We have a name for the desirable stationary states in life: states of contentment. If you can manage to be content most of the time with what you have, then you can be reasonably assured that your life has been a success. As with quantum states, numerous stationary states are possible for every individual — each of those states corresponding to a different combination of situations with which someone could be content.
Despite popular beliefs to the contrary, we don't all need to be rich and famous to be content. For example, you could be content with a stable desk job with a caring family to return to every evening in a middle-class suburb; or you could be enjoying the single life as a millionaire actor in a successful sitcom with a mansion by the beach and a Ferrari in your garage; or you could even achieve a high level of contentment working the night shift in the local four-year college where your kids can attend for free, and you enjoy your local community activities and the bowling league.
We can keep adding to the list and could potentially find stability and contentment in any one of a wide variety of life situations. Yet, as we all know, lasting contentment is not easy to find, and that is because there is something very particular about stationary states — in life, as well as in quantum mechanics. After all, if stability were all there was to stationary states, Bohr would hardly have had to start a whole quantum revolution on account of them.
You see, the most interesting thing about stationary states is that stationary states are very specific; we can't just pick any available state of the system and call it a stationary state. And the reason goes straight to the heart of what is quantum about quantum mechanics. Although pretty much any quantum system can have stationary states, the clearest way to understand them is in terms of the states of an electron inside an atom.
We all learn in school that every atom is like a little solar system, with a tiny compact nucleus made of protons with positive electric charge and neutrons with no electric charge , with even tinier particles called electrons with negative electric charge in orbit around the nucleus just like the planets around the sun.
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However, there is a fundamental difference: In the solar system, the planets could in principle revolve around the sun at any radius or distance from the sun, so the earth could have been arbitrarily closer or farther than where it is now relative to the sun, and it could still have a perfectly stable orbit around the sun. But that is not the case with electrons. If we draw an atom as shown in Figure 1. This means that in the figure, if the circles drawn correspond to the smallest three allowed orbits, then we cannot draw some other circles in between them to create some intermediate orbits.
The situation is just like that for the floors in a multistoried building. Suppose each floor is ten feet high, then people can occupy rooms at ten, twenty, or thirty feet of elevation from the ground assuming the ground floor is a garage , as shown in Figure 1. It is likewise with electrons in their orbits. Electrons in the allowed orbits are in their stationary states, and they would remain there forever, unless disturbed. This striking phenomenon where only specific orbits are allowed is called the quantization of electronic orbits, because the orbital radii can only take discrete or quantized values.
The reason this quantization happens is rather surprising, as we will see at the end of this chapter. This finicky nature of stationary states gives a quantum perspective on the elusive nature of long-lasting personal states of contentment.
In our lives, even more so than with the relatively simple electrons, a lot of things have to be just right to achieve a stable and lasting situation that would make us content. Even the least demanding among us is unlikely to be in a perpetual state of contented bliss, under just any arbitrary set of circumstances. Things would be a lot easier if we were all that easy to please! Getting all the conditions just right almost never happens! But when it does so once in a while, some lucky ones can hold on to a stationary state of contentment for a long time — we see people like that occasionally and might envy them.
But the real trouble for most of us is that even contentment is not enough: If you are fine with being content, very good for you — most people unfortunately are not! The truth of the matter is we crave happiness, not contentment. People don't write books about "pursuit of contentment"; Hollywood would not make movies about that. Contentment lies on the path to happiness, but usually is not the same as being happy. Happiness or sadness is really all about changes. This might come as a surprise after all this talk about stationary states.
Nevertheless, it is true, because it is only when things change that we register any feelings at all. If you feel a bit skeptical about that, that's probably because when most of us think of "change," we envision only major changes in life. But, by change, I mean any change, because every little incident that happens in life has the potential for making us happier or sadder. When a change is positive, leading us to a better situation than we are currently in, we are happy, and when it is negative and things get worse, we end up being sadder and unhappy — and how happy or unhappy depends on just how big the change is.
Think about it: If absolutely nothing ever changed in your life, in the short term you would reach some sort of equilibrium where you are neither happy or sad, but eventually you would just be bored out of your mind.
The Quantum Rules
That is why very few people are ever completely content. We are driven by our feelings and our need to feel, and being content is more like an absence of strong feelings. Change needs to happen to trigger the sensations of happiness we seek. At a quantum level, changes happen all the time, but inside an atom, they happen in jumps. Since electrons only exist in very specific orbits, they cannot just ease into different orbits there are no "stairs" among the different orbits like among the floors in a building ; they have to jump to get from one orbit to another.
