On May 15, 1935, Albert Einstein co-authored a paper with his two postdoctoral research associates, Boris Podolsky and Nathan Rosen, at the Institute for Advanced Study. First published in the Physical Review, the article was titled "Can the quantum mechanical description of physical reality be considered complete?" and generally referred to as "EPR" because of the first initials of the authors' last names, this article quickly became a vital part of current and long-standing debates over the correct interpretation of quantum theory. In fact, it is ranked among the ten best papers ever published in the Physical Review journals, and the EPR always tops their list of most cited papers due to its central role in the development of the theory of quantum information. In the article itself and at the heart of the subject, two quantum systems are joined in such a way as to relate both their spatial positions in a certain direction and also their linear moments in their respective directions, even when the systems are far away from each other. one from the other. other in space. Because of this “entanglement,” determining the position or momentum of one system would respectively fix the position or momentum of the other. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get an original essay On this basis, they argue that one cannot maintain both the accepted view of quantum mechanics and the completeness of the theory; in essence, only one of the two can be correct. This essay describes the central argument of this 1935 article, explores its possible solutions, and probes the current importance of the questions raised by the article. By 1935, the conceptual understanding of quantum theory was dominated by Niels Bohr's ideas regarding complementarity as described in the Copenhagen Interpretation. These ideas focused on observations and measurements obtained in the quantum domain, because according to the theory, observing a quantum object involves an inherent physical interaction with a measuring device that affects both systems in an uncontrolled way. The best picture to think of would be a photon observing device trying to measure the position of an electron, where the photons inherently hit the electrons and move them a certain distance. The effect this has on the measuring instrument as a "result" can only be predicted statistically, leading to inherited errors within the measuring system. Furthermore, the effect suffered by the quantum object limits the other quantities that can be co-measured with the same level of precision, and according to the complementarity of the Heisenberg uncertainty principle, when the position of an object is observed , its momentum is affected in some cases. capacity unknown. So the position and momentum of the particle cannot be known at exactly the same level. In fact, a similar situation arises for the simultaneous determination of energy and time. Thus, complementarity requires a doctrine of unknowable physical interactions which, according to Bohr, are also the origin of the statistical nature of quantum theory. Einstein was initially enthusiastic about quantum theory and even expressed ardent support for its general approval. By 1935, however, while recognizing the theory's significant achievements, his enthusiasm had turned into something else: disappointment. His reservations were twofold. First, he believed that theory had completely abandoned the historical task of natural science, which was to provide knowledge of the fundamental laws of natureindependent of observers or their observations. Instead, the dominant understanding of the quantum wave function in theory was that it treated only the results of any measurement as probabilities, as described by Born's rule. In fact, the theory made no mention of what, if anything, would likely be true if no observations had ever occurred. The fact that there may be laws for a system subject to observation, but no laws of any kind dictating how the system behaves independently of observation, has portrayed quantum theory as unrealistic at best. and false at worst. Second, quantum theory as defined by the Copenhagen interpretation was essentially statistical. The probabilities built into the wave function were fundamental and, unlike classical mechanics, they were not understood as a simple case of moving decimal places to achieve finer and finer precision in instrument readings. In this sense, the theory was indeterministic, and Einstein began to examine how quantum theory was closely related to indeterminism and the concept of determinism in general. He wondered whether it was possible, at least in principle, to attribute certain properties to a quantum theory. quantum system in the absence of measurement. Is it possible, for example, that the decay of an atom actually happens at a given time, even if such a decay time is not implied by the quantum wave function? In trying to answer these questions, Einstein began to wonder whether quantum theory's descriptions of quantum systems were in fact complete. In other words, can all physically relevant truths about systems be derived from quantum states? In response, Bohr and other sympathizers of his complementarity theory made bold claims, not only about the descriptive adequacy of quantum theory, but also about its "finality", claims which enshrined the hallmarks of indeterminism which worried Einstein. Thus, complementarity became Einstein's target of investigation. In particular, Einstein had reservations about the uncontrollable physical effects touted by Bohr in the context of measurement interactions and their role in fixing the interpretation of the wave function. Accordingly, the EPR's emphasis on comprehensiveness was intended to support these reservations in a particularly dramatic way. The EPR text is primarily interested in the logical links between two statements. The first claim is that quantum mechanics is incomplete, and the second claim is that incompatible quantities, such as the value of the x coordinate of a particle's position and the value of the linear momentum of that same particle in the direction x, cannot simultaneously have a “reality”. » ; in other words, they cannot have real and discrete values ​​simultaneously. The authors declare the contradiction of these two hypotheses as their first premise: one or the other must be verified. It follows that if quantum mechanics were complete, which would indicate that the first assertion fails, then the second would be valid; that is, incompatible quantities cannot have real values ​​simultaneously. They further assume that if quantum mechanics were complete, then incompatible quantities, particularly position and momentum coordinates, could indeed have simultaneous real values. They then conclude that quantum mechanics is incomplete for the reasons mentioned above. This conclusion certainly follows from their logic, because otherwise, ifthe theory was complete, we would have a contradiction on the simultaneous values. To establish these two premises more fully and flesh them out so that no doubt remains, the EPR begins with a discussion of the idea of ​​a complete theory. Here, the authors propose a single necessary condition: for a theory to be complete, “each element of physical reality must have a counterpart in the physical theory.” Although they do not explicitly define an "element of physical reality" in the text, this expression is used to refer to values ​​of physical quantities, such as positions, momenta and spins, which are determined by a "physical state real” underlying. The picture that EPR constructs in this section is that quantum systems have real states that assign values ​​to certain quantities, and while the authors vacillate between saying that the quantities in question have "definite values" or "if there is an element of physical reality corresponding to the quantity", let us assume that the simplest terminology is adopted. If this hypothesis is true, a system can therefore be defined as definite if this quantity has a definite value; that is, whether the actual state of the system attributes a value, or an “element of reality,” to the quantity. Furthermore, without a change in the actual state, there will be no change among the values ​​assigned to these quantities. With this understanding now in place, in order to study the question of completeness, the major question that the EPR must now answer is when, exactly, a quantity has a definite value. For this, they propose a minimum sufficient condition: if, without disturbing a system in any way, the prediction with absolute certainty of the value of a physical quantity is possible, then there must exist at least one element of reality corresponding to this greatness. . This condition for an "element of reality" is known as the EPR reality criterion, and for illustration purposes, the EPR refers to the specific case where the solution of the quantum wave function is an eigenstate, since in an eigenstate, the corresponding eigenvalue has a probability of one. Thus, it has a defined value that can be determined, and therefore predicted with absolute certainty, without disturbing the system. With this understanding in place, the mathematics of eigenstates shows that if, for example, the position and momentum values ​​of a quantum system were defined and, therefore, elements of reality, then the description provided by the The wave function of the system would be: incomplete, because no wave function can contain equivalents to the eigenvalues ​​of one for both elements due to the generally accepted postulates of Heisenberg. The authors therefore verify the first premise: either quantum theory is incomplete, or there cannot be “defined” values ​​that are simultaneously real and “defined” for incompatible quantities. The next challenge is to show that if quantum mechanics were complete, then incompatible quantities could have simultaneous real values, which forms the basis of the second premise. This assertion, however, is not so easy to demonstrate. Certainly, what the EPR does from this point on is rather strange. Instead of assuming completeness, and on that basis, inferring that incompatible quantities can actually simultaneously have real values, they simply set out to infer the latter claim without assuming any completeness. This “derivation” turns out to be the central and most controversial part of the article. To prove this derivation, they sketch then dissect an emblematic thought experiment whose variations continue to be widely discussed to this day..