Math and Science FAQs

Here contains all the FAQs from all sciences and maths. These are common questions and misconceptions that people have. Inside these questions and myths are put to rest.

infinity

Why Division by Zero Is Impossible: 10 Mathematical Reasons

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33 Comments
A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs:What if it was…
tensors relativity

Tensors Explained: Beginner’s Essentials for Relativity

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If you try learning general relativity, and sometimes special relativity, on your own, you will undoubtedly run into tensors. This article will outline…
Evidence for Big Bang

Big Bang Evidence: CMB, Redshift & Element Abundances

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Big Bang: Key PointsHubble's law (redshift of galaxies) and the Doppler effect provide direct evidence that the universe is expanding away from our…
perpetual motion machines

Why We Don’t Discuss Perpetual Motion Machines (PMM)

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12 Comments
Authorship Authorship Contributions From Anorlunda Introduction You may want to believe the article you read, or the video you saw, or you may be very…
what are the black hole thermodynamics

Black Hole Thermodynamics: Four Laws Explained — Guide

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Overview Black hole thermodynamics is summarized by four laws that closely parallel the laws of ordinary thermodynamics. Below I present each law, the…
what is impedance

Impedance in AC Circuits: Definition & Key Equations

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Definition / Summary The impedance of a load (a combination of components) in an AC circuit is a complex number [itex]Z = R + jX[/itex], where [itex]R[/itex]…
What is Mass Inflation

Mass Inflation Inside Black Holes — Explanation & Equations

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Definition and summary Abstract from Poisson and Israel (1990), "Internal structure of black holes": "The gravitational effects associated with the radiative…
What is potential energy

Potential Energy Explained — Definitions & Formulas

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Definition / Summary Potential energy is the negative of the work done by a conservative force. It represents stored mechanical energy associated with…
How to Find Potential Functions

How to Find a Potential Function of a Vector Field

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Definition and summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Conditions and equations $$\nabla \phi(x,y,z)…
Moment of Inertia

Moment of Inertia: Definitions, Formulas & Tensor Guide

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Definition / Summary The moment of inertia is a property of a rigid body that relates torque (rotational force) to rotational acceleration in the same…
What is a linear equation

First-Order Linear Equation: Definition & Solutions

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Definition / Summary This article summarizes the first-order (linear) polynomial equation in one variable, its solution, and natural extensions to matrices…
What are significant figures

Significant Figures: Rounding Rules & Examples for Science

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Definition / Summary Significant figures (commonly called "sig figs") are the digits in a number that are considered when rounding a value to reflect…
What is a fibre bundle

Fibre Bundle: Definition, Examples & Intuitive Guide

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Definition / Summary Fibre bundle — intuitively, a fibre bundle is a space E that locally looks like a product B × F but may have a different global…
What are real numbers

Real Numbers: Definition, Properties & Completeness

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Definition of real numbers Real numbers are the set of all values that can appear on the continuous number line. They include rational numbers (fractions…
What is the double split

What is the Double Slit? A 5 Minute Introduction

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Definition/Summary The double-slit is a simple configuration used to demonstrate interference effects in waves.Equations At distances that are…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

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Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
What is a parabola

Parabola Explained: Properties, Equations & Practical Uses

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What is a Parabola? A parabola is a U-shaped curve that appears frequently in mathematics, physics and engineering. It is a conic section defined by a…
Limit of a Function

Limits of Functions for Calculus: Definition & Examples

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What is a limit? In mathematics, a limit describes the behavior of a function or sequence as its input approaches a particular value. Limits are a cornerstone…
Lie Algebra Intro

Lie Algebra Basics: Definitions, Equations & Examples

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Definition / Summary A Lie algebra (pronounced "Lee") is the tangent-space algebra of a Lie group at its identity element. Concretely, it is a vector…
What is a Tangent Line

Tangent Line and Hyperplane: Definitions & Circle Example

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Definition / Summary Informal idea The tangent to a curve in a plane at a particular point has the same gradient as the curve at that point. Generalization More…
What are virtual particles

Virtual Particles Explained — Quantum Field Theory

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Definition / Summary Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) for interactions…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

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Introduction Let me start with a counter-question. What is a number? Before you laugh, there is more to this question than one might think. A number can…
lensfocus

Lenses and Pinholes: What Does “In Focus” Mean?

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11 Comments
Introduction In introductory physics, the optics unit often teaches about virtual and real images, focal lengths, indexes of refraction, etc. Some questions…
universestart

Did the Big Bang Have a Center? Explaining Cosmology

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28 Comments
Did the Big Bang Have a Center? What the standard models say According to standard cosmological models based on general relativity — and which agree…
personaltheories1

Why Won’t You Look at My New Theory?

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290 Comments
In any forum where science is discussed, there will always be people who have a great new personal theory and can't understand why no one else is interested…
universeexpansion

At What Velocity Does the Universe Expand and Can It Be Faster than Light?

Neither of these questions makes sense in the form in which it was posed. To see why, let's start by thinking about how we know the universe is expanding.The…
quasarredshift

Evidence that Galaxy and Quasar Redshifts Are Cosmological

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How do we know that the redshifts of galaxies and quasars are cosmological and not "intrinsic"? Evidence for the cosmological interpretation Historical…
speedlightframe

Why Is the Speed of Light the Same in All Frames of Reference?

Why ask "why" about physical laws? The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you…
earlyuniverse

Was the Early Universe in a Disordered State?

No. The second law of thermodynamics says that entropy can only increase, so if the early universe had been in a state of maximum entropy, then the cosmos…
blackholeexists

Do Black Holes Really Exist?

