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What ‘Publishable’ Means 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…
Full Chapter List – So You Want To Be A Physicist… Series Part I: Early Physics Education in High schools Part II: Surviving the First Year of College Part III: Mathematical Preparations Part IV: The Life of a Physics Major Part V: Applying for Graduate School Part VI: What to Expect from Graduate School Before…
Full Chapter List – So You Want To Be A Physicist… Series Part I: Early Physics Education in High schools Part II: Surviving the First Year of College Part III: Mathematical Preparations Part IV: The Life of a Physics Major Part V: Applying for Graduate School Part VI: What to Expect from Graduate School Before…
From Concept to Manuscript You’ve done the science. You had an idea, performed an extensive literature review, designed an experiment, ran the experiment, mucked the experiment up, repeated the cycle until you generated meaningful results, conducted a rigorous analysis, and now, finally, you’ve written up your results complete with fancy graphs. You want to share…
In Memoriam In Memory of Dr. Thomas J. LeCompte (1964-2025), Detector Designer and Champion of Education and Science. Prologue Defining “the box” Someone who shows interest in science is initially a welcome development. So are fresh ideas from unexpected quarters. In contrast, there is a scientific community that is meticulously organized down to the last…
Introduction: “Convenient Notation” In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra: [tex]\delta^j_k =\left\{\begin{array}{lcl}1&\text{ if }…
Abstract Fermat’s Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book…
The Concept A vector space is an additively written abelian group together with a field that operates on it. Intuitive picture vs abstract definition Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That’s where the term linear to describe…
Introduction The concept of a group is as simple as it gets: a set with a binary operation like addition and a couple of natural laws like the requirement that the order of two consecutive operations does not matter: ##(1+2)+3=1+(2+3).## That’s it. The concept of a group is so simple that I still wonder why…
Introduction 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…
Abstract It took until the last century for physicists and mathematicians in the Netherlands to question the Euclidean concept of dimension as length, width, and height. Luitzen Egbertus Jan Brouwer published a ground-breaking paper On the Natural Concept of Dimension (Amsterdam, [2]) in 1913 about the mathematical definition of dimension picking up a thought from…
Direct answer: Cosmologists classify the universe as open, flat, or closed based on spatial curvature. Current cosmic microwave background (CMB) measurements indicate the universe is very close to flat, but small curvature remains observationally allowed. Whether the universe is ultimately finite or infinite cannot be settled by theory alone, since all three curvature types are…
The Einstein Field Equations (EFE) are ten coupled, nonlinear differential equations that describe how matter and energy determine the curvature of spacetime. First published by Albert Einstein in 1915, they form the mathematical core of general relativity, linking spacetime geometry to its energy and matter content through the equation [itex]G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}[/itex]. Key…
Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century BC) and Archimedes of Syracuse (##3##-th century BC), to the fundamental building blocks of calculus from the ##17##-th century on, up to modern Lie theory which is crucial for our understanding of quantum theory….
