The basic equations of physics involve a time variable t and are invariant under the transformation t → −t. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with thermodynamics. But equations written on the blackboard are not the whole story in physics. In prior work we sharpened a distinction obscured in today’s theoretical physics, the distinction between obtaining evidence from experiments on the laboratory bench and explaining that evidence in mathematical symbols on the blackboard. The sharp distinction rests on a proof within the mathematics of quantum theory that no amount of evidence, represented in quantum theory in terms of probabilities, can uniquely determine its explanation in terms of wave functions and linear operators. Building on the proof we show here a role in physics for unpredictable symbol-handling agents acting both at the blackboard and at the workbench, communicating back and forth by means of transmitted symbols. Because of their unpredictability, symbol-handling agents introduce a heretofore overlooked source of irreversibility into physics, even when the equations they write on the blackboard are invariant under t → −t. Widening the scope of descriptions admissible to physics to include the agents and the symbols that link theory to experiments opens up a new source of time-irreversibility in physics.
The basic equations of physics involve a time variable t and are invariant under the transformation t → −t. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with thermodynamics. But equations written on the blackboard are not the whole story in physics. In prior work we sharpened a distinction obscured in today’s theoretical physics, the distinction between obtaining evidence from experiments on the laboratory bench and explaining that evidence in mathematical symbols on the blackboard. The sharp distinction rests on a proof within the mathematics of quantum theory that no amount of evidence, represented in quantum theory in terms of probabilities, can uniquely determine its explanation in terms of wave functions and linear operators. Building on the proof we show here a role in physics for unpredictable symbol-handling agents acting both at the blackboard and at the workbench, communicating back and forth by means of transmitted symbols. Because of their unpredictability, symbol-handling agents introduce a heretofore overlooked source of irreversibility into physics, even when the equations they write on the blackboard are invariant under t → −t. Widening the scope of descriptions admissible to physics to include the agents and the symbols that link theory to experiments opens up a new source of time-irreversibility in physics.
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given results is analyzed, leading to the conclusion that any quantum description comes as an element of a family of related descriptions, entailing multiple statements of results and multiple explanations. Facing this multiplicity opens avenues for exploration and consequences that are only beginning to be explored. Among the consequences are these: (1) statements of results impose topologies on control parameters, without resort to any quantum explanation; (2) an endless source of distinct explanations forces an open cycle of exploration and description bringing more and more control parameters into play, and (3) ambiguity of description is essential to the concept of invariance in physics.
This is Part 1 of a four part paper, intended to redress some of the most fundamental confusions in the subject of physical time directionality, and represent the concepts accurately. There are widespread fallacies in the subject that need to be corrected in introductory courses for physics students and philosophers. Parts 1 and 2 are about quantum mechanics, Part 3 is about fundamental concepts, and Part 4 is about cosmology. We start in Part 1 by analysing the time reversal symmetry of quantum probability laws. Time reversal symmetry is defined as the property of invariance under the time reversal transformation, T: t -> -t. It is shown that quantum mechanics (classical or relativistic) is strongly time asymmetric in its probability laws. This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric or reversible. This is widely claimed as settled scientific fact, and large philosophical and scientific conclusions are drawn from it. But it is an error. The fact is that while quantum mechanics is widely claimed to be reversible on the basis of two formal mathematical properties (that it does have), these properties do not represent invariance under the time reversal transformation. A recent experiment (Batalhao at alia, 2015) showing irreversibility of quantum thermodynamics is discussed as an illustration of this result. Most physicists remain unaware of the errors, decades after they were first demonstrated. Orthodox specialists in the philosophy of time who are aware of the error continue to refer to the ‘time symmetry’ or ‘reversibility’ of quantum mechanics anyway – and exploit the ambiguity to claim false implications about physical time reversal symmetry in nature. The excuse for perpetrating the confusion is that, since it is has now become customary to refer to the formal properties of quantum mechanics as ‘reversibility’ or ‘time reversal symmetry’, we should just keep referring to them by this name, even though they are not time reversal symmetry. This causes endless confusion, in attempts to explain the physical irreversibility of our universe, and in philosophical discussions of implications of physics for the nature of time. The failure of time reversal symmetry in quantum mechanics changes the interpretation of modern physics in a deep way. It changes the problem of explaining the real irreversibility found throughout nature.
This paper contributes to a burgeoning area of investigation, the ambiguity inherent in mathematics and the implications for physics of this ambiguity. To display the mathematical form of equations of quantum theory used to describe experiments, we make explicit the knobs by which the devices of an experiment are arranged and adjusted. A quantum description comes in two parts: (1) a statement of results of an experiment, expressed by probabilities of detections as functions of knob settings, and (2) an explanation of how we think these results come about, expressed by linear operators, also as functions of knob settings. Because quantum mechanics separates the two parts of any description, it is known that between the statements of results and the explanations lurks a logical gap: given any statement of results one has a choice of explanations. Here we work out some consequences of this openness to choice. We show how quantum theory as mathematical language in which to describe experiments necessarily involves multiple descriptions: multiple explanations of a given result, as well as multiple statements of results and multiple arrangement of knobs. Appreciating these multiplicities resolves what otherwise is a confusion in the concept of invariance. Implications of multiplicity of description for the security of quantum key distribution are noted.
