If you are even a little bit interested in modern physics, you know that there is a big cloud on the field right now. We need two theories to describe what we know about the universe today, Einstein's theory of general relativity for large-scale physics, like what happens in the solar system, and quantum mechanics for very small things, like what happens in atoms. The problem is, the two theories are mathematically incompatible, we will see why in a moment. This incompatibility has been a serious problem for several decades now, and it's considered a very tough nut to crack. Well, what if this video proposed a solution to that problem? I know, right? It sounds crazy. But it's true. Please give us just five minutes of your time to convince you. Then you can decide by yourself if it's worth watching the other videos in this playlist. The fundamental idea is that we must really understand what measurements are in physics. For that reason, the approach we are going to discuss is called a theory of incomplete measurements, because it focuses on what measurements are, what they tell us, and what we learn from them. In short, it answers the question, how do we build knowledge in physics? Here is a short summary of the theory of incomplete measurements in just five bullet points. First, physics is all about measurements. Everything we know about the universe, we know through measurements. Second, all our measurements are discrete, not continuous. Your pocket ruler has only so many tick marks. Third, our knowledge is statistical in nature. We know something is true because it happens often. Fourth, we correlate measurements with one another. That's what laws of physics really are, correlations between different measurements. Fifth, there are different ways to measure the same thing. Measurements are a very relative thing. That's it. That's the basis for the theory of incomplete measurements in one page. The problem is that these five points, as innocuous and simple as they look, hide five deep issues. Actually, they deeply shadow the known way to do physics. First, we need to precisely define what makes a good physical measurement. We must revisit what this x means in your equations. Ouch. Second, continuous mathematics are the wrong way to represent physics. Goodbye continuum. Third, if our knowledge is statistical, then we need something like quantum mechanics even for large scale stuff. Isn't that great? Fourth, if laws of physics are correlations, then equations are an inexact way to talk about physics. Equations began. Fifth, Einstein told us that the laws of physics remain valid even in an accelerating spaceship. This theory claims that they remain valid even if your voltmeter is broken. If you thought Einstein had a problem with mathematics, wait until we discuss that one. Is there some good news? Well, yes, there is. The good news is that the tools to use, while very complicated, are largely familiar to computer scientists, in particular in the field of digital photography or signal processing. We know the answers, we just did not realize how general they were. We have the discrete mathematics we need. We use it every time we take a picture with our smartphone. We just did not really consider that picture to be a faithful representation of what quantum mechanics calls a wave function. What about discrete mathematics? We have that too. Our computers know how to draw lines in circles. We did not really realize until now that this means they solve continuous equations in a discrete way. It means you don't need continuous mathematics to model physics. You don't need the square root of two, with all its infinity of decimals, to draw the diagonal of a square. You don't need to compute the last digit of pi to be able to draw a circle on a screen. How does that solve the problem exactly? How can measurement help us unify quantum mechanics and general relativity? Remember we talked about mathematical incompatibilities. The problem is really that when you introduce general relativity and quantum mechanics, this leads to theories that predict infinite values where only finite values are observed in reality. To address that, a technique called renormalization was invented, where you arbitrarily cut out the parts of the integrals that do not converge. This crude technique gives the right results, but nobody really understood why. Richard Feynman reportedly summarized this philosophy of physics as shut up and calculate. It turns out that these infinities result from continuous mathematics and infinite sums. If you use discrete mathematics, you just can't hit the problem. So the incompatibility is essentially gone. Albert, wait. Does that means you need to rewrite Einstein's equations, as well as all of quantum mechanics, using only discrete mathematics? Yes, exactly. And that, my friend, is something we obviously won't be able to cover in just five minutes. The theory of incomplete measurement solves a number of mysteries in quantum mechanics, like the so-called measurement problem, or why the wave function is complex valued, or whether Schrodinger's cat is really both dead and alive. But explaining that takes time. This playlist contains several short videos addressing each topic individually. You can watch them in any order you like. Or, if you prefer, just watch the whole playlist.