Introduction When doing mathematics, we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. Going from rational numbers to reals is more complicated. The easiest way at the start is probably infinite decimals. Dedekind Cuts can be used to get a bit more fancy. A Dedekind cut is a…
Abstract Famous Science Communicators There is so much to say about the many endeavors by professional scientists to explain to us the world. The list is long: Carl Sagan, Harald Lesch, Neil deGrasse Tyson, Sabine Hossenfelder, Michio Kaku, and I even saw Roger Penrose and Steven Hawking on TV. The list is – of course…
A central principle of Physics Forums regarding homework help is not to provide solutions on demand but to guide students along a path to the answer. The rationale behind this principle is articulated in the familiar saying, “If you give a hungry man a fish, you feed him for a day; if you teach him…
In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic pressure. We will look at the two known cases of this, white dwarfs and neutron stars; but it should be noted that similar arguments will apply to any postulated…
Part 1: Overview Part 2: Mathematical Details Part 3: Implications In a previous article, I described in general terms the model of gravitational collapse of a spherically symmetric massive object, first published by Oppenheimer and Snyder in their classic 1939 paper. In this follow-up article, I will give further mathematical details about the model, using…
Part 1: Overview Part 2: Mathematical Details Part 3: Implications Most people who have spent any time at all studying GR are familiar with the Schwarzschild solution. (A series of Insights articles discusses the key properties of that solution.) Much of that familiarity probably derives from the fact that the Schwarzschild solution describes a black…
Introduction I often read questions about our classification scheme that we use on physicsforums.com to sort posts by science fields and subjects, what has to be studied first in order to learn something else, what is a good way through physics or mathematics in self-study or simply about the desire to understand, e.g. general relativity…
An entire book could easily be written about the history of numbers from ancient Babylon and India, over Abu Dscha’far Muhammad ibn Musa al-Chwarizmi (##\sim ## 780 – 845), Gerbert of Aurillac aka pope Silvester II. (##\sim ## 950 – 1003), Leonardo da Pisa Fibonacci (##\sim## 1170 – 1240), Johann Carl Friedrich Gauß (1777 –…
* Oct. 25th, 1811 † May 31st, 1832 … or why squaring the circle is doomed. Galois died in a duel at the age of twenty. Yet, he gave us what we now call Galois theory. It decides all three ancient classical problems, squaring the circle, doubling the cube, and partitioning angles into three…
P or NP This article deals with the complexity of calculations and in particular the meaning of ##P\stackrel{?}{\neq}NP## Before we explain what P and NP actually are, we have to solve a far bigger problem: What is a calculation? And how do we measure its complexity? Many people might answer, that a calculation is an…
Riemann Hypothesis History The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the field of number theory. It’s named after the German mathematician Bernhard Riemann, who introduced the hypothesis in 1859. RH: All non-trivial zeros of the Riemannian zeta function lie on the critical line. ERH: All…
We use integration to measure lengths, areas, or volumes. This is a geometrical interpretation, but we want to examine an analytical interpretation that leads us to Integration reverses differentiation. Hence let us start with differentiation. Weierstraß Definition of Derivatives ##f## is differentiable at ##x## if there is a linear map ##D_{x}f##, such that \begin{equation*} \underbrace{D_{x}(f)}_{\text{Derivative}}\cdot…
Superdeterminism as a way to resolve the mystery of quantum entanglement is generally not taken seriously in the foundations community, as explained in this video by Sabine Hossenfelder (posted in Dec 2021). In her video, she argues that superdeterminism should be taken seriously, indeed it is what quantum mechanics (QM) is screaming for us to…
(based on https://www.physicsforums.com/threads/teaching-sr-without-simultaneity.1011051/post-6588952 and https://physics.stackexchange.com/a/689291/148184 ) In my earlier Insight Spacetime Diagrams of Light Clocks, I stated without proof that the areas of all light-clock diamonds are equal. In my article, “Relativity on Rotated Graph Paper”, Am. J. Phys. 84, 344 (2016) I provided algebraic proof. In the penultimate draft, I had a non-algebraic motivating…
Introduction Every secondary school student who has encountered trigonometry in his/her Math syllabus will most likely have come across the sine, cosine, and area rules which are typically used to solve triangles in which certain information is supplied and the remainder are to be calculated. Somewhat surprisingly (because it is relatively simple to derive), the…
