Science and Math Articles

Here is the collection of expert STEM 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.  These articles are all peer-reviewed by the community.

spacetime

Struggles With the Continuum: Is Spacetime Really a Continuum?

/
29 Comments
 Is spacetime really a continuum?  That is, can points of spacetime really be described---at least locally---by lists of four real numbers…
photoelectric

“Violating” Einstein’s Photoelectric Effect Model

/
4 Comments
One of the most spectacular theoretical descriptions that Einstein had ever produced is the corpuscular nature of light that he used in his 1905 photoelectric…
CosmologicalHorizons

Inflationary Misconceptions and the Basics of Cosmological Horizons

/
45 Comments
Introduction It is a common saying that during inflation "space expanded faster than the speed of light."  This statement is meant to articulate the…
lightswitch

What Happens When You Flip the Light Switch: From Zero Seconds to 20 Years

/
47 Comments
Introduction Few people know what happens when a customer does something like flipping a light switch. The full explanation requires descriptions of topics…
relativitytherorm

Learn the Relativistic Work-Kinetic Energy Theorem

/
20 Comments
I was bothered for a long time by the reasons for the relativistic validity of the work-kinetic energy relation ##\Delta E=Fd##, which holds without any…
supergravity

Emergence From the Superpoint

/
6 Comments
 In the previous article we saw that the generalization of super-Lie algebras to homotopy super-Lie n-algebras (super L-infinity algebras)…
liealgebra

Homotopy Lie-n Algebras in Supergravity

/
1 Comment
 The previous article in this series claimed that the mathematics of the 21st century that had fallen into the 1970s in the form of string…
string theory

It Was 20 Years Ago Today — the M-theory Conjecture

/
2 Comments
  While the world didn't end, after all, 15 years back at the turn of the millennium, in hindsight it is curious that, almost unnoticed,…

Why You Should Not Use Wikipedia As Your Primary Source

/
108 Comments
It is no secret to anyone who has read my posts in this forum for a while that I do not like Wikipedia. I think that there's a fundamental flaw with the…
hupmisconceptions1

Learn a Misconception of the Heisenberg Uncertainty Principle

/
26 Comments
One of the common misconceptions about the Heisenberg Uncertainty Principle (HUP) is that it is the fault of our measurement accuracy.A description…
learnfrompf

The Most Important Thing You Can Learn from Physics Forums

/
15 Comments
It is a bit pompous of me to think that I can tell you the most important thing you can learn from Physics Forums (PF). After all, each one of us here…
errorbars

Plus/minus What? How to Interpret Error Bars

/
20 Comments
People sometimes find themselves staring at a number with a ± in it when a new physics result is presented. But what does it mean? This Insight aims to…
LCDM4

Approximate LCDM Expansion in Simplified Math (Part 4)

/
14 Comments
  Part 4: Cosmic Recession Rates An astronomer, accompanied by his amateur relativist friend, aimed a telescope at a distant galaxy and measured…
theoex

False Physics Major Dichotomy: Theorist or Experimentalist?

/
27 Comments
Many physics majors believe that pursuing a Ph.D. in physics requires them to choose between theory and experiment. Due to my weaknesses in math, I…
LCDM3

The LCDM Cosmological Model in Simplified Math (Part 3)

/
5 Comments
  Part 3: Important Cosmological Horizons and Distances A question that often comes up is: "how big is the observable universe?"The question…
lcdmjorrie

Approximate LCDM Expansion in Simplified Math (Part 2)

/
14 Comments
  Part 2: Time and Distance In Part 1 we have seen how one of the simplest ways of expressing the fractional expansion rate of the universe,…
neutrino

Learn About Neutrino Masses and Speed

/
28 Comments
It was hard to miss the 2011 OPERA neutrino speed measurement that indicated superluminal neutrino speeds (and turned out to be a measurement error), but…
gravity

Understanding the General Relativity View of Gravity on Earth

/
102 Comments
Often students have difficulty reconciling the General Relativity (GR) view of gravity versus their own experience with gravity on the surface of Earth.…
cosmo

Approximate LCDM Expansion in Simplified Math

/
11 Comments
 If we restrict ourselves to a spatially flat LCDM universe model (and ignore the early radiation energy density), the first Friedmann equation…
math obvious

Lessons From My Experience Teaching Math

/
20 Comments
My #1 goal, when I teach a math class, is to convey a certain way of thinking about math. It's quite different from what my students have done before,…
physics love

Should You Do Science for Love or for Money

/
19 Comments
When I look over the most highly cited papers and my favorite accomplishments, I am struck by the fact that most of the projects were not funded by…
measuringentanglement

Can You Measure Quantum Entanglement?

/
23 Comments
Though any pair of particles, given their history, might happen to be entangled, some pairs are more entangled than others.Since at least the 1990s,…
garrett

Garrett Lisi’s Superparticle Bet With Frank Wilczek

/
52 Comments
There is an interesting story unfolding in particle physics. The main motivation for building the Large Hadron Collider was to search for new particles.…
qftintegrals

Some Useful Integrals In Quantum Field Theory

/
2 Comments
In my paper on renormalisation I mentioned what most who have studied calculations in Quantum Field Theory find, it's rather complicated and mind-numbing.…
arrowoftime

Retrocausality: How Fundamental is the Arrow of Time?

