Physics and Mathematics Guidance

[Matthewkind]

Before I ask my question, first allow me to introduce myself. My name is Matthew Pendleton, and I am a seventeen-year-old currently in high school. Two years ago, I was purely interested in philosophy. But during one of my readings, I came across Albert Einstein and his contributions and I began to think, "What -is- relativity?" Back then I didn't even know there was special and general, but now I'm fairly familiar with the concepts (not the mathematics thereof). Anyways, I fell in love with his way of thinking upon reading a few biographies and quote-books. His humility at facing the universe is simply astounding. And his ideas were pure genius! Even without the relativity theory, he has the "biggest blunder of his life" (cosmological constant) going for him; not to mention the myriad of other contributions to science he's made - for example, in black holes and wormholes.

It's been two years now, and I'm willing to take on any amount of insane mathematics if I can help Einstein achieve his dream of a grand unified theory which encompasses all of the fundamental forces. I've heard a lot of good things about string theory, although to be quite honest, I'm barely familiar with the concepts - so I don't know a lot about the mathematics of string theory.

I am currently studying physics and mathematics independently, as - due to lethargy prior to becoming a senior - I've been placed in 'Introduction to College Algebra'. So far I've pretty much covered all of algebra, and a lot of Calculus. As of right now, I'm studying Linear Algebra and am just getting acquainted with matrices. I am very thankful to Khan Academy for the chance to study such mathematics whilst still in high school.

Right now I'd like to know what I should be doing in terms of preparing to become a theoretical physicist. I want to know what I should be studying so that I may help my dear friend. I know that this may seem a bit silly, but this has become my life's goal.

I'm sorry if any of this either doesn't make sense or doesn't flow - I'm in a very loud library in a public school right before lunchtime.

Thank you very much for taking the time to read all of this.

 

[Matthewkind]

I suppose if I had to ask a condensed question it would be: what branches of mathematics + branches of physics should I begin with, and what then?

I thought I should start with linear algebra, then move onto Euclidean geometry. As for the physics, I'm studying classical mechanics and am actually currently working with angular motion in a plane. Should I be doing something else, or am I on the right track?

 

[Marin]

Hi, Matthew!

Welcome to Physics Forums!

It's great you're so enthusiastic about Einstein's General Relativity (GR) and theoretical physics only at the age of 17. It's also a very good decision to post a thread in the forum, since you're going to get many different answers and suggestions, some of them you wouldn't consider yourself. (I myself started visiting this forum shortly before I entered university and have only benefited from it)

As to your question, first, be aware of the fact that GR is an advanced theory of physics, and in order to be able to understand its concepts several years will be needed. You already know you'll need a bunch of hard mathematics and it's great you're planning to study the main concepts of maths parallelly as well. GR is a theory based primarily on differential geometry. To be able to grasp the concepts of the latter, you'll definitely need all courses in analysis (calculus in n-dimensions, ODE's, maybe even PDE's) and linear algebra offered. Don't worry, there's plenty of time for you to do them all. The physics curriculum during the bachelor is doing almost only basics, so I'd suggest you follow the standard classes and focus on understanding as much details as time permits, at least in the beginning.

After taking differential geometry you'll be able to fully understand the mathematics of Einstein's theory. As to the physics, by this time you'll probably have developed some own intuition about how physics works, but GR is really conceptually different, so only time and experience (a one semester course will definitely be insufficient) will help you understand it's physical meaning.

As to the grand unified theories, don't worry about them now. Your point of view of looking at them will be changing from year to year as you begin to understand how physics works (this is my experience at least)

so much from me,
marin

PS: it will be a hard way to go and probably you're going to experience difficulties as well, so keep your main motivation throughout clear and never ever dare to forget it!

 

[Matthewkind]

Thank you so much! ODE's and PDE's... are you referring to ordinary differential equations and partial differential equations? I've heard of them, but I'm only vaguely aware of what they are. Something to do with calculus, right? And as for the courses in analysis... that's real analysis and complex analysis? Again, I don't really know where to study those. Are you telling me that colleges actually have courses on ODE's and PDE's, those sorts of analysis, etc.? If so, that'll make organizing my studying a lot easier; I was under the impression that I was surrounded by an insurmountable wall of mathematics and complex physical distortions and such. Obfuscation was the only certainty!