What Does the Double-Slit Experiment Prove About Quantum Reality? The double-slit experiment demonstrates that light and matter exhibit both wave and particle behavior depending on what is measured. When no measurement of “which slit” is made, particles produce an interference pattern typical of waves. When that measurement is made, the pattern disappears and particles behave…
Introduction A recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch site being a fixed height above the ground upon which the projectile was eventually impacted. Several interesting methods of solution arose so the idea of this article is to present all…
Confessions of a moderate Bayesian part 3 Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian Probability Bayesian statistics by and for non-statisticians https://www.cafepress.com/physicsforums.13280237 Background One of the things that I like about Bayesian statistics is that it rather closely matches the way that I think about…
Confessions of a moderate Bayesian, part 1 Bayesian statistics by and for non-statisticians https://www.cafepress.com/physicsforums.13265286 Background I am a statistics enthusiast, although I am not a statistician. My training is in biomedical engineering, and I have been heavily involved in the research and development of novel medical imaging technologies for the bulk of my career. Due…
All undergraduate physics majors are shown how the counterintuitive aspects (“mysteries”) of time dilation and length contraction in special relativity (SR) follow from the light postulate, i.e., that everyone measures the same value for the speed of light c, regardless of their motion relative to the source (see this Insight, for example). And, we can…
Answer: AI, and more specifically machine learning, is already reshaping STEM through faster image and data analysis, automated grading and mastery-learning systems, and accelerated drug discovery in fields like pharma and biotech. Five Physics Forums advisors agree AI will keep expanding into labs, classrooms, and industry, but none expect it to fully replace human instructors,…
Physics Forums advisors expect AI to arrive unevenly across STEM: faster in narrow, well-defined tasks like long-haul trucking routes or lab data analysis, and slower in classrooms and jobs requiring human judgment. Most contributors caution against buzzword-driven adoption and stress that AI’s usefulness depends on whether the underlying problem is genuinely suited to automation. Key…
Big Bang: Key Points Hubble’s law (redshift of galaxies) and the Doppler effect provide direct evidence that the universe is expanding away from our reference point. Expansion has cooled the universe from the initial high temperatures at the Big Bang; radio astronomy detects signals from stars, galaxies, radio galaxies, quasars, and pulsars that trace this…
Mary Somerville and Caroline Herschel were jointly honored by Google’s 2 February 2020 Doodle as the first two women elected honorary members of the Royal Astronomical Society (RAS). Somerville, a Scottish polymath born in 1780, became known for her 1831 work “The Mechanism of the Heavens,” and her scientific standing helped open the RAS to…
Authorship Authorship Contributions From Anorlunda Introduction You may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention. It can be very difficult to analyze what is inside the box to find the flaw. Maybe we can’t find it. Maybe nobody can find…
Note: This Insight was previously titled, “Answering Mermin’s Challenge with Wilczek’s Challenge.” While that version of this Insight did not involve any particular interpretation of quantum mechanics, it did involve the block universe interpretation of special relativity. I have updated this Insight to remove the block universe interpretation, so that it now answers Mermin’s challenge…
Introduction In a previous article “Calculating the Balmer Alpha Line” we mentioned how accurate predictions of the spectral lines of singly ionized Helium were of considerable importance in persuading the scientific community that Danish physicist Niels Bohr was on the right track in respect of his groundbreaking atomic model first published in 1913. In this…
For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common ground. There is no consensus about the interpretation of quantum mechanics, and – not surprisingly – there is disagreement even among the mentors and science advisors here on Physics…
Don’t forget to read Part 1 of this interview. Peak Oil and Future Energy Sources Professor Kaku, what do you think of “peak oil”? How serious is it, and what alternative sources of energy do you think will best provide the world’s needs in the coming decades after fossil fuels start to decline (whether it…
We are happy to present this archived interview with Dr. Michio Kaku, conducted in 2004. Michio Kaku is an American theoretical physicist, futurist, and popularizer of science. He is a professor of theoretical physics at the City College of New York and the CUNY Graduate Center. Kaku has written several books about physics and related…
