The problem with the measurement problem

It is not really a topic I want to discuss. In fact, I don’t think it is worthy of including under my Demystifying Quantum Mechanics series. However, since even physicists don’t seem to get it, it is necessary to clarify a few things.

So the argument seems to go that even of one were to consider a completely mixed quantum states with equal probabilities for different outcomes then a measure would convert this mixed state into one with only one outcome and zero for all other outcomes. This transformation is then interpreted as a quantum collapse and the fact that this process is not understood is called the measurement problem.

The problem with this interpretation of the situation is just that: it is an interpretation. So it falls under the general topic of interpretations of quantum mechanics. Currently, there are no known experimental conditions that can distinguish between different interpretations of quantum mechanics. As such it is not physics, because it is not science. It falls under philosophy. As a result, it would not be possible to solve the so-called measurement problem.

Just in case you are wondering whether this measurement scenario can be interpreted in any other way that does not involve collapse, the answer is yes. The obvious alternative is the Many World interpretations. In terms of that interpretation the mixed quantum state describes the different probabilities for all the different world in which measurement are to be performed. If one would restrict the quantum state to any one of these worlds (or realities) then it would have 100% probability for a specific outcome even before the measurement is performed. Hence, not collapse and no measurement problem.

So, yes indeed, the measurement problem is a pseudo-problem. It is not one that can (or need to be) solved in physics.

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Garlic and tomatoes

It cannot be said, with any stretch of the imagination, that I am afflicted with green fingers. In fact, many years ago when I told my friends about my gardening attempts, they would burst out laughing. So, for years, prior to being presented with the opportunity to employ a gardener, I would think of that place outside my backdoor as a tortured garden. It is challenging to have a nice garden in a water scarce country.

So, why I decided to venture into this direction again, I don’t know. But it is fun, sort of.

I decided to harvest the pips of an overripe tomato and put them in some soil. Amazingly enough, they germinated. As they got bigger, I transferred them to individual containers. Now they are starting to become big enough to put into a big pot where they can stay until they would (hopefully) produce tomatoes.

I also had a garlic pod that started to look a bit sad. Although I like garlic in my food, I don’t seem to use it at a fast enough rate. So the garlic does not last. The thing made it quite clear that it wishes to burst forth and … grow. So, I relented and planted the thing. Now you wouldn’t believe just how must life there is in that pod. It sprouted leaves, all bunched together, like there’s no tomorrow. Soon I’ll have to find a bigger container and separate the thing into different pods, I guess.

Anyway, it would be a proud day, some time in the hopefully not too distant future, if I can harvest my own tomatoes and garlic and prepare some dish with them. It would mark a personal triumph, but I guess I still would not tell my friends, lest they laugh at me again.

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Hermitian existence

South Africa has the dubious honour to be among the top ten countries in the world with the highest number of confirmed COVID-19 cases. Of these ten countries, South Africa has the highest rate of daily increase in cases, over 4%.

Why? Perhaps one can blame the existing culture of disdain for the government’s regulations. It doesn’t matter that the government is trying to impose regulations to curb the spread of the virus. People ignore it and try to life as they like. One can understand why the government has lost it credibility looking at the recent history of corruption, state capture, and general incompetence.

I’m a scientist and not a politician. So I don’t want to discuss politics. Any reasonable person that sees the statistics can decide for themselves that it makes sense to isolate oneself as far as possible. So, what the government is trying to do makes sense, even if it is sometimes a bit too little too late.

The bottom line is, here I’m sitting in my house like a hermit. The hermitic existence is not so bad. The idea of living as a hermit has been part of western culture for centuries. It is intend to improve spiritual growth. I guess, it very much depends on the kind of person that you are. Not everybody can handle such seclusion for an extended period of time.

Charles Hermite
Charles Hermite

As a theoretical physicist, one can perhaps take some inspiration from Charles Hermite, whose last name sounds like hermit. He was a French mathematician who made significant contributions that are still widely used in quantum mechanics, among other fields. For example, a Hermitian operator is one that equals it Hermitian adjoint. It always has real eigenvalues. All physical states are represented by Hermitian operators

It this sound like twaddle to you. Don’t worry. What I’m try to get at is that if you currently also experience a “Hermitian “existence (as opposed a hermetic existence), then you can know that you are a real (valued) physical person. (Haha – just kidding. Perhaps only the mathematically inclined would find that funny.)

