2025 is the year of Quantum Science and Technology. It celebrates 100 years since the invention of quantum theory (as previously mentioned, in 1925 Heisenberg published what is considered the first paper on quantum mechanics). How is quantum theory doing on her 100th birthday? It is thriving! Its successes continue in quantum chemistry, condensed matter, molecular, optical, nuclear and particle physics, and new areas of quantum information and quantum computation that utilize non-classical information theoretic properties of quantum systems have burst upon the scene, and many researchers are involved in the new area of quantum biology. The achievements of quantum theory are phenomenal, and there does not exist a single experiment that contradicts its basic tenets. As illustrated by the magic cube of physics, the structure of the fundamental framework of physics is completely dominated by quantum theory, which is intrinsically probabilistic and contextual, and by spacetime physics, which is not intrinsically probabilistic and it is not contextual. In the area of overlaps between quantum and spacetime physics, we find local quantum field theory, where spacetime appears as a glorified index of quantum fields—and yet is important in defining what we mean by locality, causality, etc. Nevertheless, local quantum field theory, especially in the form of effective field theory has scored (and continues to score) impressive successes in particle, nuclear and condensed matter and statistical physics, as well as in the realms of quantum field theory in curved but not dynamical backgrounds, including weakly gravitational fields and cosmology.
2025 is the year of Quantum Science and Technology. It celebrates 100 years since the invention of quantum theory (as previously mentioned, in 1925 Heisenberg published what is considered the first paper on quantum mechanics). How is quantum theory doing on her 100th birthday? It is thriving! Its successes continue in quantum chemistry, condensed matter, molecular, optical, nuclear and particle physics, and new areas of quantum information and quantum computation that utilize non-classical information theoretic properties of quantum systems have burst upon the scene, and many researchers are involved in the new area of quantum biology. The achievements of quantum theory are phenomenal, and there does not exist a single experiment that contradicts its basic tenets. As illustrated by the magic cube of physics, the structure of the fundamental framework of physics is completely dominated by quantum theory, which is intrinsically probabilistic and contextual, and by spacetime physics, which is not intrinsically probabilistic and it is not contextual. In the area of overlaps between quantum and spacetime physics, we find local quantum field theory, where spacetime appears as a glorified index of quantum fields—and yet is important in defining what we mean by locality, causality, etc. Nevertheless, local quantum field theory, especially in the form of effective field theory has scored (and continues to score) impressive successes in particle, nuclear and condensed matter and statistical physics, as well as in the realms of quantum field theory in curved but not dynamical backgrounds, including weakly gravitational fields and cosmology.
Why yet another book on quantum mechanics? Quantum mechanics was born in the first quarter of the twentieth century and has received an enormous number of theoretical and experimental confirmations over the years. It is considered to be the fundamental physical paradigm, and has a wide range of applications, from cosmology to chemistry, and from biology to information sciences. It is one of the greatest intellectual achievements of the past century. As an effect of its invention, the very concept of physical reality was changed, and “observation,” “measurement,” “prediction,” and “state of the system” acquired a new and deeper meaning. Probability was not unknown in physics: it was introduced by Boltzmann in order to control the behavior of a system with a very large number of particles. It was the missing concept in order to understand the thermodynamics of macroscopic bodies, but the structure of the physical laws remained still deterministic. The introduction of probability was needed as a consequence of our lack of knowledge of the initial conditions of the system and of our inability to solve an enormous number of coupled non-linear differential equations. In quantum mechanics, the tune is different: if we have 10 6 radioactive atoms no intrinsic unknown variables decide which of them will decay first. What we observe experimentally seems to be an irreducible random process. The original explanation of this phenomenon in quantum mechanics was rather unexpected.
The theory of Quantum Mechanics is one of the mainstay of modern physics, a well-established mathematical clockwork whose strength and accuracy in predictions are currently experienced in worldwide research laboratories. As a matter of fact, Quantum Mechanics laid the groundwork of a rich variety of studies ranging from solid state physics to cosmology, from bio-physics to particle physics. The up-to-date ability of manipulating single quantum states is paving the way for emergent quantum technologies as quantum information and computation, quantum communication, quantum metrology and quantum imaging. In spite of the impressive matemathical capacity, a long-standing debate is even revolving around the foundational axioms of this theory, the main bones of content being the non-local effects of entangled states, the wave function collapse and the concept of measurement in Quantum Mechanics, the macro-objectivation problem (the transition from a microscopic probabilistic world to a macroscopic deterministic world described by classical mechanics). Problems that, beyond their fundamental interest in basic science, now also concern the impact of these developing technologies. Without claiming to be complete, this article provides in outline the living matter concerning some of these problems, the implications of which extend deeply on the connection between entanglement and space-time structure.
From the very beginning, Quantum Mechanics has been accompanied by crucial foundational questions: the possibility of visualizing physical processes, the limits of measurement epitomized by the Heisenberg uncertainty principle, the existence of a deeper underlying reality with additional degrees of freedom, the role of measurements, and the status of locality. Long regarded as philosophical speculations, these issues were progressively reformulated into precise mathematical statements and ultimately subjected to experimental verification. The trajectory proved unpredictable: questions once dismissed as metaphysical gave rise to experimental platforms, which in turn matured into devices and technologies powering quantum computation, communication, and sensing. Yet this development is not unidirectional: advances in technology also feed back into foundations, enabling tests of principles that were previously out of reach, for example, whether quantum superposition persists at larger and larger scales and whether reality, gravity included, is fundamentally quantum. In this way, the dialogue between foundational inquiry and technological progress continues to shape both our theoretical understanding and the practical realization of quantum phenomena.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from special relativity, quantum optics, general relativity, quantum communication and quantum computation. The high level of current interest in these subjects is exemplified by the recent award of the 2012 Nobel Prize in Physics to Serge Haroche and David J Wineland for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems. It is our hope that this issue will encourage new researchers to enter this rapidly developing and exciting new field. R B Mann and T C Ralph Guest Editors
Quantum physics emerged from the failures of classical physics to explain many physical phenomena. Quantum physics has contributed immensely to science and underpinned modern technologies. The UN-designated International Year of Quantum Science and Technology (2025) recognizes the centenary of the birth of quantum mechanics as a complete theory and its profound contribution to the first quantum revolution, which has given us computers, mobile phones, lasers, GPS and MRI. Also a second quantum revolution is poised to provide unprecedented computing ability through quantum computers, secure communication with quantum cryptography and ultrasensitive quantum sensing devices for various diagnostic tools.