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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Physics employment

Recently, I heard somebody talking on the radio about ways to start a day with positive energy. The person suggested all sorts of things, ranging from the things to eat or not to eat, the kinds of exercises to do and also even meditation. It occurred to me how fortunate I am that I don’t need to waste all that time on getting positive energy. When I wake up and I ask myself “what am I going to do today?” The answers is “physics!!!” and there I get all the positive energy that I need. It is my profession, my purpose and my passion.

Then I read the lamentations of Peter Woit in a blog post on the job situation in theoretical high energy physics. So, while it may be great to have a passion for physics, it is not a given that one can make it your profession. Indeed, I can remember that for as long as I’ve been in this field, the job situation was challenging. 

Students at University of Toronto
Students at University of Toronto

Part of the problem is the way that physics as a profession is being practiced. One typically starts as a student studying physics, but what are the career expectations? Most physics students apparently expect to become physics professors at universities. Well, if you look at the number of students compared to the number of faculty positions in physics, then it is obvious that such expectations are quite unreasonable. Moreover, if every physics professor produces scores of physics PhD’s during his or her career, then obviously there would be a huge oversupply of physics PhD to replace that professor.

So where do these PhD’s go to work? First they become postdocs. The ideal postdoc is a person that basically runs the research program for a professor. They come up with the ideas of what to investigate and they even supervise the professor’s PhD students. But what are the professors doing then? They travel and give talks, raising their profile, building their networks, and increasing their impact. Some of them don’t even touch any research. It’s all about fame and glory. The postdocs basically become cheap labor to produce the content on which these professors are riding their ego trips. More than once, when I’ve asked such “eminent researchers” questions after their talks at conferences, I’ve discovered that they don’t really understand what they are talking about.

So what can be done? Firstly, the poor students studying physics need to understand this situation and be realistic about their expectations. Other career choices include teaching (in schools, not universities) or industry. The latter represents the idea of an “industrial physicist.” However, in this case there is a different form of competition. The industry is better geared for engineers, for obvious reasons.

Another thing. When you decide to do physics, please do it for the right reasons. If physics is you passion and will remain your passion for the rest of your life, by all means proceed. Somehow you’ll find a way to live out your passion. But, if you want to do physics because you want to show off how bright you are, then rather join Mensa and leave physics to those that are passionate about physics. And, if you want to do physics because you want to be famous, like Einstein and those guys, rather consider a career as a rock star or a movie star. Very few physicists ever become really famous, contrary to what they may think.

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COVID-19 numbers

In a time like this, there is much uncertainty. It may be the first time that the world is experiencing such a pandemic, but similar situations have been encountered before. People have lots of questions and they are looking for information. Unfortunately, there is a lot of misleading information available. It seems that most people don’t check such information. They just believe what they read. It is for this reason tragic when “official” websites provide misleading information.

One example is the incorrect representations of numerical quantities about the COVID-19 pandemic. Two such quantities that is for obvious reasons quite important for people is the recovery rate and the mortality rate. They give an estimate, based on the currently available statistics, of the chances for a person to recover or die from COVID-19, given that the person has contracted the decease.

The statistics, which is generally available (see for example Wikipedia), consist of three numbers provided for every country on a daily basis. These number are: the number of confirmed cases (CC), the number of deaths (D) and the number of recoveries (R). For example, on 14 June 2020, the quoted number for the whole world are:

CC = 7 763 921
D = 429 632
R = 3 682 950

From these numbers, one can now compute the mortality rate and the recovery rate. The mistake that one often finds is that these rates are computed by dividing D or R by CC. That gives a misleading result, because CC also contains the currently active cases that does not form part of D or R yet.

The correct way to compute the mortality rate is to divide D by the sum of D and R and multiply the result by 100 to express it as a percentage. In a similar way, the recovery rate is obtained to dividing R by the sum of D and R and then multiply it by 100. You will note that when you add up the mortality rate and the recovery rate you get 100%. That makes sense, because one would either die or recover. There is no other option.

Applying these calculations to the above statistics for the world, we find the mortality rate to be just over 10% and the recovery rate just under 90%. These rates differ from country to country. For instance, the current morality rate in the USA is about 15%, while for SA it is only 3.7%.

Why is it different for the different countries? This is an important question, because it affects people’s behavior. There are many possible reasons, including the age demographic of a country and the availability of medical facilities in the country. The mortality rates for different age groups are different: it increases for older people. If the number of active cases becomes too high, there may not be enough hospital beds and equipment to treat all those that need treatment. As a result, one can expect the morality rate to increase.

The government of a country needs to try and keep the number of active cases low enough so that those that need to treatment can get it. For that reason, they impose restrictions that are aimed to reduce the rate at which the virus is spreading. Restrictions may seem to be a violation of people’s freedom, but in this case it is necessary. However, a government can only do so much. If the people decide to ignore the regulations imposed by the government, because they want to exercise their freedom, then the virus would spread too fast, with the result that the number of active cases can increase above the level where the country would have enough medical facilities.

There are more numbers that are important, for instance the growth rate in the number of confirmed cases. That is a topic for another day.

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