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A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then triangulating your location based on that information [1]. Since light travels at 300 million meters per second, your location will be off by about 1 meter if the clock times are off by only…
It is said that you should accomplish three things in life: Plant a tree. Have a child. Write a book. Out of the three, I have completed at least one. At the time of writing this Insight, my textbook “Mathematical Methods for Physics and Engineering” just hit the virtual online shelves. This Insight will…
This is an introduction to cosmology for someone who has some knowledge of calculus and basic physics. In this tutorial, we will take a journey into the cosmos to study cornerstone ideas in cosmology and their derivations. Let’s begin our journey, by explaining the meaning of cosmology. Cosmology is the study of the origin, evolution,…
Please give us a brief background on yourself Over 40 years ago, I studied mathematics, physics and computer science in Freiburg and Berlin (Germany). My Ph.D. thesis was in pure mathematics, but I was later drawn more and more into applied mathematics. Since 1994 I am a full professor of mathematics at the University of…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 8. Phase space. The next chapter is 10. Gauge symmetries. 9. Propagators In this chapter we discuss the following topics: Background Fourier analysis and Plane wave modes Microlocal analysis and UV-Divergences Cauchy principal values Propagators for the free scalar…
The following is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 6. Symmetries. The next chapter is 8. Phase space. 7. Observables In this chapter we discuss these topics: General observables Polynomial off-shell observables and Distributions Polynomial on-shell observables and Distributional solutions to PDEs Local observables and Transgression Infinitesimal…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 4. Field Variations. The next chapter is 6. Symmetries. 5. Lagrangians Given any type of fields (def. 3.1), those field histories that are to be regarded as “physically realizable” (if we think of the field theory as a…
The following is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 1. Geometry. The next chapter is 3. Fields 2. Spacetime Relativistic field theory takes place in spacetime. The concept of spacetime makes sense for every dimension ##p+1## with ##p \in \mathbb{N}##. The observable universe has macroscopic dimensions…
This is the beginning of a series that gives an introduction to perturbative quantum field theory (pQFT) on Lorentzian spacetime backgrounds in its rigorous formulation as locally covariant perturbative algebraic quantum field theory. This includes the theories of quantum electrodynamics (QED) and electroweak dynamics, quantum chromodynamics (QCD), and perturbative quantum gravity (pQG) — hence the…
The CMB establishes a record of ancient acoustic oscillations in the baryon-photon plasma. We’ve been studying how these primordial sound waves evolve, and how to analyze the last scattering surface to learn about them. Now it’s time to confront their origin: what process composed the cosmic symphony? A few different proposals have been advanced…
The EPS conference was a week ago, and many new results and future plans were shown. A good general overview has been collected by Paris Sphicas in his Summary slides. I had a look at some presentations and collected things I personally found interesting. Warning: The selection is heavily biased, I cannot cover everything, and…
This article won’t contain much about physics that typical readers of this site don’t already know. However, deconstructing improper physics in literature and film can be a good exercise for physics teachers to share with their students. I’ll focus on one story, in particular, Edmond Hamilton’s The Second Satellite. Second Satellite Key Points The article focuses…
Tensor Key points The author begins by questioning the nature of numbers and their deeper significance. Numbers can represent various mathematical constructs, from scalars to linear mappings of one-dimensional vector spaces. These numerical representations can be described as elements of fields, dual spaces, and matrices. The concept of tensors is introduced, which are multi-dimensional arrays…
This Insights article is about dissipative forces (friction, air resistance, viscosity…). Damping by friction forces is one of the concepts that is encountered earliest by physics students. The reason for its importance is that almost all moving objects in everyday life are affected by friction and air resistance, which is why Newton’s 1st law is…
Please give us a bit of background into your educational and professional life. I’m a public school kid through and through. After going to the local high school where I grew up in Westford, Massachusetts, I attended Michigan State University to get Bachelors degree in astrophysics (with several extra classes in Computer Science). From snowy…
In terms of wavelength, peak solar radiation occurs at about 500 nm. Interestingly, this is well within the range of human vision. When solar radiation is plotted against frequency instead of wavelength, the peak is found to be at about 340 THz. It may come as a shock that when 340 THz is converted to…
Undergraduate interest in research is a good thing; it’s even better if they aspire to publish their work for review and consideration from a broader audience. First, we should consider what it means to be publishable. Usually, “publishable” means a paper contains a novel and interesting result in either theory or experiment that is more…
This is a compilation of my blog entry on this singular “project” to change the way we conduct the introductory physics laboratory in most US universities. I think we are missing a tremendous opportunity to educate a general audience on how we acquire and learn something in physics, and how we analyze something that we…
Traditional presentations of special relativity place emphasis on “velocity”, which of course has an important physical interpretation… carried over from Galilean physics. However, in many situations, working only with velocities can be tedious in calculations and may obscure the underlying geometry. First, a story (inspired by my post in the recent Relativistic Relative Velocity thread)….