And there is magic in those jumps — just as magical as true happiness. Bohr did not get a Nobel Prize just for suggesting stationary states; he realized the wonderful thing that happens when electrons jump between stationary states: light happens! That's right, the tiny electrons dancing and jumping between stationary orbits is the origin of all the light in the universe. Here's how it works: An electron in an orbit with a larger radius has more energy than one in a smaller radius, and so when some perturbation triggers an electron to jump from an outer orbit to an inner one, the excess energy is released as a little packet or "quantum" of light, as shown in Figure 1.
The Quantum Guide to Life
The reverse process can also happen: If a quantum of light with just the right amount of energy comes long, it can be absorbed by an electron to enable it to jump to an outer orbit. And just as the electron states are very specific, all the properties of the packets of light, so absorbed or emitted, are also very specific. Every jump between the same two energy levels will create clones of the exact same quantum of light, which, by the way, are called photons hence photon torpedoes in Star Trek 1.
We can visualize the changes in the state of our mind as happening similarly to the little quantum jumps of electrons inside an atom. Our mind remains in a stationary state until stimuli, external ones or internal ones say due to bodily chemical shifts or memory flashbacks , lead to transitions in our mental state. At every waking moment of our life, there are things happening that influence our mood, with metaphorical quanta of happiness floating in and out: You could have been on your way to work at a job that you hate, and then the car radio confirms that you have won the lottery — that's a big quantum jolt of happiness — you go from being downright miserable to deliriously happy.
Then there are the small quanta that change your mood a bit this way and that all the time: an attractive stranger smiled at you, and that made you a just a bit happier instantaneously. Someone behaved like a jerk for no good reason; your happiness drops a quantum. Most of the time, we simply receive too many stimuli on our mind and senses during our waking hours to distinguish individual "quanta" of happiness, so our change of mood might seem just as fluid as a beam of light composed of countless photons.
Viewed this way, perhaps it is not a coincidence that we have always associated light and brightness with happiness, and its absence and the descent into darkness with despair and gloom. The quantum analogy just reinforces all those metaphors we use to express feelings of joy: "Everything seems bright again," "The clouds are gone," "There is light at the end of the tunnel," "Every cloud has a silver lining," "If it is winter, can spring be afar?
And then all the ones for sadness: "The light is gone from my life," "It's all gone dark," "Why such a dark view of life? Light is the absolute favorite metaphor and tool in literature, poetry, art, and movies to express the state of the mind, and as we now see, with some primordial roots in the very origin of light. Spread the quanta of happiness, spread the light! Now let's get to the heart of the matter.
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What is it that defines the stationary states? Why is it that electron orbits can be of only specific radii? What is the reason for quantization? On the human side, what can we do to significantly change our stationary states of mind? To answer all that, we need to understand really what makes quantum mechanics, well The word was coined by the German physicist, Max Planck, in , when he suggested that the observed spectrum of electromagnetic waves which includes visible light, x-rays, ultra-violet rays, gamma rays, microwaves, and radio-waves could be explained only by assuming that such waves including ordinary visible light actually come in discrete packets of energy that he called quanta.
The idea was slow to catch on at first, but when it did, it caught fire and spurred intense research over the next three decades, which ushered in a completely new way of looking at the universe that has come to be known as quantum mechanics. The name underscores the fact that, as with light, many of the things in nature that were thought to exist as a continuum like a fluid actually come in discrete form like grains of sand. But there is a common misconception that everything in quantum mechanics is discrete or "quantized" and, vice versa, that discreteness is a unique feature of quantum physics.
The discreteness is not so much about quantum mechanics per se, but is related to the fact that every system we deal with is finite and has boundaries. It is just that in the very small systems where quantum mechanics is most relevant, that discreteness is particularly conspicuous. But how can boundaries make something discrete? It might seem obvious because all discrete or grainy little things have boundaries, due to their finite size. However, it is more subtle than that, because a river has boundaries, too, and we all think of water as a fluid.
The way boundaries lead to discrete behavior in quantum mechanics is rather ironic, because to understand it, we need to look at waves, and waves essentially represent quite the opposite of discrete-ness — they are associated with continuous media like fluids. Therein lies a lingering mystery of the quantum world — the wave — particle duality: Most quantum entities behave both like waves and like particles depending on how you look at it!
Let us now see how waves and boundaries lead to quantization.
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