Quantum Mechanics in a cup of coffee

Updated: June 30, 2006

Quantum Mechanics is problematic. It talks about probabilities. On the other hand, we, the humans, use to think in absolute terms. We like to think in a binary fashion - yes or no. Quantum Mechanics is a maybe. And it's a curious maybe. It says: maybe, why don't you go and have a look?

But let's say that adult people, after spending a few years in the recesses of a dark library in some university, actually manage to cope with the concept of this trickstery physics. The question is, how do you explain Quantum Mechanics to a child?

Well, I have an idea.

## Coffee machine

Your average teenager (13-16 or so) will not like the use of heavy words like wave equation, energy states, eigenvalues. But it could relate to a coffee machine. And for all practical purposes, coffee machine is our experimental setup.

The question we want to ask ourselves is: If I press the Drink button (after inserting the coin), I'm supposed to get a drink in a plastic cup. Will the plastic cup actually drop down from its internal holder or will the coffee spill out onto our feet?

It's a risk we take in our lives every time we insert a coin into any of food-and-drinks automated machines, at least the older, greedy models that do not warn the customer about the lack of necessary ingredients. And it's a rather linear risk for a person who might spend an hour in front of a machine and drink one cup after another; with each new attempt, the chances for getting the drink contained in a cup drops. However ...

Let's assume that you are in a mood for a nice espresso. You walk up to your coffee machine, insert the coin and select your drink. As a customer without any knowledge about how many people used the machine since the last refilling, you face the crucial issue of yes or no - will the cup drop down? For you, the system is completely unknown. In other words, it's in a mixed state. It's a mesh of yes and no, entangled in uncertainty.

To know the answer, you must press the Drink button. You must conduct the experiment. And by doing that, you actually change the environment. Beforehand, the coffee machine was dormant. It just sat there. Now, it's active, because of your external input. It does things. It starts mixing various powders and heating the water. It changes. It flexes its muscles.

But eventually, it settles down. And you get your drink. And you know for sure, if you have a cup or not.

This is your typical Quantum Mechanics. It's about black boxes, which contain a number of answers, and you can get only one. People have a hard time understanding the mixed states. How can electron simultaneously rest in several energy states. The answer is - it cannot. Not when you look at it (measure it). But in potentia, it can be just about anywhere. That ugly waveform, it's the electron specifications sheet. It tells the little electron where and for how long it may stay there. Instead of instructions and actual times, electron gets this information in fancy physical terms, in probabilities.

Our coffee machine is a black box. Inside of it, various conflicting states can exist - cups and no cups. And they exist, as a concept, simultaneously, even though they defy our binary thinking.

Think of a quantum system as a list of all that can be. Think of an experiment that measures the quantum system as a judge that will decide which one of the items on the list will come true. This judge is not completely unbiased though. This judge will choose one of the items based on its color. The brighter the color the more chance it will be selected. Now, think of color brightness as probabilities.

One of the Quantum Mechanics rules is that the measurement affects / changes the experiment. But of course it does. Beforehand, you have a black box, full of might-bes (or cats). Afterwards, you have opened the black box and pulled out one of the might-bes and turned it into a yes.

 "Where is me cat?" Erwin Rudolf Josef Alexander Schroedinger (1887-1961)

Now, our coffee machine was a rather simple example. It only has 2 options. But we could also make a machine that could have cups, glasses and mugs. Then, our problem would be a bit more complicated, but essentially it would remain unchanged.

The best way to think of anything in our lives in terms of Quantum Mechanics is to deprive our senses of its physical presence. If we see, hear, smell, feel, or taste something, we are actually measuring it. That's not quantum. Estimating how fast a car by watching it is going is not quantum; jumping above a wall and taking a peek at a car race in a closed stadium  - it is not quantum.

## Principle of Uncertainty

The last thing that I want to discuss is the Principle of Uncertainty. In Quantum Mechanics, they say you cannot measure both the location (x) and the velocity or momentum (P) of a particle simultaneously. Or rather, you can, with a certain error. You can never be absolutely sure in the values of these two at one time.

And the answer for this is simple! Again, it's like our coffee machine! Our particle is a black box. It has velocity and it has direction it which it goes. You can sample one of these two maybes and know it for sure. The other will remain a mystery until we sample again.

But what if we did the two samplings really really really fast? Could we not measure its speed first and then a fraction of a fraction of the tiniest time unit possible, measure its location? Sure, we could. But we will never have the precise numbers we desire. Each of these measurements will point to a different state. And we have no idea what things are like within the black box, no matter how small the time separation between two separate peeks into it.

Of course, there's a practical limit to how fast we can do this. I will not go into this. It's boring. But it comes down to a funny value of h/2, and that's the bottom limit of our Quantum world. And so, the best we can do is pixilize our world to very small squares and treat each one as a black box. If our particle is within one of these boxes, the box will light up, but we can never be sure if it's in the center of the box or bouncing off the edge of it.

So, next time you come across a coffee machine, give it a little pat and thank it for making the world so much less complicated to comprehend.

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