In this Insight I will introduce the quantum mystery called “Wigner’s friend” using Healey’s version [1] of Frauchiger and Renner’s (FR’s) version [2] of Wigner’s version [3]. As with much of physics, the explication becomes more succinct and comprehensible with each successive rendering. I will show how this mystery results from treating classical information (behaving…
Introduction Financial options — the right to purchase (call) or sell (put) stock or other assets at a fixed price on a future date — have been around for a long time. They are attractive to the option buyer because the buyer’s total risk is limited to the premium (price) paid for the option, unlike…
About Physics Forums Physics Forums is an independent online community for people who want to learn and discuss science as it is actually understood and practised by scientists. It was founded in 2001, it is moderated by working and retired physicists, mathematicians and engineers, and it has been running continuously ever since. Mission and Values…
We asked our PF Advisors to tell us what academic advice would you tell your 18 year old self. Here are their responses… PF Advisors’ Academic Advice Thanks & Next Steps Thanks to all the PF Advisors that shared their academic advice. We have more questions for them in the near future. Stay tuned for…
Adam Becker is an astrophysicist and science writer whose first book, What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics, has just been published. Give us some background on how you got interested in physics and formative youth experiences I don’t remember a time when I wasn’t interested in science. Some of…
This is one chapter in a series on Mathematical Quantum Field Theory The previous chapter is: 15. Interacting quantum fields. 16. Renormalization In this chapter we discuss the following topics: Epstein-Glaser normalization Stückelberg-Petermann re-normalization UV-Regularization via Counterterms Wilson-Polchinski effective QFT flow Renormalization group flow Gell-Mann & Low RG Flow In the previous chapter we have…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 14. Free quantum fields. The next chapter is 16. Renormalization. 15. Interacting quantum fields In this chapter we discuss the following topics: Free field vacua Perturbative S-matrices Conceptual remarks Interacting field observables Time-ordered products (“Re”-)Normalization Feynman perturbation series Effective…
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…
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 have been a full professor of mathematics at the University…
Intransitive dice are sets of dice that don’t follow the usual rules for “is better/larger than”. If A<B and B<C, then A<C. If Bob runs faster than Alice and Charlie runs faster than Bob, then Charlie runs faster than Alice. If die B wins against die A (a larger number wins) and die C wins…
Macromolecules Paper overview A joint computational-experimental paper that I worked on was just published in MacroLetters, a journal that covers all topics relating to macromolecules (polymers and the like). In it, we looked at simulations of knotted polymer chains being stretched by an external flow field and studied how the knot affected the response of…
Twirling DNA Around a Rotating Wire A new paper from a group of Canadian physicists has demonstrated how simply twirling a wire through a solution of DNA molecules can align the molecules around the wire, similar to the way that twirling a fork can align noodles around it. The paper was published in Physical Review…
Why I’m a Bohmian and Questioning Orthodox QM Many people here know that I am a “Bohmian”, i.e. an adherent of a very non-orthodox interpretation of quantum mechanics (QM). Indeed, in the past, I have published a lot of papers on Bohmian mechanics in peer-reviewed journals from 2004 to 2012. So how can I not…
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…
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…
We have an amazing count of over 320 Insights published at Physics Forums. Now we test to see how much you remember from some of them. If you need a hint feel free to read the corresponding Insight which is linked at the end of the question. Good Luck and remember to read future Insights…
Read part 1 -Backyards, Barns, Bayous Air Force Academy appointment 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…
Fake News, Data, and the Need to Check Sources During and even after the recent US election campaign, numerous reports of fake or misleading news were circulated: outright fabrications, inaccurate summaries, and incomplete reporting designed to push one point of view or another. Outright fabricated stories are often exposed eventually, but subtler misreports — especially…
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…
Challenging the Myth of Institutional Labs 21st-century science labors under the myth that good experimental science requires expensive lab facilities in a university or institutional setting. We have the example of Marie and Pierre Curie discovering radium in an abandoned shed, Lavoisier’s seminal Chemistry work in his home laboratory, and Isaac Newton’s seminal work in…
