To be, and not to be, that is the question

Recently, a friend of mine asked me: "René, why did you study physics?" This question literally taking me brought back to the past... When I still was an undergraduate student that was a recurring question, not only for me but for my colleagues who, like me, were studying physics and all the time I used to hear answers like: "To understand the wormholes", "I'm interested in the string theory", "I heard about of the QCD and I would like to challenge my knowledge by working on this" and last but not least, the most frequent answer, "To understand the quantum world." To this question, I have a more modest answer: "I like thermodynamics and teaching, and if I study physics I can do both of them"  and these days I think the same way. However, in these past years, I was uncomfortable as no one was interested in thermodynamics (at least at my University), everyone is more interested in understanding hamiltonians, trying to solve complex integrals, wave functions, or anything else different from thermodynamics.

To announce the glad tidings

At that time, once I read the very interesting (and funny) quote:

"The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

from the great English astrophysicist, Sir Arthur Stanley Eddington. This encouraged me to want to evangelize the importance of thermodynamics and how everything is thermodynamics I wanted everyone to feel the love that I felt for it. Notwithstanding, despite all my effort, I don't remember gaining any followers and I knew the reason (or at least I thought that)... Everyone only wants to know about quantum mechanics and it doesn't matter how much I try to explain some interesting thermodynamic phenomena as the easterlies, or why the freezer is on the top of the fridge. In the majority of cases, I was just cut off during my explanation with an "ah ok! let me ask you one question, is it true that everything is a wave and the waves have a dual nature being particle and waves at the same time? It' s really crazy, isn't it? "

The devil's advocate

Since all my attempts to gain thermodynamic followers didn't work, I thought of a different strategy. I'll study quantum mechanics, but only so I can speak against it properly (how far is a spoiled human being capable of going?). I still remember how my first quantum mechanics class was, the topic was: "The superposition principle in quantum mechanics"... And a surprise!!! I liked it very much, and I'd been all set to loathe it.

To be, and not to be

I'll try to explain easily how this was the first lesson and why for me, it was a real epiphany. The professor started saying: "To understand how strange the quantum world is, I propose a game. Imagine that you have a set of balls, quantum balls in the sense that they present quantum behavior different from normal balls described by classical mechanics. These quantum balls have two binary properties namely, color (That could be red or blue) and direction (that could be up or down), and since these are quantum properties we are not capable of knowing color nor direction if we do not measure beforehand. Therefore, we also have two apparatus, one called Color gauge, to measure the color and the other called Direction gauge to measure the direction".

Quantum ball game

The professor continued: "We'll study four possible setups of this experiment. I'll give you the answers of the three first setups, and I want you to infer from these answers the fourth case".

"Case 1: we start with a bag full of the quantum balls with random properties and throw them directly into a Color gauge. Then, what do we expect to obtain at the end of the experiment? The answer is based on the probability, if the balls in the bag are uniformly distributed, the probability to choose one ball to be blue or to be red is the same. Therefore, at the end of the experiment, we have 50% of the balls going out from the blue side and the other 50% going out from the red side".

Schematic representation of the case 1

Someone asked the professor: "what happens with the direction?" and the professor rapidly answers, "well, we are measuring color, then the direction doesn't matter at that point, but for similar probability reasoning we expected that in each bag we have to be 50% up and 50% down". 

 

The professor continued:

"Case 2: now, we're going to use two Color gauges but for the input of the second one, we only allow blue particles to pass. Based on your common sense, what do you expect will happen?". Because it was a physics lesson and the answer seemed very obvious, everybody thought that it was a trick and no one answered anything. The professor, feeling a little disappointed, said: "come on guys, this is the easy part, the answer is clearly 50% blue at the end of the experiment!!!"

Schematic representation of the case 2

 

After that, the lesson seemed more like a probability instead of a quantum mechanics lesson. However, the professor went on: "In the next case we'll enter in the quantum realm. Thus, is everyone ready?"

"Case 3: Consider now a system similar to the previous one, but this time the second apparatus is a Direction gauge. If I asked you what would happen, you'd all say we'd get 25% of the blue balls with the up direction would be one bag and 25% in the other one with the down direction. Notwithstanding, this answer is half correct, because it is here when the nature of the quantum world forces us to abandon our common sense. It's correct that we found 25% of the balls in each bag. However, some red balls appear inside of each of them. This new phenomenon that completely contradicts our Aristotelian vision of the world establishes that the measure of the direction completely destroys any previous knowledge of the color and vice-versa".

