Quantum Mechanics, The Uncertainty Principle, Schrodinger's Cat, & Other Misconceptions
By Jon Therkildsen, MSc MBA from University of Århus (2004)
THIS ARTICLE WILL ADDRESS AND ANSWER THE FOLLOWING:
WHAT IS AN ATOM?
WHAT IS A QUANTUM MECHANICAL WAVE-FUNCTION?
WHAT IS THE OBSERVER EFFECT?
WHAT IS SCHRODINGER’S CAT?
WHAT IS THE UNCERTAINTY PRINCIPLE?
The study of Quantum Mechanics is quite complex, and yet it has found its way to the popular media and mainstream culture. Its marvelous wonders have encaptivated the minds of many. Unfortunately, there is much misinformation or fundamental inaccuracies out there about several of the more popular quantum mechanical theories. I will try to explain some of them here - brief, simple, and to the point, accurate enough to avoid the more general misinformation I often meet.
WHAT IS AN ATOM?
There is a beautiful story here. It is about how a simple thought can grow into perhaps the most important concept in Science today.
The idea that all matter is made up of tiny indivisible particles goes back two and half millennia to the Greek philosopher Leucippus of Miletus and his pupil Democritus of Abdera.
Now, of course, you may wonder; how on Earth could someone like Leucippus get such a profound idea when sliced bread was not even invented (took another 2 400 years, btw)? The answer is simple and, I think, beautiful. It was logic.
He wondered (and I am paraphrasing);
“… what if we were to break a stick. And then break one of its halves, and again break one of its halves and continue to do so for as long as it would be possible. Eventually, we should get such a tiny piece of the stick that we cannot - not even in principel - break it any further...”
He envisioned that all matter fundamentally (by the purest meaning of the word) consists of a collection of smaller indivisible particles or pieces. And incidentally, “atom” is Greek and means “indivisible” or “uncuttable” for this very reason.
Beautiful, isn’t it?
By simple deductive logic, he laid down the theory of atom and particle physics. And he did so to the extent that he (or rather Democritus) speculated that all of the Universe consisted of only atoms and empty space, and nothing else. Bold statement.
Today we call this “The Standard Model of Particle Physics.” We know of 17 such fundamental particles that, when grouped correctly, define all matter. They are the final piece of anything, including Leucippus’ stick. These 17 fundamental particles cannot be broken any further. They are indivisible. They are uncuttable. They are atoms.
Now indeed, the informed will note that “Atoms” are not understood as fundamental particles, and in fact, “Atoms” are a collection of the fundamental particles themselves (quarks, leptons, and bosons). While this is true, it is only true because we once thought what we called an “Atom,” was indeed what Leucippus also called an "Atom." Since then, we have learned that even Atoms can be subdivided into protons and neutrons, and those again can be subdivided further into our list of the 17 particles I reference above.
We call those fundamental particles or elementary particles, but a rose by any other name is still a rose. And the fundamental particles are atoms in every sense of the way Leucippus and Democritus meant them to be.
So what is Quantum Mechanics then?
Well, it is the science that describes and explains the nature and behavior of matter and energy on the atomic and subatomic levels. The mechanics of these smallest constituents of reality is quantum mechanics.
The Quantum Mechanical Wave-Function & The Observer Effect
Quanta or quantum systems is a common label often used for the tiniest constituents of reality, be it atoms or subatomic particles like those mentioned above. However, quanta is not a very informative term. It doesn’t instinctively or figuratively tell us what we are dealing with.
The odd thing about the quanta is that they do not behave quite like we would imagine particles or even waves would. They behave like something else entirely.
A particle is generally (and inaccurately) imagined as a small grain of sand. Add enough, and we can build a sandcastle. Quanta, on the other hand, are not like small grains of sand. They are more like a sea of floating possibility, if this can be imagined. The behavior of these quanta is best described by the so-called “wave-function” (abbreviated to Ψ), authored by Erwin Schrödinger. This mathematical function or equation describes the fundamental nature of reality. And, as it shows, quanta are not little grainy particles in absolute positions in space. They hold all positions (aka superposition.) Imagine a cloud where some parts of the cloud have higher concentrations. Even though the cloud is everywhere, these higher contractions are where we typically find what we call the particle or the collapsed wave - yet the whole “cloud” is this whole quantum. They are not in one place; they are everywhere at once (with varying degrees of probability).
They can still build a sandcastle, but they are neither grains of sand nor anything else easily imaginable in their natural state. This, naturally, contradicts our experience up here in the macro world, where things are either one or another, and never both. You are either dead or alive, not both. Or you are in Paris or New York, not both. The wave-function kind of disagrees; however, the wave-function describes our base reality impeccably.
