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Showing posts with the label My research

Is 0.999... = 1? (spoiler alert: no it is not)

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 ...

Forced correlations & In search of lost rationality, part 2.

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As promised, I'm back for some more lost rationality! And ranting. Yeah, mostly ranting. But before I go there, I'll lay out the research that this rant is related to. This one was about temporal coherence, where we look at correlations between different points in time instead of space. To measure those correlations, you need a device such as a  Michelson interferometer  where you split the incoming light to two, delay one of the copies, and then recombine them. This simple setup is sufficient only for some special cases, and measuring the correct correlations is way more complicated. There actually isn't a general method to do that, modern detectors are far too slow! Let's just say that if you need to measure the temporal coherence of a pulse train, then one way to do it is to isolate individual pulses and measure them with a  FROG  (yes, that is a real scientific instrument) and then study their correlations from the measured data. Anyhow, if you have a...

Is it possible to make a laser out of wood?

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Wood is a precious material. It has been used for thousands of years as fuel, in construction, for tools and weapons, as well as for furniture and paper. It is also important for biochemistry in the production of purified cellulose and its derivatives, such as cellophane and cellulose acetate. Wood has unarguably been the most important raw material that allowed civilizations to flourish and it will probably remain that way. But quite recently the usefulness of wood has expanded to a completely new area: photonics and optics. When you think about it, it sounds improbable, or even down right stupid to use wood as a material in optical physics, but that's really what has been going on! Let me be clear, this is not the type of wood you would traditionally use, but chemically treated so that it transmits light. The process is simple in principle, you just soak some wood in a chemical that dissolves lignin. Then you take the delignified wood and add epoxy to it, and voila! You...

Update on the double-slit experiment

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After two papers on something that I did not receive an education for, I finally got a topic in photonics, my bread and butter to be. I started working as a part of the coherence coherence group of UEF in the summer of 2015 and my first task was to design and build an interferometer, which would be used to quantify spatial coherence. Thin film interference. Physics is pretty, ain't it? Now, one might ask, what is spatial coherence? The idea behind this concept is simple: it describes how well different parts from a beams cross-section correlate with each other. If the correlation is strong, then we talk about high coherence and low when the correlations are weak. A very good overview of spatial coherence and its measurement can be found  here . The usual way to measure it is to use the  Young's interferometer  (a double slit experiment, variations of this are used in quantum mechanics), but there are some problems. First of all, a single measurement is not eno...

Chaos in the sky

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While I was writing my  first article , I noticed that there were almost no models that describe how the radioactive fallout settles to the ground (or deposits, as they say). The models that I found were either extremely primitive or simply mathematical fittings to data, with next to none predictive power! The crudest model is that you take the radioactive concentration (Becquerel/cubic meter) and multiply it with the amount of rain (millimeters). I have no idea what motivated this (maybe that the dimensions work out to be correct?), and it's just as reliable as it sounds. The most advanced model I found was actually quite reliable in estimating deposition, but as it was just a mathematical fit to measured data, it did not offer any insight to the physics behind it. So, I started drafting a simple model to introduce in the first paper. I had a small notebook where I would scribble whatever I had come up with. The notebook filled up quickly and I realized that there was n...

Radiation poisoning from reindeer

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I was doing a summer internship at the Finnish  Radiation and Nuclear Safety Authority  a few years back, where I got the opportunity to try my hand at writing. It was very interesting work and the internship went by reaaally fast. Oh, and I was also in charge of monitoring the radiation levels in the air of northern Finland, while my supervisors were on summer vacation (yay). Thankfully, the radiation stayed at safe levels throughout the summer, although it would have been interesting to see what happens when they are elevated. I did get to see some action as well, since we hosted a drill with other authorities, the emergency services and the military. The setting was that there was an unknown source of radioactivity spotted in Northern Finland and fighter jets were sent to collect samples from the clouds. Our job was to determine what the cause was and what needs to be done to avoid further damages. It was partly exciting and partly dull, since I was assigned to spe...