Expert Math and Science Articles

Welcome to our 100% community authored science and math blog. All of our blog authors are experts in their respective STEM fields. You’ll find high quality, engaging and interesting math and science articles (physics, mathematics, engineering, chemistry, biology, technology…). Even better we have science and math tutorials, guides, quizzes and interviews too.


Emergence From the Superpoint

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

Centrifugal Force Reversal Near A Black Hole

My goal in this article is to derive a simple equation for the proper acceleration of an observer traveling on a circular path around a Schwarzschild black…

Homotopy Lie-n Algebras in Supergravity

 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…

A Short Proof of Birkhoff's Theorem

Birkhoff's theorem is a very useful result in General Relativity, and pretty much any textbook has a proof of it. The one I first read was in Misner, Thorne,…
string theory

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

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

Why You Should Not Use Wikipedia As Your Primary Source

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…

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

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…

Misconception of the Heisenberg Uncertainty Principle

One of the common misconception about the Heisenberg Uncertainty Principle (HUP) is that it is the fault of our measurement accuracy.A description…

You Will Not Tunnel Through a Wall

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…

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

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…

The Most Important Thing You Can Learn from Physics Forums

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

Plus/minus What? How to Interpret Error Bars

People some times find themselves staring at a number with a ± in it when a new physics result is presented. But what does it mean? The aim of this Insight…

Approximate LCDM Expansion in Simplified Math (Part 4)

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

False Physics Major Dichotomy: Theorist or Experimentalist?

Many physics majors believe that pursuing a PhD in physics requires they make a choice between theory and experiment. Due to my weaknesses in math,…
physics course

Your Curriculum Vitae As a Physics Graduate

  I am going to backtrack a little bit and talk about writing your Curriculum Vitae (CV) and what you should focus on in search for…
issac newton

The Isaac Newton Quiz

One of the great heavy weights of history. How much do you really know about him? Let's find out!"To myself I am only a child playing on the beach,…

The LCDM Cosmological Model in Simplified Math (Part 3)

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

How to Get a Postdoctoral Physics Position

  If you intend to pursue an academic/research career, chances are, you will need postdoctoral experience. This is typically a 2…

Approximate LCDM Expansion in Simplified Math (Part 2)

  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,…
physics jobs

How to Get a Physics Job!

  In the previous chapter, we have reached the point where you have finished with your thesis defense, and also thesis submission…

Neutrino Masses and Speed

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…

Understanding the General Relativity View of Gravity on Earth

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

Approximate LCDM Expansion in Simplified Math

 If we restrict ourselves to a spatially flat LCDM universe model, the first Friedmann equation can be written in a very simple form. Marcus…
math obvious

Teaching Math and the Obvious

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

Science for Love or for Money

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…

Measuring Quantum Entanglement?

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,…
thesis defense

Your Physics Thesis Defense Guide

  At this point, you have completed writing your thesis, your adviser has approved of it, and you have distributed it to all the…

Garrett Lisi's Superparticle Bet With Frank Wilczek

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

Writing Your Doctoral Thesis/Dissertation As a Physics Major

  At this stage, you have performed your doctoral research work, maybe even have published (or about to publish) a paper or two,…

Some Useful Integrals In Quantum Field Theory

In my paper on renormalisation I mentioned what most who have studied calculations in Quantum Field Theory find, its rather complicated and mind numbing.…
oral presentation2

Oral Presentations - Addendum | Physics Career

I'll try not to make a habit out of this, but I believe there's something to add to this chapter of the series.In Part XIV, I mentioned the APS Meetings…
physics journals2

Publishing in a Physics Journal (Addendum)

 When I first wrote this part of the series, I wasn't quite sure if I should include this. for most people submitting to most of the physics…
oral presentation

Oral Presentations As a Physics Major

  I mentioned earlier that there are two ways for physicists to communicate their work. The first is via publications in peer-reviewed…

Writing a Master Degree Thesis As a Physics Major

Your First Scientific Paper Ought to be good! Structure and Contents of a Master Degree Thesis This guide was written some years ago as a guideline for…

Retrocausality: How Fundamental is the Arrow of Time?

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…
physics journals

Publishing in a Physics Journal As a Physics Major

  At this stage, you are well into your Ph.D research work, and depending on what area of physics you are in, you may already start…
lab work

Research Work and The Lab Book As a Physics Major

  Now where were we? Oh yes! You have now started with your actual research work. You and your adviser have agreed on at least the…
research work

Initiating Research Work As a Physics Major

  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…
advisor research

Choosing a Research Area and an Advisor As a Physics Major

  In the previous part, I described the trials and tribulations of going through the qualifying exam that almost all graduate physics…
gas compression

Reversible Vs Irreversible Gas Compression and Expansion Work

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

Causal Perturbation Theory

Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound…
LHC quiz

Think You Know about the LHC?

News of the LHC progress has dazzled scientists and hobbyists alike. It's now time to show just how much you know about the operation.Please share…
grad exam

First years of Graduate School from Being a TA to the Graduate Exams

 You are now entering your first year of graduate school. In terms of academic aspect, you will have a set of required courses that you must…
other majors

Entering Physics Graduate School From Another Major

  I have decided to tackle this issue because it became a very common question in many physics forums. Can someone, without a degree…
heat errors

Frequently Made Errors in Heat: Elementary Level

1. Heat, Work, Internal Energy and Kinetic Energy "If heat is the motion of molecules, why isn't it Kinetic Energy?"In everyday use, we may think…

Errors in Probability: Continuous and Discrete Distributions

1. Classifying as discrete, continuous or mixed These statements (or equivalents) can be found in authoritative-seeming websites:X "A random variable…

Weak Values Part 2: The Quantum Cheshire Cat Experiment

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

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

Negative absolute temperatures

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…
publishing in journals

Guide to Publishing in Peer Reviewed Journals

From Concept to Manuscript You've done the science.  You had an idea, performed an extensive literature review, designed an experiment, ran the experiment,…
What is Energy

What is Energy?

What is energy?For some reason, this perfectly legitimate question seems to spawn far more than its share of bad threads. So what is energy and how do…