Is a string theory science project feasible in highschool?

[MusicTheorist]

Hi,

I just joined this forum a few minutes ago because I'm thinking of joining my high school science research program to research string theory. For those of you who don't know about the programs, basically you research something for three years and then you enter it in the Intel Talent search. I really would like to research string theory, however I'm not sure if it's possible due to the high level of math needed. I'm currently taking trigonometry, do you think there's anyway I could do a project on this?

Thanks in advance!

 

[tiny-tim]

Welcome to PF!

Hi MusicTheorist! Welcome to PF!

Well, string theory is a clever mathematical way of summing infinite series in quantum field theory, and quantum field theory requires knowledge of quantum theory and linear algebra, and …

so I'd recommend against it.

(and it's mostly maths, so would that satisfy the program anyway?)

How about something related to music, or to sound generally?

 

[Bob_for_short]

As soon as you learn waves, you will be able to understand "the wave mechanics". It is all about different wavy motions.

 

[MusicTheorist]

Thanks for the replies.

I was thinking of doing a project on music, but I don't particularly want to because being a composer myself I feel that researching music scientifically would make it lose it's magic.

I am a pretty fast learner, even faster if I teach myself. I'm not a great math student I'll say that, except most of that is because when I was in 7th, 8th, and 9th grades I either couldn't pay attention (I needed glasses and couldn't see) or was too immature to pay attention so I missed out on a lot of the important concepts that everything I do in math now is built on.

I find though that when I teach myself the math from a book I can learn it really fast and really well. Do you think I could teach myself the math in a year and then use the next two years to do the research?

 

[Bob_for_short]

Frankly, I have no idea. I am too different - I am a slow learner and slow researcher.

 

[MusicTheorist]

Hmmm, well, could you recommend a book or something that is pretty dense? This way I could have an idea of what I'd be getting myself into.

 

[Bob_for_short]

I am afraid you have to follow the school program at least. As I am a foreigner (Russian) I have no idea about books in your country.

 

[marcus]

What do you know about the physics of sound?

One of the most interesting physics courses I ever took was devoted to the physics of sound.
And it was also surprisingly easy, or maybe the teacher was just very good. His name was Crawford, at UC Berkeley. Retired now. Could do all kinds of experiments and get you to experiment with sound on your own.

Unfortunately I don't see much on Google about physics of sound.

I do see this bit about "acoustic illusions" which are the auditory analogs of optical illusions.
http://www-cip.physik.uni-bonn.de/~scheller/acoustic-illusions/main.html

My advice would be to learn all you can about vibration and sound, especially if it can relate to something you can hear or see or experience in some way.

Do you know about dispersion and dispersive media? There are channels in which different frequencies travel at different speeds---there is not just one single fixed speed of sound, but it depends on the pitch. Strange effect. A tunnel can cause dispersion.

Do you know how air-temperature affects the pitch of a pipe-organ's notes? Did you know that the speed of sound determines how the length of the tube is related to pitch? And do you know how the air-temperature affects the speed of sound?

What do you know about diffraction---how waves get around barriers. It depends on wavelength. This can effect how at the beach the waves crashing onto the beach sound different when you are behind different barriers.

What do you know about resonance. About filters? Filters do not have to be electronic.
All kinds of vibration are interesting and can involve non-obvious effects.

There is a lot of hype surrounding string, raising unfounded expectations. But at least the concept involves (at a primitive level) vibration. String theory may never pan out, might just be a dead-end as a unifying ToE. And end up as a collection of special purpose mathematical techniques, useful in various limited ways. It is looking more and more like that. But at least the concept of vibration is something it shares with the real world---and the world of the senses.

 

[MusicTheorist]

Well, what I'm really interested more in is parallel worlds, baby universes, things like that, so maybe I shouldn't have called it string theory...

I barely know anything about waves. I just finished going over a basic chapter about waves in chemistry this year...but outside of that I know nothing.

 

[pzona]

OP, I would recommend against string theory in high school. I'm a first year college student (chemistry major though, not physics), and I'm pretty sure that all courses that even get into the most basic aspects of string theory are all 400 level. I have a feeling the math is just too advanced (although I could be wrong) for a high school student.

