Leifer ch 8

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Leifer ch 8

Introduction Despite its status as a core part of contemporary physics, there is no consensus among physicists or philosophers of physics on the question of what, if anything, the empirical success of quantum theory is telling us about the physical world.

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One should not be misled by this terminology into thinking that what we have is an uninterpreted mathematical formalism with no connection to the physical world. Rather, there is a common core of interpretation that consists of recipes for calculating probabilities of outcomes of experiments performed on systems subjected to certain state preparation procedures.

Much of the Leifer ch 8 literature connected with quantum theory centers on the problem of whether we should construe the theory, or a suitable extension or revision of it, in realist terms, and, if so, how this should be done.

There are, however, other questions of philosophical interest. These include the bearing of quantum nonlocality on our understanding of spacetime structure and causality, the question of the ontological character of quantum states, the implications of quantum mechanics for information theory, and the task of situating quantum theory with respect to other theories, both actual and hypothetical.

Frances M Cowan

In what follows, we will touch on each of these topics, with the main goal being to provide an entry into the relevant literature, including the Stanford Encyclopedia entries on these topics. Quantum Theory In this section we present a brief introduction to quantum theory; see the entry on quantum mechanics for a more detailed introduction.

For systems of a great many degrees of freedom, a complete specification of the state of the system may be unavailable or unwieldy; classical statistical mechanics deals with such a situation by invoking a probability distribution over the state space of the Leifer ch 8. A probability distribution that assigns any probability other than one or zero to some physical quantities is regarded as an incomplete specification of the state of the system.

In quantum mechanics, things are different. There are no quantum states that assign definite values to Leifer ch 8 physical quantities, and probabilities are built into the standard formulation of the theory.

Construction of a quantum theory of some physical system proceeds by first associating the dynamical degrees of freedom with operators on an appropriately constructed Hilbert space see the entry on quantum mechanics for details. These assignments are required to be linear. That is, if one physical quantity is a linear combination of others, the corresponding expectation values stand in the same relation.

A complete set of such expectation values is equivalent to a specification of probabilities for outcomes of all experiments that could be performed on the system.

Incompatible observables give rise to uncertainty relations; see the entry on the uncertainty principle. A pure state, that is, a maximally specific assignment of expectation values, may be represented in a number of physically equivalent ways, for instance by a vector in the Hilbert space or a projection operator onto a one-dimensional subspace.

In addition to pure states, one can also consider non-pure states, called mixed; these are represented by operators called density operators.

THE CORTEX

If a pure state assigns a definite value to a physical quantity, a vector that represents the state will be an eigenvector of the corresponding operator. The noncontroversial core of quantum theory consists of rules for identifying, for any given system, the appropriate operators representing its dynamical quantities, and an appropriate Hilbert space for these operators to act on.

In addition, there are prescriptions for evolving the state of system when it is acted upon by specified external fields or subjected to various manipulations see section 1.

Leifer ch 8

Whether we can or can expect to be able to go beyond this noncontroversial core, and take the theory to be more than a means for calculating probabilities of outcomes of experiments, is an issue that remains a topic of contemporary philosophical discussion.

Classically, a field, such as, for example, an electromagnetic field, is a system endowed with infinitely many degrees of freedom. Quantization of a field theory gives rise to a quantum field theory.

The chief philosophical issues raised by quantum mechanics remain when the transition is made to a quantum field theory; in addition, new interpretational issues arise. There are interesting differences, both technical and interpretational, between quantum mechanical theories and quantum field theories; for an overview, see the entries on quantum field theory and quantum theory: The standard model of quantum field theory, successful as it is, does not yet incorporate gravitation.

The attempt to develop a theory that does justice both the quantum phenomena and to gravitational phenomena gives rise to serious conceptual issues see the entry on quantum gravity.

Leifer ch 8

For our purposes, the most important features of this equation is that it is deterministic and linear. The state vector at any time, together with the equation, uniquely determines the state vector at any other time. The collapse postulate Textbook formulations of quantum mechanics usually include an additional postulate about how to assign a state vector after an experiment.

Process 1, which occurs upon performance of an experiment, and Process 2, the unitary evolution that takes place as long as no experiment is made see von Neumann Thus after the first measurement has been made, there is no indeterminacy in the result of the second. This conclusion must still hold if the second measurement is not actually made.

In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement Dirac Neither von Neumann nor Dirac, however, seem to think of it this way; it is treated by both as a physical process.

Though, in his extended discussion of the measurement process, von Neumann, Ch. VI does discuss the act of observation, he emphasizes that the collapse postulate may be applied to interactions with quantum systems with measuring apparatus, before an observer is aware of the result.

A formulation of a version of the collapse postulate according to which a measurement is not completed until the result is observed is found in London and Bauer They deny, however, that it represents a mysterious kind of interaction between the observer and the quantum system; for them, the replacement of the pre-observation state vector with a new one is a matter of the observer acquiring new information.

These two interpretations of the collapse postulate, as either a real change of the physical state of the system, or as a mere updating of information on the part of an observer, have persisted in the literature.Read and Download Leifer Chapter 8 Free Ebooks in PDF format - QUESTION AND ANSWER READING COMPREHENSION INTRODUCTION TO ANIMALS ANSWER KEY QUESTION PAPERS OF NTSE QUESTION PAPERS PREVIOUS YEARS 12 CHEMISTRY QUESTION.

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