# Science and Math Articles

Here is the collection of expert science and math articles that span all the sciences and mathematics. Some examples include physics, mathematics, biology, chemistry, cosmology and earth sciences. For math we cover algebra to advanced calculus.

### A Pure Hamiltonian Proof of the Maupertuis Principle

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Here is another version of proof of Maupertuis's principle. This…

### Fermi-Walker Transport in Kerr Spacetime

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In the last two posts in this series, we developed some tools…

### How to Create a Universe - Instructions for an Apprentice God

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(-: ##~~~## A fantasy to be read at leisure time ##~~~## :-) Written…

### A Classical View of the Qubit

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This Insight article is part of my paper Foundations of quantum…

### Fermi-Walker Transport in Schwarzschild Spacetime

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In the first post in this series, we introduced the concepts…

### Aiming High and Managing Distractions as Keys to Success for Science Majors

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Over the years, I've noticed some distinct trends among the physics…

### The Sum of Geometric Series from Probability Theory

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Here I present a simple (but to the best of my knowledge, new)…

### 9 Reasons Quantum Mechanics is Incomplete

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I argue that all interpretations of quantum mechanics (QM) are…

### Against "interpretation"

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I am against "interpretations" of Quantum Mechanics (QM) in a…

### Lie Algebras: A Walkthrough The Representations

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Part III: Representations  10. Sums and…

### An Introduction to the Traditional Abacus of China and Japan

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Introduction Abacuses are commonly seen in ancient civilizations…

### An Accurate Hooke's Law Laboratory

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Learning Objectives * Gain confidence and experimental care…

### Lie Algebras: A Walkthrough The Structures

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Part II: Structures5. Decompositions.Lie…

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### Demystifying the Often Misunderstood Bernoulli's Equation

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Introduction Bernoulli's equation is one of the most useful…

### Are Magnetic Field Lines Real?

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We recently had a question in the relativity forums that mentioned…

### When Vehicle Power Dictates Acceleration

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One interesting problem when dealing with a vehicle of a certain…

### The Quantum Mystery of Wigner's Friend

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In this Insight I will introduce the quantum mystery called Wigner's…

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### The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

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In this Insight, I will show how the Popescu-Rohrlich (superquantum)…

### A Simplified Synthesis of Financial Options Pricing

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Financial options (the right to purchase ("call") or sell ("put")…

### Why the Quantum | A Response to Wheeler's 1986 Paper

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Wheeler's opening statement in his 1986 paper, How Come the…

### The 10 Commandments of Index Expressions and Tensor Calculus

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Having more than 10 years of experience in teaching vector and…

### Direct Echo-Based Measurement of the Speed of Sound

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Figure 1: Distance vs. time a firecracker report echoed off…

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### Intro to Algorithms for Programming

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Many threads here at PF include some question about how to learn…

### Lessons From the Bizzaro Universe

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The terms Bizarro and Bizarro World originated in Superman comics,…

### Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

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Paper discussion: Solar system expansion and strong equivalence…

### Statistical Mechanics: The Ideal Gas

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Read Part 1: Equilibrium Systems The Ideal Gas: Boltzmann's…

### "Classical Physics Is Wrong" Fallacy

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One of the common questions or comments we get on PF is the claim…

### Hilbert Spaces And Their Relatives: Operators

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Operators. The Maze Of Definitions. We will use…

### Hilbert Spaces and Their Relatives: Basics

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Basics Language first: There is no such thing as…

### Mathematical Quantum Field Theory - Renormalization

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Interacting Quantum Fields

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This is one chapter in a series on Mathematical Quantum Field…

### Mathematical Quantum Field Theory - Free Quantum Fields

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This is one chapter in a series on Mathematical Quantum Field…

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### The Fundamental Difference in Interpretations of Quantum Mechanics

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A topic that continually comes up in discussions of quantum mechanics…

### Mathematical Quantum Field Theory - Quantization

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The following is one chapter in a series on Mathematical Quantum…

### Coordinate Dependent Statements in an Expanding Universe

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In this Insight we will discuss the general Robertson--Walker…

### The Schwarzschild Metric: A Newtonian Comparison

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A Short Proof of Birkoff's Theorem derived the Schwarzschild…

### The Schwarzschild Metric: The Photon Sphere

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A Short Proof of Birkoff's Theorem derived the Schwarzschild…