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68 Comments
Introduction The purpose of this article is to discuss the title question from several different viewpoints, to show that it isn't as simple as it looks.…
observableuniverse

Why the Observable Universe Radius Exceeds Its Age

The radius of the observable universe is about 46 billion light-years, which is considerably greater than its age of about 14 billion years. The radius…
heat

What Is Heat? Definition in Thermodynamics Explained

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One of the most frustrating misconceptions in thermodynamics centers on the actual definition of heat. Many science and engineering students refer to a…
steadystate

What Is the Steady-state Model and Why It’s No Longer Viable

Introduction to the Steady State Model Back in 2011, I wrote a FAQ entry for Physics Forums on the steady state model and why it is no longer viable.…
electronatom

Why Electrons Don’t Crash Into the Nucleus — Quantum View

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Atoms and Coulomb forces If atoms were described only by Coulomb attraction, the electron and nucleus would attract each other and, according to classical…
airplanelift

How Does an Airplane Wing Work? A Primer on Lift

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56 Comments
Many people ask how an airplane wing works, and several answers are commonly given. You might have even seen vigorous arguments between proponents…
blackholesuniverse

Why the Early Big Bang Universe Didn’t Form a Black Hole

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Why the Big Bang Is Not a Black Hole In the early universe, the matter was gathered together at very high density — so why wasn't it a black hole?Big…
electrostaticfield1

Learn About Energy Gained by Charge in an Electrostatic Field

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Energy gain of an electron in a potential V I have seen this question being asked frequently on here. A lot of students have a bit of an issue in understanding…
twinparadox

A Geometrical View of Time Dilation and the Twin Paradox

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90 Comments
Based on the number of questions we receive on the topic at Physics Forums, there is a lot of confusion in the general public about how time dilation works…
universespinning

Is the Universe Rotating? Evidence, Tests & Limits

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Can we tell whether the universe is rotating? If you believe wholeheartedly in Mach's principle, there is no way to test empirically for the rotation…
uncertaintyenergy

Does Heisenberg Uncertainty Violate Energy Conservation?

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The short answer is: No — there is no violation. The longer answer Given the probabilistic aspect of quantum theory, what do we mean now by "conservation…
999equals1

Why 1 Equals 0.999… — Explanations & Rigorous Proofs

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111 Comments
Why do people say 1 and 0.999... are equal? Aren't they two different numbers? No — 1 and 0.999... really are the same number, although that can feel…
photonsmedium

Do Photons Move Slower in a Solid Medium?

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Scope and context This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower…
lightspeedrod

Why Rigid Rods Can’t Send Faster-Than-Light Signals

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Why a rigid rod can't send faster-than-light signals One common proposal for achieving faster-than-light (FTL) communication is to use a long, perfectly…
proofs

Mathematical Proofs: How to Understand and Write Them

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Introduction This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is a skill many people find hard to master. There are two…
blockuniverse

PF’s policy on Lorentz Ether Theory and Block Universe

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What is the PF's policy on Lorentz Ether Theory and Block Universe?Debates about the superiority or "truth" of modern Lorentz Ether Theory (LET) and…
gravitate

Does Gravity Gravitate?

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 The title question of this article is one that often comes up in PF threads, and I would like to give my take on it. This will be the first…
gravityacceleration

Why Is Acceleration Due to Gravity a Constant?

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5 Comments
This question has popped up many times. So here is an attempt to address it.To answer this question at the elementary level, several assumptions will…
what_is_evolution

What Is Evolution? How It Works — Mechanisms & Evidence

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What is evolution? In every field of scientific endeavor there sometimes comes a quantum shift in knowledge, a grand denouement that changes how we see…
speedoflight

Why Does C Have a Particular Value, and Can It Change?

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Short answer: Because c (speed of light) has units, its value is what it is only because of our choice of units, and there is no meaningful way to test…
gravitywaves

How Fast Do Changes in the Gravitational Field Propagate?

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20 Comments
Overview General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational…

Understanding Zero: History, Division, Exponents, 0!

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7 Comments
The goal of this FAQ is to clarify the concept of 0, and specifically the operations that are allowed with it.The best way to start this FAQ is to…
matterphoton

Will All Matter Be Converted to Photons?

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41 Comments
Will all matter be converted into black holes and then photons? No. There is a misconception that a lot of laypeople seem to be picking up recently from…
photonmass

Do Photons have Mass?

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Do photons have mass? The quick answer: NOCommon source of confusion However, this is where it gets a bit confusing for most people. This is because,…
spaceship

Bell Spaceship Paradox: Why the String Breaks in SR

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33 Comments
Bell spaceship paradox — setup Bell describes two spaceships that start out at rest relative to each other with an elastic string between them, one…
quantum_tunneling

Why You Can’t Quantum Tunnel Through a Wall

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64 Comments
Can You Quantum Tunnel Through a Wall? Short answer The short and sweet answer if a tennis ball, a bowling ball, or any other kind of ordinary macroscopic…
relmass

What is relativistic mass and why it is not used much?

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58 Comments
It happens that the term relativistic mass is used, in particular in the introductory text on special relativity. It should be noted that whether or not…
space law

Space Law Explained — Outer Space Treaty & Satellite Rules

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*This Insight is intended to have a logical basis but not to be taken as purely factual or legal advice. Key PointsOuter Space Treaty does not provide…
evolution_faq

Evolution Explained: FAQs, Evidence & Common Misconceptions

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[CONTENT] Key PointsEvolution is a scientific theory supported by multiple independent lines of evidence. In science, the term "theory" denotes a…