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!]

Prelims.

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!

All-in-one!