They are introductory in the sense that they are more about the horizontal bar of the T than about going in depth in a particular topic. But I guess I have to admit it was a poor choice of words.
Indeed, anyone who can seriously grok all the material in the entire series will gain a very deep and wide understanding of theoretical physics that very few people possess.
Depends on your definitions of "introductory" and "mathematically sophisticated reader". In the university I attended, the first physics course (Mechanics & Optics) introduced the concept of Lagrangian fairly early.
Thanks for the comments about links of related interest, for example links about studying advanced mathematics. One comment here suggested that the original author's selection criteria of free and online[1] have allowed in some links that are not really very good.
With that idea in mind, it occurs to me that we could help Gerard t'Hooft, Nobel laureate in physics and the author of the site submitted here, by sending him the best links that his site doesn't already have that would help people learn more background for physics and physics proper. He surely hasn't been able to find all the best links by himself.
[1] "It is my intention to search on the web where the really useful papers and books are, preferably downloadable as well. This way, the costs of becoming a theoretical physicist should not exceed much the price of a computer with internet connection, a printer, and lots of paper and pens."
Spot check of his links yielded a quite disappointing 100% failure rate: the lecture notes he links to for "phenomenology" (which ordinary people would call high energy physics) are all bad.[1]
Also, I don't think you can discount the value of community when studying anything as fundamentally social as theoretical physics. Maybe a modern Gauss could make his way to the edge of human understanding, and beyond, on his own, but most of us need the insights and encouragement of our peers. I would say that a smart, intrepid physicist should audit classes. Impress the professor with your effort, earnestness, and ability, and there's no way you'd be kicked out of class no matter what the rules say.
Call me old-fashioned but I think the previous, less fashionable version of this page (site?) was much more usable [1]. At least it gave you a much better idea of all it takes by having it all the links in one page.
The "Intermediate" section contains the canonical texts for undergraduate first and second courses in the "mainstream" mathematics subjects. The "advanced" section contains mostly intro and/or reference texts for research in each area (ie assume an undergraduate degree in Mathematics).
Some less main-stream areas (e.g. logic) aren't particularly well-represented.
this site isn't exclusive to theoretical physics. most of the material is broad. It's not until the later topics that it becomes more theoretical: general relativity, super gravity, string theory...
physics may also interest those who don't want to be come any type of physicist, hence the popularity of television shows like Cosmos, etc. for those that want to dive into something a little more technical, but very approachable, there are the feynman lectures, which are freely available online here: http://www.feynmanlectures.caltech.edu/
i say this because most the people i know that are doing graduate studies focused on general relativity are in theoretical physics. we're not at the point, technologically, where experimental physics can cover the full range of what general relativity describes. it would be nice to have a black hole in a lab that is not an analogue, though. and one day, we probably will. so, i agree that eventually it will be on par with electromagnetism, but for now it describes a lot that is still very theoretical.
But EM as a subject, as its usually taught, is still theoretical. Experimental EM would be better known as either electronics or statistics. You make it sound like theoretical means lacking experimental support, perhaps that is what the word means in, say, politics, but certainly not in physics.
This depresses me a lot. It depresses me because it is something I may (the may is the first problem here) want, but I feel I can never achieve it.
When I was a child I wanted to become an astronaut. But from the age of 8 or 9 onwards I was always a fat kid, and fat kids can't become astronauts, so I quickly buried this dream and stayed the fat kid, instead of becoming lean and pursuing it. Don't get me wrong: I never had much problem with being the fat kid besides that. There was almost no bullying, I had friends, got a girlfriend (later) and everything. The point is, I buried the specific dream of becoming an astronaut but I was still fascinated by technology, computers and science. And dinosaurs, like every proper kid in the 90ies.
I was always a lazy kid. Lazy, but with good to very good grades. (That's the other part of the problem.) I may have suffered early from the challanges of being gifted; though it is possible that I only was ahead of my classmates because I was 1 year older, because of my day of birth - I doubt myself a lot nowadays. So after primary school I got only sent to the "Realschule", it's the middle layer in the german school system, not the Gymnasium where you are on track for the abitur (the diploma to enter universities). Everything was pretty easy there, I never had to practice, never did my homework and had always good to very good grades. Except in French. For French I would have had to practice, memorize words and do the homework but i could not bring myself to do it.
During my time at the realschule I was interested in almost everything. Being it physics, history, politics, computers, etc. I wanted to understand every aspect of the world. I read books by Gell-Mann, Feynman, Hawking an others in the physics field, same for history, politics, computers and aspects of math, but already at this time, I never went too deep (this may be the third part of the problem). But I intended to go to a gymnasium (with a technical profile) after the Realschule and study physics after that. In 9th and 10th grade I developed an additional interest in economics.
