, yes I saw that. I lean into her. Checked shirt, dhothi, puny guy with a mustache is the description I get. We are at the Chinna Malai bus stop. People begin to get off. I turn around and there he was. Looking innocent and apparently minding his own business. Bus gets on its way. Five minutes. Then it turns into the Saidapet bus stop. I know a lady behind me wants to get off here. Under normal circumstances, I would have leaned into the seat near me and would have let her pass between me and the guy. These being extraordinary circumstances, I do the opposite. I move towards the guy to allow the lady to pass between me and the seat. Just as she gets behind me I pretend to loose balance, lurch towards the guy, use his shoulders for leverage and knee him in his groin precisely the way my Karate master taught me. My master would have been proud of me had he seen the guy go down. I hastily but vaguely apologize to the people around, not meeting anybody’s eyes and hurry behind the lady and get off the bus. Only then do I look in and see two people staring at me. The girl who was my accomplice and another guy who must have seen what actually happened. The girl’s eyes convey approval. I feel vindicated and rush off into the crowd to wait for another bus to complete the rest of my journey.

Walking in winter

As the title suggests, this post is about my experiences with walking in winter in upstate New York. But first let me start with a preamble. I love to walk. And I hate waiting for buses. If it is only 2 or 3 miles and my options were take the bus, take your car but fight for a parking spot or walk, I would any day choose walking. This is perhaps one of the reasons I liked living in Europe because there I could walk anywhere any time of the day. In suburban United States which is where I have lived, nobody walks anywhere. There are only cars on the road. In spite of this I walked a lot when I was in Florida, especially in the months of October through March, when Florida has the most perfect walking weather. Temperature in the 60’s most of the time and clear blue skies with a bright sun, heaven! And then I moved to the godforsaken hinterland of upstate New York, inside the Snow Belt. But, I stubbornly refused to change my predilection of walking everywhere and the following is an account of the experience.

I walk to work everyday. I walk through small roads and not-quite-roads that are not cleared regularly and almost never salted by the looks of them. I walk this way because it is the straight line from home to work. In any case everything was fine and dandy in the fall. And then, first came November. My sneakers started getting wet by the time I reached my office every morning and I had to take them off and let them dry. Then later in the month it got so cold that walking with wet sneakers made my feet so numb they hurt. So I went out and bought myself a pair of Faux leather shoes that did not get wet and were thick soled. And then the walking continued. Then came January and with it a whole lot of snow. First, there was may be 10 inches or so of snow on the ground. So I went out and bought myself a pair of boots that allowed me to walk through it with no damage done. And so the month progressed and the walking continued.

Then came the winter storm a few weeks back. We got 30 inches of snow in a span of 2 days. When I walked into work through this, I realized through first hand experience the hazards of walking through waist deep snow. If you lose your balance and fall (as you are bound to do) you actually go under the snow and getting back up is not easy at all as you have no surface that can lend any support! By this time I thought I had seen it all with respect to “winter walking hazards”. But then, this morning I walked in “freezing rain”, a meteorological phenomena that I don’t quite understand (something about not enough time between nucleation and precipitation for snow flakes to form). And do you know what freezing rain does to snow on the ground? It forms a layer of ice on top of it. So with every step one of two things will happen, either the ice will make you skid or the ice will give under your weight and you will find your leg disappearing into the snow and you have to use your other leg (which is hopefully free and clear) to extricate yourself from this hole! Is there more in store for me? I hope not! Oh Spring! When are you getting here?