That doesn't mean you can't get into some really interesting things though. I'm covering some basic quantum chemistry right now, and I feel like the Schrodinger Wave Equation might be a good topic if you want to do something really advanced. It's a highly physical approach to describing electron behavior in atoms, and once you understand some of the basics, it leads to some really interesting and counterintuitive implications. String theory involves infinite series, some of which are absolute hell to calculate, while the SWE usually only goes as high as differential equations (still not easy, but not as hard as infinite series summations).

I'm not going to tell you what to do, since I don't know your abilities or interests, but I would definitely recommend starting with something a little easier than string theory. The best physicists in the world are still stuck on a lot of problems with it, so it may be too advanced for you. I might be biased toward the wave equation because I'm a chemistry major, but if you're looking to get into some more advanced physics for a project, the SWE (or anything in quantum mechanics really) might be a little more realistic (and just as interesting!).

 

[pzona]

Well, what I'm really interested more in is parallel worlds, baby universes, things like that, so maybe I shouldn't have called it string theory...

I barely know anything about waves. I just finished going over a basic chapter about waves in chemistry this year...but outside of that I know nothing.

Sorry, I didn't read this until after I posted my response. A good place to start looking for a topic would be "Physics of the Impossible" by Michio Kaku. Some of the things he says are pretty idealistic and impractical, but the science behind his ideas is pretty solid as far as I can tell. If you read through a few chapters of his book, you'll definitely come across some really interesting things. You could easily make a list of possible project topics just from reading a few sections; he covers a lot of the things you mentioned that you're interested in. Even if you don't use any of his ideas, he has some pretty interesting things to say.

 

[MusicTheorist]

Funny you should mention Kaku, my father picked up a copy of Kaku's Parallel Worlds at the bookstore today and I've been skimming through it. I was going to start reading it within the next few days.

I'll look into the SWE. I'm interested in pretty much anything that's really abstract.

Thanks for the really helpful responses!

 

[atyy]

Decoupling Gravity in F-Theory
http://arxiv.org/abs/0910.2955

Clay Cordova wrote the above string theory paper in 2009, and he was a high school student in 2003 as I learned from http://motls.blogspot.com/2009/10/f-theory-papers-go-3d.html - 3 years is well within an order of magnitude of 6, so by back of the envelope physics reasoning :tongue2: something like that could be well within your reach.

 

[Haelfix]

Actually you could make a decent presentation about string theory at the high school level. Something along the lines of 'the Elegant Universe' b/c stating the facts and general ideas isn't particularly hard.

Generically the material (without the math) is too simple for a college undergrad presentation, but just about right for high school.

 

[humanino]

I was thinking of doing a project on music, but I don't particularly want to because being a composer myself I feel that researching music scientifically would make it lose it's magic.

I think you should reconsider this position. Very few things offended me as much as when I was told I can no longer enjoy a rainbow since I understand how they happen. Let me tell you, it's wrong.

You can easily decipher the tricks Mozart drives you into, study a piece for weeks, yet still enjoy it possibly even more.

Music theory is very much developed mathematically. Composers such as Boulez have thought of the way waves travel in space and time, included constraints for the space and time positions of their orchestra. He even lead a group creating the necessary electronic tools for his visions. Music just as physics or mathematics is a story written by humanity as a whole, every composer sitting on the shoulders of giants.

 

[atyy]

You can easily decipher the tricks Mozart drives you into, study a piece for weeks, yet still enjoy it possibly even more.

easily?

 

[atyy]

BTW, humanino is of course right (except for the "easily") - all the great composers were very, very interested in musical technique.

 

[MusicTheorist]

I think you should reconsider this position. Very few things offended me as much as when I was told I can no longer enjoy a rainbow since I understand how they happen. Let me tell you, it's wrong.

You can easily decipher the tricks Mozart drives you into, study a piece for weeks, yet still enjoy it possibly even more.

Music theory is very much developed mathematically. Composers such as Boulez have thought of the way waves travel in space and time, included constraints for the space and time positions of their orchestra. He even lead a group creating the necessary electronic tools for his visions. Music just as physics or mathematics is a story written by humanity as a whole, every composer sitting on the shoulders of giants.

