Scientific World

Besides being one of the most important relationships in all of quantum physics, Heisenberg's Uncertainty Principle is something that a lot of disgruntled high schoolers will complain about having to learn in grade 12 Chemistry. Unfortunately, a lot of people will toss the principle to the side because they won't take the time to understand it. If said student does decide to tackle the principle at a deep level, they too will often end up dismissing it because it just sounds absurd.  Like most of quantum mechanics, I will concede that the principle does indeed sound bizarre, especially if you try to relate to our macroscopic world. In this post, I'll try to take a different angle and attempt to explain it mathematically (to some degree). For some, I think this may be more helpful. Now, there are a couple of important things to take note of here: For starters, there absolutely is experimental backing to this idea. This is not just something we pulled out of a hat and h

Numbers, arithmetic, calculators and completely pointless word problems are what usually come to mind for most people when they think about math (I'm sorry, but I don't care enough about Sally to calculate how much her 72 watermelons are going to cost her!). Though this is true in high school, things get weird once you enter the realm of higher mathematics, due in large part to the fact that math eventually leaves the "real world" and enters a land of abstraction beyond the comprehension of our puny brains. But we can still sit back and scratch our heads at some of the more ridiculous mathematical results, such as… 5. 1 + 2 + 3 + 4 +….. = -1/12  The above is what is called an infinite sum. It does exactly what it sounds like: it takes an infinite number of elements and adds them up. This sounds like a really weird idea, but many people (much smarter than you or I) have developed methods of actually performing infinite sums (even though it's actually impossibl