Tuesday, May 27, 2008

Fail to Pass, Hate to Love & Dying to Live

Such oxymorons make one think what do words mean after all???

As Gopaldas 'Neeraj' says "शब्द तो केवल छल है..." (Words are just illusions...) So true... words often hide or reveal too much... relevant or irrelevant information!!!

Gopaldas 'Neeraj' @ IIT Roorkee

Now you would be wondering why am I being philosophical and starting a blog with such 'debatable facts'! Well, because they say the beginning of any article should be catchy and what is better than a controversy or quotes (shayaris if you prefer) from a Great Poet!!!

Anyway lets get to our usual stuff, i.e. Physics and stuff related to it. Just to make an explicit connection with the few lines above, lets consider a statement: "Lifetime of the Muon is 2.2 μsec". Now is this statement really that simple and conveys all relevant info? No. The words have hidden a lot of info and hard-work that goes into arriving at that seemingly simple statement. In addition, the word 'Lifetime' as used here has a specific meaning which is implied but not at all obvious to someone who is not conversant with the terminology!

Have a look at this file that gives a precise meaning for the word 'Lifetime' and some details on the experimental aspect (μ source, detector, electronics, analysis/simulation software, etc.) to get an idea of what all you 'missed' in the above statement. Much more than that, you will notice that there is a formula for μ lifetime (on page 10) containing various constants and its mass. Experimental determination of some quantity is all right but how do you get a formula for it in terms of a finite number of basic constants?

This is going to be done below i.e. what follows is a 'derivation' of that formula (in the framework of QFT). Those who are unsure of whether to continue or not, should probably stop as this blog post got over somewhere around the 3rd paragraph! [ I started this post just to put this derivation here! Muhahahaha :)) As some of you may have guessed, this was indeed an assignment problem in GS's QFT-II course!]


Evaluating M^2...

Within M^2...

M^2 Evaluated.

Decay Rate...

Total Decay Rate...

Calculation finally over.

Number at last!

Now, you 'know' how the lifetime of Muon is calculated theoretically and the amazing fact remains that it matches very well with experiments! In summary, I can say that I have managed to pass through it all, have come around to love it and am definitely living to die not the other way around!


Wednesday, May 7, 2008

Willingness to Come...

We are familiar with the fact that as one grows old (read transition from high school kid to undergrad to grad to...) the willingness to come to classes decreases 'proportionately'. To find an exact relation between these two variables: Willingness to Come to Class (WCC) and Age of Student (AoS) is the prime objective of this post. The data collection is carried out by carefully studying two recent absolutely uncorrelated events:

1) An undergrad's tenacious admission that he can attend 10 classes of one hour duration in a row on all days of a week (by week, I mean an academic week = 5 days). Now, many reading this post will wonder what was I doing talking to an undergrad and that also about coming to classes??? That is definitely not like me and you would be perfectly justified to wonder that! But if you wonder a little more, it'll all start making sense. If you don't have time to wonder more, let me walk you through a syllogism:

a) I am a Teaching Assistant (TA);

b) I grade quizzes & tests;

=> It is likely that someone will be dissatisfied with my grading and will confront me.

That takes care of me talking with an undergrad but why talk about coming to classes? Lets again consider a syllogism:

a') I am Just a TA;

b') I Just grade quizzes & tests;

=> It is highly likely that there was a question on one of the tests regarding coming to classes and someone was dissatisfied with my grading and confronted me.

That should now stop you from wondering more. But maybe not! So what was the question? That does not matter, what matters is that after a heated discussion on the grading style, the unexpected admission surfaced and rest is history! In laymen's term, I found that undergrad's resolve to come to classes awe-inspiring and we get our first 'solid' data point on the WCC vs. AoS graph... I put it on the upper left (not too left) corner!

2) At the beginning of Prof. Sterman's QFT-II 'extra' class at 5:40 PM (after Spring Sem's last colloquium!) he stated "I appreciate your willingness to come to class at this time. Hell, I appreciate my willingness to come to class at this time..." !!! [Though quotation marks are used, it (obviously) does not mean this is the exact wording!] I don't think there is anything to explain here as this event is self-explanatory. I'd like the Renormalisation of QCD Lagrangian to be as self-explanatory as this but then life is not that simple or as overheard in the same class "it is as it is" (though in a totally different context). I already hear some of you urging me to end this verbiage which is leading us away from the objective of this post! So from this rather trivial event, we get another 'solid' data point on the WCC vs. AoS graph... I put it on the extreme lower right corner!

Our data collection is now complete and we start with data analysis. And we all know what can be said about the relation between two variables when we have just two points at diametrically (almost) opposite corners of the graph: Yes, you guessed it right!!! Absolutely Nothing with 95% Confidence Level.

So there we have it: a systematic analysis of WCC across various age groups. No objective and/or subjective biasing of the author was involved in choosing the sample which is random to the best of the author's knowledge. To that extent, no grad students were involved as the author coincidentally happens to be one.

These are some preliminary results and this is a work-in-progress. Thus, deviations from the results presented here should not be totally surprising and are anticipated. Apart from this, an extensive study on who all are interested in reading such survey reports is also being planned for near future.

Creative Writing