Wanted: Schrodinger's Cat, Dead or Alive !

(Disclaimer: Just when i thought my selection of topics couldn't get any worse! That's what a girl could do to you. Apparently the only use my lady love finds of my geeky side is quenching her 'negligibly rare' doubts on mainstream scientific jargon. :) )

Schrodinger's cat! The most talked about cat after Tom i assume - of course given you have boring friends like mine. Quick recap of trivia: yes, we are talking of a cat as in the animal; something to do with being dead and alive at the same time (!!); belongs to the mysterious world of quantum mechanics - something mere mortals find amusing just because it rhymes with ehem ehem..

Lesser known trivia: It is a thought experiment proposed by an Austrian physicist Erwin Schrodinger in 1930s (When is the last time you have heard of a scientist named simply Jack or Tim?). A thought experiment is just a fancy way of saying 'Suppose you manage to do this utterly ridiculous thing, wonder what would happen ? '. Schrodinger put forward this 'thought' experiment to prove that quantum mechanics might confuse you if you start applying it to real life macro objects.You bet! To be a bit more specific, he wanted to show that the 'Copenhagen interpretation of Quantum mechanics' cannot be applied to big objects, say cats for example. (yes, quantum mechanics can only be applied to nano-sized objects and it has different interpretations or explanations proposed by different people). What exactly is Copenhagen's take on quantum mechanics would be too much detail, and to quote the holy grail of knowledge, wikipedia, "Despite an extensive literature which refers to, discusses, and criticizes the Copenhagen interpretation of quantum mechanics, nowhere does there seem to be any concise statement which defines the full Copenhagen interpretation." Phew!

To give you a better perspective, lets zoom out a bit. We all know classical physics - the physics which we did at high school, the f=ma stuff. Unfortunately it seems that these rules just don't apply if you zoom in onto nano objects like fundamental particles. The reason simply being, at this scale, individual particles of an object tend to have a good effect on it - as opposed to bigger objects, where the behavior is an 'average' of all the particles inside. And hence quantum mechanics was proposed! To explain why particles behave they way they do at nano-scales.

Hope that's clear. Moving on, the biggest difference between classical physics and quantum mechanics is that classical physics gives you exact rules whereas quantum mechanics always talks in terms of what is 'more probable' - playing it safe, if you may. So, whereas classical physics tells you if a ball is moving or at rest, Quantum would tell you what are the different probabilities that the ball is moving at different speeds.

What Shcrodinger has done through his experiment is to transfer this element of 'probability' or 'doubt' from a micro-scale object (a subatomic radio-active particle) to a macro object (a cat). The setup for the experiment can be easily found on the internet. To summarize, a cat's life depends on if a radio-active atom has decayed. But the decay of an atom is not certain according to quantum mechanics. Hence the cat (inside a closed box) has chances of being both dead AND alive. We would never know unless we open the box (duh!). Opening the box is called 'taking a measurement' and hence when you take a measurement of the system it practically 'kills' the probabilities and the system converges to one 'reality' - dead OR alive.

NB: The low-level explanation for such a complex idea is merely to stay fair to this blog's intent. No disrespect is meant to the geniuses or the quality of their works. If the topic still boggles you with questions, i am sure you can find great detail online. And do remember, as this is a purely theoretically topic, all resources may fail to satisfy your search for something tangible.

Fourier Transforms - why is it everywhere ?!

What a topic for my first post ! I risk scaring away 90% of my sane audience. Yet I take the risk because I love this concept and its everywhere! Even people allergic to engineering might have come across it somewhere or the other. So do we really need another article about Fourier Transform on the internet? Probably not. But let me try to explain it to you as simple as it can get. This could very well be the first write-up of FT that has almost no mathematical equations!

So what exactly is it?
Well, the general idea is pretty simple. And fascinating too! Imagine having a secret potion from which you can make any food in the world ! All the food - from veggies to bacons - can be made by mixing this single potion in different ways ! The only ingredient in all cookbook recipes would be just one- the potion. That would be pretty amazing right? Well it turns out the world of wave-forms have such a magic potion. In other words, there is a magic 'waveform' from which all wave-forms in the world can be made . When i say waveform it includes all shapes of wave-forms you have ever seen -  from giggly oscillating waves like the ripples on water to sharp steps like that of a staircase. And that magic waveform isss *drumroll* - the SINE wave ! Believe it or not, those wiggly oscillating sine waves can be added up to create any waveform we want ! And that is pretty much what Fourier Transform is all about. Given a waveform it tells you the recipe! It tells you exactly what kind of sine waves are to be added together to get the particular waveform.

No way! What about sharp edges?
If that question came to your mind, you are pretty smart. And more importantly, you understood what i was trying to say! :-) . Totally agree with you - how can we create sharp wave-forms (steps for example) by adding up smooth wiggly sine waves ? Well, you cannot. But wait, you can get pretty close! If you are careful enough, you can keep adding almost infinite (ouch!) sine waves until your result looks almost like a step for example. In fact, the following figure is very common in textbooks to illustrate this.

You can see that the black waveform is a perfect sine wave. The blue in fact is a sum of many sine waves. And the red is sum of even more sine waves. Notice how it gets closer and closer to a square wave ? Like i promised, i won't go into the details of how its done. Plenty of people have done that already. Google !

Interesting! But what's the big deal?
Good to know. But why would anyone want to waste time on something pointless as creating wave-forms from sine waves right? How does it affect me or things around me? Biased with my background, let me try to explain this from an engineering point of view. It so happens that there are many systems in engineering where you know how the system would respond if you try to feed it a sine wave. In fact, a large portion of systems would always output a sine wave if you give it a sine wave input - only the amplitude,frequency etc. change (no! not going there). Here lies the beauty! So, if you know how the system responds to sine waves, and any wave can be decomposed into sine waves, you can pretty much predict how the system would respond to any wave !!  I rest my case.   

The Motive

I love to explain stuff  - stuff i believe i understand a bit. I am among those for whom the content look of an 'aaha' moment on the listener's face is the most rewarding experience ! (Partly feeds my ego too, i admit.) But I hate explanations, the complicated once that is. If you haven't guessed it yet, one of my favorite quotes is by Einstein : " If you can'ts explain it simply, you don't understand it well enough! ". Now, I agree not everything under the sky can be expressed in simple terms or Layman's terms, so to say. After all, Einstein would be the first to know that! But that doesn't mean you bypass the intuition and start learning/teaching concepts as blind facts.

Intuition! If this blog is to be summarized in one work, Intuition would be it! The topics are going to be random, ranging from signal processing to religious beliefs. The common thread - me, my understanding. These are topics i 'believe' i understand the intuition behind. It is very possible that i am wrong (very very in fact); or that my proud intuitive explanations are too naive and known to all ! My only aim is to give some new face somewhere that 'aaha!' look of comprehension.

Please bear in mind that the discussions on any topic are for light reading and should serve as a 'fundamental understanding' of the concepts. A lot of details would be deliberately avoided and simplifying assumptions will be plenty. Experts keep this in mind before criticizing the accuracy of claims ;). All of you are always welcome to correct me or guide everyone to better explanations! Happy reading!