You're right, though! I won't waver in my convictions! I will definitely solve the mysteries of the universe, and I will push humanity further! Although, that does seem rather...selfish sounding. Perhaps I should shoot for assisting my fellow humans in their overall understanding. But it's rare that I even talk to people who are even remotely interested in this sort of thing, so you'll have to excuse my excited ramblings and confused typing. I've been on my own so far. I'm very excited...!

 

[Marin]

ODE's = Ordinary Differential Equations
PDE's = Partial Differential Equations (much harder)

They are both needed ubiquitously in physics. Every equation of motion is a differential equation, since it has to predict the rate of change of some quantity in/of the system. (evolution of a system). You'll have a lot of headache with them. And yes, they both heavily rely on calculus and analysis.

Complex analysis you'll not need for differential geometry and also not for GR. It has, of course, applications in physics, but every single bit of mathematics has.

I cannot give you any info on what is being done in US colleges, since I'm not familiar with the US system at all, but the guys here will definitely be able to answer these questions.

 

[Matthewkind]

Where's 'here'? Perhaps I can make myself known in the physics community and be transferred 'there'?

 

[Dembadon]

Hi, Matthewkind! Welcome to PF!

The courses you'll be taking, should you decided to major in physics, will greatly depend on the university you attend. At my school, Real and Complex Analysis are courses that mathematics majors might take during their senior year, and they focus more on proving theorems rather than applications. Instead, physics majors take a semester-long course called "Mathematical Methods in Physics," offered by the physics department.

Here is the course description from my university's catalog:

"Applications of mathematics frequently used in physics, including vector calculus, tensors, linear algebra, ordinary differential equations, partial differential equations and complex analysis."

Of course, one is still required to take Calc I-III, Probability & Statistics, and DiffEq's, but the course I mentioned above will cover the subjects it mentions as they pertain to physics. There might be proofs involved, but proofs won't be the focus of the course. Hopefully that made sense.

If you haven't started getting information from the colleges to which you're going to be applying, I'd suggest doing that right away.

 

[Matthewkind]

Thanks! Einstein actually mentioned that tensors were a big part of his mathematics. Aren't they a step-up from vectors? But if scalars are quantities with magnitude, and vectors are quantities with both direction and magnitude, what then are tensors?

 

[Matthewkind]

Actually, therein lies the problem. I don't have any money whatsoever - my mom works at McDonalds. Unfortunately, owing to the slowness of public high schools and my own aforementioned lethargy, getting into college doesn't seem very likely. I'm actually rather frustrated at the put-downs of my mother calling my physics endeavors nothing more than a waste of time. I'm lost as to what to do.

My apologies for complaining. I'm scared and under a lot of pressure. Do you have any advice as to my current predicament?

 

[symbolipoint]

Matthewkind discusses what he is studying:

I am currently studying physics and mathematics independently, as - due to lethargy prior to becoming a senior - I've been placed in 'Introduction to College Algebra'. So far I've pretty much covered all of algebra, and a lot of Calculus. As of right now, I'm studying Linear Algebra and am just getting acquainted with matrices. I am very thankful to Khan Academy for the chance to study such mathematics whilst still in high school.

You study independently currently? How were you "placed" into College Algebra? This is a fairly advanced course from the point of view of what a student would do in high school. Some of the topics are tough ones to study.

If you are doing well in College Algebra, then you will do well with Mathematics and some other science and technical courses from a college.

I don't have any money whatsoever - my mom works at McDonalds. Unfortunately, owing to the slowness of public high schools and my own aforementioned lethargy, getting into college doesn't seem very likely. I'm actually rather frustrated at the put-downs of my mother calling my physics endeavors nothing more than a waste of time. I'm lost as to what to do.

How would she respond if you replace "engineering" for "physics"? How would she respond if you replace "computer programming" or "computer science" for "physics"? Based on practicality or interest, could change direction, at least temporarily, to some vocational field and attend a community college?

 

[Matthewkind]

Well, I'm not about to take Engineering. I don't care much for luxury or hedonism. I'm fairly convinced that I'm ready to dive right into studying all of the mathematics required of me to understand the universe - even if that means having to make up my own math as I go along.

