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.

Evidence for Big Bang

Universe FAQ ‘Is there Evidence for the Big Bang?’

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Evidence for the big bang can be provided from observational astronomy using Hubble’s law (redshift of galaxies) also known as the ‘Doppler effect’…
perpetual motion machines

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

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Authorship Contributions From: Anorlunda You may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention.…
what are the black hole thermodynamics

What Are the Thermodynamics of Black Holes? A 5 Minute Introduction

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Definition/Summary The four laws of black hole thermodynamics are as follows... The Zeroth Law Surface gravity [itex](\kappa)[/itex] is constant…
what is impedance

What is Impedance? A 5 Minute Introduction

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

What is Mass Inflation? A 5 Minute Introduction

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Definition/Summary Abstract from Poisson and Israel's 1990 paper, 'Internal structure of black holes'- 'The gravitational effects associated with the…
What is potential energy

What is Potential Energy? A 5 Minute Introduction

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Definition/Summary Potential energy is simply another name for (minus) the work done by a conservative force. Since the work-energy theorem states…
How to Find Potential Functions

How to Find Potential Functions? A 10 Minute Introduction

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

What is the Moment of Inertia? A 10 Minute Introduction

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Definition/Summary Moment of Inertia is a property of rigid bodies. It relates rotational force (torque) to rotational acceleration in the same way…
What is a linear equation

What is a Linear Equation? A 5 Minute Introduction

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Definition/Summary A first order polynomial equation in one variable, its general form is [itex]Mx+B=0[/itex] where x is the variable. The quantities…
What are significant figures

What are Significant Figures? A 5 Minute Introduction

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Definition/Summary Significant figures (commonly called "sig figs") are the number of figures (digits) included when rounding-off a number. For example,…
What is a fibre bundle

What is a Fibre Bundle? A 5 Minute Introduction

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Definition/Summary Intuitively speaking, a fibre bundle is space E which 'locally looks like' a product space B×F, but globally may have a different…
What are real numbers

What is a Real Number? A 5 Minute Introduction

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Definition/Summary The real numbers are most commonly encountered number system, familiar to the layman via the number line, and as the number system…
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

What is a Parabola? A 5 Minute Introduction

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Definition/Summary A parabola has many definitions, a classical one being, "A Parabola is the locus of all points equidistant from a given point (called…
Limit of a Function

What Is a Limit of a Function? A 5 Minute Introduction

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Definition/Summary Limits are a mathematical tool which is used to define the 'limiting value' of a function i.e. the value a function seems to approach…
Lie Algebra Intro

What is Lie algebra? A 5 Minute Introduction

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Definition/Summary A Lie algebra ("Lee") is a set of generators of a Lie group. It is a basis of the tangent space around a Lie group's identity element,…
What is a Tangent Line

What is a Tangent Line? A 5 Minute Introduction

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Definition/Summary The tangent to a curve in a plane at a particular point has the same Gradient as the curve has at that point. More generally, the…
What are virtual particles

What are Virtual Particles? A 10 Minute Introduction

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

What Is a Tensor?

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

Lenses and Pinholes: What Does "In Focus" Mean?

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

Where Did the Big Bang Happen?

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According to standard cosmological models, which are based on general relativity and are found to agree well with observations, time and space did not…
personaltheories1

Why Won't You Look at My New Theory?

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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 actually 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…
quasarredshift

Could Redshifts Be Intrinsic Rather than 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 The purpose…
speedlightframe

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

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be…
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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The purpose of this article is to discuss the title question from several different viewpoints, in order to show that it isn't as simple as it looks. We…
observableuniverse

Radius of the Observable Universe in Light-years Is Greater than 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

Building a Definition for Heat

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One of the most frustrating misconceptions in Thermodynamics centres on the actual definition of heat. Many science/engineering students often refer to…
steadystate

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

[Back in 2011, I wrote a FAQ entry for physicsforums on the steady state model and why it is no longer viable. I've learned more about the theory since…
electronatom

Why Don’t Electrons Crash into the Nucleus in Atoms?

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If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms could exist. Obviously this…
airplanelift

How Does an Airplane Wing Work: a Primer on Lift

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Many people ask how an airplane wing works, and there are any number of answers that are commonly given. You might have even seen vigorous arguments…
blackholesuniverse

Is the Universe a Black Hole?

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In the early universe, matter was gathered together at very high density, so why wasn't it a black hole? The first thing to understand is that the Big…
electrostaticfield1

Energy Gained by Charge in an Electrostatic Field

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I have seen this question being asked frequently on here. A lot of students have a bit of an issue in understanding why, if an electron is placed in a…
twinparadox

A Geometrical View of Time Dilation and the Twin Paradox

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Based on the amount 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

Can We Tell Whether the Universe Is Rotating?

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If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing…
uncertaintyenergy

Does the Heisenberg Uncertainty Principle Imply Energy Nonconservation?

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The short answer is: no, there's no violation. The longer answer can be this: Given the probabilistic aspect of quantum theory, what do we mean now,…
999equals1

Why Do People Say That 1 And .999 Are Equal?

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Why do people say 1 and 0.999... are equal? Aren't they two different numbers? No, they really are the same number, though this is often very counterintuitive…
photonsmedium

Do Photons Move Slower in a Solid Medium?

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

Can I Send a Signal Faster than Light by Pushing a Rigid Rod?

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One common proposal for achieving faster than light communication is to use a long perfectly rigid object and mechanically send signals to the other end…
proofs

What Proofs are in Mathematics and Why Bother?

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This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is for many people a skill that is hard to master. There are actually 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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This question has popped up many times. So here is an attempt to address it. To answer this question at the elementary level, a number of assumption…
what_is_evolution

What Is Evolution and How Does It Happen?

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What is evolution? In every field of scientific endeavor, there comes now and then a quantum shift in knowledge, a grand denouement of the way things…
speedoflight

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

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Short answer: Because c has units, its value is what it is only because of our choice of units, and there is no meaningful way to test whether it changes.…
gravitywaves

How Fast Do Changes in the Gravitational Field Propagate?

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

The History and Concept of the Number 0

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The goal of this FAQ is to clear up the concept of 0 and specifically the operations that are allowed with 0. The best way to start this FAQ is to look…
matterphoton

Will All Matter Be Converted to Photons?

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FAQ: In the very distant future, will all matter be converted into black holes and then photons? No. There is a misconception that a lot of laypeople…
photonmass

Do Photons have Mass?

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Do photons have mass? The quick answer: NO. However, this is where it gets a bit confusing for most people. This is because in physics, there are several…
spaceship

What Is the Bell Spaceship Paradox, and How Is It Resolved?

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Bell describes two spaceships that start out at rest relative to each other, with an elastic string between them, one end attached to each ship, which…
quantum_tunneling

You Will Not Tunnel Through a Wall

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We periodically get questions on PF about people wanting to know of a tennis ball, a ping pong ball, a person, a cow, etc. can tunnel through a wall, or…
relmass

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

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

7 Basic Space Law Questions Explored

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*This Insight is intended to have logical basis but not to be taken as purely factual. 1. Would 'Star Wars' have been legal? Well, I'm afraid I cannot…
evolution_faq

Evolution Frequently Asked Questions

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Q: Isn't evolution just a theory? A: As opposed to what? Yes, evolution is just a theory, but theories are the foundations of the idea of science. We…