Testable proposals for the measurement problem

In a previous post, I made the statement: “Currently, there are no known experimental conditions that can distinguish between different interpretations of quantum mechanics.” Well, that is not exactly true. Perhaps one can argue that no experiment has yet been performed that conclusively ruled out or confirmed any of the interpretations of quantum mechanics. But, the fact is that recently, there has been some experimentally testable proposals. Still, I’m not holding my breath.

Recently, seeing one such proposal, I remembered that I also knew about another testable proposal made by Lajos Diósi and Roger Penrose. The reason I forgot about that is probably because it seems to have some serious problems. At some point, during a conversation I had with Lajos, I told him I have a stupid question to ask him: does quantum collapse travel at the speed of light? His response was: that is not a stupid question. So, then I concluded that it is not something that any of the existing collapse models can handle correctly. In fact, I don’t think any such model will ever be able to handle it in a satisfactory manner.

Thinking back to those discussions and the other bits and pieces I’ve read about the measurement problem, I tend to reconfirm my conviction that the simplest interpretation of quantum mechanics (and therefore the one most likely to be correct) is the so-called Many Worlds interpretation of quantum mechanics. However, the more I think about it, the more I believe that “many worlds” is a misnomer. It is not about many worlds or many universes that are constantly branching off to become disjoint universes.

Perhaps one can instead call it the “multiple reality” interpretation. But how would multiple realities be different from “many worlds”? That fact is that these realities are not disjoint, but form part of the unitary whole of a single universe. These realities can be combined into arbitrary superpositions. What more, these realities are not branching of to produce more realities. The number of realities remains the same for all time. (There are actually an infinite number of them, but the cardinality of the set remains the same.) The interactions merely change the relative complex probability amplitudes of all the realities. 

Anyway, just thought I should clear this up. I don’t see myself ever writing publication on this topic.

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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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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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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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