Introduction The historical development of scientific progress teaches us that every theory that was established and broadly accepted at a certain time was later inevitably replaced by a deeper and more fundamental theory of which the old one remains a special case. One celebrated example is Newtonian (classical) mechanics, which was superseded by quantum mechanics at the beginning of the last century. It is natural to ask whether in a similar manner there could be logically consistent theories that are more generic than quantum theory itself. It could then turn out that quantum mechanics is an effective description of such a theory, only valid within our current restricted domain of experience. At present, quantum theory has been tested against very specific alternative theories that, both mathematically and in their concepts, are distinctly different. Instances of such alternative theories are non-contextual hidden-variable theories [1], local hidden-variable theories [2], crypto-nonlocal hidden-variable theories [3, 4], or some nonlinear variants of the Schrödinger equation [5–8]. Currently, many groups are working on improving experimental conditions to be able to test alternative theories based on various collapse models [9–14]. The common trait of all these proposals is to suppress one or the other counterintuitive feature of quantum mechanics and thus keep some of the basic notions of a classical worldview intact. Specifically, hidden-variable models would allow us to preassign definite values to outcomes of all measurements; collapse models are mechanisms for restraining superpositions between macroscopically distinct states, and nonlinear extensions of the Schrödinger equation may admit more localized solutions for wave-packet dynamics, thereby resembling localized classical particles.
Introduction The historical development of scientific progress teaches us that every theory that was established and broadly accepted at a certain time was later inevitably replaced by a deeper and more fundamental theory of which the old one remains a special case. One celebrated example is Newtonian (classical) mechanics, which was superseded by quantum mechanics at the beginning of the last century. It is natural to ask whether in a similar manner there could be logically consistent theories that are more generic than quantum theory itself. It could then turn out that quantum mechanics is an effective description of such a theory, only valid within our current restricted domain of experience. At present, quantum theory has been tested against very specific alternative theories that, both mathematically and in their concepts, are distinctly different. Instances of such alternative theories are non-contextual hidden-variable theories [1], local hidden-variable theories [2], crypto-nonlocal hidden-variable theories [3, 4], or some nonlinear variants of the Schrödinger equation [5–8]. Currently, many groups are working on improving experimental conditions to be able to test alternative theories based on various collapse models [9–14]. The common trait of all these proposals is to suppress one or the other counterintuitive feature of quantum mechanics and thus keep some of the basic notions of a classical worldview intact. Specifically, hidden-variable models would allow us to preassign definite values to outcomes of all measurements; collapse models are mechanisms for restraining superpositions between macroscopically distinct states, and nonlinear extensions of the Schrödinger equation may admit more localized solutions for wave-packet dynamics, thereby resembling localized classical particles.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function ( e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.
How it all began In 1935, a decade after the invention of quantum theory by Heisenberg (1925) and Schrödinger (1926), three papers appeared, setting the stage for a new concept, quantum entanglement. The previous decade had already seen momentous discussions on the meaning of the new theory, for example by Niels Bohr (see his contribution to Albert Einstein: Philosopher-Scientist in Further reading); but these new papers opened up the gates for a new, very deep philosophical debate about the nature of reality, about the role of knowledge, and about their relation. Since the 1970s, it has become possible for experimenters to observe entanglement directly in the laboratory and thus test the counter-intuitive predictions of quantum mechanics whose confirmation today is beyond reasonable doubt. Since the 1990s, the conceptual and experimental developments have led to new concepts in information technology, including such topics as quantum cryptography, quantum teleportation, and quantum computation, in which entanglement plays a key role. In the first of the three papers, Einstein, Podolsky, and Rosen (EPR) realized that, if two particles had interacted in their past, their properties will remain connected in the future in a novel way, namely, observation on one determines the quantum state of the other, no matter how far away. Their conclusion was that quantum mechanics is incomplete and they expressed their belief that a more complete theory may be found. Niels Bohr replied that the two systems may never be considered independent of each other, and observation on one changes the possible predictions on the other. Finally, Erwin Schrödinger, in the paper which also proposed his famous cat paradox, coined the term “entanglement” (in German Verschränkung ) for the new situation and he called it “not one, but the essential trait of the new theory, the one which forces a complete departure from all classical concepts.”
Erwin Schrodinger first used the phrase “quantum entanglement” in 1935 to describe a mechanical phenomenon at the quantum level where two (or more) particles’ quantum states must be defined in relation to one another even if they may be geographically apart. This paradoxical event has confounded us for a very long time. Entangled particle behavior appears to be mysterious, illogical, and akin to sorcery at work. The successful and dependable principle of locality has led us to the achievements of twentieth-century physics. However, some theorists may doubt the locality itself due to the “spooky” and nonlocal effects of the local laws of quantum theory. Could there truly be an instant connection between two subatomic particles located on the extreme edges of the universe? Is there a theory that predicts such a relationship that is fundamentally faulty or lacking? Are the outcomes of the experiments that show this connection being read incorrectly? These questions challenge our most fundamental understanding of space and time. The universe is currently being disassembled by modern physics, and it will never be the same. Utilizing cutting-edge technology, quantum entanglement will have a positive impact on society. The history of quantum entanglement is outlined in this work, along with several hypotheses regarding the puzzling behavior of entangled particles. Quantum entanglement may also be an instance of nonlocality in action, in which what occurs in one location affects what occurs in another. Entanglement can also be compared to a situation in which a light switch is used to control two (or more) light bulbs, causing them to turn on at the same time when the switch is switched on. The key question is whether one of the aforementioned theories actually accounts for the odd behavior of entangled particles, in which case experimental evidence would unquestionably support the theory.
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the other). Hence, every time that a certain construal of reality encounters a problem, there is a choice between a modification to the mathematical formalism of the physical theory and a change in the model of reasoning. A case in point is negative construal of quantum superposition causing the problem of definite outcomes. To be sure, according to the said construal, it is not the case that a system being in a superposition of states is exclusively in one of the states constituting the superposition, which in turn implies that macroscopically differing outcomes of observation may appear all at once. The usual approach to the problem of definite outcomes is to modify the quantum mathematical formalism by adding to it some extra postulates (for instance, the postulate of wave function collapse). However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model of reasoning. This possibility is studied in the present paper.