Browse All Articles Here is an alphabetical list of all Physics Forums Insights grouped by format and then discipline. It is auto updated as new Insights are published. Enjoy! Articles FAQs Guides Tutorials Interviews Quizzes
For those who don’t know the great David Hestenes, he is the inventor of the geometric algebra formalism of physics. Here we go! 1) What is the best application of geometric algebra in theoretical physics that you can think of? In other words, what application shows the power and elegance of geometric algebra best? The…
Introduction The article, “Governmental policy is wrecking science,” makes some interesting points but is fundamentally in error, because government policy is only a small part of the problem. The government is depending on scientists and teachers to police students and each other regarding scientific and academic integrity. To a harmful extent, scientists and teachers are…
We are pleased to introduce David J. Griffiths, one of the most successful physics textbook authors. Odds are if you studied physics in college, you’ve used one of his textbooks. We are honored to share some of his insights on quantum mechanics and the academic world. Please give us a background on your educational background…
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…
On Hardware Quality Designing Quality vs Testing It is impossible to test quality into a product. Quality must be designed into the product. Production Yield Responsibility The hardware designer is always responsible for the production yield. The purpose of production tests is to check production quality, not product quality. Prototype to Product When the prototype…
Give us a little background on yourself? I was born in Washington DC, grew up in Texas, bachelor’s in physics from Harvard in 1978 but found a career in system software instead. Son of two law professors and grandson of a third, raised a Quaker although it didn’t stick, keep a small fleet of well-rusted…
Bayes’ Theorem: Balancing predictive success with falsifiability Despite its murky logical pedigree, confirmation is a key part of learning. After all, some of the greatest achievements of science are unabashed confirmations, from the discovery of acquired immunity to the gauge theory of particle physics. However because we cannot isolate a unique hypothesis from the…
We are pleased to introduce Sean Carroll. Sean Carroll is a theoretical physicist at Caltech specializing in cosmology and quantum mechanics. He has a new book, The Big Picture, which addresses “On the Origins of Life, Meaning, and the Universe Itself.” Key Points Sean Carroll grew up near Philadelphia and studied at Villanova University. His…
We are pleased to introduce Peter Krautzberger. Peter is a manager for MathJax, the technology behind the display of equations on Physics Forums. “The core of the MathJax project is the development of its state-of-the-art, open source, JavaScript platform for display of mathematics.” Please give us a bit of background on yourself I was born…
Roger Babson and His War on Gravity 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…
Click for Full Series Part 1: Logical induction ain’t logical Part 2: We don’t need no stinkin’ induction Part 3: Balancing Predictive Success with Falsifiability Introduction Three million years ago, the grandfathers of our genus used sharpened stones to chop wood and cut bone. Today, surgeons use fiber optic-guided lasers to clear micro blockages in…
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 in it. Here at PF we have rules about this, but I want to look at the more general question of why there is so little interest…
Newtonian limit and spacetime curvature It’s a calculation that you can find in any textbook on General Relativity (GR): when gravity is weak and does not vary with time, and when particles are traveling slowly concerning the speed of light, GR becomes good old Newtonian gravity again. However, this is done at the level of…
Abstract Over the past few years, the author and his wife have served as teachers, qualified scientists, mentors, and/or parents on dozens of science projects assisting students ranging from elementary school projects that can be completed in a weekend to high school and college freshmen projects that take a semester or year to complete and…
Instantaneous Power The formula for power is: ##P=V\cdot I## , power= voltage*current. We call that, instantaneous power. Even when ##V## and ##I## are changing in time, ##P=V\cdot I## applies for each instant. It matters not if the ##V## or ##I## changes are `sinusoidal, what their frequency is, or even if they are aperiodic. ##P=V\cdot…
Please give us a bit of background on your life and professional experience Life: Born and educated in Italy; I then spent 10 years in the United States and 15 in France. I came to physics late: before that I was more into hippie dreams and even trying to overthrow the Italian government. Professional: In…