I went to a gymnasium with an economic profile, instead of the technological one; for various reasons, my interest in economy played a role, but also that the girl I had a crush on went there and all in all it was the most convenient choice. There I did well in every subject except spanish. I almost never learned, I almost never did homework. I was still one of the best and considered very smart by everyone. So probably not the age.
During this time I got engaged in politics (a local chapter of a party), more involved with the voluntary firefighters of my home village. This is about to become important. I also noticed that I struggle with the more complex math (integral calculus), not so much because of the concepts, but because I didn't train it enough. So I figured physics may not be the right thing for me and neither computer science. I was pretty arrogant at that time and also decided for myself that I only want to attend a "real" university, and not a university of applied science (Fachhochschule). The other factor was that I did not want to leave my home town because of the firefighters and the party and because I did not want to ask my parents for the money to pay rent in another city when I can study in the next city and live at home.
So I decided to go for Economics at the university. I figured the math can't be that bad. After the first year it became apparent that I'm going to fail, I also had never made a lot of contacts with other students (I had a 1+ hour public transport commute each way every day) to learn together and motivate me, and later I was ashamed to talk with anybody about it.In the end I switched subjects to law (I lied to myself that I'm interested in it). This way I could stay at the same university, I did not even tell my parents at first, though everybody else knew. All the time I was still interested in everything (even economics), and quickly felt that I may get problems diving deeper into law topics. I began to become a bit depressed and anxious to even enter the university. One day the new semester started and I could not bring myself to enter the lecture hall. I phoned my girlfriend and said to her: "I can't enter the lecture hall. This has to end." Finally I felt free and she felt free too, because she had felt that something wasn't right with me, but was afraid to ask, because my reactions can be horrible.
I started to look for alternatives. I figured that it's time to leave the university, I did not want to try anything else at the university (it would have been computer science) for fear of failing again. So I decided to apply for vocational training as a programmer (this is a thing in germany.) I had luck, it was early in 2008 before the economy crashed and burned, so I quickly found a spot. I got the job, did the training and work now as a business software developer, doing ABAP developement in some of our companies SAP systems for several years now. Sometimes it's fun and it enables my lifestyle of buying fancy stuff and clothes and huge steaks. Sometimes I'm bored to hell and want to do "real programming", though. I procrastinate a lot during my job, but I usually finish in time, because when I need to I can be very fast, and occassionally deadlines get pushed back, so I am lucky and am not late. I learned the valuable skill of "asking for help". At least sometimes I am able to. I still have the fear that other may notice that I'm not so smart and don't know stuff I'm supposed to know.
I have Ideas but I don't pursue them. Because I don't know everything. I can't think them through and suddenly there is the next idea or interest.
I noticed a few things in the last years. I can only learn (or bring myself to learn) if i have a real task. Abstract learning is very difficult for me, I search for distractions and excuses. Those tasks need to be given to me from someone else, because I can't give myself tasks, because if I give myself I task I can cancel it by myself.
When I begin to dive into a topic, being it maths, or economics, or puzzles, I tend to stop at the first obstacle, if it is not the most exciting thing in the world.
I think I am stuck with programming software, and I think that's fine. But even in this field I have troubles rooting in everything described above.
And there is still the love for physics somewhere deep in me. But I simply can't pursue it. For all those reasons.
So my problems are:
1. I still don't know what I really want.
1.1. I want everything
1.2. I want it now.
2. I need to know everything before I continue, decide,
2. I don't want to give up, what I already achieved
3. Good enough is often good enough for me, I can't force myself to go on and further
4. I never learned to ask for help.
5. I avoid conflicts
6. I never learned to cooperate in education
7. I have been lucky too often.
8. I can't stay focused except under high external pressure
9. My mind may not be best suited for the symbolic language of math. (that's what I think)
10. Nowadays I doubt if I am really smart
11. ?
I could continue for another hour, but this text alreadyis an incoherent mess.
Edit: And I turn 30 next months. I increasingly get the feel that I'm too old for anything now.
What you've described is very much the classic "curse of being gifted". Breaking out of the curse is really quite hard and I think there's really two ways to go about it.
1) Give up, just be a normal, non-gifted person. Do normal non-gifted people stuff and enjoy life.
2) Realize that you're smart, and if you're so smart, figure out a way out. For any problem you have, use your smarts to figure it out. Figure out how to study, how to motivate yourself, use your gifts on yourself. Then once you've figured yourself out, turn your new skills outward and use your gifts properly.
It sounds obvious, but people "cursed" with being gifted don't often realize they have the single gift they can use to get themselves out of their mess. Instead they simply coast on it like a ship adrift at sea rather than using it as a ship of exploration that can take them anywhere.
Have you known people to have successfully gone down path 2? Any stories or tips to share?
I'm in a similar situation. Despite having been moderately successful, I lacked passion. Now I'm a 30 year old graduate student, working three times as hard and making a third the money that I used to, but I couldn't be happier.