And the College Algebra course is nothing more than a review of quadratics and fractions; things of that sort. I actually do have a lot of problems with geometry. I'm still trying to hit the core of it. Same goes for trigonometry, but only because I don't know what radians "are". I can do the identities and the inverse functions fairly effortlessly. And I'm even well-trained in derivative calculus. Integral is a little tricky by yourself, but I'll definitely tough it out.

 

[MaxwellsDemon]

When it comes to paying for college there are always plenty of options, student loans, scholarships etc. In my experience knowledge is never a waste of time or money. If I may make a suggestion though, have a backup plan. Its difficult to find employment in theoretical physics. I finished my masters degree a few years ago and wasn't able to find work in the field. My backup plan was teaching high school science, but after trying that I discovered that I didn't enjoy the child psychology part of the job. Now I'm working as a dishwasher while I wait to go back to university again...this time to study mechanical engineering. So while studying theory and working on problems and topics that interest you, be sure to also gain skills that you can fall back on if the dream job of physics professor or theoretical researcher doesn't work out. There are many careers that compliment an education in physics that wouldn't require you to take a large number of additional courses. You could get a second major or a minor in things like computer programming, or electrical/mechanical engineering, or accounting, or medical physics...things like that. If you want to win your mom over to physics, tell her that people who use physics in their jobs: computer guys, engineers, and medical physicists make lots of $$$. :)

 

[Matthewkind]

Well... I'm incredibly idealistic and hard-headed. There's no way I'd do anything other than spend my time working through physics and trying to understand the inner workings of Nature. I'm not too worried about my living conditions - just so long as I'm living.

 

[MaxwellsDemon]

Well... I'm incredibly idealistic and hard-headed. There's no way I'd do anything other than spend my time working through physics and trying to understand the inner workings of Nature. I'm not too worried about my living conditions - just so long as I'm living.

I thought the same thing when I was your age, but trust me...you won't feel much like working on your theories if you're having to toil eight hours a day every day at a low paying job you hate just to put food on the table and a roof over your head. Unless of course the life of a garbage eating hobo appeals to you. Einstein didn't get his dream job of theoretical physicist immediately out of college. He worked as a patent clerk while developing his special theory of relativity. I'm not saying you shouldn't study theoretical physics, I'm just suggesting that you also have non theory career path or skill that you can fall back on just in case you don't land that dream job right away. It doesn't mean you'd have to take a ton of additional classes either. Learn from my mistake and don't be a thirty year old dishwasher with a masters in physics.

 

[symbolipoint]

I thought the same thing when I was your age, but trust me...you won't feel much like working on your theories if you're having to toil eight hours a day every day at a low paying job you hate just to put food on the table and a roof over your head. Unless of course the life of a garbage eating hobo appeals to you. Einstein didn't get his dream job of theoretical physicist immediately out of college. He worked as a patent clerk while developing his special theory of relativity. I'm not saying you shouldn't study theoretical physics, I'm just suggesting that you also have non theory career path or skill that you can fall back on just in case you don't land that dream job right away. It doesn't mean you'd have to take a ton of additional classes either. Learn from my mistake and don't be a thirty year old dishwasher with a masters in physics.

Disappointing you had to settle for dishwashing job, yet you have Masters degree in Physics. Why not maybe technical job or work as independant tutor or for a professional tutoring company? Any programming skills that you could use for a job?

 

[MaxwellsDemon]

Disappointing you had to settle for dishwashing job, yet you have Masters degree in Physics. Why not maybe technical job or work as independant tutor or for a professional tutoring company? Any programming skills that you could use for a job?

The dishwashing job was kind of a circumstacial thing. I got my masters in physics, was going for my PhD but wasn't interested in the research they were doing at my university...so I decided to move back to my home city and get a second masters in high school education. I got a part time job as a dishwasher to pay the bills at that time, but then after getting some classroom experience I found I didn't enjoy teaching. So the dishwashing thing went to full time while I applied to some engineering schools. Now the plan is mechanical engineering...I'd like to design and build robots I think. Still stuck with the dishwashing for at least a couple more months though. My programming skills aren't currently very strong, otherwise I'd probably look for a local job in computers. I'm in a relatively small city, so there isn't much for technical employment...its pretty much all food, customer service, or healthcare. Its a bit depressing that I don't get to use my knowledge for anything currently, but I've taken the six months off from formal learning to play around with some pet theories, learn piano, and read some classic literature. I've also met some really interesting people, my fellow employees, that I would never have met otherwise.

