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...

Starting from 1889 and scheduled to become emeritus (emerita?) sometime in 2019, the International Prototype Kilogram (also known as Le Grand K) had a service of 130 years. Which is a remarkably long time for a standard of measurement based on a metallic cylinder. The change is rather massive (pun intended), because it affects every SI-system unit. However, the biggest change is not the kilogram, but the fact that some of the old SI units had a dependence on measured values. The new definition relates the base units to constants of nature, which will be redefined as being exact. The speed of light is a good example of setting some constant to be exact. We used to measure it's value, which leads to experimental error. But then in the 15th General Conference on Weights and Measures in 1975 it was decided to set it at exactly 299 792 458 meters per second . This also allowed us to define the meter in a very precise way, by establishing some temporal yardstick. Simil...

Quantum mechanics, the brainchild of some of our greatest scientific minds, is broken. Some may object to this, since the theory is one of the most successful ones we have ever had. Indeed, it gives correct results, but that doesn't mean everything is okay. Let me illustrate with an analogy. Imagine you are driving along and suddenly the check engine light turns on (or whatever indicator your car has). But everything seems to be working fine, so you just keep on driving, although the on-board analytics is trying to show that something is wrong. And you just keep on driving, hoping that it doesn't blow up. You can't know how terribly wrong things are before you take the car apart and look inside. I am in no way saying that there is necessarily something wrong in the results of the theory. What I am saying is that although we have every indication that there is something wrong with it, we keep on using it. We've been ignoring the quantum check engine lig...

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...

Time travel is a popular concept in works of fantasy, with many different flavors. In the Back to the Future trilogy, Doc Brown built a time machine out of a DeLorean just because he could. In Harry Potter and the Prisoner of Azkaban, Hermione Granger uses a time-turner  so she could study every subject in Hogwarts, and even Superman turns back time to undo the death of Lois Lane. Seems like Superman really is quite super. But scientifically speaking, how much sense does time travel actually make? Let's start from the most obvious type of time travel: forward in time. Clearly we are all automatically traveling towards future time by default, since we age and seasons shift and whatever. But the interesting thing is that according to the theory of relativity, it is possible to slow down the passage of time for yourself, while everything else around you continues to age normally. This effect is called time dilation , and it is an important effect in the universes dynamics....

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...