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 because Lisa was on the other coast, so I spent a lot of evenings on the computer. We had the…
Garrett Lisi is a theoretical physicist and Physics Forums member who developed the E8 Theory, a proposed geometric framework for unifying particle physics using the E8 Lie group. He splits his time between physics research in Maui and surfing, and in 2007 his E8 Theory paper drew both mainstream media attention and sharp criticism from…
Background: Ethernet vs Fieldbus in the 1990s The 1990s saw the widespread adoption of network technology on two fronts: Office automation and factory automation. But while office automation soon standardized on Ethernet (for volume reasons) and TCP/IP (due to the Internet explosion), factory automation fragmented into several incompatible field busses (a Fieldbus is a common…
Give us a brief history of Borek Note: text below is of a negative pedagogical value, don’t read it if you are younger than 20, attending school or still naïvely hoping for the best. I was born half a century ago, in a galaxy far, far away. So far away our laws were all shifted…
Eukaryote evolution and cellular complexity Historically, life is categorized into three broad domains: bacteria, archaea, and eukaryota. Whereas bacteria and archaea are almost all relatively simple, single-celled microorganisms, humans and all other forms of complex, multi-cellular life (including all other animals, plants, and fungi) are classified as eukaryotes, so understanding the evolution of eukaryotes is…
This is a new Interview category for Insights. While I line up some great new interviews I’ll be migrating some previous mentor interviews. ZapperZ is a staff emeritus at Physics Forums Can you give us a brief history of ZapperZ? Without reveal things that are answers to a few of the security questions to my accounts,…
Resistance to complex math seems to never die out. I see it frequently in PF posts. Often it takes the form of challenges rather than questions. First challenge: Complex is just a mathematical trick that has nothing to do with physics. Second challenge: Everything that complex does can be accomplished by ordinary real numbers. My…
Background: textbook accounts 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: Historical observations: Zwicky…
Galaxy and quasar redshifts are classified as cosmological, not “intrinsic,” because they match predictions from general relativity’s expanding-universe solutions, because independent tests (quasar-host redshift matches, the Lyman-alpha forest, the Gunn-Peterson trough, and gravitational lensing geometry) all confirm the same picture, and because every specific observational claim for an alternative “intrinsic redshift” mechanism has been shown…
LightCone 8 is a versatile tabulating/charting cosmological calculator, useful for understanding the expansion history of the universe (and even some future expansion), based upon the Lambda-Cold-Dark-Matter (LCDM) model. Part I of this mini-series gives a broad overview of the user interface and the main functions. Follow-on parts will highlight some specific uses and techniques. 1.1…
Introduction What this Insight Covers 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. Hilbert’s 1900 Problems In 1900, David Hilbert presented 23 of the most important open problems in mathematics…
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…
What causes cancer? For the most part, cancer is a disease that arises from mutations in the body that accumulate over time. These mutations knock out key tumor suppressor genes involved in repairing DNA or regulating cell division and activate oncogenes that can drive cells to divide uncontrollably and invade other tissues. But where do…
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…
To self-study calculus, work through four core areas in order: differentiation, integration, sequences and series, then multivariable calculus. Each builds directly on the last, so skipping ahead creates gaps. A strong starting text is Keisler’s “Elementary Calculus: An Infinitesimal Approach,” which is freely available online and covers both standard and infinitesimal methods. Key Takeaways Calculus…
All current astronomical observations are consistent with zero global rotation of the universe. Solar-system data set a model-independent upper limit of roughly 10−7 radians per year on cosmic rotation (Clemence 1957), while cosmic microwave background analyses push that limit far tighter, to as low as 10−15 rad/yr under some model assumptions (Barrow, Juszkiewicz & Sonoda…
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 general relativity (GR) and brought BW to bear on general relativistic cosmology to ‘explain’ what puzzles so many people about big bang cosmology, i.e., the origin of the universe. The bottom…
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 general relativity (GR) and brought BW to bear on general relativistic cosmology to ‘explain’ what puzzles so many people about big bang cosmology, i.e., the origin of the universe….
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…