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no tidal bulge

Beyond the Tidal Bulge

Overview That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet the tidal bulge is still used to portray why the Moon is receding the Earth. If there is no tidal bulge, some other explanation is in order. That other explanation uses gravitation as…

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lineartransformations

Learn About Matrix Representations of Linear Transformations

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Let X and Y be finite-dimensional vector spaces. Let ##T:X\to Y## be a linear transformation. Let ##A=(e_1,\dots,e_n)## and ##B=(f_1,\dots,f_m)## be ordered…
electronatom

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

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Atoms and Coulomb Forces If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms…
airplanelift

How Does an Airplane Wing Work? A Primer on Lift

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

Is the Universe a Black Hole?

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In the early universe, the matter was gathered together at very high density, so why wasn't it a black hole?The first thing to understand is that the…
pythondebug2

Simple Python Debugging with Pdb: Part 2

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This Insight article is the continuation of the first article, Simple Python Debugging with Pdb: Part 1.In this article, let's look at another important…
pythondebug1a

Learn Simple Python Debugging with Pdb

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I'm pretty new to Python, so I was looking around for some debugging tools. At first, I dismissed Pdb (Python debugger) as being too primitive, but after…
goingbacktoschool

A Guide to Going Back to School For Math or Science

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Motivations for creating the series I came to Physics Forums originally to read ZapperZ’s thread about becoming a physicist back in 2013. It was one…
electrostaticfield1

Learn About 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…
studymath

How to Self-Study Basic High School Mathematics

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  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…
studymath2

A Guide to Self Study Calculus

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  We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order.…
studymath1

The Essential Guide to Self Study Mathematics

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  How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead,…
seeelectron

Have Scientists Seen an Electron?

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This is not about seeing an electron, but rather, the notion that seeing something with our eyes is the end-all requirement for the validity of anything.…
peterblockuniverse

The Block Universe – Refuting a Common Argument

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The "block universe" interpretation of SR has come up repeatedly in threads here on PF. Rather than link to them, I want to summarize a common argument…
twinparadox

A Geometrical View of Time Dilation and the Twin Paradox

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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…
Retrocausality

Understanding Retrocausality and Blockworld

In an Insights series “Blockworld and its Foundational Implications,” I quoted Huw Price and Ken Wharton in several places advocating a blockworld…
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 the rotation of the universe as a whole, since there is…
blockuniverse5

Blockworld and its Foundational Implications: Delayed Choice and No Counterfactual Definiteness

 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity. In part 3, I introduced…
blockuniverse4

Blockworld and its Foundational Implications: General Relativity and Closed Timelike Curves

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 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity (SR). In part 3, I introduced…
blockuniverse3

Blockworld and its Foundational Implications: General Relativity and the Big Bang

 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity (SR). Geroch sums up the…
blockuniverse2

Blockworld and Its Foundational Implications: The Relativity of Simultaneity and Blockworld

 In part 1 of this 5-part Insights series, I introduced two consequences of the second postulate of special relativity (SR): time dilation…
blockuniverse1

Blockworld and Its Foundational Implications: Time Dilation and Length Contraction

 This is the first in a 5-part series of Insights that will introduce blockworld (aka "block universe”) and use it to address a puzzle…
DNA

Atomic Positioning with DNA Hinges

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DNA Hinge Key PointsFunke and Dietz created a DNA hinge which is adjustable by varying the length of one of the DNA molecules, allowing positioning…
prequantum4

Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories

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  At the end of this page, we will have come full circle back to the first article in the series 20 years ago -- The M-Theory Conjecture.We…
prequantum3

Examples of Prequantum Field Theories III: Chern-Simons-type Theories

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  After having constructed gauge fields and higher gauge fields in the previous article by systems of ##L_\infty##-algebroid-valued…
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,…
guagetheory

Examples of Prequantum Field Theories II: Higher Gauge Fields

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   After having recalled ordinary gauge fields from a dg-algebraic perspective in the previous article, here I discuss…
prequantumft

Examples of Prequantum Field Theories I: Gauge Fields

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  After having motivated the need for prequantum field theory and having laid out its principles (i. extremal action, ii. global…
animationwalk

Fun with Self-Avoiding Walks Simulations

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This post is about some simulations I did of self-avoiding random walks. These are what they sound like with each step, the position of the walk moves…
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…
prequantumgeometry5

Higher Prequantum Geometry V: The Local Observables – Lie Theoretically

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 This article discusses how the previous considerations naturally follow the concepts of local observables of local field theories and of…
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 a vacuum.…
prequantumgeometry4

Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively

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  The Euler-Lagrange ##p##-gerbes discussed in the previous article are singled out as being exactly the right coherent refinement…
prequantumgeometry3

Higher Prequantum Geometry III: The Global Action Functional – Cohomologically

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  The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…
blackbody

A Poor Man’s CMB Primer: Bumps on a Blackbody

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 Astronomers Arno Penzias and Robert Wilson discovered the cosmic microwave background in 1965. They were not looking for it.They were…
prequantumgeometry2

Higher Prequantum Geometry II: The Principle of Extremal Action – Comonadically

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  The previous article motivated the importance of considering "pre-quantum field theory" in-between classical and quantum field…
redshiftblackholes

Learn Time Dilation and Redshift for a Static Black Hole

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The following is an overview of the time dilation and gravitational redshift effects of a static (Schwarzschild) black hole. By general relativity, a strong…
prequantumgeometry

Higher Prequantum Geometry I: The Need for Prequantum Geometry

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 Before proceeding with a discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article,…
atoms

Can We See an Atom?

