Partially Coherent

You may have encountered the popular claim that \( 0.999... = 1 \), where the three dots signify that the decimal continues forever. This is a somewhat weird claim, since it would mean that mathematics is broken. There should be no way for two different numbers to have the same value. What makes it weirder is that this is quite popular claim. I've even seen mathematicians say that it's true! But is it though? One popular proof is to first denote \( S = 0.999...\) and then multiply by \(10\) to get \( 10S = 9.999...\) and subtract \( S \) from it, to get  \( 10S - S = 9.000...\) and finally dividing by \(9\) yields  \( S = 1.000... = 1 \) and we see that  \(0.999... = 1\)! However, there's a problem. This short derivation is not strictly speaking correct. It is veeeery close to being correct, and to see why let's look at finite decimals first. Let's say that \(S = 0.999\) (note that this is not the same as \(S = 0.999...\) ). Let's do the same trick as ...

A while back I came across the article: The Lowest-Bid Universe , where the idea of whether we live in a simulation is examined. The premise of the text is that if this really is the case, then we should lodge complaints of our own reality. Because, apparently, the reality we live in is not that well made. The article starts by superficially mentioning some of the wilder ideas in physics, and then moves on to a "more philosophically motivated" idea that the reality as we experience it is the product of an experiment or a simulation. The standard motivation behind this is to argue that even if only a few civilizations evolve so far that they can produce simulations of whole universes, they inevitably will do a large number of them. Therefore, if there are a large number of simulated realities, it is very likely that our reality is also simulated. Then the writer concludes that if this is truly the case, then our simulation is poorly built. Why would he say so? Becau...

I wrote some weeks ago about the basic concepts behind entropy and the arrow of time . It also conveniently served as test of MathJax . If you have a blog or website where you want to show some equations, you can apply MathJax with a short string of html code, and voila, nice clean LaTeX typesetting becomes available! Okay, enough advertising and let's get on with it. The two main reasons I wrote about entropy last time, is because 1. it is one of the most fascinating concepts in all of physics and 2. there are some fairly recent studies I wish to write about, and one needs to understand some basics before I go deeper into those. There was this one study that was circulated widely in popular science channels, which got hyped into the form: "scientists reversed the arrow of time!" Spoiler alert, no they didn't. I'm not saying that what the group did wasn't seriously cool and a great advancement, it's just that they didn't do what it sai...

Last Friday a collaboration between MIT and Harvard made the headlines with their research on quantum photonics, and I must say, the hype is particularly strong with this one. Here's my pick of the headlines from some of the popular science outlets: "Physicists Created a New Form of Light" - Motherboard "Photons entangled to make new form of light" - New Atlas "MIT Physicists Have Constructed a Bizarre Form of 'Molecular' Light With 3 Photons - photon's shouldn't do this" - ScienceAlert "Scientists create a new form of light in breakthrough that could pave the way for everything from ultra-fast quantum computers to real-life LIGHT SABERS" - Daily Mail I cannot overstate how badly overhyped this study is. First of all, the team did not find a new form of light, and no entanglement was involved. Neither did they make "molecular" light and photons are supposed to do exactly this. Oh, and you definit...