FAQs

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

/
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

/
0 Comments
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

/
2 Comments
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)

/
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

The Four Laws of Black Hole Thermodynamics Explained

/
0 Comments
Black hole thermodynamics consists of four laws that mirror the ordinary laws of thermodynamics: a zeroth law of uniform surface gravity, a first law relating…
what is impedance

Impedance Explained: Formulas, Equations & AC Circuit Basics

/
0 Comments
Impedance is the AC (alternating current) equivalent of resistance. It is a complex number, Z = R + jX, combining resistance R and reactance X, and it…
What is Mass Inflation

Mass Inflation in Black Holes: Poisson-Israel Theory Explained

/
0 Comments
Mass inflation is the phenomenon in which the internal mass parameter of a rotating or charged black hole grows without bound near the Cauchy horizon,…
What is potential energy

Potential Energy Explained: Formulas, Units & Derivations

/
0 Comments
Potential energy is the negative of the work done by a conservative force on an object, representing mechanical energy stored due to position within a…
How to Find Potential Functions

How to Find a Potential Function of a Vector Field

/
0 Comments
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: Formulas, Tensor, and Key Equations

/
0 Comments
What Is Moment of Inertia? Moment of inertia is a rigid body property that relates torque to rotational acceleration, playing the same role that mass…
What is a linear equation

First-Order Linear Equation: Definition & Solutions

/
0 Comments
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

/
0 Comments
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 Bundles Explained: Definition, Examples & Visualization

/
3 Comments
A fibre bundle is a mathematical structure consisting of a total space that looks locally like a simple product of two spaces but may have a different…
What are real numbers

Real Numbers Explained: Definition, Axioms & Properties

/
0 Comments
Real numbers are the complete set of values on the continuous number line, denoted ℝ, and they include both rational numbers (fractions and repeating…
What is the double split

What is the Double Slit? A 5 Minute Introduction

/
0 Comments
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

/
0 Comments
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

What Is a Parabola? Equations, Focus, and Real Uses

/
0 Comments
A parabola is a U-shaped curve where every point is equidistant from a fixed point called the focus and a fixed line called the directrix. Its standard…
Limit of a Function

What Is a Limit of a Function? Definition, Laws & Examples

/
0 Comments
A limit describes the value a function or sequence approaches as its input gets arbitrarily close to a specific point, without requiring the function to…
Lie Algebra Intro

Lie Algebras Explained: Commutators, SU(2), SO(3), Euc(n)

/
0 Comments
A Lie algebra is the vector space of infinitesimal generators attached to a Lie group at its identity element, equipped with a bilinear antisymmetric commutator…
What is a Tangent Line

Tangent Line Equations: Circles, Curves & Surfaces Explained

/
0 Comments
A tangent line or tangent hyperplane to a curve or surface at a given point shares the same gradient, or first-order linear approximation, as that curve…
What are virtual particles

Virtual Particles Explained: On-Shell vs Off-Shell in QFT

/
1 Comment
What Is a Virtual Particle? A virtual particle is a mathematical device, not a physical entity, that appears in perturbation expansions of the S-operator…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

/
58 Comments
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?

/
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? The Physics Explained

/
28 Comments
The Big Bang did not happen at a single point in space, so it has no center. Standard cosmological models based on general relativity treat the Big Bang…
personaltheories1

Why Won’t You Look at My New Theory?

/
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

Are Galaxy Redshifts Cosmological? The Evidence Explained

/
0 Comments
Galaxy and quasar redshifts are classified as cosmological, not "intrinsic," because they match predictions from general relativity's expanding-universe…
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

Why Wasn’t the Early Universe at Maximum Entropy?

No. The second law of thermodynamics states that entropy can only increase over time. If the early universe had begun in a state of maximum entropy, the…
blackholeexists

Do Black Holes Really Exist?

/
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 Is Bigger Than Its Age

The observable universe has a radius of about 46 billion light-years, far larger than its age of roughly 14 billion years. This happens because space itself…
heat

What Is Heat? The Real Thermodynamics Definition Explained

/
13 Comments
Heat is not something a body possesses. Heat is a transfer mechanism: the non-mechanical exchange of energy between a system and its surroundings that…
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 Don’t Electrons Crash Into the Nucleus? Explained

/
12 Comments
Atoms are stable because electrons do not behave as classical orbiting particles. Quantum mechanics describes electrons using wavefunctions and stationary…
airplanelift

How Does an Airplane Wing Work? A Primer on Lift

/
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 Big Bang Wasn’t a Black Hole: Cosmology Explained

/
7 Comments
The Big Bang was not a black hole because it happened everywhere in space at once rather than at a single point, and because the near-perfect homogeneity…
electrostaticfield1

Learn About Energy Gained by Charge in an Electrostatic Field

/
2 Comments
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

/
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? What Physics Tests Reveal

/
3 Comments
All current astronomical observations are consistent with zero global rotation of the universe. Solar-system data set a model-independent upper limit of…
uncertaintyenergy

Does Heisenberg’s Uncertainty Principle Break Energy Conservation?

/
2 Comments
Direct answer: No, the Heisenberg time-energy uncertainty relation does not violate conservation of energy in quantum mechanics. The relation describes…
999equals1

Why 1 = 0.999…: Four Simple Proofs Explained

/
111 Comments
Yes, 1 and 0.999... are exactly the same real number, not merely two numbers that happen to be extremely close. This surprises many people because 0.999...…
photonsmedium

Do Photons Move Slower in a Solid Medium?

/
5 Comments
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 a Rigid Rod Can’t Send Faster-Than-Light Signals

/
52 Comments
A perfectly rigid rod cannot send faster-than-light (FTL) signals because no such rod exists. Every real material transmits mechanical disturbances at…
proofs

Proofs in Mathematics: Methods, Examples, and How to Write Them

/
28 Comments
A mathematical proof is a logical argument, built only from definitions, axioms, and previously established results, that shows a statement is true in…
blockuniverse

PF’s policy on Lorentz Ether Theory and Block Universe

/
81 Comments
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?

/
9 Comments
 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?

/
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

How Evolution Works: Variation, Inheritance, Selection

/
0 Comments
Evolution is the process by which populations of organisms change over generations through three interacting mechanisms: random genetic variation, inheritance…
speedoflight

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

/
53 Comments
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?

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

The Concept of Zero: History, Rules, and Why 0/0 Fails

/
7 Comments
Zero is neither positive nor negative, is defined as the additive identity so that x + 0 = x for every number x, and produces 0 when multiplied by any…
matterphoton

Will All Matter Be Converted to Photons?

/
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?

/
5 Comments
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

/
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

/
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?

/
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: Lasers, Spying, Broadcasting & the Moon

/
0 Comments
This piece is intended to have a logical basis but should not be taken as purely factual or legal advice.Outer space law leaves several activities…
evolution_faq

Evolution FAQ: Theory, Evidence & Common Misconceptions

/
0 Comments
Evolution is the scientific theory explaining how species change over generations through mutation, heredity, and natural selection. It is supported by…