The Problem Of Time: Quantum Mechanics Versus G...

The Problem Of Time: Quantum Mechanics Versus G... >>> __https://bltlly.com/2tkKSb__

In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative.[1][2] This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws at the microscopic level seem to require a single direction.[3] For macroscopic systems the directionality of time is directly linked to first principles such as the second law of thermodynamics.

In classical mechanics, a special status is assigned to time in the sense that it is treated as a classical background parameter, external to the system itself. This special role is seen in the standard formulation of quantum mechanics. It is regarded as part of an a priori given classical background with a well defined value. In fact, the classical treatment of time is deeply intertwined with the Copenhagen interpretation of quantum mechanics, and, thus, with the conceptual foundations of quantum theory: all measurements of observables are made at certain instants of time and probabilities are only assigned to such measurements.

The dynamical nature of spacetime, via the hole argument, implies that the theory is diffeomorphism invariant. The constraints are the imprint in the canonical theory of the diffeomorphism invariance of the four-dimensional theory. They also contain the dynamics of the theory, since the Hamiltonian is zero (identically vanishes). The quantum theory has no explicit dynamics; wavefunctions are annihilated by the constraints and Dirac observables commute with the constraints and hence are constants of motion. Kuchar introduces the idea of \"perennials\" and Rovelli the idea of \"partial observables\". The expectation is that in physical situations some of the variables of the theory will play the role of a \"time\" with respect to which other variables would evolve and define dynamics in a relational way. This runs into difficulties and is a version of the \"problem of time\" in the canonical quantization.[5]

Avshalom Elitzur and Shahar Dolev argue that quantum mechanical experiments such as the Quantum Liar[18] provide evidence of inconsistent histories, and that spacetime itself may therefore be subject to change affecting entire histories.[19] Elitzur and Dolev also believe that an objective passage of time and relativity can be reconciled, and that it would resolve many of the issues with the block universe and the conflict between relativity and quantum mechanics.[20]

The thermal time hypothesis has been put forward as a possible solution to this problem by Carlo Rovelli and Alain Connes, both in classical and quantum theory. It postulates that physical time flow is not an a priori given fundamental property of the theory, but is a macroscopic feature of thermodynamical origin.[29]

One often hears the claim that decoherence solves the measurementproblem of quantum mechanics (see the entry on philosophical issues in quantum theory). Physicists who work on decoherence generally know better, but it isimportant to see why even in the presence of decoherence phenomena,the measurement problem remains or in fact gets even worse.

Indeed, as pointed out already by von Neumann (1932, Section VI.3),one cannot reproduce the correct probabilities by assuming that theyarise because we are ignorant of the exact state of a macroscopicapparatus. But whatever the exact initial state of the apparatus, ifthe system (say, an electron) is described by a superposition of twogiven states, say, spin in \\(x\\)-direction equal \\(+\\frac{1}{2}\\) and spin in\\(x\\)-direction equal \\(-\\frac{1}{2}\\), and we let it interactwith a measuring apparatus that couples to these states, the finalquantum state of the composite will be a sum of two components, one inwhich the apparatus has coupled to (has registered) \\(x\\)-spin \\(= +\\frac{1}{2}\\), and one in which the apparatus has coupled to (has registered)\\(x\\)-spin \\(= -\\frac{1}{2}\\).[13] This is the measurement problem in the narrow sense of the term.

Indeed, what happens if we include decoherence in the descriptionDecoherence tells us, among other things, that plenty of interactionsare taking place all the time in which differently localised states ofthe apparatus registering, say, different \\(x\\)-spin values of anelectron couple to different states of the environment. But now, bythe same arguments as above, the composite of electron,apparatus and environment will be a superposition of (i) a statecorresponding to the environment coupling to the apparatus coupling inturn to the value \\(+\\frac{1}{2}\\) for the spin, and of (ii) a state correspondingto the environment coupling to the apparatus coupling in turn to thevalue \\(-\\frac{1}{2}\\) for the spin. We are thus left with the following choice,whether or not we include decoherence: either the compositesystem is not described by such a superposition, because theSchrödinger equation actually breaks down and needs to bemodified, or it is described by such a superposition, but then we needto either to supplement quantum mechanics with appropriate hiddenvariables, or to give an appropriate interpretation of thesuperposition.

