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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The non-locality mess

Demystifying quantum mechanics VII

The title comes from a section heading in a paper a recently saw. Due to a serious issue with some confusion that exists in the literature, the author advocates that the physics community abandon the notion of non-locality in favor of correlations that can be observed experimentally.

The problem with the community is that it consist of a very diverse collection of people with diverse perspectives. So, the chances are small that they’ll abandon the notion of non-locality. However, it is not unreasonable that one may be able to clarify the confusion so that the community will al least know what they are talking about.

The problem comes in because people mean different things when they use the term “non-local.” The traditional meaning is associated with “spooky action at a distance.” In other words, it refers to a non-local interaction. This meaning is best understood in the context of special relativity.

Consider two separate events, which one can think of as points in space at certain moments in time. These events are separated in different ways. Let’s call them A and B. If we start from A and can reach B by traveling at a speed smaller than the speed of light, then we say that these events have a time-like separation. In such a case, B could be caused by A. The effect caused by A would then have travelled to B where a local interaction has caused it. If we need to travel at the speed of light to reach B, starting from A, the separation is called light-like and then B could only be caused by A as a result of something traveling at the speed of light. If the separation is such that we cannot reach B from A even if we travel at the speed of light, then we call the separation space-like. In such a case B could not have been caused by A unless there are some non-local interactions possible. There is a general consensus that non-local interactions are not possible. One of the problems that such interactions would have is that one cannot say which event happened first when they have a space-like separation. Simply by changing the reference frame, one can chance the order in which they happen.

As a result of this understanding, the notion of non-local interactions is not considered to be part of the physical universe we live in. That is why some people feel that we should not even mention “non-locality” in polite conversation.

However, there is a different meaning that is sometimes attached to the term “non-locality.” To understand this, we need three events: A, B and C. In this case, A happens first. Furthermore, A and B have a time-like separation and A and C also have a time-like separation, but B and C have a space-like separation. As a result, A can cause both B and C, but B and C cannot be caused by each other.

Imagine now that B and C represent measurements. It would correspond to what one may call “simultaneous” measurements, keeping in mind that such a description depends on the reference frame. Imagine now that we observe a correlation in these measurements. Without thinking about this carefully, a person may erroneously conclude that one event must have caused the other event, which would imply a non-local interaction. However, based on the existence of event A, we know that the cause for the correlation is not due to a non-local interaction, but rather because they have a common cause. In this context, the term “non-local” simply refers to the fact that the observations correspond to events with a space-like separation. It does not have anything to do with an interaction.

When it comes to an understanding of entanglement, which we’ll address later in more detail, it is important to understand the difference between these two notions of non-locality. Under no circumstances are the correlations that one would observe between measurements at space-like separated events B and C to be interpreted as an indication of non-local interactions. The preparation of an entangled state always require local interactions at A so that the correlated observations of such a state at B and C have A as their common cause. The nature of the correlations would tell us whether these correlations are associated with a classical state or a quantum state.

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Einstein, Podolski, Rosen

Demystifying quantum mechanics VI

When one says that one wants to demystify quantum mechanics, then it may create the false impression that there is nothing strange about quantum mechanics. Well, that would be a misleading notion. Quantum mechanics does have a counterintuitive aspect (perhaps even more than one). However, that does not mean that quantum mechanics need to be mysterious. We can still understand this aspect, and accept its counterintuitive aspect as part of nature, even though we don’t experience it in everyday life.

The counterintuitive aspect of quantum mechanics is perhaps best revealed by the phenomenon of quantum entanglement. But before I discuss quantum entanglement, it may be helpful to discuss some of the historical development of this concept. Therefore, I’ll focus on an apparent paradox that Einstein, Podolski and Rosen (EPR) presented.

They proposed a simple experiment to challenge the idea that one cannot measure position and momentum of a particle with arbitrary accuracy, due to the Heisenberg uncertainty. In the experiment, an unstable particle would be allowed to decay into two particles. Then, one would measure the momentum of one of the particles and the position of the other particle. Due to the conservation momentum, one can then relate the momentum of the one particle to that of the other. The idea is now that one should be able to make the respective measurements as accurately as possible so that the combined information would then give one the position and momentum of one particle more accurately than what Heisenberg uncertainty should allow.

Previously, I explained that the Heisenberg uncertainty principle has a perfectly understandable foundation, which has nothing to do with quantum mechanics apart from the de Broglie relationship, which links momentum to the wave number. However, what the EPR trio revealed in their hypothetical experiment is a concept which, at the time, was quite shocking, even for those people that thought they understood quantum mechanics. This concept eventually led to the notion of quantum entanglement. But, I’m getting ahead of myself.

John Bell

The next development came from John Bell, who also did not quite buy into all this quantum mechanics. So, to try and understand what would happen in the EPR experiment, he made a derivation of the statistics that one can expect to observe in such an experiment. The result was an inequality, which shows that, under some apparently innocuous assumptions, the measurement results when combine in a particular way must always give a value smaller than a certain maximum value. These “innocuous” assumptions were: (a) that there is a unique reality, (b) that there are no nonlocal interactions (“spooky action at a distance”) .

It took a while before an actual experiment that tested the EPR paradox could be perform. However, eventually such experiments were performed, notably by Alain Aspect in 1982. He used polarization of light instead of position and momentum, but the same principle applies. And guess what? When he combined the measurement result as proposed for the Bell inequality, he found that it violated the Bell inequality!

So, what does this imply? It means that at least one of the assumption made by Bell must be wrong. Either, the physical universe does not have a unique reality, or there are nonlocal interactions allowed. The problem with the latter is that it would then also contradict special relativity. So, then we have to conclude that there is no unique reality.

It is this lack of a unique reality that lies at the heart of an understand of the concept of quantum entanglement. More about that later.

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