My previous Insight, Frames of Reference: A Skateboarder’s View, explored mechanical energy conservation as seen from an inertial frame moving relative to the “fixed” Earth. Shifting one’s point of view to the moving frame proved to be somewhat controversial as far as mechanical energy conservation was concerned. Here I will examine shifting into accelerating frames…
Read part 1 -Backyards, Barns, Bayous When I was offered a job at the Air Force Academy, it seemed like an opportunity to exercise both my commitment to academic rigor and my desire to serve my country while continuing with the basement and boat ramp approach to research. Since I was a faculty in the Department…
In the last article, we looked at various counterintuitive features of the Schwarzschild spacetime geometry, as illustrated in the Kruskal-Szekeres spacetime diagram. But counterintuitive, in itself, does not mean physically unreasonable or unlikely. So the obvious next question is, how much of the entire spacetime geometry we have been looking at is actually believed…
Not long after Einstein published his Field Equation, the first exact solution was found by Karl Schwarzschild. This solution is one of the best known and most often discussed, and its properties have played a significant role in the development of General Relativity as a theory, as well as in efforts to find a…
1. Some Background on Dimensional Analysis … if you are not already familiar with it. 1.1 Dimensions Dimensional Analysis is a way of analyzing physics equations that consider only the qualitative dimensions – mass, length, time, charge .. – of the quantities involved, not the values that they take in the given problem. This is not to…
A tripod holds a camera still while the shutter is open, preventing motion blur. The tripod must be able to maintain this stability in the presence of uneven ground, wind, ground vibrations, etc. Generally, tripods are most easily characterized in terms of their size (weight and height) and the maximum load they can support. …
My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue the idea of shifting one’s frame of reference because its use is relatively uncommon in introductory physics courses. Students are asked to solve problems mostly in the (approximately) inertial frame of…
Although rolling wheels are everywhere, when most people are asked “what is the axis of rotation of a wheel that rolls without slipping?”, they will answer “the axle”. It is an intuitively obvious answer shared by 3/4 or more of the students in an introductory physics class. It is also the wrong answer. Here I…
We are pleased to introduce David J. Griffiths. Professor Griffiths is one of the most successful physics textbook writers. Odds are if you studied physics in college, you’ve used one of his textbooks. We are pleased and honored to obtain some of his insights on the quantum and academic world. Here we go! Please give us a…
The Connes-Lott-Chamseddine-Barrett model is the observation that the standard model of particle physics — as a classical action functional, but including its coupling to gravity and subsuming a fair bit of fine detail — may succinctly be encoded in terms of operator algebraic data called a “spectral triple”. This involves some non-commutative algebra, and…
Introduction First, congratulations! Camera technology has advanced to the point where a complete novice, using an entry-level camera right out of the box, can take photos that (under certain circumstances) appear identical to professional photos. Regardless if you only use your camera in the ‘automatic’ setting or if you explore the art of photography, the…
Before decoupling, photons and charged particles were in good thermal contact: though the primordial plasma might have varied in temperature from place to place, the photons and baryons were in local thermal equilibrium and shared a common temperature. If some physical process caused the baryons to heat up in some place, this temperature change…
We’ve been looking at how the continuum nature of spacetime poses problems for our favorite theories of physics — problems with infinities. Last time we saw a great example: general relativity predicts the existence of singularities, like black holes and the Big Bang. I explained exactly what these singularities really are. They’re not points…
Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this caused. But combining gravity with relativity led Einstein to something equally remarkable: general relativity. In general relativity, infinities coming from the continuum nature of spacetime are deeply connected to its most dramatic successful…
How do you determine the change in entropy for a closed system that is subjected to an irreversible process? Here are some typical questions we get at Physics Forums from confused members: If I have an irreversible adiabatic process, shouldn’t the change in entropy be zero since q/T is zero? Since entropy is a function of…
