I want to understand the universe

[Looh]

Hello!

As I'm new on the forum, I might as well start off with an introduction as that may be helpful given the purpose of the thread. I'm 19 years old and I'm currently in high school; my scientific knowledge is quite limited, I do have a basic knowledge of maths reaching up to and around calculus, I've taken courses in physics due to a genuine interest but I failed them because I've been such a lazy fool. I have a basic understanding of forces, but I lack knowledge in most other necessary fields within physics. Besdies that, I have a very limited understanding of basic chemistry and I'd say I'm quite well versed in biology and genetic engineering at basic levels.

Now, to the true purpose of the thread. As the topic says, I want to understand the universe. My current goal is a complete understanding of both the special and general theories of relativity; and as I want to truly understand it, I assume knowing the maths behind it is essential. I'm also very interested in uncertainty and quantum mechanics, but I know close to nothing about those subjects. Nor do I know about string theory, but it does indeed look interesting as it, as far as I understand, could very well turn out to be a complete theory of everything.
So I'm basically asking for help here; where do I start? Are there any good e-books or online courses that you can recommend? Am I in need of an education at a university, or could I find enough material on the internet or in the library? I won't be able to attend courses that costs money, but I'll check the library for books that could help me reach my goal.

Thank you for reading, I hope that I'll be able to evolve intellectually during my time here on this forum.

 

[genericusrnme]

Mary Boas - Mathematical Methods in the Physica Sciences
That book will get you started on the basic maths you need to know
Landau & Lifgarbagez - Mechanics - Vol 1 of A Course of Theoretical Physics
That book will get you started on the basics of physics (aka lagranges equations)

You'll also want lots of linear algebra
Gilbert Strang - Introduction to Linear Algebra
Kunze & Hoffman - Linear Algebra (I'm pretty sure I spelled the first guys name wrong)
Steven Roman - Advanced Linear Algebra

Maybe some mathy algebra too;
Poalo Aluufi - Algebra: Chapter 0
Bourbaki - Theory of Sets and Algebra Vol 1 &2 (although these are a little out dated)

For quantum mechanics
Landau and Lifgarbagez - Non Relatavistic Quantum Mechanics (a little out dated but it gives you a better feel for it than the more elegent modern books do imo)
JJ Sakurai - Modern Quantum Mechanics

You'll also want to know a little analysis;
Tom Apostol - Mathematical Analysis

Once you've got thatunder your belt, I recently found a nice little textbook you may enjoy
Mikio Nakahara - Geometry Topology and Physics

But really, once you've got the first two books read you'll know the general jist of what it is you're looking for..

In my opinion you can learn whatever you want and at a pace more suited to you without going to university (provided you have some will power and discipline). Getting a job at the end of it however is a different matter, you pretty much need a university degree for that part.

Good luck!

 

[Looh]

Thank you very much for your suggestions, genericusrnme, I'll check them out immediately!

 

[Nabeshin]

Mary Boas - Mathematical Methods in the Physica Sciences
That book will get you started on the basic maths you need to know
Landau & Lifgarbagez - Mechanics - Vol 1 of A Course of Theoretical Physics
That book will get you started on the basics of physics (aka lagranges equations)

You'll also want lots of linear algebra
Gilbert Strang - Introduction to Linear Algebra
Kunze & Hoffman - Linear Algebra (I'm pretty sure I spelled the first guys name wrong)
Steven Roman - Advanced Linear Algebra

Maybe some mathy algebra too;
Poalo Aluufi - Algebra: Chapter 0
Bourbaki - Theory of Sets and Algebra Vol 1 &2 (although these are a little out dated)

For quantum mechanics
Landau and Lifgarbagez - Non Relatavistic Quantum Mechanics (a little out dated but it gives you a better feel for it than the more elegent modern books do imo)
JJ Sakurai - Modern Quantum Mechanics

You'll also want to know a little analysis;
Tom Apostol - Mathematical Analysis

Once you've got thatunder your belt, I recently found a nice little textbook you may enjoy
Mikio Nakahara - Geometry Topology and Physics

But really, once you've got the first two books read you'll know the general jist of what it is you're looking for..

In my opinion you can learn whatever you want and at a pace more suited to you without going to university (provided you have some will power and discipline). Getting a job at the end of it however is a different matter, you pretty much need a university degree for that part.

Good luck!

I'll say that this is a very ambitious book list, especially for a high school student. Most of these books are written for 3rd or 4th year university students, and some for graduate students.

