Author: Simply Curious
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Measurement, Decoherence, and Why Quantum Outcomes Appear Stable
Quantum mechanics is often presented as fundamentally mysterious, especially when it comes to measurement. A quantum system can exist in a superposition of possibilities, yet measurements yield definite outcomes. This apparent tension has motivated a wide range of interpretations, from wavefunction collapse to many-worlds to strongly observer-centered views. A more…
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What’s the connection between spin and statistics – a simple argument
The Painted Ball Trick: Seeing the Connection Between Spin and Statistics Quantum mechanics is famous for being counter-intuitive. Two of its weirdest features are “spin” and the rules about how identical particles behave when you swap them. Spin isn’t really things spinning like tops, but it acts a bit like…
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Why the Universe Isn’t Overflowing with Vacuum Energy: A Curious Field Theory Detour
Taming the Vacuum Energy: A Quantum Field Theory Twist on the Cosmological Constant Problem If you (or your friendly quantum field theorist friend) ever tried to calculate the energy of empty space using quantum field theory (QFT), you’ve both likely stumbled into a cosmic-sized embarrassment. The math predicts a vacuum…
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The Great(er) American solar eclipse of 2024
The title of this post is a variation on the title of my previous post, which was written after the 2017 eclipse. This time, I had resolved, with some friends, to travel to Indianapolis and prowl around the outskirts near criss-crossing highways so we could chase clear skies (which I…
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Hawking radiation: a weight-loss program for black holes – another black hole conundrum and a cute connection between black holes and quantum field theory
Coming on the heels of the apparent success of Wegovy and Ozempic for obese humans, a situation that I am still very skeptical about for its long-term effects, I thought I would write a post about how Hawking radiation causes black holes to lose mass. It is subtle and not…
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Black hole conundrums – how to extract information from a black hole
There is a problem that has been in the science news and blogged about a lot in recent years. It is called the Black Hole Information Paradox and essentially boils down to this. I throw some information into a black hole. It vanishes and can’t be retrieved. However, what does…
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Unruh and Hawking – or how I get randomness from order, i.e., something ordered that looks random.
I have been planning to write a post about something rather esoteric, called the Unruh effect (and its intellectual descendant, the Hawking effect) and wanted to find a way to explain it to a high-school student. In the process, I discovered a new way to look at the effect, which…
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Do we live in a hologram? How could we tell?
A neat way to show how we could tell experimentally that we live in a holographic universe
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The universe in a grain of sand
This article attempts to explain a paper I wrote that is published in Europhysics Letters. The English engraver William Blake in a piece of poetry, the stories, the colossal orders of magnitude of sizes from the humongous to the very small make us wonder if somehow the very large is…
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A story of commutators
The conceptual step that took humans from their pre-conceived “classical” notions of the world to the “quantum” notion was the realization that measurements don’t commute. This means, as an example, that if you measure the position of a particle exactly, you cannot simultaneously ascribe to it an infinitely precise momentum.…
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Schrodinger’s Cat Lives again!
This article concerns a new paper I just submitted and now published . It concerns a peculiar feature of quantum mechanics (and also of classical mechanics). The feature is this. The Laws of Physics appear indifferent to the direction of time. If you play a video of two balls colliding…
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Three pieces – and some puzzles
I just finished a bit of summer reading – in particular, three books with very similar scope. The first is by a well-known physical chemist and author – it is called “Four Laws that drive the Universe“. The second is by a well-known quantum information expert, and called “Decoding reality:…
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Tales of Karatsuba
This article is based on a brilliant essay in Quanta magazine, behind which lies a lovely story of a mathematical discovery. I take the essay a little further and describe an algorithm we posted on arxiv to increase the speed of the calculation even further (though not as fast as the…
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Error Correcting Codes and the Quantum version
This article was inspired by a very nice article in Quanta magazine (by Natalie Wolchover) about the connection between error-correction codes and space-time. I thought the quantum mechanics concepts were glossed over, so decided to expand on it a little. Electrical engineers and digital-signal-processing engineers study error correction for a…
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Modulo arithmetic & cards
Another week, another Manjul Bhargava delight. Arithmetic is usually taught in base 10. We have 10 unique symbols (0,1,2,3,4,5,6,7,8,9) and a place value system with the lowest value being , the next being , the next being and so on. So a number like . So far so good, but…
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Gauge invariance, Global and Local Symmetry
This post, aimed at people with some knowledge of Maxwell’s equations, is aimed at connecting a bunch of concepts that are all central to how we understand the universe today. Nearly every word in the title has the status of being a buzz-word, but for good reason – they help…
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Binary/Ternary codes and card tricks
This trick uses the representation of numbers in a different base. Solution in a post in a day!