In 2002, Pierre Deligne proved a remarkable theorem on what mathematically is called Tannakian reconstruction of tensor categories. Here I give an informal explanation what this theorem says and why it has profound relevance for theoretical particle physics: Deligne’s theorem on tensor categories combined with Wigner’s classification of fundamental particles implies a strong motivation…
The Schwarzschild Metric A Lagrangian that can be used to describe geodesics is [itex]F = g_{\mu\nu}v^\mu v^\mu[/itex], where [itex]v^\mu = dx^\mu/ds[/itex] is the four-velocity. In the equatorial plane of the Schwarzschild metric this is $$F = (1 – 2m/r)^{-1} (dr/ds)^2 + r^2(d\phi/ds)^2 – (1 – 2m/r)(dt/ds)^2$$ The canonical momenta are [itex]p_\mu = \partial F/\partial v^\nu…
The LHC experiments are in full swing collecting data this year (more information in the forum), and a while ago the collaboration of the CMS experiment released 300 TB of old (2011) data that everyone can analyze (forum thread). But how do these analyses look like? There are two main analysis types: Searches for…
Polymer Key Points DNA is a good model system for polymer physics as it is small enough to observe single–molecule dynamics and large enough to be thermodynamically driven When DNA is coiled in the cell nucleus, it has no direct correlation between spatial position and genetic position When stretched out in a nanochannel, there is…
This Insight is a follow-up to my earlier tutorial Insight (Spacetime Diagrams of Light Clocks). I gave it a different name because I am placing more emphasis on Relativity and invariance, and I want to discuss more advanced methods involving “causal diamonds” (rather than just the “clock diamonds” in the earlier Insight). I will assume…
The following problem was inspired by reading Greg Egan’s “Incadescence”. Consider a body, orbiting a Schwarzschild black hole and tide locked to it, as in figure 1 below. The body itself has negligible mass, but due to the tidal gravity around the black hole, an observer on the body will feel “weight”. The basic problem…
We occasionally have students ask for help on software, “My software is perfect, but it doesn’t work!” Your software is never perfect. My software is never perfect. I recently found that I made someone’s top ten list of software that I had written 37 years ago. It’s not a top ten list anyone would aspire…
We are pleased to introduce Sean Carroll! Sean Carroll is a theoretical physicist at Caltech, specializing in cosmology and quantum mechanics. Sean has a new book out called The Big Picture, where the topic is “On the Origins of Life, Meaning, and the Universe Itself”. Key Points Sean Carroll’s educational journey took him from suburban Philadelphia to Villanova University,…
In the early 20th century, an eccentric businessman named Roger Babson declared gravity to be mankind’s greatest threat. He devoted part of his fortune to defeating it, creating the Gravity Research Foundation which sponsors a yearly essay contest focused on the understanding of gravity. This contest has been won by the likes of Stephen Hawking…
This Insight Article is a sequel to the Insight Article ”The Physics of Virtual Particles”, which contains an exposition of definitions that are physically justified, and in particular, makes precise what a virtual particle is and what being real means. As discussed in detail in the companion article, virtual particles are defined as (intuitive imagery…
A couple of weeks back, a thread was started about whether or not most of the stars we see at night are brighter than our Sun. The consensus was yes. I’d like to delve back into that subject in a little more detail. Just how representative is the night sky to what is out there?…
In discussions on the internet (including a number of Wikipedia pages) and in books and articles for non-experts in particle physics, there is considerable confusion about various notions around the concept of particles of subatomic size, and in particular about the notion of a virtual particle. This is partly due to misunderstandings in the terminology…
The “ordinary Big Bang and expansion” (no inflation, no dark energy) Einstein’s General Relativity allows a solution (FLRW metric) where an empty Universe expands. Imagine you have particles (say, hydrogen atoms) in a cubic grid with exactly 1 light-year between the nearest particles. (We assume their mass is so tiny that this Universe essentially behaves…
Read part 1 of this interview. Tell us about your experience with past projects like “This Week’s Finds in Mathematical Physics”. I was hired by U.C. Riverside back in 1989. I was lonely and bored, since Lisa was back on the other coast. So, I spent a lot of evenings on the computer. We had…