 

[Matthewkind]

I could handle teaching high schoolers as a fallback. Thanks for warning me, though. And you say you've been reading classic literature. Have you tried philosophy? The ancient Greek philosophers were astounding. You might also find Thomas Aquinas fascinating. And if medieval Christian philosophy isn't your thing, go for Nietzsche. He's one of my personal favorites.

 

[MaxwellsDemon]

I could handle teaching high schoolers as a fallback. Thanks for warning me, though. And you say you've been reading classic literature. Have you tried philosophy? The ancient Greek philosophers were astounding. You might also find Thomas Aquinas fascinating. And if medieval Christian philosophy isn't your thing, go for Nietzsche. He's one of my personal favorites.

I've gone on stints where I read philosophy. Plato is my personal favorite. I've read a lot of his works. I haven't read much of Nietzsche...of the Renaissance and Enlightenment philosophers I've read some of Descartes, Pascal, Spinoza, Kant, Leibniz...a few others, but I'm more of a dabbler in philosophy than a serious student I would say.

 

[Matthewkind]

You and I should correspond more frequently. I don't have any physics friends - perhaps you could teach me? Do you have an MSN?

 

[Tensor_law]

sigh good luck with your quest to become the next einstein and to come up with a unified field theory.

You need imense talent in theoretical physics. Unless you have qualified for USAMO or Some National Olympiad your dream is through. Spare yourself the pain and do engineering. Double major in physics if you want, but i can tell you now, you have a 1 in 10 shot of becoming a professor even if you were in the top 1% of talented students. Which you are not.

You remind me of a younger me. I wish someone had told me this earlier. You dream about theoretical physics and yet have a weak grasp of mathematics. There is more to physics then string theory and Quantum field theory. It is a siqn of your ignorance that you want to work in them!

 

[Matthewkind]

Thanks for the concern, but unfortunately I'm extremely hard-headed. I will definitely study hard and become a wonderful physicist. After all, I have Einstein with me. :)

 

[Tensor_law]

Kid. Please. You are not going to be einstein.

Einstein lived in a different time.

You are not going to revolutinize physics. Inface if i bet you $10 000 that you would not become a professor, the odds are 9/10 in my favour of making some money. In fact i will gladly enter that bet with you if you want! Ill let you off though, as going down the theory path, you will need all the money you can get.

Have you ever seen a theoretical physics paper? Its not about extra dimensions of space and time flying around with pretty equations describing them. Its not about particles traveling faster than light. It is not about what existed before the big bang!

Sure it sounds cool to be hawking, describing black holes, but hawking will die without knowing for sure if his ideas are anything more than speculation. Physics is about experiment not about sitting in your office dreaming about tiny strings, which might or might not exist.

You are dreaming a dream.

I bet you think experimental physicists are less worthwhile then theorists?
I bet you think your the smartest kid alive?
Wait till college, when even the english lit majors are smarter than you!

 

[Tensor_law]

I bet you look down on philosopher, historians and economists, because they are not "discovering the secrets of the universe". Honestly you know some vectors and how to take a derivative. The big boys were doing that at 8 years old, if not earlier!

I bet engineers, doctors and lawyers are practical scumbags to you? Anyone that actually tries to do anything beside look at equations is a lesser being! I am tired of this rubish, grow up!

 

[Tensor_law]

also being hard headed is not a good sign for a future physicist!

 

[Matthewkind]

Well, I never really thought down on anyone. I merely wish to assist Einstein. I don't believe that anyone is more intelligent than anyone else. I just refuse to do anything but theoretical physics.

 

[Tensor_law]

then you refuse to be paid.

Tell that to the government when you finish your phd. With that attitude industry won't even take you. Good luck, enjoy the trash cans!

 

[hadsed]

Well, I never really thought down on anyone. I merely wish to assist Einstein. I don't believe that anyone is more intelligent than anyone else. I just refuse to do anything but theoretical physics.

You sound like a crazy person talking about Einstein like that.