I do know that theory is very much based in mathematics - I'm in AP Theory now and it's almost like a math course. It has helped me appreciate music more actually so I agree with you.

Still, for some reason I'm just not that interested in doing a project on music. I'm not sure why. It tends to be that when I really want to do something (in this case string theory) it's extremely hard to get myself out of that mindset. Maybe I just have to do a little convincing.

 

[humanino]

easily?

Well, of course it helps it have a teacher, and I meant that it is easier with Mozart than with more recent composers.

 

[arivero]

I had noticed a lot of musicians hating the math of harmony, scales, etc, but I though that it was just a consequence of the self-teached approach to music, plus hate of academic formalism. I had neved thought about "losing magic"; but yes it could. Note that the same applies, by the way, to parallel universes, baby bangs or whatever science exotics.

Were I to think on a math/music project for high school, I would go for theory of scales: pythagorean, well-tempered, pentatonal, etc. On a physics/music project, I would go for drum waves. The classical experience, putting flour in the membrane of the drum and vibrating it with a violin arc, is still pretty, and it allows for modern variations (high speed photography, wave input from modern music instead of the violin arc ...)
http://www.cuatro.com/el-hormiguero/videos/ciencia-flipa-ensena-ciencia-miley-cyrus/20090422ctoultpro_5/ min 2:42 for an example in a pop program.

 

[DreadyPhysics]

Still, for some reason I'm just not that interested in doing a project on music. I'm not sure why. It tends to be that when I really want to do something (in this case string theory) it's extremely hard to get myself out of that mindset. Maybe I just have to do a little convincing.

I bet I can convince you to stay away from string theory.

If you want to approach string theory in any meaningful sense, you can't just rely on Kaku and Green's elegant universe- that is, pop sci books and features. Especially if this is a 3-year research contest/event I would hope that you could offer more than a book report on Green. The problem is, these treatments, though readable, offer none of the meat of higher physics; they're totally stripped of math (stripped of the actual physics and *reasoning*), and what you're left with is a very blurry, hand-wavey picture and you certainly can't draw any meaningful conclusions from that alone. In short, you need to look at what string theorists themselves write about string theory amongst themselves, which means YOU NEED THE MATH.

So what math, exactly, would you need to learn in order to make any sort of headway with string theory? It sounds like you've got algebra and trigonometry under your belt, which is a good start. Let's crack those books.

First a solid background in calculus is necessary for basic-level physics. Learning up to multivariable calculus is at least a year's worth of material, normally. Hand-in-hand with calc is usually taught linear algebra, which is a generalization of systems of algebraic equations, and fundamental to understanding quantum mechanics.

After calc you'd have to learn differential equations, which is the language of classical physics. This is not a trivial matter, ususally a mid-level college course or two.

Most of the language of analyzing fields and equations in the standard model and beyond uses the tools of functional analysis: real and complex analysis are high-level undergrad courses if not graduate level mathematics. These are very abstract notions and complex analysis relies on an understanding of imaginary numbers.

After all that basic framework is out of the way, you can start learning differential geometry and group theory, specifically lie groups, lie algebra and topology. Now we're approaching the language that string theory is written in.

To tackle ST itself, you would have to understand the fiber bundle formalism of the standard model, which also requires knowledge of cohomolgy. It would also behoove you to study up the basic ideas in extensions of the standard model: supersymmetry is required for string theory, but you should also have a working understanding of kaluza-klein-type extra dimensions.

Somewhere along the way you'll have to pick up statistics, most likely, for quantum. Oh yeah, and all the physics between here and there- which is to say, start from advanced Newtonian mechanics (lagrangians), extend this to an understanding of quantum mechanics, then quantum field theory, and then the standard model.





Now on the other hand, a physical treatment of music is both fascinating and within your immediate mathematical reach from the sounds of it. But don't take my word for it...

 

[DreadyPhysics]

It sounds like you might be interested in cosmology (based on what you posted earlier.) You could, for example, look at the development of the Big Bang theory. This is something that can be understood in a more qualitative manner: without much mathematical formalism you can come to understand the scientific arguments at each step of the way that leads us to postulate the big bang event.