We are pleased to introduce you to Theoretical Physicist and PF Member Garrett Lisi. Known for riding waves and developing a unique theory of everything. Read on! Tell us a little bit about growing up in San Diego The part of San Diego where I grew up — Rancho Santa Fe — was pretty idyllic. I…
PET Key Points Paul Dirac first theorized positrons in 1928 and they were observed four years later by Carl Anderson. Positron Emission Tomography (PET) was developed in the 1950s–1980s as a medical diagnostic technology. PET works by administering a radioactive isotope, Fluorine–18, to the patient and detecting the positron emission and the subsequent gamma photons….
A vector has magnitude and direction. Pictorially, a vector can be imagined as a location in n-dimensional space relative to some fixed origin. The magnitude is represented by the distance from the origin to the point. In Mechanics and Introductory Physics, we mostly deal with 2- and 3-dimensional vectors. Some physical entities that behave…
Introduction Many times, we encounter ourselves tangled in some Quantum Mechanics (QM) interpretations debates. Unfortunately, the standard of discussion in these debates is often low in comparison to the standard in the debates of the more technical aspects of the theory, standards which tend to be more precise and rigorous. A consequence of this is…
Last time I sketched how physicists use quantum electrodynamics, or ‘QED’, to compute answers to physics problems as power series in the fine structure constant, which is $$ \alpha = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{\hbar c} \approx \frac{1}{137.036} . $$ I concluded with a famous example: the magnetic moment of the electron. With a truly…
Many are familiar with the “fundamental forces” of nature: gravity, electromagnetism, and the strong and weak nuclear forces. Three of these tend to bind things together in stable ways: as orbits, as atoms, or as nucleons. Once these systems are stable, there are still “residual” effects that the objects can have on one another through…
Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics and special relativity into account. It makes many wonderfully accurate predictions. And yet, it has embroiled physics in some remarkable problems: struggles with infinities! I want to sketch some of the…
Look in your standard cosmology textbook (in my case, the closest one at hand is Barbara Ryden’s Introduction to Cosmology) and go to the section that describes the experimental discovery of dark matter. Two of the things you will likely find in there are the following pieces of information: The virial theorem was applied to…
In this series, we’re looking at mathematical problems that arise in physics due to treating spacetime as a continuum—basically, problems with infinities. In Part 1 we looked at classical point particles interacting gravitationally. We saw they could convert an infinite amount of potential energy into kinetic energy in a finite time! Then we switched…
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 satisfying. If you ask Euclid why the Pythagorean theorem is true, he’ll show you a proof based on his five postulates. But it’s also possible…
Introduction In this Insight, I will go over the background information for the Millennium Prize problems and briefly describe three of them. A future Insight will contain brief descriptions of the remaining four problems. In 1900, David Hilbert presented 23 of the most important open problems in mathematics at a conference of the International Congress…
Earth’s gravitational field at the surface is approximately 9.8 Newtons/kilogram, or equivalently, 9.8 meters/second/second. But how does that change due to its shape, rotation, and composition and various locations along its surface and within its interior? This article will answer those questions. Earth’s Gravity Key Points Earth’s gravitational field at the surface is approximately 9.8…
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. We will look at some common misconceptions that lead people to think the answer must be “no”, and we will look at some of the issues involved that prevent…
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. Since then, I’ve learned more about the theory, and it turns out that Fred Hoyle was a lot cleverer than I’d assumed. The following is an…
In this Insights article we’ll look at a limited class of ordinary differential equations — homogeneous linear ODES with constant coefficients. Although there are many differential equations that are outside the scope of this article, there are many applications in mechanics and electronics of the types of differential equations we’ll be looking at. Homogeneous Equations A…
Many people ask how an airplane wing works, and several answers are commonly given. You might have even seen vigorous arguments between proponents of competing theories, such as Bernoulli’s principle and Newton’s laws. So who is correct? First, we must discuss what Bernoulli’s equation means. Bernoulli’s equation First, what is Bernoulli’s principle? Bernoulli’s principle (or…
