December 6, 2010
A lot has been said on the implications of quantum mechanics. If there is any theory of the physical world, which is astoundingly successful despite of what a rusty philosopher would make out of such implications, it is that these implications are enhanced by the validity of quantum mechanics via experiments.
I just finished reading the 4th chapter on Stephen Hawkings recent book, the Grand Design, this chapter named, Alternative Histories, describes through a clarity of masterful examples and brilliance, the idea that the world, where it all matters how tiny the objects are, is determined on a basis of laws which directly invalidate all our intuition and contravenes all our everyday experience. The idea of this idea is, such tiny creatures of which we never heard of and never formed any impression of, because they are beyond our reach, they all lie in a world which behaves funny.
Have you ever heard of an object called a neutrino or a gluon, or a pentaquark. This last one may not exist, but scientists have got a hint of such a particle, especially I know a scientist who worked out all the details of a pentaquark candidate, I used to play tennis with this scientist guy, so believe me you, on everything I tell you about science.
Hawking gives the example of bucky balls instead of objects like neutrinos, a large molecule of 60some atoms in it, which is still essentially a quantum object, that is, it exhibits all the funny scenario of quantum mechanics. What’s funny? Imagine Schrödinger’s kitten extending both left wards and rightwards on a right turn at a signal on the highway. Both at the same time!! Without splitting into two separate kittens or anything like that, which could be shown in a movie. The real kitten can’t do that, but an electron can do that.
It can extend like a wave in two separate directions. That is, if more than 10 of such funny electrons are in a group and they do this left right trick, the radar of the Schrödinger’s cops will show up half of the electrons on the detector at the left hand shoulder of the highway irrespective of the signal. And half of the electrons will show up on the detector placed at the right hand side, this without any electron actually turning wholly into one of the side. That’s the way these tiny objects behave. If one of the electrons registers half a hit on the left hand side detector and half a hit on the other detector at the same time, it just means the likelihood of the electron hitting on any of the detector is complete when there are sufficient electrons, for us to make any sense of that.
But we can, NOT question, if it makes sense how an object can really register half a hit or simultaneously occupy two paths, it makes sense for the tiny objects and not for us because we never have such facilities to realize such weird phenomenon. Hawking explains the behavior through the Davison Germer experiment and the modern forms of the Young’s double slit experiment the phenomena of quantum level interference.
Much of it though reminds me of everything Feynman explained in his famed Feynman Lectures, which I had studied in depth at least 3 times, 13 years ago, the first three chapter of volume 3 where all the quantum mechanical drama is explained in the most interesting fashion, ever done until today. Only Feynman could have explained drama and increased its fun and pleasure. He was a showman in the attires of a physicist.
Lets not go into who else is like that, it may not cut enough pleasure to some. But Feynman had explained the true jest of the nature of the quantum world. All of it reconstructed into his own thinking and his own ways of explaining it, accessible to anyone who can understand verbal, chatty, English. That was the reason why he was so famous and add to that, his colorful ways. If I remind you of any of that, pardon me.
The other thing that Hawking explained is what he borrowed from Feynman approach; the addition of phases decides which path is to be followed. This is one of the most brilliant aspects of quantum mechanics. I will explain it a little more. Before that here is what the implications of alternative histories is. Instead of calling it multiple histories we have tried to keep it as interesting as it could be in simpler language. Multiple sounds like mathematical jargon.
While mathematics gives all the physics its charm, truth be told, its all virtual, its internal, its in our making. The real charm of physics lies in its intuition and conceptual imagination of which Feynman was the real master and with which he explained his Physics. Since in classical mechanics, as an example say the cricket ball travels only one path. Otherwise the umpire has to take a 6, a 4, a 2 and a 1 and add them up and divide by three so the batsman scores 4.33333.
The umpires job is done pretty simple the way nature adds it all up before the umpire adds things up in his mind. The umpire may be a math Olympiad owner, but nature prefers pretty simple maths, it just does not live any clue how this may be worked out, unless Feynman arrives. So what nature did to save the umpire guy some humiliation is it added up all the paths the cricket ball could have taken to reach its destination. Nature did everything at the quantum level. Nature is a gigantic rulebook (see my other recent article), immensely complex and subtle but it does things that we get a clue only when we work at it for decades, the most intelligent ones and painstakingly reach only at some of its laws.