You may wonder how we can see them as “particles” of bigger structures, if they exhibit several states simultaneously and are generally fuzzy by nature?
It is only when observed, measured, or interacted with that they become one quality over another. Werner Heisenberg described it as the transition from the possible to the actual. We call this “The Observer Effect,” which is a consequence of the so-called; “The Copenhagen Interpretation.” This is when their superposition becomes a position. They “become” a grain of sand, so to speak, only when observed.
“Observed,” in this case, means any sort of subatomic interaction that happens when a quantum system of superpositions becomes entangled with its environment. It is not tied to the human eye, as I have read some articles postulate. It is any interaction or environmental entanglement - dumb, smart, or dull. Matters not. When they arrive as particles (meaning, when they are observed), we call this a collapse of the wave-function. And it can uncollapse hereafter again. It doesn’t change form or even nature. It remains a wave-function. You may view a collapsed one, as a kind of compressed “packed-wave” instead of a more spread-out wave-function. This fact is by far - in my view - the part of quantum mechanics that most struggle with understanding.
Everything in the quantum realm can be described entirely in terms of waves, or entirely in terms of particles, whichever one prefers. Paul Dirac proved both versions are exactly equivalent. However, they cannot both be right. Even Niels Bohr believed that they were neither waves nor particles, let alone both. He, however, was content with not asking this question further. A way to view it, is, that they travel like waves, and arrive like particles. The “like” here is important, as we have no way of knowing what they actually are. The problem is, there is nothing in our theories that explain what goes on in between the “transition from the possible to the actual” - experiments show waves, and they show particles, not the transition. There has never been an experiment ever to catch a wave-function in the act of a collapse. Leslie Ballentine argues there never is a collapse. Schrödinger hoped, at one point, to show what happens in between these states, but he never did - and for good reason.
The wave-function is describing this nature of quanta and quantum systems accurately. To Schrödinger, this wave-function is the literal description of quanta. To him, the tiniest particles are wave-functions. In their true form, they are not waves, and they are not particles; they ARE wave-functions that react to their quantum environment. There is no better description, and it is an accurate description. However, and if we have to get anal about it, the wave-function does not live in our ordinary Euclidean space; it lives in Hilbert space - which for all sense and purposes is the space of quanta, and so demands, at the very least, a mentioning in an article like this.
The takeaway here is that the tiniest constituents of our reality are fluctuating wave-functions rather than particles or manifested waves - more like some third sort of indefinable mix between these two. Impossible for us to imagine, but possible for us to describe.
The truth is that neither “wave” nor “particle” are good labels for the tiniest constituents - but it is the best we can think of when figuratively describing something like this beyond the elegant language of mathematics. A more adequate label would simply be to acknowledge these quanta as wave-functions and call them this:
Meticulous, the above description may be, but it is not very satisfying when writing an essay. Alas, we continue to call them particles or waves or both, depending on what we are trying to communicate. Neither, unfortunately, are correct, but often correct enough.
“The Observer Effect” is still being interpreted and discussed, and there are indeed different views on what it actually is. We call them interpretations of quantum mechanics.
The most popular one is “The Copenhagen interpretation,” followed by the more far-out “Many-World interpretation.” There are about 15+ vastly different interpretations out there. However, whichever one subscribes to, changes nothing. They all work (and in that sense, they are all correct) as the underlying mechanics and results are the same. It does not show any unsureness or conflict with the macro worlds of sandcastles or cats. It shows that there is still much to be learned, but what we do know (or claim to know) about it cannot be described as an effect of an inherent unknowability. It is rather a quality of the quantum realm reality. It is, simply put, different down there.
The best theory we have today is the so-called “Quantum Field Theory” (QFT), and it is essentially collecting several theories and theorems under a common conceptual framework, viewing all of reality as propagating fields. And interestingly, it describes “particles” as excited states of these fields. This perhaps helps to visualize how quanta are not really “atoms” or “grains of sand” but something else.
A wave function. Un-observed. Un-collapsed. A true representation of our TINIEST constituents
Schrödinger's Cat
The famous “Schrödinger’s Cat” thought example is meant to illustrate the absurdity of superpositions from the above-mentioned Copenhagen interpretation, by showing a mechanism where the consequence of an uncollapsed wave-function can make a cat both alive and dead simultaneously. Its destiny, in this mechanism, is determined by an unobserved/uncollapsed atom.
Quantum Mechanics states that subatomic particles will be in all states (superstates), not one over the other until they collapse or are observed. Therefore, Schrödinger argues; until it is observed, by looking inside the box, this atom has both killed and not killed the cat. It is what I describe above as having several states simultaneously. The fate of the cat is not 50/50 in this experiment. It is 100% alive and 100% dead - simultaneously. And as we know “classically,” this is not possible. A cat is either dead or alive, not both. Yet, this is what the thought example aims to prove.
