## Wednesday, September 16, 2009

### Arrow of Time

Last month (Aug 09), the world of physics was enthralled by a mathematical work that led to an explanation to the arrow of time. The paper was by Lorenzo Maccone, one of the biggest names in quantum physics in this generation. The physicists in the universities (at least big universities) around the world have a hard copy of this paper in their hands, gearing themselves up for lunch time debates on its merits and demerits. As a result, now we have a paper that provides a counter-argument for Maccone's proposal. Moreover this paper says that quantum explanation given by Maccone actually complicates the arrow of time rather than resolving it. This paper is actually written by professors from Imperial College, London. Before taking a deep-dive into it, let's look at what arrow of time means.

The term Arrow of time was first coined by English Astronomer, Arthur Eddington. The name rings any bell? Yes, he is the same Eddington who studied the 1919 solar eclipse to confirm the theory of relativity. The mathematical equations of physics are always time symmetric. That is, whatever happened in a period of time can be reversed without affecting any physical law. It's like rewinding your VCR. But the crystal jar that I broke last week, did not rebuild itself. And it is ridiculous to think that it would.

When we look at the real world, if we leave things alone it always goes towards chaos. In the words of thermodynamics, entropy always increases in the real world as per the second law of thermodynamics. In the movie Godzilla, when running through Manhattan, Godzilla dashes against Chrysler building and it falls down and breaks. It is possible and realistic, if we make proper assumption about the strength of Godzilla and weakness of the building. If we look at it reverse, Godzilla runs through the rubble and it forms into a tower and moves up the top of the building. Does it sound realistic? No. But in a universal, completely mathematical sense, any object can return to lower entropy eventually. So arrow of time is this phenomenon that we always move forward in time in reality with a monotonous increase in entropy. At quantum level, the evolution of quanta is given by Schrodinger's equation, which is time-symmetric. Here, the term entropy is not about heat, but it is about information.

Lets look at some quantum level example. I have built a particle accelerator at the back of my house. I power it up and it generates a quantum particle. But how would I know whether it did generate a particle or not? Copenhagen interpretation says that unless I observe that particle, I cannot say. In other words, unless I observe the particle, I cannot assume that the particle exists, because I don't have the information about its existence. I decide to test the accelerator and I use a Geiger-Muller counter and it ticks. Wow! Now I know, my accelerator works. But what I did by observing its presence is that I collapsed the wave function of that particle. So I know that I generated a particle in past, because it leaves a trace of information.

The time-symmetry of maths and the second law of nature can be looked at as a paradox. If there is a time-symmetric dynamics, as in thermodynamics, it should be impossible for me to have a working system that is time-asymmetric. But everybody knows that the second law works. This paradox is called Loschmidt's paradox. Maccone in his work has made an attempt to answer this Loschmidt's paradox.
"How wonderful that we have met with a paradox. Now we have some hope of making progress." -Niels Bohr
Now let us get back to the particle-accelerator-in-my-backyard example to explain what Maccone says. Assume that my Geiger-Muller counter ticks, but I have a selective amnesia and I forget the count immediately after I heard it. Or in other words, what if somebody shot down the neuron of my brain, in which I saved the information that I heard a count? OK. My example is bad. Let me make it more classical. What if the crystal jar that I broke has comeback from shards, but I just don't remember the happening of that event? So the point is, the activity that results in a decrease in entropy is accompanied by the erasure of its observer's memory. At quantum-level, some instantaneous memory reduction is observed, but never at macroscopic-level because of decoherence. Here is the finding in Maccone's own words:
... any decrease in entropy of a system that is correlated with an observer entails a memory erasure of said observer, in the absence of reservoirs (or is a zero-entropy process for a super-observer that keeps track of all the correlations). That might seem to imply that an observer should be able to see entropy-decreasing processes when considering systems that are uncorrelated from her.
Quick Note: That particle observation problem that I took as an example is one process in quantum physics that is considered to be irreversible. It is called Born Rule. Even that would be reversible according to this paper, if somebody shoots the neuron of the observer at the instance of observation, as I said earlier.