Decoherence is clearly neither a dynamical evolution contradicting theSchrödinger equation, nor a new supplementation or interpretationof the theory. As we shall discuss, however, it both reveals importantdynamical effects within the Schrödinger evolution, andmay be suggestive of possible interpretational moves. As suchit has much to offer to the philosophy of quantum mechanics. At first,however, it seems that discussion of environmental interactions shouldactually exacerbate the existing problems. Intuitively, if theenvironment is carrying out lots of spontaneous measurements evenwithout our intervention, then the measurement problem ought to applymore widely, also to these spontaneously occurringmeasurements.

Indeed, while it is well-known that localised states of macroscopicobjects spread very slowly with time under the free Schrödingerevolution (i.e., if there are no interactions), the situation turnsout to be different if they are in interaction with the environment.Although the different components that couple to the environment willbe individually incredibly localised, collectively they can have aspread that is many orders of magnitude larger. That is, the state ofthe object and the environment could be a superposition of zillions ofvery well localised terms, each with slightly different positions, andthat are collectively spread over a macroscopic distance,even in the case of everyday objects.[14] Given that everyday macroscopic objects are particularly subject todecoherence interactions, this raises the question of whether quantummechanics can account for the appearance of the everyday world evenapart from the measurement problem.

Despite the fact that decoherence interactions extend the measurementproblem to the wider problem of the classical regime, decoherenceis relevant to the solution of both problems because at thelevel of components of the wave function the quantum descriptionof decoherence phenomena (tantalisingly!) includes both measurementresults and other quantum phenomena (such as quantum jumps) as well asclassical behaviour. This suggests that to a large extent decoherenceprovides an interpretation-neutral strategy for tackling themeasurement problem and the problem of the classical regime (a thesisdeveloped in greater detail by Rosaler 2016), and that the solution tothese problems lies in combining decoherence with the mainfoundational approaches to quantum mechanics.

In the final Chapter VI of his book (von Neumann 1932), von Neumannprovided a systematic discussion of quantum mechanics with collapseupon measurement (described by what he calls an intervention of type\\(\\mathbf{1})\\), as distinct from the Schrödinger equation(intervention of type \\(\\mathbf{2})\\), and traditionally associated with arole for conscious observation. (The two types of interventions areintroduced already in Section V.1, but von Neumann postpones theirconceptual discussion to the final chapter.)

We have seen in the last section that not all approaches to quantummechanics can make full use of decoherence. In those approaches thatcan, however, decoherence is instrumental in yielding a wealth ofstructures that emerge from the unitary Schrödinger (orHeisenberg) dynamics. How far can this programme ofdecoherence (Zeh 2003a, p. 9) be successfully developed

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactionalinterpretation of quantum mechanics, The Quantum Handshake -Entanglement, Nonlocality, and Transactions, (Springer, January-2016) isavailable online as a hardcover or eBook at:

The problem arises due to a property of general relativity called reparameterisation invariance. In fact it is not unique to GR but arises in any system that has this property, but in most systems we can use a process called deparameterisation to recover the time dependence. What is different about quantum gravity is that for technical reasons deparameterisation does not work, and it is still an unresolved question how the time dependence can be recovered.

The fact we can replace the proper time by any affine parameter means the theory is reparameterisation invariant, and as discussed in the Wikipedia article I linked above, when we use Hamiltonian mechanics to describe such a system we find that the value of the Hamiltonian is always zero. This is a problem because the Hamiltonian describes the time evolution of the system and if it is zero then the system does not evolve with time.

Now this happens in purely classical mechanics, and an example is discussed in the Wikipedia article. Such systems obviously do evolve with time, and the reason we run into the problem is down to a choice of the time variable that is unphysical. Recovering the actual physically meaningful time is done using a straightforward process called deparameterisation, and this gives us the equations of motion of the system. 59ce067264

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