Schrödinger wanted to discuss how quantum mechanics must be an incomplete model of reality. He had a good point back then, one hundred years ago; however, less so now.
Interestingly, Erwin Schrödinger is the author of both the wave-function (for which he received a Nobel prize) and his cat ridiculing these consequences of the wave-function.
We have since learned that the tiniest constituents of reality (mathematically described with a wave-function) are neither classic waves nor particles. It is merely a mathematical reality that is impossible to comprehend with parallels to our macro everyday lives. And this includes cats. Plus, “observation” cannot exclusively be akin to “opening the box, to take a look.” It is any subatomic particle interaction, and so this, too, renders Schrödinger’s experiment broken.
“Schrödinger’s Cat” illustrates how profoundly strange quantum mechanics is, and it is a useful tool to try and better understand it - but it does not disprove or even discredit quantum mechanics, despite vigorous attempts from Erwin (and Einstein too).
IN THE MANY-WORLDS INTERPRETATION, THE CAT LIVES IN ONE WORLD AND DIES IN ANOTHER
A competing interpretation of the Observer Effect (as described by “The Copenhagen interpretation”) is the so-called “Many-Worlds interpretation.” In its view, the cat is 100% dead, and 100% alive, but in parallel worlds. It says the wave-function does not collapse when observed; it splits into another parallel world where the other state is the state. According to this interpretation, you are dead in one world, and alive in another. And you are in Paris in one world, and in New York in another. Or the cat continues to live somewhere else. And we won’t know which world we are in, until we have a look. It sort of satisfies the thought example, and it doesn’t contradict our experience up here in the macro world among cats. It is, in some ways, a more earnest or uncompromising interpretation of the wave-function.
We cannot say which interpretation is correct (and there are several other than these two). And one can argue that it doesn’t matter much in our reality, as the wave-function stands, regardless. The evidence tells us they are both correct.
In any case, the many-worlds interpretation mentioned above, tells us that the cat is alive in one world, and dead in another. And the fact is, we won’t know which world we are in until we observe it. Or until the cat takes its pulse.
The Uncertainty Principle
Heisenberg’s Uncertainty Principle is erroneously often described as showing that there is an inherent unpredictability in the constructs of nature.
This is false.
There is nothing unpredictable or, in some sense, uncertain about the “Uncertainty Principle.” The principle is also born of the quantum wave-function, mentioned above, and it states that any velocity or position of a particle (a quantum system) cannot, by these mechanics, be defined more accurately than by an interval - as opposed to a bit or exact point. You could say that there is a fuzziness to the tiniest constituents of reality. They are not particles; they are kind of like “packed waves.”
Relating this to the “observer effect,” as discussed above, even a collapsed wave-function is still only a “wave interval” of our reality. Reality does not have particle-bits.
The principle is not that sexy or mystical; it merely tells us how nature is. We assume(ed) the tiniest of fundaments were particle-like when Quantum Mechanics taught us that this is not quite so.
That is the core of the “Uncertainty Principle.” As said above, neither “wave” nor “particle” are good labels for the tiniest constituents of reality.
Werner Heisenberg originally called it Ungenauigkeit (inexactness) or Unbestimmtheit (un-determinedness), whereas his mentor and collaborator Niels Bohr often used Unsicherheit (unsureness). Today in German, the most commonly used term for the principle is Unschärfe (blurredness or fuzziness), which, in all respect, is a better label as uncertain it surely is not.
I think perhaps the most common confusion with the principle is rooted in how a probability-wave-function can build certainty. Like a chair or a sandcastle - consisting of a gazillion fuzzy particles. It seems counterintuitive. But it isn’t.
An analogy I use is flipping a coin. They say the chance of heads is 50/50. However, flip 2 times, and you may find 100% tail. Even a 50/50 chance is quite uncertain. Flip it 10 times, and you may get 20/80. Still far from good enough. Flip it 100 times, and the chance will be perhaps 40/60… still not quite. However, do it a gazillion times, and the probability is exactly 50/50. This distributed outcome is also called The Law of Large Numbers, which is how probability functions can produce certain results. This is how fuzzy becomes solid.
Our reality is built up of a gazillion probability functions.
To sum up
Nature (all matter and energy) consist of indivisible particles. We know of 17 elementary particles. They are, however, not particles, nor waves. They are wave-functions; in several and all states simultaneously. Once observed or interacted with, they become more like packed waves. Not, imprecisely or approximately, but accurately and absolutely.
All of this, mentioned above, is not mere speculations or ideas; it has been confirmed by experiments many a time, and beyond any reasonable doubts.
That is pretty much it. Easy.
Photos via Google