Lessons from the Double-Slit Experiment

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    Ciprian Begu

    The Double-Slit Experiment demonstrated that light and matter can display characteristics of both classically defined waves and particles; moreover, it displayed the fundamentally probabilistic nature of quantum mechanical phenomena. What lessons are to be learned from this experiment and what explanation does the Semantic Interpretation of Quantum Theory offer for this weird, seemingly contradictory behavior of light and matter?

    Ashish Dalela

    The first lesson is that light is a particle. This is a lesson because in classical physics light was treated as a wave, and the interference pattern formed on the battery of detectors was attributed to the interference between two waves emanating from the two slits. The double-slit experiment shows that if we slow down the intensity of the light emanating from the source, then we can find individual detectors in the battery clicking one by one. Based on these individual clicks we know that the light doesn’t simultaneously arrive at all the detectors (which would be the case if light was a wave). Rather, the light arrives at the detectors one by one, implying it is a particle.

    The next lesson is that even though light is detected as particles, these are not classical particles. A classical particle will have an equal probability of arriving at all the detectors which means we will see a Boltzmann distribution or Normal distribution of all the particles on the detectors—maximum intensity in the detector closest to the slits and lesser intensities as we move away from the slits in both directions. However, we observe an interference pattern, which cannot be explained by assuming that these are classical particles. So we need a new model.

    The problem is how to arrive at this new model. We have two contradictory models—individually the photons are particles, and collectively they are waves. The simplest reconciliation of this problem in modern quantum theory is that the wave is a probability function that describes the probabilities of the arrival of the individual particles at any particular detector. However, these probabilities do not tell us the order in which the particles arrive one by one. The order of arrival is empirically observed, but it is not theoretically explained or predicted. The lack of this prediction and explanation form the crux of the problem in understanding the experiment.

    There are many interpretations of this experiment that try to solve or address this issue.

    In Bohr’s interpretation, this problem in quantum theory is permanent because we are compelled to use two complementary descriptions—one a particle and the other a wave. Bohr thought that we can never get out of this complementary description and hence never complete quantum theory. Einstein on the other hand thought that probabilities in quantum theory meant that nature was playing dice, and he is quoted saying “God does not play dice”.

    John von Neumann said that there is a consciousness that “collapses” the wavefunction into a particular alternative, and the order of detection is therefore attributed to conscious choices. However, how this consciousness interacts with the wavefunction was never explained. In the many-worlds interpretation pioneered by John Everett, the wavefunction describes the observed outcomes but doesn’t tell us which universe will see which outcome. So just as we see one event in our universe, the other events are occurring in other universes. As new events are created, the number of universes increase. So, the number of universes is constantly growing. With this approach, we still have the problem that we don’t know which of these exponentially expanding universes is our universe!

    In the decoherence approach to this problem, the probability is reduced when two or more systems begin interacting. If the possibilities in the first system are A, B, and C, and the possibilities in the second system are C, D, and E, then their combination will produce the possibility C. This approach now creates a new problem, namely, that to predict the succession of events, we have to predict the succession of systems with which the observed system interacts.

    Therefore, the basic problem of quantum theory never goes away; it only changes form. Whether we call this problem a permanent limitation of human description or call it the succession of choices made by consciousness, or the inability to predict which particular universe is our universe or the specific sequence of systems with which a particular system interacts to create a definite reality, the problem resurfaces in different forms. Therefore, no interpretation of quantum theory thus far solves the problem or even shows a path on which the problem could be solved. It only restates the problem in a new way.

    The Semantic Interpretation is different. It says that the quantum world is like a book of symbols with meaning, but the current experimental method measures this book like an illiterate person, who sees the succession of words but cannot understand the meaning. The method therefore only looks at the shape of the symbols and measures probabilities. Quantum theory, in the Semantic Interpretation, can be completed if the reality was treated as a book. For example, as we read the cover of the book, we see the book completely but in an abstract sense. Then as we see the table of contents, we get a more detailed idea about the chapters in the book, but we don’t see the entire book at the same time. Then as we read the navigation menu about the sections in each chapter, we get an even better idea, but we sacrifice knowing the other sections of the book at the same time. Then as we read the paragraphs, the first sentence gives us a good idea about the whole paragraph (assuming the paragraphs are well-written, and they summarize the paragraph in the first sentence), but we defocus from the contents in the other paragraphs. The book’s content follows a tree structure in which the table of chapters is like the trunks, the sections in each chapter are the branches, the first sentence in the paragraph captures the essence of that paragraph, and so forth. As we focus on the details we lose the big picture. And yet, the full picture and the details are presented to us in a sequence.