Schematic representation of the case 3

It's completely senseless, there cannot exist any correlation between knowing whether or not one particle is in the up or the down direction with the fact that it is blue or red... It's like I asked what is the correlation between being Colombian and being the vegetarian!!! I remember saying to my colleague: "Then I'm Colombian until someone knows that I'm vegetarian. If this happens I am not Colombian,  please give me a break".

The professor continued with his explanation:

"In quantum mechanics, there are a certain set of variables that we call incompatible; these variables cannot be measured simultaneously. Thus, when we know precisely one of these properties, all our knowledge about the other incompatible variables is lost... In quantum mechanics, we called this bizarre phenomenon as Heisenberg's uncertainty principle. 

Well, now the time has come. It's time that you answer what will happen in the next case. If you get this game right, I guarantee your chances of understanding quantum mechanics are pretty high".

I could only think of two things. First, what the hell is this idea of incompatible variables? And second, one I'm really bad at games, quantum mechanics cannot be like a game...

Sadly the professor continued:

"Case 4: in this experiment, we start with a set of blue balls (we already know that all the balls are blue) and we measure the direction. After that, we use a "Mixer", which is an apparatus that rejoins the particles and send them immediately to another apparatus, in our case, they will send it to a Color gauge. The question, then, is what do you expect at the end of the experiment?"

My reasoning, as well as that of my friends, were the next: after the Direction gauge we lost all information about the color. Then, we have a 50% probability to obtain red particles and 50% to obtain blue particles. The mixer joins the particles to send them to a Color gauge because after the Direction Gauge we have equal probability to have red and blue particles. Thus, at the end of the experiment, we have two bags, one of them having 50% of the initial number of particles with only blue particles and the other one having 50% left with only red particles. these bags would have aleatory direction in the particles. Notwithstanding, this seemed like the answer he wanted us to give (and I repeat this is a physics course and rule number one is: If the question seems easy, watch out!)... Modifying slightly one of Hamlet's most famous quotes: "Something is rotten in the quantum world". 

And as all of us expected, our reasoning proved to be completely wrong, but why? The professor was enjoying watching our bewildered faces. However, he had mercy and continued:

"The problem here is deeper, your reasoning fails because in your head you are still maintaining the classic thinking. It is true that after the balls passed for the Direction gauge some of them will become red balls. However, this is a quantum property, so we don't know what specific particle are red or blue, because the Direction gauge doesn't give us this information. The mixer is here to line up the balls and throw them to the next Gauge. Nonetheless, when the particles enter on the Mixer, we loose all previous information about direction, then we are left only with original information with which we started the experiment: the set contains only blue balls. Therefore the result at the end of the experiment is: 100% of the balls are going out to the blue side of the Gauge".

   

The professor finished the class saying: "these kinds of counter-intuitive phenomena are the daily life of quantum mechanics and we need to develop a mathematical formalism to describe experiences like this. We will see that in the next lesson, have a good quantum day guys!".

And it is true that we spent almost two months in the course learning "the mathematical tools of quantum mechanics". However, I would like to give you what is the solution that physicists found for the quantum phenomena. The answer is called superposition and the idea is: the balls are blue and red, and at the same time they aren't blue and red (same thing for the direction). If you prefer, you can say "blured" or "updown". In quantum mechanics, the properties don't have fixed values, instead, they are in all of their possible states and the same time, and only when we measure a certain quantity, we really "know"  the value of this quantity.

Clearly, I needed more than two courses of quantum mechanics to understand it. However, even with all my prejudice, quantum mechanics turned out to be as interesting to me as thermodynamics... 

Thinking a little bit more, this is the first time that I actually write or try to explain something about quantum mechanics. If I could turn back time (I'm listening to this music while I write this part, God save Cher!) and meet the younger version of myself, I would say two things: 

1) Chill out, please! spend your time trying to understand quantum mechanics, you'll thank me for it, believe me.

2) One spoiler from someone that knows a little bit more physics than you... There is a branch of physics called "quantum thermodynamics" deal with this!

Thank you for reading my post, I hope that you enjoy reading it as much as I enjoyed writing it… Feel free to leave your comment about what you think about quantum mechanics or better than this what do you think about thermodynamics and follow me in the next posts :0).