Survey of the Quantum World - 2

In the previous post, I had written about three experiments, namely spraying bullets (several at a time) through the double slit and recording the pattern on the wall, keeping a candle instead of the machine gun and recording the pattern and in the third experiment, shooting a bunch of electrons (in this case we may need a detector instead of the wall) and observing the effects on the detector. Not surprisingly, in the case of the first experiment (with the machine gun bullets), we get the following pattern in which the bullet marks are around the places opposite to the two slits. i.e., we get two distributions on the wall exactly around the places corresponding to the slits.

But, in the case of the second and the third experiment, we get a pattern which is not discrete as above but shades of dark and bright bands like the following figure shows.

One can imagine this kind of dark and bright stripes correspond to the different levels of water that reach the shore on the beach. This is a clear indication that the light and the electrons do not come in discrete packets like the machine gun bullets (otherwise we would be getting two distributions) but they have some sort of a continuous ("wave-like") behavior. Let us now leave the candle light for some time and just concentrate on the electrons. We know that electrons are particles. Numerous experiments show that electron behaves like particles. But then, how do we have dark and bright bands instead of two dark bands like the one we got for the bullets? How do we test the difference between bullets behavior and electrons behavior? That's very simple. Check the behavior bullet by bullet and electron by electron. Its like coding a difficult software. When you don't understand the logic, just break it into modules. Execute it line by line and see where you are going wrong. So, we do the first experiment again this time by just shooting one bullet at a time. Again no surprises here - same pattern with two distributions correspond to the slits. But what about electrons? What will happen if we shoot them one by one and see what pattern it creates when the time progresses? To our surprise, we don't have any surprise - we still get the same dark and white bands, same as what we got when we shoot a bunch of electrons. How can that be possible? This is the beginning of one of the beautiful areas of physics - the Quantum Physics which gives life and meaning to the Hilbert space theory, which otherwise would have lived only to satisfy the whims of the so called "pure mathematicians".

To be continued.

Survey of the Quantum World - 1

In my previous blog, I had talked about several things, namely, Copenhagen interpretation of the Quantum Theory, Schrödinger's cat paradox, the famous Einstein quote "God does not play dice" and the collapse of the wave function. Frankly speaking, until recently this Einstein's quote was over and above my head although I kept saying the quote several times to myself just because it sounded "high funda" (I know it had something to do with the probability but nothing more!). Similarly, the Schrödinger's cat paradox was no paradox to me - just some strange words beyond the scope of my understanding. By this time, I guess I don't need to say anything about my ignorance of the wave function collapse or the Copenhagen interpretation. But when I managed to sneak into the world of Quantum Mechanics (QM), some of the things were clear as a crystal - especially the Einstein quote and our cat. Of course, there are several things that are still hazy and they are bound to be. Even the great practitioner of QM, Richard Feynman had said "No body really understands Quantum Mechanics". I will discuss later in what spirit he had said that but in the meantime, in the series of blogs to continue, I want to discuss QM. The idea behind writing these series of blogs are two fold:

1. To share the joy and excitement that I have had so far had in my little understanding of this amazing world.

2. To travel more closer to this world and have a 'aerial look' of the much nicer things that are abound.

I was careful when I said 'aerial look'. I will not land into this world to look at the landscapes and sunrises. That job is for the experts. They are specifically for the people who go by the Feynman words "just shut up and calculate" and I am positive that these people will have a nicer (and a closer) look of the beauties that escape the aerial survey. Having said that, by aerial survey, I don't mean the philosophical speculation of the QM alone. Although any thought out QM discussion is bound to contain quite an amount of philosophy (I am tempted to say QM itself is a philosophy, but let me not go into that right now), I don't want to ignore the beautiful white clouds of mathematics (especially, the infinite dimensional Hilbert space theory) that envelope the rich quantum world. So, without any more ado let me begin my journey. Oh and by the way, by QM I mean the traditional way (or Copenhagen interpretation) as it is typically understood.

At the heart of QM lies this famous experiment called the double-slit experiment. It is one of the most amazing and a remarkable experiment in the history of physics. In September 2002, it was voted as the "most beautiful experiment" by readers of the Physics World. It is indeed. Quite fairly one can say that this one experiment shaped the modern theory of Quantum Mechanics and still keeps baffling physicists. The philosophical implications of this experiment are abound. Feynman had remarked that this single experiment contains everything that one needs to know about Quantum Mechanics. I will briefly describe the experiment here and give the statistical interpretation (or postulates) of Quantum Mechanics completely based on this. This is the crux of the Copenhagen interpretation that I had mentioned in this blog and the Schrödinger's cat paradox is the outcome of this interpretation.

The Double-Slit Experiment

The origin of this experiment dates back to 1801 when Thomas Young wanted to study the behavior of the light and determine whether the light is a wave or a particle. The experiment is quite simple. There is a machine gun which can spray either bullets or electrons, a barrier with two slits and a wall (or a detector) which can record the place where the bullets or electron hits the wall. Something like the one shown in the figure. We now conduct three experiments.

Experiment 1: We spray the bullets from the gun and record the pattern on the wall.

Experiment 2: Instead of the gun, we keep a candle and record the pattern on the wall.

Experiment 3: We spray electrons instead of bullets and record the pattern on the wall.

To be continued...

Collapse of the Wave Function.

I was contemplating about the collapse of the Schrödinger's wave function and trying to see what it could really mean while I happen to engage in a conversation with a friend of mine. He is a physicist and he asked me two questions.

1. Suppose I have an upright glass containing water and I tilt the glass to a 90 degree so that the glass is horizontal and the water is now on the floor. Why is that we don't expect the water to get back to the glass when leaving the glass (horizontal to the floor) and the water as such? By the way, I am not holding the glass and it rests on the floor so no gravity business.

2. Why is that all the air molecules around my location move out to somewhere else so that I die by not able to breathe in any oxygen?

His point was that these things don't happen just because the probability of these things happening is very small. In other words, nature by itself is probabilistic. So does that mean the Copenhagen interpretation of the Quantum Mechanics and the collapse of the wave function is justified? How does it then answer the Schrödinger's cat paradox and the realist views of scientists such as Einstein, who famously declared "God does not play dice".

Philosophiæ Doctor

Finally the day (03/31/08) ended with my committee members and my advisor congratulating me for successfully defending my dissertation (don't know if they had any time to go through my work!). Oh by the way, it was only recently that I found out that a PhD. work is called "dissertation" in the US and a "thesis" is relatively smaller work (like the Masters' work) while the opposite is true in Europe and in India. There is a funny anecdote: When I wanted a recommendation letter from my prof in India, he gave me a open reco which had some words like "his dissertation" (referring to my Masters' work). When I asked him if that should be a "thesis", he told me "no, a thesis is for a much larger and detailed work, as in a PhD". I am wondering why this hasn't caused any major confusion so far. Anyway, coming to my defense, not too many questions, but some pointers which were not central to my focus of research. I would say its not a great work, but a decent piece of manuscript that can be potentially used in the simulation of N-body problems to reduce the computation time to a significant level. My advisor says it has good prospects but that can happen only if I have the time, patience and energy to publish the ideas. I believe earth shattering thesis like the ones produced by de Broglie and Lebesgue will have a fair share of extreme intelligence along with the researching abilities (not to undermine the hard work that went along). I have learnt/unlearnt several things along the way - the key point being: the more one studies, the more one understands academics is abyss. Standing on the shoulders of the giants would first require the ability to stand!

P.S: A faculty in a renowned institution told his students in the class "why do you guys think a PhD is a wonderful thing, all my colleagues have them, after all!"

Hello World !

Just wanted to see if there is any response...