An introduction to the quantum Hall effect. The first half uses only quantum mechanicsand is at a levelsuitable for undergraduates. The second half covers more advanced field theoretic techniques of Chern-Simonsand conformal field theories.
Understanding Relativistic Quantum Field Theory Pdf 23
An elementary course on elementary particles. This is, by some margin, the least mathematically sophisticated of all my lecture notes, requiring little more than high school mathematics. The lectures provide a pop-science, but detailed, account of particle physics and quantum field theory.
Quantum Field Theory An introductory course on quantum field theory, aimed at first year graduate students. It covers the canonical quantization of scalar, Dirac and vector fields. Videos are also included.
These notes provide an introduction to the fun bits of quantum field theory, in particular those topics relatedto topology and strong coupling. They are aimed at beginning graduate students and assumea familiarity with the path integral.
Special Relativity [pdf]
The homopolar generator: an analytical example [pdf]
Quasistationary electrodynamics - fundamentals [pdf]
Relativistic treatment of the DC conducting straight wire [pdf]
The relativistic wave equation [pdf]
The electromagnetic field in GR [pdf]
In order to understand what Everett was worried about, one must firstunderstand how the standard collapse formulation of quantum mechanicsworks. The theory involves the following principles (von Neumann,1955):
The deterministic dynamics (rule 4a) typically does nothing toguarantee that a system will either determinately have ordeterminately not have a particular property when one observes thesystem to see whether the system has that property. This is why thecollapse dynamics (rule 4b) is needed in the standard formulation ofquantum mechanics. It is the collapse dynamics that guarantees that asystem will either determinately have or determinately not have aparticular property (by the lights of rule 3) whenever one observesthe system to see whether or not it has the property. But the lineardynamics (rule 4a) is also needed to account for quantum mechanicalinterference effects. So the standard theory has two dynamical laws:the deterministic, continuous, linear rule 4a describes how a systemevolves when it is not being measured, and the random, discontinuous,nonlinear rule 4b describes how a system evolves when it ismeasured.
But the standard formulation of quantum mechanics does not say what ittakes for an interaction to count as a measurement. Without specifyingthis, the theory is at best incomplete since it does not indicate wheneach dynamical law obtains. Moreover, if one supposes that observersand their measuring devices are constructed from simpler systems thateach obey the deterministic dynamics, as Everett did, then thecomposite systems, the observers and their measuring devices, mustevolve in a continuous deterministic way, and nothing like the random,discontinuous evolution described by rule 4b can ever occur. That is,if observers and their measuring devices are understood as beingconstructed of simpler systems each behaving as quantum mechanicsrequires, each obeying rule 4a, then the standard formulation ofquantum mechanics is logically inconsistent since it says that the twosystems together must obey rule 4b. This is the quantum measurementproblem in the context of the standard collapse formulation of quantummechanics. See the section on the measurement problem in the entry on philosophical issues in quantum theory.
In order to solve the measurement problem Everett proposed droppingthe collapse dynamics (rule 4b) from the standard collapse theory andtaking the resulting physical theory to provide a complete andaccurate description of all physical systems in the context of allpossible physical interactions. Everett called the theory pure wavemechanics. He believed that he could deduce the standard statisticalpredictions of quantum mechanics (the predictions that depend on rule4b in the standard collapse formulation of quantum mechanics) in termsof the subjective experiences of observers who are themselves treatedas ordinary physical systems within pure wave mechanics.
Note that Everett did not require a physically preferred basis tosolve the determinate record problem to show that pure wave mechanicswas empirically faithful. The principle of the fundamental relativelyof states explicitly allows for arbitrarily specified decompositionsof the absolute universal state into relative states. Given hisunderstanding of empirical faithfulness, all Everett needed to explaina particular actual record was to show that is that there is somedecomposition of the state that represents the modeled observer withthe corresponding relative record. And he clearly has that in purewave mechanics under relatively weak assumptions regarding the natureof the actual absolute quantum mechanical state.
For Everett, the relative states of its subsystems provided a way tocharacterize branches of the absolute state of a composite system.Insofar as the principle of the fundamental relativity of statesallows one to consider the quantum-mechanical state in any specifiedbasis, there is no canonical way to individuate branches. This makesit natural perhaps to think of the existence of branchesoperationally, as Everett did. Rather than take the branchesdetermined by a physically preferred basis or those determined by, orroughly determined by, some decoherence condition to determine whichphysically possible worlds were real, he took every branch in anybasis to have observational consequences and hence to be real inhis operational sense. Given how he understood branches and their rolein determining the empirical faithfulness of the theory, Everett neverhad to say anything concerning how a particular physically preferredbasis is selected because none was required.
On the standard sort of many-worlds theory, worlds are taken to splitover time as new branches are produced in measurement-likeinteractions. One problem with this is that the forward-lookingprobability of an observer getting each quantum-mechanically possibleoutcome for a measurement is simply one inasmuch as each possiblemeasurement outcome is in fact recorded by some future copyof the observer one of the post-measurement branches. One way to getthe right forward-looking probabilities, the standard probabilisticpredictions of quantum mechanics, is to postulate worlds that neverbranch. Such worlds might be characterized by their completehistories. If one is in such a world, then one simply experiences itshistory.
quantum mechanics quantum mechanics: Bohmian mechanics quantum mechanics: many-worlds interpretation of quantum mechanics: modal interpretations of quantum mechanics: relational quantum theory: philosophical issues in
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