/
26 Comments
In this Insight, I'll discuss a recent experiment ([1]  [2] [3]) by some Australian physicists that has brought a thought experiment into the real world…
research work

How to Initiate Research Work As a Physics Major

/
1 Comment
  It has been a while since the last installment of this series, so let’s recap on where you are right now. You should already…
gas compression

Reversible vs Irreversible Gas Compression and Expansion Work

/
26 Comments
Introduction In learning Thermodynamics, one of the difficult concepts that many students struggle with is the difference between reversible and irreversible…
perbation theory

Introduction to Causal Perturbation Theory

/
30 Comments
Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound…
cheshirecat

Weak Values Part 2: The Quantum Cheshire Cat Experiment

/
0 Comments
In a previous Insight, Weak Values Part 1: "Asking Photons Where They Have Been," I showed different methods for computing the relative intensities in…
askingphotons

Weak Values Part 1: Asking Photons Where They Have Been

In a previous Insight on retrocausality, I explained an experiment by Danan, Farfurnik, Bar-Ad, and Vaidman (DFBV)[1], “Asking Photons Where They Have…
negative temperature

What are Negative Absolute Temperatures

/
9 Comments
It's a famous result in thermodynamics that you can't reach absolute zero no matter how hard you try. Also, the definition of absolute zero makes it obvious…
What is Energy

A Definition and Controversy of Energy

/
44 Comments
Energy SummaryThe article addresses the fundamental question, "What is energy?" and explores why discussions about energy can be challenging. It…
LHC

LHC Part 3: Protons as Large as a Barn

/
8 Comments
Introduction See also part 1 and part 2 of the series.The LHC commissioning phase is coming to and end. On Wednesday May 20th 2015, the first collisions…
earth year

How to Scientifically Measure How Many Days Are in a Year

/
75 Comments
Days in a Year SummaryThe article explores the measurement of the number of days in a year, considering various definitions of a "day" and a "year." …
Alzheimers

Can Gene Editing Eliminate Alzheimer’s Disease?

/
13 Comments
The development of the CRISPR/Cas9 system has made gene editing a relatively simple task.  While CRISPR and other gene-editing technologies stand to revolutionize…
subway

A Brachistochrone Subway Is Not a Cost-effective Idea

/
6 Comments
It is apparent that a subway tunnel could be built without the need for supplied energy like electricity, assuming zero friction everywhere.  The tunnel…
redlights

Learn About the Greenberger-Horne-Zeilinger Experiment

In two previous Insights, I shared Mermin's explanation of the Hardy experiment[1] and the Mermin device[2]. Both of his corresponding AJP papers…
mermin

The Quantum Liar Experiment: An Instantiation of the Mermin Device

In 1981, Mermin published a paper[1], "Bringing home the atomic world: Quantum mysteries for anybody" in which he explained the mystery of quantum nonlocality[2]…
classroom

Explore Some Sins in Physics Didactics

/
203 Comments
Introduction There are many sins in physics didactics. Usually, they occur, because teachers, professors, textbook or popular-science-book writers, etc.…

LHC Part 2: Commissioning

/
23 Comments
Introduction Last month, I wrote a FAQ about working at the LHC, at the time the first beams were circulating in the machine after a stop of two years.…
CrispR DNA

Why CRISPR Technologies Won’t Lead to Designer Babies

/
37 Comments
The prospect of designer babies has been a staple of the dystopian futures imagined by science-fiction writers, evoking fears of eugenics (e.g. Brave New…
abstract_algebra

Is Zero a Natural Number?

/
0 Comments
Using: Anderson-Feil Chapter 1.1 Is zero a natural number? This is a pretty controversial question. Many mathematicians - especially those working in…
micro1

What is a Property Formally in Mathematical Logic

/
0 Comments
** Hrbacek-Jech Chapter 1.2Hrbacek and Jech do not go into full detail about what a property is formally. This is a part of mathematical logic, but…
bioethics

The New Bioethics: A 21st Century Overview

/
0 Comments
Bioethics Key PointsWorrying about the future now means recognizing the advances in technology, such as genetic engineering, that have arisen. …
supernova

What are the Fates of Massive Stars

/
0 Comments
Star Fate Key PointsStars are born in primordial nebulae, gaseous molecular clouds on the spiral arms of galaxies Stars smaller than 1.4 suns…
hand_to_hand_combat

Learn the Physics of Hand-to-Hand Combat

/
0 Comments
Physics of Hand-to-Hand Combat Key PointsMartial arts effectively use principles of physics to achieve goals quickly and forcefully. Athletic…
evolution_evidence

5 Pieces of Evidence that Support Theory of Evolution

/
0 Comments
Evidence for evolution First, read the following article as a precursor:What is Evolution: A Beginner’s Guide, What Is Evolution and How Does It…