    The point of the Semantic Interpretation is that if we begin from the big picture, then we can better predict the details. However, if we begin in the details we cannot predict the big picture. For instance, as you read the book’s title, you can eliminate a number of possibilities about the book (e.g. from the title of the book you can know that the book is fiction or non-fiction). As you go through chapter titles you can further eliminate even more possibilities. Therefore, by approaching the book hierarchically we are able to reduce the uncertainty.

    Just like you look at a forest from a distance and you can see greenery but you don’t know what types of trees exist in the forest. Then you come a little closer and you can see the species of the trees but you cannot count the number of branches on the tree. If you go even closer, you can count the branches and then leaves, and then veins on each leaf, and then the cellular structure inside each vein, etc. The knowledge of the forest is true and complete. The knowledge of the species of the tree is true, but incomplete because when we see the individual tree we don’t see the other trees. The knowledge of the number of trunks and branches is true but incomplete because when we see the individual branches and trunks we don’t see the other branches, other trees, and the entire forest.

    Therefore, we can know the truth at many levels. Each of these levels constitutes the truth but if you look at the whole truth you see the reality completely and yet the knowledge is abstract. As you delve into more details, you know the truth partially. Therefore, you tradeoff the completeness with the detail; looking at the detail forces you to renounce the big picture. In terms of quantum theory, we can progressively reduce the uncertainty by looking at the world in a hierarchical manner—from forest to trees to trunks to branches to leaves, and so forth.

    In the everyday world, we use macroscopic objects—e.g. tables, chairs, and cars—without knowing everything about the molecular structure. We call this the science of macroscopic objects. It is abstract knowledge; it works and it is true. For most practical purposes we don’t need to know the details because we can manipulate the macroscopic object without knowing its molecular structure. There is no contradiction between the macroscopic and microscopic sciences, but there is a contradiction between classical (macroscopic) physics and quantum (microscopic) physics. The reason is that classical particles are indivisible, whereas macroscopic objects are divisible. At the macroscopic level, we are dealing with summarized information, whereas at the microscopic level we are dealing with detailed information.

    Both summarized and detailed pictures of reality constitute information; which means they have to be both treated as information—namely associated with each bit of information is the hierarchical level of abstraction or detail. Physics doesn’t have this ability to indicate whether a physical particle represents abstract or detailed information. We cannot say that some particle is the summary of a hundred other particles. So we just see the particles but we don’t know what they mean. But in the everyday world, there are many levels of knowledge—from summarized to detailed. And to know anything we have to define the level at which we are knowing the same reality.

    So, the semantic interpretation opens up the idea that the same world is infinite descriptions—some of which are detailed and the others are abstract; the abstract description is complete whereas the detailed description is partial. If we want to know everything in a detailed manner, we have to collect the experiences of the entire tree and organize them in a hierarchy. Similarly, when we uncover the experience we have to describe it from the root to the leaves, and the summary information reduces the uncertainty in the detailed information. If we progress from the root to the leaves we can progressively make better and better predictions, provided we understand that something is the root and something is a leaf. If we ignore this hierarchy, then we cannot use the previous events to predict the next event.

    So, this interpretation recognizes the reality of both macroscopic and microscopic realities and tells us that they can be consistent, dissolving the quantum-classical conflict. It also says that macroscopic knowledge is abstract—e.g. tables, chairs, cars—but also more complete. And because it is more complete we don’t need atomic physics in the day to day life to manipulate the world. If, however, we wanted to know more deeply about matter the doors are open to keep refining the knowledge. It follows that both macroscopic and microscopic reality is meaning and not just physics and we have to view even the material world as meaning rather than meaningless particles and waves.

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