What nature did is it took all the paths the cricket ball could have taken, considering that the cricket ball might even have exploded in the path into 3 pieces, the ball is made of millions of quantum particles and the nature is concerned about each one of them per its own rule book. So the path of all the tiny components is actually taken into consideration. Say a little bump, and since all the components are connected to each other and sans the explosion scenario will traverse only one path as seen by the person who is watching the cricket show (oh it’s a match but as grand as a show) all the possible paths of this tiny bump adds up to zero except the one that we see as its motion. Isn’t it brilliant?
Now Feynman had explained this and Hawking recounted how this is possible. The nature of quantum mechanics is such that there are always two parameters, which decide a path, the so-called phase and amplitude. Now the phase is like an angular variable and the amplitude is like a total value for something, say, the speed of the tiny bump. So every possible path the tiny bump can take is associated with a phase and amplitude. That is, if path A, is taken then at each point on path A, there is a phase (angular position of the direction of the path) and amplitude (speed allowed for the tiny bump on that path)
When nature takes all the million paths allowed for the tiny bump or the ball, which includes all the paths in the vicinity of the actuated path (that is the actual trajectory of the ball seen on TV) all of them cancel each other out. If Path A is the actuated path, then its surrounded on both sides by, Path A minor up and path A minor down, A minor up, has a phase 30 degree and A minor down, minus 30 degree, since nature isn’t going to give any special priority to any of the path but add them up to see any value, it finds that at each instant only the actuated path Path A survives with a non zero value and all other do not give any sufficient phase or amplitude to the actual motion of the ball.
So the ball continues on path A, which is constantly calculated by the conditions of the environment. Now the conditions of the environment are such for the cricket ball that it’s hardly influenced by say, moisture content. It will spin a little less or so on and so forth. But moisture may mean something for the bowling team; it may change the conditions on the ground so it may be inconvenient for the batsman and so on. But the conditions for a bucky ball are quite different. Its actuated path is quite impossible to determine in advance (future) and in retrospect (past) as well. Here probability rules play a different game. Here the wave nature of the bucky ball is prominent as well, so expect funny behavior, here you can easily make the environment turbulent for the bucky ball and it may have an actuated path that may land it in the lap of Queen Victoria or ghost land. What queen is going to do with a 60 atom erratic fluke is not much of a choice, she may not even notice this and little turbulence on her lap may land the super atom in further trouble because this time it may get stuck in Madonna’s Silicon forte.
But the nature of quantum mechanics is such that if you apply its rule by constantly dividing each component of a large object for careful scrutiny small errors that you think did not matter may show up to be a hint for a large demise. No I am not even talking about butter fly effect or error propagation. But ever thought about a sticky thermodynamics problem or a jet simulation problem. They all need to be reunderstood, from the perspective of a mathematical formulation that is respectful of so called alternative histories or a multiple path formulation.
Well it’s not about detecting the trajectory of an airplane or a fighter jet; it’s about understanding this problem like a physicist. If it makes you laugh to think, an electron can hit the wing of an airplane and the airplane is going to come apart like a shoddy toy, think again, remember the Challenger episode, where the rubber lost its tenacity at a subzero temperature. And watch the movie Final Destination to keep yourself in good humor.
Well I can not tell you directly how even quantum mechanics is related here and neither can you directly or indirectly ask me such a question how quantum mechanics is responsible for thermodynamics. We can not ask how it is that quantum mechanics rules the roost when it comes to deciding the laws of nature and its in nature of nature that the principles of quantum mechanics are over ruling on every other principle we know.
Think about it this way if it bothers you, the world is made up of tiny creatures in millions, the cumulative effect is what we see as an effect of the daily world, when there is a doubt, some new form of quantum mechanics is waiting to happen because we are in direct violations of the rule books of nature of which we have no idea where it is kept, how it is to be read and how it needs to be worked out and interpreted. When we have celebrated Feynman and his contributions are just a reminder that strikingly difficult problems in physics are always in need of crazy, interesting, off the board thinking we must continue with hardships of Physics problems rather than find an easy way out.