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 field with potential V, the energy gain after going through the field is always eV, no matter how far away it has to move. For…
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 BW perspective nicely with this quote[1]: There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. In particular, one does not think of particles as…
DNA Hinge Key Points Funke and Dietz created a DNA hinge which is adjustable by varying the length of one of the DNA molecules, allowing positioning of molecules attached to the hinge by as little as 0.04 nanometers. DNA origami was one of the first successful methods of “bottom–up” nanotechnology, allowing structures such as cubes,…
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 randomly, with the constraint that it can’t visit the same spot more than once. These are mathematically somewhat interesting and crop up in a few areas of physics;…
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 to many beginning students. Here are some non-rigorous proofs that 1=0.999…: Proof #1 For any two unequal numbers, there is always another number in between them. (That is…
Astronomers Arno Penzias and Robert Wilson discovered the cosmic microwave background in 1965. They were not looking for it. They were using the comically distorted Holmdel Horn Antenna at Bell Labs, New Jersey, to study the reflection of radio waves off NASA balloon satellites. Despite all efforts to remove interference while calibrating the instrument…
The following is an overview of the time dilation and gravitational redshift effects of a static (Schwarzschild) black hole. By general relativity, a strong gravitational field can slow downtime. The closer you get to the event horizon of a black hole (if you can survive the gravity gradients, and g-forces and have some means of…
Before proceeding with a discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article, we need to speak a bit about the fundamentals of local Lagrangian field theory in general, of which these sigma-models are examples. The geometry that underlies the physics of Hamilton and Lagrange’s…
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 there have been many attempts, claims, and misconceptions surrounding what atoms look like and how we can photograph them. Let’s set that all straight below!…
In the first two posts in this series, we looked at different ways of interpreting the question “does gravity gravitate?” We left off at the end of the last post with an open question: what do the various “mass integrals” look like in a spacetime where gravitational waves are being emitted? Let’s look at…
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 to the answer “yes”. However, this will leave a lot of people who ask our title question unsatisfied, because the usual motivations for asking the question have…
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 skills that one must master: finding the proof and communicating the proof. We will try to focus on the former here, but we will try to say…
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 of several posts on this subject. Short answer: mu. (The terms of the question are not well-defined, so it doesn’t have a well-defined answer.)…
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 see, namely that the universe is expanding uniformly and that there is no center (and no edge). The analogy is disliked (often intensely disliked) by serious physicists because it causes…
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 be made, which will become obvious later on. Still, at this point, we will simply deal with objects with spherical symmetry and no complicated mass distribution. In other words,…
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 as lists of real numbers. We’re not asking if this idea is true: there’s no clinching evidence to answer that question, so it’s too easy to let one’s philosophical…
The Planck length is an extremely small distance constructed from physical constants. There are a lot of misconceptions that generally overstate its physical significance, for example, stating that it’s the inherent pixel size of the universe. The Planck length does have physical significance, and I’ll talk about what it is, and what it isn’t. Key…
Last time we saw that nobody yet knows if Newtonian gravity, applied to point particles, truly succeeds in predicting the future. To be precise: for four or more particles, nobody has proved that almost all initial conditions give a well-defined solution for all times! The problem is related to the continuum nature of space:…
Key Points Scaling arguments are powerful tools in physics between vague descriptive arguments and rigorous formulae. Examples of scaling arguments include the Square–Cube Law and Terminal Velocity. A paper by Nicole Meyer–Vernet and Jean–Pierre Rospars examines the top speeds of organisms of varying sizes from bacteria to blue whales. The paper finds that the time…