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p-‘s and q-‘s redux
Continuing our saga, trying to be intellectually honest, while a little prurient (Look It Up!, to adopt a recent political slogan), let’s look at the ridiculous “measured” correlation in point 3 of this public post. Let’s call it the PPP-GDP correlation! The scatter graph with data is displayed below Does…
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Minding your p-‘s and q-‘s
In the practice of statistical inference, the concept of p-value (as well as something that needs to exist, but doesn’t yet, called q-value), is very useful. So is a really important concept you need to understand if you want to fool people (or prevent yourself from being fooled!) – it’s…
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Math, Rhythmic patterns & A Card Trick
Another Wednesday, another session of Manjul Bhargava’s entertaining and instructive class at the National Museum of Mathematics, in New York City. This time, the topic was that of rhythmic combinations and their connection to mathematics. As the sentence itself suggests, combinations of rhythms lead to combinatorial arithmetic – the notions…
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Of Baby Hummers and clock arithmetic with Aryabhata and Archimedes
I spent a pleasant evening at the National Museum of Mathematics this week – the first session of a semester long program of lecture demonstrations about mathematics and magic. The instructor is Manjul Bhargava, the famous Princeton mathematician. I thought the ideas were worth discussing in a more public forum,…
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Gedankenexperiments #1
Albert Einstein is well known to be one of the most creative scientists of the last couple of centuries. He produced fascinating theories that really burnished this reputation. But he also had several ideas (trying to undermine, for instance, ideas about quantum mechanics) that didn’t work – often the exact…
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The Indian musical drums
There is a well-known paper by the famous scientist and Nobel laureate C. V. Raman about the harmonic drums of India – the mridangam and the tabla. While the paper was written in the 1930s, it is quite detailed and refreshing in its clear description of how these instruments work.…
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The Rule of 72 – and what does the Swiss National Bank have to do with it
I was listening to an academic talk and someone mentioned the “Rule of 72”. Apparently invented by Einstein, it is a simple numerical approximation that helps you understand the power of compound interest. This, according to legend, became popular when interest rates offered on deposits by the Swiss National Bank…
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Bucking down to the Bakhshali manuscript
The Bakhshali manuscript is an artifact discovered in 1881, near the town of Peshawar (in then British India, but now in present-day Pakistan). It is beautifully described in an article in the online magazine of the American Mathematical Society and I spent a few hours fascinated by the description in…
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Schrodinger’s Zoo
I have been enjoying reading Richard Muller’s “Now: The Physics of Time” – Muller is an extremely imaginative experimental physicist and his writings on the “arrow of time” are quite a nice compendium of the various proposed solutions. Even though none of those solutions is to my liking, they are…
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Why do chocolate wrappers stick to things
Here’s something I saw while lazily surfing the net this morning. Someone throws a candy wrapper towards the floor and it sticks to the curtain or a book cover. How long will it stick? First, the reason this happens is because of static electricity – and this is why this…
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Is the longest day the warmest day?
I woke up to a snowy day on the 30th of December, here in New Jersey and immediately realized two things! It was colder and darker than at the same time on the shortest day of the year, the 21st of December. I suppose you could blame the colder weather…
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Can you travel faster through time?
If you watch science fiction movies, the most dramatic effects are obtained through some form of time travel. Pick some time in the future, or the past and a fabulous machine or spell swoops you away to that time. I have always had a problem with this simple approach to…
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Coffee, anyon?