My most difficult project remains mastering myself. I'm doing okay now, but I know I can be much better. I'm worried I won't be able to master myself and will be stuck with mediocrity because I'm my own worst enemy after decades of terrible work habits.
I often spend too much time on "self-hacks", and not actually doing stuff that needs to get done. It feels like paralysis by analysis, so that's why I'm questioning this advice.
I don't know, I think the answer is to figure out what motivates you.
It took until the point that I was so irritated at my station in life that I finally had to just stir myself into action. I couldn't handle the crap pay I was receiving, and watch people who were clearly not at my level (or so I believed) surpassing me in basic life accomplishments without major effort, like making enough money to pay for the gas I used commuting to/from work. So for me, anger and frustration worked pretty well.
I also got heavily involved in some very physically demanding martial arts and really learned what my limits were, mentally and physically. I think it helped me both work off the anger and get some perspective in a constructive way while I started planning how I was going to get out of my rut. I also was incredibly physically fit during that time too, which wasn't bad. One thing I learned, I really need a coach barking at me to do my crunches, or get back in the ring or run another lap or whatever. So one solution I learned is to optimize my life so I have a motivating person keeping me moving forward.
In my case, I found a wife who's been incredible. I'm more afraid of her than I am of failing. So having an ever present challenger has helped push me along.
But ultimately, you have to use your smarts to figure it out yourself.
"This, and much more, she accepted - for after all living did mean accepting
the loss of one joy after another, not even joys in her case - mere
possibilities of improvement. She thought of the endless waves of pain
that for some reason or other she and her husband had to endure; of the
invisible giants hurting her boy in some unimaginable fashion; of the
incalculable amount of tenderness contained in the world; of the fate of
this tenderness, which is either crushed, or wasted, or transformed into
madness; of neglected children humming to themselves in unswept corners;
of beautiful weeds that cannot hide from the farmer and helplessly have to
watch the shadow of his simian stoop leave mangled flowers in its wake, as
the monstrous darkness approaches."
― Vladimir Nabokov, Signs and Symbols
You are not to old. Five years ago I started training martial arts again. I had only done it of a few months in my twenties and it was the only "sport" I ever enjoyed.
It is great, as I really sucked at it, but so did everyone else. Five years later I am still not particularly good at it. But I am better than the beginners and it gets better every few months. But, the key thing is not what it did for my martial arts, it is what it did for my life.
I am much more disciplined in everything I do. I have more stamina. I get up at least an hour earlier in the morning. I am not suffering as much from a mostly static job, sitting behind a computer all day (these days I stand). I take stress better. The list goes on.
It has thought me to deal with the issues you list, specially: 1.2, 2, 3, 4, 5, 6, 8.
I can't really say it will do the same for you, but if you find a serious club, where competition is not the focus, but collaboration. Maybe it could work for you too.
You have two options: Change your mindset or continue burying/ignoring your ambitions. Burying your ambitions can make you relatively satisfied in life, but I believe they will always haunt you regardless of how hard you try.
You can change your mindset by developing habits that turns your mind into a force for achieving your ambitions, instead of an obstacle that prevents you from achieving your ambitions (which it appears to be now). Through this you will achieve MUCH more, and I believe be much more satisfied in life.
You're only 30. I would suggest you continue reading, looking inward and learning about yourself, and continue searching for answers concerning why you aren't full of passion and motivation for achieving your ambitions. Everyone's journey is different, however here are a smattering of books/resources that may be insightful and have helped me:
1. Carol Dweck on mindset:
- Mindset: The New Psychology of Success
- Self-theories: Their Role in Motivation, Personality, and Development (Essays in Social Psychology)
2. About the inner journey of high performance, removing mental obstacles, cross-disciplinary learning, and nature vs. nurture:
- The Art of Learning: A Journey in the Pursuit of Excellence - Josh Waitzkin
- Way of the Peaceful Warrior
- The Talent Code - Coyle
- Bounce - Syed
3. Add some insightful structure to your perspective. Do you have a pessimistic and deterministic mindset that is a detriment to your success?
I'm guessing that this is likely to be more depressing.
I like to consider myself as one of those amateur physicists who Hooft talks about. .. but instead of the deep academic physicist researcher kind, I prefer to be the playful kind. I've filled a notebook with such play. It is likely to be of no use to a professional physicist, but I certainly had fun thinking about things.
A couple examples -
1. I tried to work out a formula for refractive index of a material assuming that photons get slowed down by it through repeated absorption and re-emission.
2. I asked "what if gravity obeyed maxwell's equations?" Iirc some approximate calculations based on it turned ou something like newtonian laws would hold if we're living on the inside of an exploding blackhole (or something like that).
I don't know whether I went anywhere with those, but they were interesting to think about when I knew enough math to do them.
I'm quite sure such play is well within the reach of amateur theoretical physicists even if you may not end up solving the domain's pressing problems.