Introduction Understanding the behavior of infinity is one of the major accomplishments of mathematics. Sadly, the infinite is often misunderstood and could lead to various paradoxes when used or interpreted the wrong way. This FAQ attempts to explain the role of infinity in mathematics and tries to resolve a few apparent paradoxes. 1. Infinity is…
Is spacetime really a continuum? That is, can points of spacetime really be described—at least locally—by lists of four real numbers ##(t,x,y,z)##? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances? Rather than trying to answer this hard question, let’s look back at the struggles…
Yes. First, we have not addressed what 0.999… actually means. So it’s best first to describe what on earth the notation [tex]b_0.b_1b_2b_3…[/tex] means. The way mathematicians define this thing is [tex]b_0.b_1b_2b_3…=\sum_{n=0}^{+\infty}{\frac{b_n}{10^n}}[/tex] So, in particular, we have that [tex]0.999…=\sum_{n=1}^{+\infty}{\frac{9}{10^n}}[/tex] But all of this doesn’t really make any sense until we define what the right-hand side means….
Introduction It is a common saying that during inflation “space expanded faster than the speed of light.” This statement is meant to articulate the extreme rates of expansion seen during inflation, and this it does successfully. Unfortunately, it is at least a little wrong, and what little there is right about it is not unique…
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 at a bit of history A short history of 0 Historically, there are two different uses of zero: zero as a placeholder and…
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 popularizations, which is that all the matter in the universe will first be sucked into black holes, and then recycled into photons in the distant future through…
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 need for corrections. We’ve discussed this before here on PF, but I think at this point I understand it better, so I thought I’d post a summary of my present…
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 hole at some constant radius [itex]r > 2M[/itex]. (Note that this is not the same as being in a stable circular orbit about the hole; we allow for…
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 give a fast overview of how physicists (and other scientists) tend to present their results in terms of statistics and measurement errors. If we are faced…
Part 3: Important Cosmological Horizons and Distances A question that often comes up is: “how big is the observable universe?” The question can have more than one answer, depending on the context, so cosmologists have given it a technical name and a precise definition. It is called the ‘particle horizon’, here indicated by Dpar,…
Often students have difficulty reconciling the General Relativity (GR) view of gravity versus their own experience with gravity on the surface of Earth. This article covers some of the basic concepts and explains how they work with “every day” gravity. Important Concepts Spacetime: the combination of 3 dimensions of space and 1 dimension of time into…
If we restrict ourselves to a spatially flat LCDM universe model (and ignore the early radiation energy density), the first Friedmann equation can be written in a very simple form. Marcus started several PF threads in a collaborative effort to develop this simplified approach.[1] It is still a work in process, but here I…
There is an interesting story unfolding in particle physics. The main motivation for building the Large Hadron Collider was to search for new particles. And in July of 2012, the LHC found the Higgs boson, confirming the existence of this entirely new, but widely expected elementary particle. But the Higgs wasn’t the only particle most…
Introduction In learning Thermodynamics, one of the difficult concepts that many students struggle with is the difference between reversible and irreversible work in the expansion/compression of a gas. They wonder, 1. Why is it that we need to use two different equations to calculate the work done by the system on the surroundings, one for…
Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound very arbitrary and counterintuitive. But it doesn’t have to be this way… Traditional approaches The starting point of any quantum field theory is free fields that serve to define irreducible representations of…
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 your results Ready for your next quiz? How well do you know about the Periodic Table of Elements? 1. What is the Large Hadron Collider (LHC)? The Large Hadron…
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 of a hot body as containing heat, but in Physics Heat and Work refer to the transfer of energy from one body to another. Correspondingly, Internal Energy and Kinetic…