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Here is a simple analogy that helps to understand the basic idea of the Bohmian interpretation of quantum mechanics.
Assume that you have recipes for two different meals. These recipes are written on papers. Hence, these recipes are real. However, when you make the meal, you use only one of the recipes. Only one meal is real. The unused recipe is not real as a meal. But it is still real as a recipe. Now, wave functions are recipes, and particles are meals.
At least this is so in the Bohmian interpretation. But such a view of recipes and meals is not widely accepted. Most physicists find such a view too complicated. For example, why one should deal with both recipes and meals, when recipes alone are enough? There are much simpler ways to make the food.
For example, in the Copenhagen interpretation meals do not exist at all. Only the recipes, which collapse to a single recipe when you decide to eat. Very simple indeed.
In the many-world interpretation the meals also do not exist, but the recipes do not collapse. Instead, they all exist all the time. But we see (and eat) only one of them. Why only one? It's obvious, each recipe exists in another parallel universe, of course.
So who is right? I think it's obvious. But if you are a pragmatic person, you will not care about that. You will just shut up and eat.
The goal of this entry is to provide a simple everyday-life analogy to explain quantum wave-particle duality, which-way experiments, delayed choice experiments, and quantum erasers. This analogy resulted from my attempt to explain the paper http://xxx.lanl.gov/abs/quant-ph/9903047 [Phys.Rev.Lett. 84 (2000) 1-5] to a psychologist.
Are photons particles or waves? Instead of dealing with such an abstract question, we deal with an analogous one: Are humans individuals ("particles") or social groups ("waves")? Well, in a sense they are both. But, there is a social-individual (wave-particle) complementarity principle: If you observe the social properties of humans, you cannot observe their individual properties at the same time. Analogously, if you observe their individual properties, you cannot observe their social ones.
Or can you? Let us try to do that in a specific way analogous to the experiment in the PRL paper mentioned above. Consider a society that contains two kinds of people: those with white skin and those with black skin. Nevertheless, they do not care about this difference; they live together, their friendships do not depend on the color of their skin, etc. So, your observation of their social properties tells you nothing about their individual property - their color.
Or does it? Let us observe how they are distributed as the audience during a football match. In order to see their color, they do not wear shirts. From a long distance, each individual looks as a black or a white dot. Hence, what you see is a random uniform distribution of black and white dots.
Now you watch for the coincidences: you take into consideration only the dots that are black (or only the dots that are white). Still, you only see a random uniform distribution of dots with a specified color. You do not see anything that looks like social interference. You do not observe the social (wave) properties.
Now you make a trick. You make a loud collective command to all of them: "Show your social properties!". And then something remarkable happens. The overall distribution of dots is still uniform, but if the coincidences are taken into account, i.e., if you observe the distribution of only black (or only white) dots, you observe a nonuniform distribution. Some large regions contain only black dots, while other large regions contain only white dots. The dots are grouped according to their colors. Now the effects of social interference are seen.
But how is that possible? What has happened? To be sure, there was no time for a lot of black and white people to exchange their positions. So does it mean that something like a social "wave function" has suddenly and mysteriously collapsed owing to the collective command? We could not see this effect if we did not observe their colors, so does it mean that the observation of colors is essential? If so, does it mean that the consciousness of the observer plays a crucial role? This is the analog of the wave-function collapse problem in quantum mechanics.
Now we can also erase the interference information that we obtained above. Just give them a new collective command: "Hide your social properties!" and everything will "collapse" to the initial uniform distribution again. (This is the analog of the quantum eraser.) You can repeat it as many times as you want, you can delay the decisions to give the collective orders as much as you want (analog of the delayed choice in quantum mechanics), every time you recover or erase the social interference information as you wish.
But still, how this happens? It looks very mysterious. Nevertheless, the explanation is actually very simple, provided that you allow the existence of something that you do not see (the analog of Bohmian hidden variables in quantum mechanics). Namely, all the time these people are fans of different football clubs. As is well known, in the audience, fans of the same club allways stick together, which explains the origin of social interference. Fans of one club wear black shirts, while fans of the other club wear white shirts. When you give them the command "Show your social properties!" they just put their shirts on. When you give them the command "Hide your social properties!", they just take the shirts off. Trivial, isn't it? No fast exchange of people positions, no collapse, no role for the observers or consciousness, no mystery at all!
But still, how the social-individual complementarity is avoided? How can you observe both their individual properties (their colors) and the social property (the grouping)? The point is that you can't. Namely, unlike the color of the skin, the color of the shirt is NOT an individual property. The color of the shirt is the social property, it expresses the devotion to a specific football club. There is no correlation between the skin color and the shirt color. These are different things. Only if you ASSUME that the measurement of the color always reveals an individual property, you obtain a contradiction with the complementarity principle. On the other hand, if you make a distinction between the observation of the skin color (an analog of the true quantum measurement) and the observation of the shirt color (an analog of the weak quantum measurement) then the complementarity principle is saved. Indeed, in quantum mechanics, the which-way experiments are weak measurements, not true measurements. You cannot truly measure both the interference and the which-way. To truly measure the which-way you should put detectors on the whole way itself, which you don't.