In present-day physics the fundamental dynamical laws are taken as a time-translation-invariant and time-reversal-invariant one-parameter groups of automorphisms of the underlying mathematical structure. In this context-independent and empirically inaccessible description there is no past, present or future, hence no distinction between cause and effect. To get the familiar description in terms of causes and effects, the time-reversal symmetry of the fundamental dynamics has to be broken. Thereby one gets two representations, one satisfying the generally accepted rules of retarded causality (no effect can precede its cause). The other one describes the strange rules of advanced causality. For entangled (but not necessarily interacting) quantum systems the arrow of time must have the same direction for all subsystems. But for classical systems, or for classical subsystems of quantum systems, this argument does not hold. As a cosequence, classical systems allow the conceptual possibility of advanced causality in addition to retarded causality. Every mathematically formulated dynamics of statistically reproducible events can be extended to a description in terms of a one-parameter group of automorphisms of an enlarged mathematical structure which describes a fictitious hidden determinism. Consequently, randomness in the sense of mathematical probability theory is only a weak generalization of determinism. The popular ideas that in quantum theory there are gaps in the causal chain which allow the accommodation of the freedom of human action are fantasies which have no basis in present-day quantum mechanics. Quantum events are governed by strict statistical laws. Freedom of action is a constitutive necessity of all experimental science which requires a violation of the statistical predictions of physics. We conclude that the presently adopted first principles of theoretical physics can neither explain the autonomy of the psyche nor account for the freedom of action necessary for experimental science.
For the first time, physicists have performed an experiment confirming that thermodynamic processes are irreversible in a quantum system—meaning that, even on the quantum level, you can't put a broken egg back into its shell. The results have implications for understanding thermodynamics in quantum systems and, in turn, designing quantum computers and other quantum information technologies. [11] Disorder, or entropy, in a microscopic quantum system has been measured by an international group of physicists. The team hopes that the feat will shed light on the of time: the observation that time always marches towards the future. The experiment involved continually flipping the spin of carbon atoms with an oscillating magnetic field and links the emergence of the arrow of time to quantum fluctuations between one atomic spin state and another. [10] Mark M. Wilde, Assistant Professor at Louisiana State University, has improved this theorem in a way that allows for understanding how quantum measurements can be approximately reversed under certain circumstances. The new results allow for understanding how quantum information that has been lost during a measurement can be nearly recovered, which has potential implications for a variety of quantum technologies. [9] Today, we are capable of measuring the position of an object with unprecedented accuracy, but quantum physics and the Heisenberg uncertainty principle place fundamental limits on our ability to measure. Noise that arises as a result of the quantum nature of the fields used to make those measurements imposes what is called the standard quantum limit. This same limit influences both the ultrasensitive measurements in nanoscale devices and the kilometer-scale gravitational wave detector at LIGO. Because of this troublesome background noise, we can never know an object's exact location, but a recent study provides a solution for rerouting some of that noise away from the measurement. [8] The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.
What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? The bulk of the physics community accepts and teaches that all these fundamental questions are rationalized within statistical mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of statistical mechanics (canonical and grandcanonica1, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. But an ever growing handful of physicists (Schrodinger among the first) have realized that, even in its explanation of the meaning of entropy, statistical mechanics is impaired by ambiguities and logical inconsistencies. They have started to search for a better theory to eliminate these stumbling blocks while maintaining the mathematical formalism that has been so successful in so many applications. This handful of upstreamers must not be confused with the many schools of physicists that have thrived on the more renowned incompleteness of statistical mechanics, namely, the lack of a quantitative (and the weakness of the qualitative) explanation of the origin of irreversibility. In these studies the thrust is provided by the discovery that the macroscopic dynamics of certain complex systems may be modeled using a few-degrees-of-freedom nonlinear Hamiltonian with singularities that give rise to bifurcations and chaotic behavior. These results have generated successful ways to describe irreversible behavior, but their link to the origin of irreversibility is still only heuristic (what is the connection between the nonlinear model Hamiltonian and the true full Hamiitonian?) and does not provide yet a rigorous resolution of the century-old paradox of the conflict between the irreversibiiity of macroscopic behavior, and the reversibility of the laws of mechanics. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of mechanics. The result is a theory that we call quantum thermodynamics that has all the necessary properties to combine mechanics and thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of statistical mechanics and the paradox on irreversibiiity, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity and therefore chaotic behavior. The mathematical formalism of quantum thermodynamics differs from that of statistical mechanics mainly in the equation of motion which is nonlinear but has solutions identical to those of the Schrodinger equation for all the states for which statistical mechanics reduces to quantum mechanics. The physical meaning of the formalism of quantum thermodynamics differs more drastically from that of statistical mechanics. The significance of the state operator of quantum thermodynamics is entirely different from that of the density operator of statistical mechanics, even though the two are mathematically equivalent. Indeed they obey different equations of motion. In particular, quantum thermodynamics is concerned only with those systems for which quantum mechanics would describe the states with vectors in Hilbert space or, equivalently, projection operators. Using a well known jargon, we can say that quantum thermodynamics like quantum mechanics is concerned only with pure quantum states. However, it postulates that the set of pure quantum states of a system is much broader than contemplated by quantum mechanics. Pure quantum states must be described by operators defined by all the features of projection operators except the condition of idempotence. As a result, an operator that within statistical mechanics would describe a mixed quantum state (that is, the average state of a statistical mixture of identical systems in different pure quantum states) in quantum thermodynamics describes a pure quantum state, a state that neither quantum mechanics non statistical mechanics would contemplate. Conceptually, the increased richness of pure quantum states is a new revolutionary postulate of quantum physics. But from the point of view of the statistical mechanics practitioners the new theory is not as traumatic as it seems. Whenever one uses a nonidempotent density operator to describe a thermodynamic equilibrium state one simply has to reinterpret it as one of the new pure quantum states. One even saves the usual ad hoc arguments on thermal baths and reservoirs that are usually required in statistical mechanics to justify the use of a nonidempotent density operator to describe the state of a system. In this paper we discuss the background and formalism of quantum thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility. As a byproduct, we discuss a long set of criteria that a theory should meet in order to afford the same claim.