On May 15, 1935, Albert Einstein wrote a paper together with his two postdoctoral researchers, Boris Podolsky and Nathan Rosen, at the Institute for Advanced Study. First published in Physical Review, the article was titled "Can the quantum mechanical description of physical reality be considered complete?", and generally referred to as "EPR" due to the initials of the authors' last names, this article quickly became a central point in debates, both current and old, on the correct interpretation of quantum theory. In fact, it is ranked among the top ten papers ever published in Physical Review journals, and the EPR still tops the list of most cited papers due to its fundamental role in the development of quantum information theory. Within the article itself and at the heart of the matter, two quantum systems are joined in such a way as to connect both their spatial positions in a certain direction and also their linear momenta in the respective directions, even when the systems are nowhere near close to each other. else in space. As a result of this “entanglement,” determining the position or momentum of one system would fix the position or momentum of the other, respectively. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay On this basis, they argue that it is not possible to maintain both the accepted view of quantum mechanics and the completeness of the theory; essentially only one of the two can be correct. This essay describes the central argument of that 1935 article, explores its possible solutions, and investigates the current significance of the questions raised by the article. In 1935, the conceptual understanding of quantum theory was dominated by Niels Bohr's ideas regarding complementarity described by the Copenhagen Interpretation. Those ideas centered on observations and measurements obtained in the quantum domain, since according to the theory, observation of a quantum object involves an intrinsic physical interaction with a measuring device that affects both systems in an uncontrolled manner. The best image to think of would be a photon observing apparatus that attempts to measure the position of an electron, where the photons intrinsically hit the electrons and move them some distance. The effect this has on the measurement instrument as a “result” can only be predicted statistically, leading to inherited errors within the measurement system. Furthermore, the effect experienced by the quantum object limits which other quantities can be co-measured with the same level of precision and, according to complementarity through the Heisenberg Uncertainty Principle, when observing the position of an object, its quantity of motion is affected in some way. unknown capacity. Therefore, both the position and the momentum of the particle cannot be known at exactly the same level. Indeed, a similar situation occurs for the simultaneous determination of energy and time. Therefore, complementarity requires a doctrine of unknowable physical interactions which, according to Bohr, are also the source 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 he recognized the theory's significant results, his excitement had turned into something else: disappointment. His reservations were twofold. First, he believed that the theory had completely abandoned the historical task of the natural sciences, which was toprovide knowledge of the fundamental laws of nature that was independent of observers and their observations. Instead, the prevailing understanding of quantum wave function theory was that it treated the results of any measurement only as probabilities, as outlined by the Born Rule. In fact, the theory made no mention whatsoever of what, if anything, would likely be true if no observation had ever occurred. The fact that there could be laws for a system under observation, but no laws of any kind establishing how the system behaves independently of observation, painted quantum theory as unrealistic at best and false at worst. Second, the quantum theory defined by the Copenhagen Interpretation was essentially statistical. The probabilities built into the wave function were critical and, unlike the case of classical mechanics, were not intended to be a simple case of moving decimals to achieve ever finer precision in instrument readings. In this sense the theory was indeterministic, and Einstein began to probe how strongly quantum theory was tied to indeterminism and the concept of determinism in general. He wondered whether it was possible, at least in principle, to attribute certain properties to an object. quantum system in the absence of measurement. Is it possible, for example, that the decay of an atom actually occurs at a precise moment in time, even if such a defined decay time is not implicit in the quantum wave function? In attempting 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 proponents of his theory of complementarity made bold claims, not only about the descriptive adequacy of quantum theory, but also about its “finality,” claims that encapsulated the features of indeterminism that worried Einstein. Therefore, complementarity became Einstein's focus of investigation. In particular, Einstein had reservations about the uncontrollable physical effects extolled by Bohr in the context of measurement interactions and their role in fixing the interpretation of the wave function. As a result, the EPR's focus on completeness was intended to shore up those reservations in a particularly dramatic way. The EPR text is primarily concerned with the logical connections between two statements. The first statement is that quantum mechanics is incomplete, and the second statement is that incompatible quantities, such as the value of the x-coordinate of the position of a particle and the value of the linear momentum of the same particle in the x-direction, cannot have a “reality ” simultaneous. ”; in other words, they cannot have real and discrete values ​​at the same time. The authors declare as their first premise the contradiction of these two assumptions: one or the other must be valid. It follows that if quantum mechanics were complete, indicating that the first statement failed, then the second would hold; that is, incompatible quantities cannot have real values ​​simultaneously. They also take as a second premise that if quantum mechanics were complete, then incompatible quantities, particularly position and momentum coordinates, could actually have real and simultaneous values. They therefore conclude that quantum mechanics is incomplete for the reasons stated above. This conclusion certainly follows from their logic since otherwise, if the theory were complete, there would be a contradiction suisimultaneous values. To establish these two premises more completely and concretize them so that no doubt remains, the EPR begins with a discussion of the idea of ​​a complete theory. Here the authors offer only one necessary condition: that for a theory to be complete, “every element of physical reality must have a counterpart in physical theory.” Although they do not explicitly define an “element of physical reality” in the text, that expression is used when referring to values ​​of physical quantities, such as positions, momentum, and rotations, that are determined by an underlying “real physical state.” The picture that EPR builds in this section is that quantum systems have real states that assign values ​​to certain quantities, and while the authors struggle between saying that the quantities in question have “definite values” or whether “there exists an element of physical reality corresponding to quantity”, let's assume that the simplest terminology is adopted. If this assumption is true, a system can therefore be said to be defined if that quantity has a defined value; that is, if the real 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 between the values ​​assigned to those quantities. With this understanding now in place, in order to investigate the question of completeness, the main question the EPR must now answer is when, exactly, a quantity has a definite value. To this end they offer a minimum sufficient condition: if, without disturbing a system in any way, it is possible to predict the value of a physical quantity with absolute certainty, then there must exist at least one element of reality corresponding to that quantity. This condition for an “element of reality” is known as the EPR Reality Criterion, and, by way of illustration, EPR points 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. It therefore 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 values ​​of position and momentum for a quantum system were defined and, consequently, elements of reality, then the description provided by the wave function of the system would be incomplete, since no wave function can contain counterpart eigenvalues ​​of one for both elements due to the generally accepted Heisenberg postulates. The authors therefore verify the first premise: either quantum theory is incomplete, or simultaneously real and "definite" values ​​cannot exist for incompatible quantities. The next challenge is to prove that if quantum mechanics were complete, then incompatible quantities could have simultaneous real values, which is the basis of the second premise. This claim, however, is not so easy to prove. Of course, what the EPR will do from this point on is rather strange. Instead of assuming completeness, and on this basis, deducing that incompatible quantities can actually have real values ​​simultaneously, they simply set out to derive the latter statement without assuming any completeness. This “derivation” turns out to be the central and most controversial part of the article. To demonstrate this derivation, they sketch and then unpack an iconic thought experiment whose variations continue to be widely discussed to this day. The experiment discusses two quantum systems that, although spatially distant from each other and perhaps quite far apart, the total quantum wave function for the pair connects both the systems' positions and their linear momenta together. Within.