Assume that you have recipes for two different meals. These recipes are written on papers. Hence, these recipes are real. However, when you make the meal, you use only one of the recipes. Only one meal is real. The unused recipe is not real as a meal. But it is still real as a recipe. Now, wave functions are recipes, and particles are meals.
At least this is so in the Bohmian interpretation. But such a view of recipes and meals is not widely accepted. Most physicists find such a view too complicated. For example, why one should deal with both recipes and meals, when recipes alone are enough? There are much simpler ways to make the food.
For example, in the Copenhagen interpretation meals do not exist at all. Only the recipes, which collapse to a single recipe when you decide to eat. Very simple indeed.
In the many-world interpretation the meals also do not exist, but the recipes do not collapse. Instead, they all exist all the time. But we see (and eat) only one of them. Why only one? It's obvious, each recipe exists in another parallel universe, of course.
So who is right? I think it's obvious. But if you are a pragmatic person, you will not care about that. You will just shut up and eat.
The goal of this entry is to provide a simple everyday-life analogy to explain quantum wave-particle duality, which-way experiments, delayed choice experiments, and quantum erasers. This analogy resulted from my attempt to explain the paper http://xxx.lanl.gov/abs/quant-ph/9903047 [Phys.Rev.Lett. 84 (2000) 1-5] to a psychologist.
Are photons particles or waves? Instead of dealing with such an abstract question, we deal with an analogous one: Are humans individuals ("particles") or social groups ("waves")? Well, in a sense they are both. But, there is a social-individual (wave-particle) complementarity principle: If you observe the social properties of humans, you cannot observe their individual properties at the same time. Analogously, if you observe their individual properties, you cannot observe their social ones.
Or can you? Let us try to do that in a specific way analogous to the experiment in the PRL paper mentioned above. Consider a society that contains two kinds of people: those with white skin and those with black skin. Nevertheless, they do not care about this difference; they live together, their friendships do not depend on the color of their skin, etc. So, your observation of their social properties tells you nothing about their individual property - their color.
Or does it? Let us observe how they are distributed as the audience during a football match. In order to see their color, they do not wear shirts. From a long distance, each individual looks as a black or a white dot. Hence, what you see is a random uniform distribution of black and white dots.
Now you watch for the coincidences: you take into consideration only the dots that are black (or only the dots that are white). Still, you only see a random uniform distribution of dots with a specified color. You do not see anything that looks like social interference. You do not observe the social (wave) properties.
Now you make a trick. You make a loud collective command to all of them: "Show your social properties!". And then something remarkable happens. The overall distribution of dots is still uniform, but if the coincidences are taken into account, i.e., if you observe the distribution of only black (or only white) dots, you observe a nonuniform distribution. Some large regions contain only black dots, while other large regions contain only white dots. The dots are grouped according to their colors. Now the effects of social interference are seen.
But how is that possible? What has happened? To be sure, there was no time for a lot of black and white people to exchange their positions. So does it mean that something like a social "wave function" has suddenly and mysteriously collapsed owing to the collective command? We could not see this effect if we did not observe their colors, so does it mean that the observation of colors is essential? If so, does it mean that the consciousness of the observer plays a crucial role? This is the analog of the wave-function collapse problem in quantum mechanics.
Now we can also erase the interference information that we obtained above. Just give them a new collective command: "Hide your social properties!" and everything will "collapse" to the initial uniform distribution again. (This is the analog of the quantum eraser.) You can repeat it as many times as you want, you can delay the decisions to give the collective orders as much as you want (analog of the delayed choice in quantum mechanics), every time you recover or erase the social interference information as you wish.
But still, how this happens? It looks very mysterious. Nevertheless, the explanation is actually very simple, provided that you allow the existence of something that you do not see (the analog of Bohmian hidden variables in quantum mechanics). Namely, all the time these people are fans of different football clubs. As is well known, in the audience, fans of the same club allways stick together, which explains the origin of social interference. Fans of one club wear black shirts, while fans of the other club wear white shirts. When you give them the command "Show your social properties!" they just put their shirts on. When you give them the command "Hide your social properties!", they just take the shirts off. Trivial, isn't it? No fast exchange of people positions, no collapse, no role for the observers or consciousness, no mystery at all!
But still, how the social-individual complementarity is avoided? How can you observe both their individual properties (their colors) and the social property (the grouping)? The point is that you can't. Namely, unlike the color of the skin, the color of the shirt is NOT an individual property. The color of the shirt is the social property, it expresses the devotion to a specific football club. There is no correlation between the skin color and the shirt color. These are different things. Only if you ASSUME that the measurement of the color always reveals an individual property, you obtain a contradiction with the complementarity principle. On the other hand, if you make a distinction between the observation of the skin color (an analog of the true quantum measurement) and the observation of the shirt color (an analog of the weak quantum measurement) then the complementarity principle is saved. Indeed, in quantum mechanics, the which-way experiments are weak measurements, not true measurements. You cannot truly measure both the interference and the which-way. To truly measure the which-way you should put detectors on the whole way itself, which you don't.