Starting with Hubble's discovery of an expanding universe and penzias and wilson's discovery of the CMB, along with other arguments such as cosmic element abundance relating to big bang nucleosynthesis. There's plenty of substance to be found here just on a qualitative level.

If you read through the history and understand the arguments enough that you can make the case for the big bang to someone else, I'd say you have a fairly good understanding of cosmology for a high school level, and there's plenty of other directions you can take it after this.

 

[Haelfix]

Apologies I didn't read the original post thoroughly. Yea a 3 year program they are going to expect something more than a book summary, and as mentioned the mathematics in string theory is far beyond a high school or undergrad level. You won't be able to do much with it in 3 years.

You are looking for something more like a science fair project that could compete in state or national competitions. For that, the original music idea is better and relatively common in hs science projects. However I strongly urge you to consult with your schools physics and math teachers for ideas and where to go for help. Some science 'camps' actually will take you on during the summer holidays and hold your hand a bit more.

Unfortunately, science fair type projects can be notoriously fickle b/c
1) You don't have access to precision instrumentation.
2) You can easily bite off more than you can chew.
3) You can easily end up with something relatively trivial.

Which is why you need the help of senior people who can anticipate some of the problems, before you actually embark on the project. For instance, if you wanted to write a report on the mathematics of music. Well be warned, the rabbit hole goes very deep. Harmonic and wavelet analysis can get into graduate level material quite easily, so it depends where you go with your project.

 

[JustinLevy]

Here's a suggestion:
Make a detailed "path" of learning you want to embark on. Work for two and a half years on this path. Regardless of how close you got to the goal, you will most likely have vaste more knowledge of linear algebra, calc, differential equations, lagrangian mechanics, hamiltonian mechanics, classical field theories, relativity, quantum mechanics, etc. than most high schoolers. At that point choose a project based on your current level of understanding to finish in the last half year.

There are all kinds of amazing things you will learn along the way.
Go bold! But always have a way to fall back on practicality.

(EDIT: I don't know the details of the program you want to enter, so maybe that is not doable. But I'd hope they'd encourage you to pursue whatever you are interested in as far as you can go.)

 

[pzona]

I think you should reconsider this position. Very few things offended me as much as when I was told I can no longer enjoy a rainbow since I understand how they happen. Let me tell you, it's wrong.

Agreed. Sunsets have been a hundred times more beautiful to me since I began to study the Tyndall effect.

 

[MusicTheorist]

I guess I'll have to steer away from the string theory, but what about something in theoretical physics in general? Or particle physics.

Maybe I should give a little bit more description of what the program is.

Starting year 1 (this year) we start thinking of a project. During the middle of the year we pick a mentor who is a professional, normally with Ph.D, in the field. Kids in my school have worked with people from Princeton, Yale, University of Wisconsin, etc.

For the rest of the year we work under the mentors guidance on our projects. We enter competitions etc.

Over the summer we have to log a certain number of hours in the field or in the lab. With theoretical physics that would mean just a certain number of hours working on the problems.

The next two years the process basically just repeats, excluding the finding a mentor step.

 

[marcus]

What is the nearest university (or college) to where you live? Knowing that might give us some ideas to suggest to you.
Is there a hands-on science museum near you? (In the SF Bay area where I live we have some great ones, but I gather you are back east somewhere or in the midwest. I don't know the situation back there.)

For the rest of the year we work under the mentors guidance on our projects...

Over the summer we have to log a certain number of hours in the field or in the lab.

Sounds like a good program. The organizers seem to be emphasizing the empirical aspect of science. Making explicit the idea that if something is not empirical (based on observation or experiment) then it is not science. Having interesting thoughts is called speculation. It sounds like they are steering kids away from merely speculating about interesting ideas, and more in the empirical direction.

"In the field" means making observations, keeping a notebook, recording observations.
"In the lab" means experiment, again it means keeping a (lab) notebook.
Empirical science involves records and documentation. I assume you know all this, so I don't have to say it. But "just for the record" I will .

Anyway, from the little you have told us, the basic aims and framework of the program sound really great.

