Quantum measurement | Interpretations of quantum mechanics
The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system. The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics in 1954. On the face of it, the ensemble interpretation might appear to contradict the doctrine proposed by Niels Bohr, that the wave function describes an individual system or particle, not an ensemble, though he accepted Born's statistical interpretation of quantum mechanics. It is not quite clear exactly what kind of ensemble Bohr intended to exclude, since he did not describe probability in terms of ensembles. The ensemble interpretation is sometimes, especially by its proponents, called "the statistical interpretation", but it seems perhaps different from Born's statistical interpretation. As is the case for "the" Copenhagen interpretation, "the" ensemble interpretation might not be uniquely defined. In one view, the ensemble interpretation may be defined as that advocated by Leslie E. Ballentine, Professor at Simon Fraser University. His interpretation does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it intends simply to interpret the wave function. It does not propose to lead to actual results that differ from orthodox interpretations. It makes the statistical operator primary in reading the wave function, deriving the notion of a pure state from that. In the opinion of Ballentine, perhaps the most notable supporter of such an interpretation was Albert Einstein: The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. — Albert Einstein Nevertheless, one may doubt as to whether Einstein, over the years, had in mind one definite kind of ensemble. (Wikipedia).
A05 Explanation of the matrix format of a system of linear differential equations
Explanation of the matrix notation used in systems of linear differential equations.
From playlist A Second Course in Differential Equations
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Description: Corresponding to our algebraic notion of invertibility, we want a geometric notion. Invertible transformations are defined, and then proven to be equivalent (thank goodness!) to invertible matrices when linear. Learning Objectives: 1) Define an invertible transformation 2) D
From playlist Older Linear Algebra Videos
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Linear algebra: Prove the Sherman-Morrison formula for computing a matrix inverse
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Linear Algebra 21j: Two Geometric Interpretations of Orthogonal Matrices
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Statistical Rethinking - Lecture 09
Lecture 09 - Ensembles & Interactions - Statistical Rethinking: A Bayesian Course with R Examples
From playlist Statistical Rethinking Winter 2015
Evgeni Dimitrov (Columbia) -- Towards universality for Gibbsian line ensembles
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From playlist Columbia Probability Seminar
No Ensemble Averaging Below the Black Hole Threshold - Edward Witten
Black Holes and Qubits Meeting Topic: No Ensemble Averaging Below the Black Hole Threshold" Speaker: Edward Witten Affiliation: Faculty, School of Natural Sciences, IAS Date: March 03, 2023 In AdS/CFT duality, at least in the case of D=3, I will argue that the basic CFT observables are n
From playlist Natural Sciences
Alexander Gorsky - Random Regular Graphs and Critical Phenomena in the Forest
The partition functions of perturbed ensembles of random regular graphs (RRG) which discretize 2d surfaces and yield perturbed pure 2d quantum gravity will be discussed. The phase transitions for the RRG perturbed by the chemical potentials for short cycles will be demonstrated numerically
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Intro to Machine Learning: Lesson 7
Today we'll finish off our "from scratch" random forest interpretation! We'll also briefly look at the amazing "cython" library that you can use to get the same speed as C code with minimal changes to your python code. Then we'll start on the next stage of our journey - gradient descent b
From playlist Introduction to Machine Learning for Coders
Random Matrix Theory and Zeta Functions - Peter Sarnak
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From playlist Mathematics
Random Matrices in Unexpected Places: Atomic Nuclei, Chaotic Billiards, Riemann Zeta #SoME2
Chapters: 0:00 Intro 2:21 What is RMT 7:12 Ensemble Averaging/Quantities of Interest 13:30 Gaussian Ensemble 18:03 Eigenvalues Repel 28:08 Recap 29:08 Three Surprising Coincidences 32:44 Billiards/Quantum Systems 36:00 Reimann Zeta ~~~~~~~~~~~~~~~~~~~~~~~~~ Errata + Clarifications ~~~~
From playlist Summer of Math Exposition 2 videos
Breaking of ensemble equivalence in complex networks by Andrea Roccaverde
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Andrew White: "Maximum Entropy Methods for Combining Physics-Based Simulation with Empirical Data"
Machine Learning for Physics and the Physics of Learning 2019 Workshop II: Interpretable Learning in Physical Sciences "Maximum Entropy Methods for Combining Physics-Based Simulation with Empirical Data" Andrew White, University of Rochester Abstract: Physics-based simulation models like
From playlist Machine Learning for Physics and the Physics of Learning 2019
Tim Palmer on Doubt: From Quantum Physics to Climate Change | Closer To Truth Chats
Tim Palmer discusses his new book, The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World. In it, he challenges conventional wisdom on quantum mechanics, free will, and more. Order The Primacy of Doubt: https:/
From playlist Closer To Truth Chats
Integration 8 The Substitution Rule in Integration Part 2 Example 1
Working through an example of substitution in integration.
From playlist Integration