At this point, if you are really confused, shocked and finds it all illogical and bulls**t, please wait for a moment and read this quote before we go to the counter-argument:
"No, no, you're not thinking; you're just being logical." - Niels Bohr.
The counter-argument by Jennings et al starts with the claim made by Maccone, as given in the quote. So during an entropy-decreasing event, the mutual information about the event is destructed as the part of the information. The important point here is what kind of mutual information has to be nullified as a part of memory erasure. Classical mutual information. Is there another kind? Oh.. yes! It is quantum mutual information. So the proof made by Maccone holds good only if a reduction in classical mutual information correlates with a reduction in quantum mutual information.

Information is usually represented as I(A:B), that is information that system A gets due to an event that happened in system B, observed by system A. So if the reduction in quantum mutual information happens without any change to classical mutual information, the earlier proof holds no good. The counter-argument does not stop there. If there is a reduction in quantum mutual information with no harm done to classical mutual information, the situation gets worse. A mathematical proof is made for a case in which, an entropy decreasing event erases the quantum information, but actually increase the classical information. What do the authors mean by this? It's possible for some people to remember observing the crystal jar reforming itself. But nobody does. So the Loschmidt's paradox still remains unsolved. I am not aware whether Maccone has responded to this yet. Or may be, like Walter Ritz and Albert Einstein, Maccone and the Imperial college professors may agree to disagree.

## Thursday, September 10, 2009

### Required: An Educational Reform

President Barrack Obama in his congressional speech on health care compared the proposed plan with the current education system in the United States. There are private universities like Stanford, and Harvard offering top class education but at a high cost, while public universities like UC Berkeley, UT Austin, UA Tucson, UMass Amherst are offering good quality education at an affordable cost. Good analogy. The US higher education system is arguably the best in the world. But that does not mean that it is the best that could ever be achieved.

Felix Salmon has wrote a blog in Reuters on changing tuition fees. Currently the tuition fees stand at 60% of the US median income. I am talking about the undergrad education. College tuition fee has increased at the double the rate of US median income - which also means that college tuition fees are increasing almost as fast as health insurance premium does. What is more alarming is that in some public schools like University of Massachusetts, only 33% of the students who enroll in UG education graduate. From socio-economic standpoint, the US higher education needs some serious reforms.

Obama conveyed a message that he did not want any American to go to a state where there is a treatment for the disease but he/she cannot afford it. Nice vision. I think the same applies to education. After all, illiteracy is a disease.

## Monday, September 07, 2009

### IDE Decision

Texas Instrument has recently made a sound decision to make their Code Composer studio's IDE to be based on Eclipse. That's a good news. Now that's not taking anything away from the old IDE of CCStudio. The old IDE is very comprehensive, very good, and very easy to learn. But the current developers do not just look for this. How easy is it to customize the old CCStudio IDE? That way, as the IDE becomes Eclipse-based, we can expect independent developers writing plugins for CCStudio and that would certainly improve the productivity in embedded systems and DSP development front. After looking at many IDEs, I can make an easy business/productivity decision. Your IDE must be based on Eclipse. That's the second best IDE (after Visual Studio IDE) that I have seen, although I personally write my JAVA codes only in Emacs.

## Saturday, September 05, 2009

### Taco Bell Revelation

Today I had my breakfast at Taco Bell. When I was waiting for my bean burrito, I observed that they sell egg burrito for \$0.89/-. And what more, it has bacon in it. Well, I don't eat bacon, but the menu board reminded me of some old stories. Back at the beginning of the year, some Ivy-League-educated people scared all my friends that the US would be stifling in inflation. But I was not scared. I said I would rather welcome some inflation. The Taco Bell menu teaches my friends that their fear was uncalled for.