 

[Haelfix]

Particle physics and string theory are essentially the same problem. Either you repeat an experiment or discuss a theory proven in the 1920s (which is doable, even for a hs student albeit hard), or you face the scope problem that the mathematics and modern experimentation is way out of reach (both conceptually and financially) for you at this time.

This is a problem, even for seniors in undergraduate physics (some 7 years of work ahead of you!). Some schools require a dissertation of original research, and that's extremely hard on them (especially in particle and string research) b/c they don't have the background yet to actually contribute much (outside of a few standouts).

So my best advice is to swallow the pride (believe me I had the same issue in hs when I was competing in Westinghouse and other science fairs) and listen to the suggestions of your supervisors to the T. If they offer you an idea, jump on it. They know what you can realistically do or not do in the timeframe.

 

[jpw]

Yes DEFINITELY you should go for it! Follow your instincts! I am a chess master,
And people assume you have to be a genius to play chess but I regularly teach kids as
Young as 4. Normal kids not young Einsteins.. So all you need to do
Is break it down, focus on concepts and ideas rather than heavy maths
And you will be sweet. As people here said check out Kaku, brian greene, stuff on you tube
Made for general audiences. Good luck!

 

[Bourbaki1123]

I don't know. I had almost no working knowledge of math before I began my college in '07, roughly two and a quarter years ago. I had taken algebra 2 in high school and gotten a B Junior year. I was a terrible student in high school and had virtually no academic interests.At first I wanted to be Salvador Dali, then I wanted to be Steve Vai. Then I finally became interested in Physics and math late in my senior year. I did well on my SAT math so I had the opportunity to take Calculus, which I had begun teaching myself over the summer, in the first semester of college. I am now studying Algebraic Geometry and have a fairly strong level knowledge of Commutative Algebra. I also am studying theory of computation and mathematical logic at the graduate level.

It seems to me that if you really, really want to learn the mathematics, maybe not quite for string theory, but for at least quantum mechanics, and you have some aptitude you could do it in two years. This is especially true if you can get through calculus over the rest of the year and request to be allowed to take the AP Calculus BC test. If you can get to that level in that amount of time maybe you could pull it off, not to mention you would have a serious head start to becoming a scientist of any kind.

There are many online resources to take advantage of. You have the help forums here to clarify any concepts you struggle with, you have wikipedia, you can get just about any book from amazon, or the library(especially at a nearby university if they will give you access) (or I guess you can torrent it if you don't have a problem with that). So supposing you are a sophomore, I don't see any reason why you can't learn mathematics up to a very high level by the time you graduate.

 

[Redd]

A lot of science is knowing what is beyond your current limits. Newton freely admitted
that he couldn't explain what causes gravity, he just took it as a given and calculated the results. My point being, you don't have to solve everything all at once. Take on something that you will be able to learn well and give a solid interpretation of rather than a hasty, general, view of String Theory.
There seems to be a whole school of people out there that are interested in String Theory or QM but they just want to skip the in between and go straight to
a Nobel Prize :P

You have plenty of time. Use it.

SO basically the same as what everyone else is saying.
I vote you do something on music.

 

[MusicTheorist]

Ok, well regardless of what project I do, does anyone have any recommendations for books I can use to teach myself the math and physics? Right now I'm reading through an old version of Resnick and Halliday's Physics textbook from the 1960s (my Dad's old college textbook). He has an old Calculus book too downstairs. Are those good or too outdated?

I was also wondering if I really need to take Pre-calculus before calculus, or if I can go right to calculus. If I need to know it, can I teach myself Pre-calc and trig in parallel or will they conflict?

EDIT: I think I'll start a new thread for this since it's a little off topic...

Thanks for all the help guys!

 

[Vanadium 50]

It may help to understand how much physics separates you from a typical graduate student working on string theory.

You need to learn trig and analytic geometry (what used to be called pre-calc). Then there is the Halliday and Resnick book, which typically is covered in two one-semester college classes. At my university, it was normal for physics majors to take 8 additional physics classes and 6 math classes, so you're 18 classes behind. The first two years of grad school are 12 more, bringing you to 30. Theorists would take a couple more specialized ones, so you are about 32 college classes away from getting to where someone would start to think about strings.