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Eating a Pink Lady

That may sound a little cannibalistic. Of course, if I added the word “apple” at the end (as you probably guessed) then it would sound less gruesome, but then it would also lose its appeal.

I could also have said “eating a Granny Smith,” but apart from the grammatical awkwardness, I don’t like Granny Smith apples much. I use to when I was younger, but these days they are just too sour for my taste. They are good for baking I hear. Not that I’ve ever baked apple pie.

The one’s I like most are Pink Lady, Royal Gala, and Fiji apples. Golden Delicious is also nice if they are properly ripened, but the shops tend to sell them when they are still very green. Then they are not so nice.

Pink Lady apples
Pink Lady apples

I mostly just eat them fresh. They are very helpful to combat heart burn. At my age that becomes a constant irritation. Instead of using some medication to control heart burn, I prefer to do that by my diet. So, I stay away from those things that tend to give me heart burn. In my case those are spicy food, breads and buttery pastry. Then I have an apple a day. That keeps the doctor away, as they say.

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Entanglement

Demystifying quantum mechanics VIII

Everything is no more or less in place to discuss one of the most enigmatic phenomena found in quantum mechanics: entanglement. It is sometimes called the quintessential property of quantum mechanics. 

We have discussed the fact that quantum mechanics introduces the concept of discrete entities that carry full sets of degrees of freedom, and which I called partites. Then we learned about the paradox introduced by Einstein, Podolski and Rosen (EPR) and how it led to the understanding that nature does not have a unique reality. Although it also allows that interactions could be nonlocal, we saw that such non-locality is not in agreement with our understanding of special relativity. The final ingredient that we need to explain quantum entanglement is the concept of a superposition. We can deal with that here.

The term superposition is a fancy way of saying that we are adding up things. Superpositions are also found in classical optics. There, one can observe interference effects when two waves are superimposed (added on top of each other at the same location). What makes the situation in quantum mechanics different is that the things that are added up in a quantum superposition can consist of multiple partites (multiple combinations of discrete entities) and these partites (discrete entities) do not have to be at the same location. Since each entity carries unique properties, as described in terms of the full set of degrees of freedom, the different terms in the quantum superposition gives complete descriptions of the state in terms of the set of discrete entities that they contain. 

Each the terms in the superposition can now be seen as a unique reality. The fact there are more than one term in the superposition, implies that there are multiple realities, just like the EPR paradox showed us. One can use the many-world interpretation to try to understand what this means.

Entangled entities
Artist impression of entangled entities

There are now different effects that these superpositions can produce. In some cases one can factorize the superposition so that it becomes the product of separate superpositions for each of the individual partites. In such a case one would call the state described by the superposition as being separable. If such a state cannot be factorized in this way, the state is said to be entangled.

What is the effect of a state being entangled? It implies that there are quantum correlations among the different entities in the terms. These correlations will show up when we make measurements of the properties of the partites. Due to the superposition, a measurement of just one of these partites will give us a range of possible results depending on which term in the superposition ends up in our measurement. On the other hand, if we measure the properties of two or more of the partites, we find that their properties are always correlated. This correlation only shows up when the state is entangled.

Some people think that one can use this correlation the communicate instantaneously between such partites if they are placed at different locations that are far apart. However, as we explained before, such instantaneous communication is not possible.

This discussion may be rather abstract. So, let try to make it a bit simpler with a simple example. Say that we form a superposition where each term contains two partites (two discrete entities). In our superposition, we only have two terms and the properties of the partities can be one of only two configurations. So we can represent our state as A(1) B(2) + A(2) B(1). Here A and B represent the identities of the partites and (1) and (2) represent their properties. When I only measure A, I will get either (1) or (2) with equal probability. However, when I measure both A and B, I will either get (1) for A and (2) for B or (2) for A and (1) for B. In other words, in each set of measurements, the two partites will have the opposite properties, and this result is obtained regardless of how far apart these partites are located.

The phenomenon of quantum entanglement has been observed experimental many times. Even though it is counterintuitive, it is a fact of nature. So, this is just one of those things that we need to accept. At least, we can understand it in terms of all the concepts that we have learned so far. Therefore, it does not need to be mysterious

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