While Tensorlaw is being kind of a jerk, he's right. There are more people than you can count that haven't been able to work in academia, and mind you these are very brilliant people. It's not like you work harder than you ever have in your life and it'll just come. Yes, you'll have to do that, sure maybe some won't take it to that level and make it, but that's because it's not just about how hard you work.

You really need to think about a fallback plan. If you don't care if you work in physics or not, then it doesn't matter much. What's the point of studying string theory, even if you do get accepted to a Ph.D program to do it (where funding is wishy-washy anyway), when getting your post-doc doesn't happen? And then the next post-doc? If you do happen to get those two, do you really think the whole of academia is in particular need of string theorists? On top of that, you will be limited by the 5 jobs there are available... which may be in Iowa, Siberia, or Alpha Centauri.

The point is, don't be stupid. You need to think about this or you'll be very sorry. This is something that happens to people all of the time, people who said the exact same things as you and refused to face reality.

 

[Fizex]

Einstein refused to believe the results of quantum theory which he was a father of. Any idea you have with modern physics these days would not please him.

 

[General_Sax]

You need imense talent in theoretical physics. Unless you have qualified for USAMO or Some National Olympiad your dream is through. Spare yourself the pain and do engineering. Double major in physics if you want, but i can tell you now, you have a 1 in 10 shot of becoming a professor even if you were in the top 1% of talented students. Which you are not.

quoted for truth

 

[twofish-quant]

It's been two years now, and I'm willing to take on any amount of insane mathematics if I can help Einstein achieve his dream of a grand unified theory which encompasses all of the fundamental forces.

Cool! What you'll find is that it's a lot harder than it looks. It may be that you'll spend a few decades of your life studying stuff that's totally on the wrong path. Or you could just get lucky.

Right now I'd like to know what I should be doing in terms of preparing to become a theoretical physicist. I want to know what I should be studying so that I may help my dear friend. I know that this may seem a bit silly, but this has become my life's goal.

Read science and math. Get involved with undergraduate research. Also don't focus too much at this one problem. Keep your mind open for other interesting problems.

 

[twofish-quant]

I thought I should start with linear algebra, then move onto Euclidean geometry. As for the physics, I'm studying classical mechanics and am actually currently working with angular motion in a plane. Should I be doing something else, or am I on the right track?

It's pretty decent.

Start with calculus and partial differential equations.

 

[twofish-quant]

Thanks! Einstein actually mentioned that tensors were a big part of his mathematics. Aren't they a step-up from vectors? But if scalars are quantities with magnitude, and vectors are quantities with both direction and magnitude, what then are tensors?

Great question! A tensor is a rule for turning one thing (like a vector) into another thing (like a vector). For example, suppose you have a sailboat. The wind is a vector. The force that the wind pushes against the sailboat is another vector. A tensor is a rule for calculating the force on the sailboat if someone gives you the direction of the wind.

In other words

vector 1 -> (magic tensor box) -> vector 2

Also that's one type of tensor. There is another type that turns two vectors into a scalar. For example, I draw two vectors on a piece of graph paper. Those two vectors form a parallelogram. So I get

vector 1 and vector 2 -> (magic tensor box) -> scalar (area)

 

[twofish-quant]

Actually, therein lies the problem. I don't have any money whatsoever - my mom works at McDonalds. Unfortunately, owing to the slowness of public high schools and my own aforementioned lethargy, getting into college doesn't seem very likely.

Community colleges are cheap and you can transfer to a state university.

 

[twofish-quant]

You remind me of a younger me. I wish someone had told me this earlier. You dream about theoretical physics and yet have a weak grasp of mathematics. There is more to physics then string theory and Quantum field theory. It is a siqn of your ignorance that you want to work in them!

Curious because he reminds me of a younger me. :-) :-) :-)

I ended up getting a Ph.D. in astrophysics, and that was a lot of fun. I work in an investment bank where I use a lot of my physics skills. For example the magic tensor box. You can write a list of stocks in Tokyo as one vector, a list of stocks in NYC as another vector, and then the magic tensor box will let you see how closely one set of stocks match another set.

 

[twofish-quant]

Kid. Please. You are not going to be einstein.

I think he could be. It's just a matter of being in the right place at the right time.

You are not going to revolutionize physics.

Not obvious why not. The cool think about physics is that it's not that hard to come up with something new and original. Pretty much everyone in physics comes up with *something* interesting.