#mathematical physics

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Exploring the Universe: Penrosian Perspectives on Space, Time, and Reality

Sir Roger Penrose's concepts have transformed our perception of the universe, from the microcosmic intricacies of quantum mechanics to the vast structures of cosmology.

Penrose's insights into space and time are most evident in his work on singularities. His collaboration with Stephen Hawking led to the Penrose-Hawking singularity theorems, which provided a solid mathematical basis for the existence of singularities in black holes. These theorems showed that under certain conditions, gravitational collapse is inevitable, leading to points where the curvature of space-time becomes infinite. This work fundamentally changed our understanding of black holes and their role in the universe.

In an effort to unify quantum mechanics and general relativity, Penrose developed the twistor theory. This mathematical framework transforms geometric objects in Minkowski space into a complex space, offering a new perspective on the fundamental structure of space and time. Although the twistor theory has not yet achieved its goal of unification, it has significantly influenced areas such as algebraic geometry and representation theory.

Penrose's conformal cyclic cosmology posits that the universe goes through infinite cycles, with each cycle beginning with a Big Bang and ending in an exponentially expanding phase. This theory challenges traditional cosmological models by suggesting that traces of previous universes may be observable in our own universe. Conformal cyclic cosmology offers a unique lens through which to view cosmic history, with an emphasis on continuity rather than singularity at the Big Bang.

Penrose has also ventured into the realm of consciousness with his theory of Orchestrated Objective Reduction, which he developed together with Stuart Hameroff. This theory proposes that quantum processes in the brain's microtubules contribute to consciousness, thus providing a potential bridge between physical phenomena and conscious experience. Although the theory of Orchestrated Objective Reduction is controversial, it underscores Penrose's willingness to explore interdisciplinary connections between physics and cognitive science.

Beyond technical contributions, Penrose's work invites philosophical reflections on the nature of reality itself. His theories suggest a universe in which mathematical structures underlie physical phenomena and reflect an internal order that transcends empirical observation. This perspective is consistent with his broader philosophical investigations into the interplay of mathematics, physics, and human consciousness.

Sir Roger Penrose (Curt Jaimungal, Theories of Everything, September 2024)

~A summary of first year~ What to do and what not to do

It’s about that time of year when the year 13s and gap yah students are starting to think about the new chapter of their life that will (pandemic allowing) commence in Autumn. First year. I’ve just submitted my last piece of coursework for the year, in my Mathematical Physics degree at the University of Edinburgh, and I feel I’ve learnt so much this year. Not just calculus and quantum mechanics, but I mean life stuff. As well as a lot of physics and maths, that is.

Tip 1 - don’t do all the work. Yes, I know your lecturers have told you the importance of working. I know your lecturers have told you to do all the exercises in the textbook as reading before the lectures. Yes I know it seems like everyone else has done all the exercises. But no, you don’t need to. I started off first semester on a course called Introduction to Linear Algebra, and in each of our reading guides were a list of exercises to do in the textbook - usually “do all the odd numbers exercises from chapters 1-2, plus question 34 and 40″ and I’d stay up until like 3am every day working through them as there were about 50-60 exercises per chapter, and a few chapters per week, and I was like ‘oh my god. How is everyone getting everything done, how is everyone doing all of this?’ and when I got texts from people like ‘hey becky have you done question 17 yet’ ‘have you read chapter 2′ but no no no and no. Yes, someone else *may* have done question 17, it doesn’t mean you have to. Pick the most important exercises to do, pick the ones you don’t understand really how to do, spend time learning the techniques behind problem solving and don’t just do questions for the sake of doing questions. I ended up just being like *nope* and just picking, sometimes only about 5 questions (rather than 120...) and doing them properly, and I got 94% on that course so - you don’t *need* to do it all to do well.

The key thing I learnt in semester 1 was - you have as much work to do as you want to do. If you finish all your work, you’ll find more to do, so the thing you have to learn is what the right amount of work is *for you* not for your friend, not for your course mates, not for that person who keeps asking you the answers to the hand ins x y and z, for you.

Tip 2 - don’t take extra courses unless you have to

I inflicted extra course credits on myself, meaning I was taking 1/3 more courses than most (I think all...) people in my year. My advice - don’t. It may make you, or even other people think you’re ‘academically driven’ or something, but in reality, it means your spreading yourself too thin and you don’t have the time to invest in other stuff, like reading around the bits you find interesting. Just because you *can* take extra courses don’t mean you *should*.

Tip 3 - ask questions I have become *known* in my yeargroup, in the School of Physics, by my lecturers and TAs and tutors, for being literally the first person to ask questions. I’ve had drunk classmates come up to me on pub crawls saying “omg Becky thanks for asking those questions in lectures, I was too scared to ask but I didn’t understand that either,” - trust me, you’re not the only one who doesn’t understand something. The general rule of thumb is, in the lectures, if your lecturer is up for answering questions (some lecturers on content heavy course are very pushed for time so prefer questions at the end), then stick to those questions about the content of the course - eg. clarifying something on the slides, asking for them to explain a concept you don’t get. If you want to know something *extra* that isn’t on the syllabus but you’re curious about knowing, go up to them at the end for that, or drop them an email, or if it’s too long to put in an email, ask to see them in their office. Trust me when I say, once you’ve established a relationship with the people who teach you, it’s much easier to ask them stuff. Once you get to know who’s good at answering questions, and who isn’t so good at answering questions, and you have a lil circle of people you can go ask stuff, it becomes a lot easier.

On a side note, sometimes the best people to ask your questions to are you TAs/tutors. They’re usually PhD students and so they’ve done this stuff a lot more recently, and remember more recently being a student, so they can be a good person to ask and often have more time and are more chill than lecturers and easier to approach if you’re intimidated by Chair-Royal-Professor-Sir-MBE because you don’t want to look ‘stupid’, then try asking the TAs.

This has become quite a long post... so I’ll stop here for now, but I will have more general adjusting to uni posts coming up throughout the summer, so stay tuned.

My DMs & Asks are always open if you have any questions about studying physics or studying at Edinburgh or studying Physics at Edinburgh ;)