Ask Ethan: Could Octonions Unlock How Reality Really Works?
The octonions themselves will never be “the answer” to how reality works, but they do provide a powerful, generalized mathematical structure that has its own unique properties. It includes real, complex, and quaternion mathematics, but also introduces fundamentally unique mathematical properties that can be applied to physics to make novel — but speculative and hitherto unsupported — predictions.
Octonions can give us and idea of which possibilities might be compelling to look at in terms of extensions to known physics and which ones might be less interesting, but there are no concrete observables predicted by the octonions themselves. Pierre Ramond, my former professor who taught me about octonions and Lie groups in physics, was fond of saying, “octonions are to physics what the Sirens were to Ulysses.” They definitely have an allure, but if you dive in, they may drag you to a hypnotic, inescapable doom.
Their mathematical structure holds an incredible richness, but nobody knows whether that richness means anything for our Universe or not.
Have you ever heard of an octonion? Many have been speculating over the past few years that they might hold the key to the mathematical structure that underpins our reality, as there are deep connections between physical ideas that extend the Standard Model (such as string theory) and the mathematics of the octonions. Exploring the math with a view to what it might mean for physics is fascinating.
I started studying physics one year ago and my blog still lacks activity – thus it’s time to do a recap of my experiences and give you, the new freshmen, some hints!
To be honest despair was my constant companion during the first semester. In the beginning confusion is ominpresent because you have to learn an immense amount of new mathematical stuff you have never imagined before. But as time is passing you get used to it and you start understanding the connections between the topics. The most important advice is to keep going, no matter how frustrated you might be.
In my case I did earnestly not believe to pass any exams for the first months of uni. Each single day showed me how much I did not understand. In retrospect I realize that this feeling is absolutely normal – your endurance is being tested. Gladly I did never resign and kept on learning. As a result free time was not really existent during these months. But this proved to be worthwile – I passed all exams and with some luck I finished the first semester even with good grades.
At LMU Munich you have three lectures in the first semester: E1 (experimental physics – classical mechanics), M1 (mathematics for physisicsts – calculus) and T0 (mathematical methods for theoretical physics). At least E1 sometimes resembles the physics you are used to. There the math is not as heavy as the stuff you need to use later. But you learn all of this heavy math in T0 – the most challenging lecture as I experienced it. And well yeah – calculus was just a bunch of confusion for me. To prove Lemmas, Propositions etc. in correct mathematical language was something absolutely new. To calculate and to prove are completely different things – but you can get used to it, even if it takes a lot of time! Practice makes perfect.
Luckily the second semester was way better than the first. I proved to myself that I can make this and got a higher frustration tolerance. I believe that most of the students feel this way. The lectures then were E2 (experimental physics – thermodynamics and electrodynamics), T1 (theoretical physics – classical mechanics) and M2 (mathematics for physicists – linear algebra). Though it is still damn difficult, your fundament of knowledge you earned during the first semester helps you everyday. Still you won’t be safe from failing exams – I did not pass linear algebra this semester. About 80% didn’t. But I have a lot of hope for the retry exam – It’s okay to fail sometimes.
Now let’s give you some tips for your first months as a freshman!
Go to each lecture and tutorial The moment you start not going to lectures is a dangerous step. In some cases (if the professor gives an absolutely terrible lecture) it might make sense. But not going to uni because of despair and resignation is the worst thing you can do. Once you started this it becomes a vicious circle. It’s way more difficult to learn absolutely everything by yourself. It’s really helpful to get a better start into new topics with attending lectures. Otherwise it gets more difficult than it is anyway and you lose motivation more and more.
Get used to work by yourself Try to get a balance between discussing with others and solving problems on your own. Both extremes do not ensure effective learning. You need to ponder by yourself. But when you’re struck for hours, you should get help – discussing is important, even if you do not get the right results.
Do not let bad habits overwhelm you Going to uni everyday for often more than eight hours can lead to very unhealthy habits, such as not eating the whole day, not making real breaks because you’re under pressure, smoking a lot, etc. At least these had been my problems. Maybe I have the tendency for bad habits anyway 😀 I think it’s still important to say: Don’t forget to eat, drink and take breaks – otherwise your brain won’t work properly.
Get enough sleep Really – get enough sleep. Plan in your daily routine when you’re going to bed. Sometimes it is in fact not possible to sleep enough. As long as this is the exception, everything is fine. It should simply not be the rule. At the latest when you’re constantly falling asleep during lectures you should rethink your sleeping habits.
Do something that gives you compensation You need to get your head free. Often you think about a physics problem for hours and stay struck, even after discussing with your mates. Get a hobby or better to say, don’t stop the hobbies you’ve been doing before. Sports, drawing,… anything – but do something which is not physics.
Remember that it is possible to pass the exams Although it might be difficult to believe in the beginning, it is really possible to pass. As long as your work hard enough. The exercise sheets are most of the time much harder than the exams. Get additional exercises from books etc. and you can properly learn for them. (Honest edit: Sometimes the exams seem actually impossible to pass. e.g. my linear algebra exam that 80% failed, but even then: you’re at least not alone).
Don’t compare yourself with others Simply don’t start thinking that all the others are better than you. There are always these genius guys who seem to have less problems with the sheets and lectures. But these are no ordinary people and not the average student. It’s okay to belong to the struggling “mainstream”.
Don’t give up Already after a few weeks you are going to see that there are many more free seats in the auditorium, because many guys give up. You need tenacious adherence to the idea that you do not belong to them because of the following:
Most important: Don’t forget why you are doing this! All my points make physics look like some masochistic burden, but it is not. You are doing all of this in order to understand the world a bit better and get to the borders of human knowledge. It takes a lot of time and costs a lot – but it is worth it. I never regretted doing physics even in my most frustrated moments. I earnestly believe it’s the best you can study – your mind gets more analytically, you think outside the box and you see the fundaments of nature – even it is only a glance.