Based on the stats I receive from WordPress.com, most readers of this blog live in the US, India and the UK. In addition, there are several readers in Canada, Saudi Arabia, China, Romania, Turkey, Nigeria and France. Suppose you live in the first three of these countries. In addition, let’s…
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The unreasonable importance of 1.74 seconds
1.74 seconds. If you know what I am talking about, you can discontinue reading this – its old news. If you don’t, its interesting what physicists can learn from 1.74 seconds. Its all buried in the story about GW170817. A few days ago, the people who constructed the LIGO telescope…
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New kinds of Cash & the connection to the Conservation of Energy And Momentum
Its been difficult to find time to write articles on this blog – what with running a section teaching undergraduates (after 27 years of ), as well as learning about topological quantum field theory – a topic I always fancied but knew little about. However, a trip with my daughter…
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The Normal Distribution is AbNormal
I gave a talk on this topic exactly two years ago at my undergraduate institution, the Indian Institute of Technology, in Chennai (India). The speech is here, with the powerpoint presentation accompanying it The Normal Distribution is Abnormal And Other Oddities. The general import of the speech was that the…
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Mr. Olbers and his paradox
Why is the night sky dark? Wilhelm Olbers asked this question, certainly not for the first time in history, in the 1800s. That’s a silly question with an obvious answer. Isn’t that so? Let’s see. There certainly is no sun visible, which is the definition of night, after all. The…
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The Great American Eclipse of 2017
I really had to see this eclipse – met up with my nephew at KSU, then eclipse chasing (versus the clouds) all the way from Kansas to central and south-east Missouri. The pictures I got were interesting, but I think the videos (and audio) reflect the experience of totality much…
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Mr. Einstein and my GPS
I promised to continue one of my previous posts and explain how Einstein’s theories of 1905 and 1915 together affect our GPS systems. If we hadn’t discovered relativity (special and general) by now, we’d have certainly discovered it by the odd behaviour of our clocks on the surface of the…
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Master Traders and Bayes’ theorem
Imagine you were walking around in Manhattan and you chanced upon an interesting game going on at the side of the road. By the way, when you see these games going on, a safe strategy is to walk on, since they usually reduce to methods of separating a lot of…
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Fermi Gases and Stellar Collapse – Cosmology Post #6
The most refined Standard Candle there is today is a particular kind of Stellar Collapse, called a Type 1a Supernova. To understand this, you will need to read the previous posts (#1-#5), in particular, the Fermi-Dirac statistics argument in Post #5 in the sequence. While this is the most mathematical…
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Coincidences and the stealthiness of the Calculus of Probabilities
You know this story (or something similar) from your own life. I was walking from my parked car to the convenience store to purchase a couple of bottles of sparkling water. As I walked there, I noticed a car with the number 1966 – that’s the year I was born!…
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Arbitrage arguments in Finance and Physics
Arbitrage refers to a somewhat peculiar and rare situation in the financial world. It is succinctly described as follows. Suppose you start with an initial situation – let’s say you have some money in an ultra-safe bank that earns interest at a certain basic rate . Assume, also, that there…
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The earth is flat – in Cleveland
I stopped following basketball after Michael Jordan stopped playing for the Bulls – believe it or not, the sport appears to have become the place to believe and practice outlandish theories that might be described (in comparison to the Bulls) as bull****. There’s a basketball star, that plays for…
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Special Relativity; Or how I learned to relax and love the Anti-Particle
The Special Theory of Relativity, which is the name for the set of ideas that Einstein proposed in 1905 in a paper titled “On the Electrodynamics of moving bodies”, starts with the premise that the Laws of Physics are the same for all observers that are traveling at uniform speeds…
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Can a quantum particle come to a fork in the road and take it?
I have always been fascinated by the weirdness of the Universe. One aspect of the weirdness is the quantum nature of things – others relate to the mysteries of Lorentz invariance, Special Relativity, the General Theory of Relativity, the extreme size and age of the Universe, the vast amount of…
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A digression on statistics and a party with Ms. Fermi-Dirac and Mr. Bose (Post #5)
To explain the next standard candle, I need to digress a little into the math of statistics of lots of particles. The most basic kind is the statistics of distinguishable particles. Consider the following scenario. You’ve organized a birthday party for a lot of different looking kids (no twins, triplets,…
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Cosmology: Cepheid Variables – or why Henrietta couldn’t Leavitt alone …(Post #4)
Having exhausted the measurement capabilities for small angles, to proceed further, scientists really needed to use the one thing galaxies and stars put out in plenty – light. The trouble is, to do so, we either need detailed, correct theories of galaxy and star life-cycles (so we know when they…
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Cosmology: Distance Measurements – Parallax (Post #3)
This post describes the cool methods people use to figure out how far away stars and galaxies are. Figuring out how far away your friend lives is easy – you walk or drive at a constant speed in a straight line from your home to their house – then once…
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Cosmology and the Expanding Universe ..(Post #2)
Continuing the saga about the cosmological red-shift.
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A simple sum
This calculation was inspired, a few years ago, by trying to find a simple way to explain the sum of the first natural numbers to my (then) twelve-year-old daughter, without the use of calculus. As many people know, the sum of the first natural numbers is found very easily, using…
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A course correction – and let’s get started!
I have received some feedback from people that felt the posts were too technical. I am going to address this by constructing a simpler thread of posts on one topic that will start simpler and stay conceptual rather than become technical. I want to discuss the current state of Cosmology,…
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A simple connection between Entropy and Information
This article follows a simple example laid out by Jaynes (1996). Jaynes’ example is one that shows how one’s computation of the change in entropy in a physical / chemical process depends on the precise variables that one uses to label the macro state. If you use different variables (say…
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