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In this article, I will discuss how these images of atoms are made, what exactly we are looking at, and what it means to see an atom. Over the decades…
gravity3

Does Gravity Gravitate: The Wave

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 In the first two posts in this series, we looked at different ways of interpreting the question "does gravity gravitate?" We left off at…
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…
gravitate2

Does Gravity Gravitate? Part 2

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 In the first post of this series, I talked about two ways to answer the title question, one leading to the answer "no" and the other leading…
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 two separate…
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…
doubt

Dealing with Doubt as a Science Student

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Doubt, as odd as this may sound, can be essential to our living.  We all make decisions and later have questions on whether we made the right choice or…
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…
pluto

Pluto Quiz: Think You Know Pluto?

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Pluto has been in the news quite a bit these past several months. Let's see if you've been paying attention. Feel free to share your score in the comments…
birthcmb

A Poor Man’s CMB Primer: The Birth of a Cosmic Background Radiation

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 The early universe was hot. So hot that nuclei boiled. The great thermal energy of the universe overwhelmed the confining efforts of the…
modulation

Understand the Acoustic Modulation vs. Beating Confusion

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A long time ago I read a paper in the IEEEProceedings recounting the history of the superheterodyne receiver. Overall it was a very interesting and informative…
balloonanalogy

Learn Inflation Balloon Analogy Misconceptions

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The Balloon Analogy is a simple-minded way to help describe (but not completely describe) two facts of cosmology that are difficult for many people to…
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, several assumptions will…
spacetime4

Struggles With the Continuum: Point Particles and the Electromagnetic Field

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 In these posts, we're seeing how our favorite theories of physics deal with the idea that space and time are a continuum, with points described…
bubbles

Explosion-Generated Collapsing Vacuum Bubbles Reach 20,000 Kelvin

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Key PointsJérôme Duplat and Emmanuel Villermaux published a paper in Physical Review Letters (PRL) to generate centimeter-sized vacuum bubbles…
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…
cardinalnumbers

Informal Introduction to Cardinal Numbers

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Cardinal numbers We will now give an informal introduction to cardinal numbers. We will later formalize this by using ordinal numbers. Informally, cardinal…
cmb

A Poor Man’s CMB Primer: Orientation of the Universe

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 This is a picture of the cosmic microwave background:Fig 1. The cosmic microwave background as seen by the European Space Agency's…
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…
planck

What Planck Length Is and It’s Common Misconceptions

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The Planck length is an extremely small distance constructed from physical constants. Many misconceptions generally overstate its physical significance,…
spacetime2

Struggles With The Continuum: Quantum Mechanics of Charged Particles

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 Last time we saw that nobody yet knows if Newtonian gravity, applied to point particles, truly succeeds in predicting the future. To be precise:…
procrastination

The Best Methods to Deal with Procrastination

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It's 6:30 in the morning. You've just woken up and you feel so sleepy you think to yourself "A few more minutes can't hurt." And so you drift on to sleep…
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…
imagination

Why Imagination Without Knowledge Is Ignorance Waiting to Happen

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Introduction My feelings on people who think that imagination is more important than knowledge are well-known. These people simply are parroting Einstein's…
animal speeds

Exploring a Paper on Scaling Laws and the Speed of Animals

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Key PointsScaling arguments are powerful tools in physics between vague descriptive arguments and rigorous formulae. Examples of scaling arguments…
infinity_faq

Learn the Top 5 Misconceptions About Infinity

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Introduction Understanding the behavior of infinity is one of the major accomplishments of mathematics. Sadly, the infinite is often misunderstood and…
man_on_moon

Last Man On The Moon | Look Back at Previous Missions

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On December 11, 1972, astronaut Eugene Cernan became the last person to walk on the lunar surface, marking the conclusion of NASA's Apollo missions—a…
spacetime

Struggles With the Continuum: Is Spacetime Really a Continuum?

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 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

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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…
999

Is There a Rigorous Proof Of 1 = 0.999…?

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Yes.First, we have not addressed what 0.999... means. So it's best first to describe what on earth the notation [tex]b_0.b_1b_2b_3...[/tex] means.…
CosmologicalHorizons

Inflationary Misconceptions and the Basics of Cosmological Horizons

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

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…
lightswitch

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

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

Will All Matter Be Converted to Photons?

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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: NOHowever, this is where it gets a bit confusing for most people. This is because, in physics, there are several…
relativitytherorm

Learn the Relativistic Work-Kinetic Energy Theorem

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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

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

An Equation for the Centrifugal Force Reversal Near A Black Hole

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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…
liealgebra

Homotopy Lie-n Algebras in Supergravity

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 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…
birktheo

Learn A Short Proof of Birkhoff’s Theorem

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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

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  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

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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…
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…
hupmisconceptions1

Learn a Misconception of the Heisenberg Uncertainty Principle

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

Why You Can’t Quantum Tunnel Through a Wall

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What is quantum tunneling? Quantum tunneling is a phenomenon in quantum mechanics where particles exhibit the ability to pass through energy barriers…
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 the introductory text on special relativity. It should be noted that whether or not…
learnfrompf

The Most Important Thing You Can Learn from Physics Forums

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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

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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)

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  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?

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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…
physics course

Your Curriculum Vitae As a Physics Graduate

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

Isaac Newton Quiz: Test Yourself on Isaac Newton

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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,…
LCDM3

The LCDM Cosmological Model in Simplified Math (Part 3)

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  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

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

Approximate LCDM Expansion in Simplified Math (Part 2)

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  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

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

Learn About Neutrino Masses and Speed

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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

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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

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 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

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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

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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?

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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

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