Furthermore, if it's physics you're interested in, I wouldn't recommend most of these either. They are very heavy on (abstract) mathematics, which isn't really the core of physics. Sure, many of us find it interesting in its own right, or as a means to an end, but if you just start out reading Boas, Strang, Apostol, etc. you don't really see where the material is applicable to the real world. I'd say this is a way to get demotivated fast. This is maybe a list of books one should have read to start approaching string theory from a more formal perspective, which is itself a tall goal even for a university student.

I don't really see anything terribly wrong with the standard textbooks used in university. I don't really have the time to list them off here, or to come up with a list of my own, but there are tons of threads on the subject here. So, for example, if you want a book for an introduction to quantum mechanics, search in this forum and you'll see dozens of threads with people asking the same question. There are also some free books online if you're unable or unwilling to get texts from the library. I'm not too familiar with them, but Ben Crowell who posts here at PF has his own set of free books you might be interested in checking out: http://www.lightandmatter.com/books.html

 

[micromass]

Anyway, here's a book list:

For mathematics:

A first course in calculus - Lang
Like the title says, it's quite a good introduction to calculus. You said you know calculus, so this book might not be necessary.

Calculus - Spivak
OK, this is a pure math book. But knowing calculus is so very important in everything you will do, so I guess it's better to do it right. If you want to do physics, then understanding this book isn't necessary. But there might come a time that you want to know the math behind physics. For example, you might want to study functional analysis for QM or manifolds for relativity. This involves pretty heavy math. Understanding this book is a very good tool.

Introduction to linear algebra - Lang
An excellent treatise on linear algebra with lots of motivation from geometry and algebra. It has many computational exercises, but also conceptual proofy questions.

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach - Hubbard
One of the best calculus 3 books out there, and not terribly difficult. It also contains a unique view on linear algebra and develops differential forms in view of that.

Elementary differential equations - Boyce, Diprima
This is a bit of a cookbook text. Got this equation? Do that. But unfortunately, most differential equations texts are like this. Still, I think it's a very decent book.

Mathematical methods for the physical sciences - Boas
An extremely good book, but you need some prerequisite knowledge to fully appreciate it. Knowledge of calculus and linear algebra would be good and probably some knowledge of physics. But this book contains about all the math you need to appreciate most of physics (of course, if the physics becomes more advanced, so does the math!)

As for physics, I can't give you much advice as I'm no physicist. But here are two books:

Physics for scientists and engineers - Halliday and Resnick
This book, or books like it, are very good starters if you want to begin in physics. They a very basic knowledge of calculus, but no advanced math. Personally, I find books like this pretty boring, but you have to got through them. You will likely not understand more advanced texts if you don't get the basics.

Classical Mechanics - Taylor
A very good and comprehensive text on classical mechanics. A very good second book to read.

 

[phinds]

I agree w/ Nabeshin that genericusrnme's list is too heavy for someone at your level, too much focused on the math, and could well be demotivating. Depending on how quickly you want to jump into the math, or rather, I should say, if you want to AVOID jumping into the math too quickly but get a broad perspective on the subjects you name, I'd suggest you start out with the more accessible popularizations that are light on math. Try a book or two in each of several fields (cosmology, string theory, quantum mechanics, etc) to get an overview and see where you might be most interested in jumping into more rigorous detail. I'd suggest Steven Weinberg's "The First Three Minutes" as a good starting point.

Should you take that approach, BE CAREFUL about one thing --- even the really serious professional physicists sometimes make VERY poor choices of terminology and make overly simplified statements, so take everything with a grain of salt. The point would be to get an overview, not to feel that you have learned the details.

 

[WannabeNewton]

Halliday and Resnick "Fundamentals of Physics" is a great textbook for the Physics I, II level. Its "calculus" based but all the calculus problems in the book tend to be very easy and not too insightful; the very annoying / difficult problems tend to be algebraic. Its a pretty standard text. I think Landau would be a bit of a stretch for a person starting out with physics. The motivation for Lagrangian and Hamiltonian mechanics would be better appreciated if he/she first understands the usual Newtonian formulation.

 

[Nabeshin]

The motivation for Lagrangian and Hamiltonian mechanics would be better appreciated if he/she first understands the usual Newtonian formulation.

This is a true point, but even if one understands the Newtonian formulation, L&L is not the best place to start learning Lagrangians and Hamiltonians. It's very terse, which I can see giving a lot of students (ESPECIALLY self-studying ones) a very difficult time. Something like Thornton & Marion, Goldstein, or Taylor would be better in my opinion.

 

[BruceW]

yes, it's probably best to get very familiar with the Newtonian formulation first, then go on to Lagrangian. I agree with Nabeshin really. The best way to learn stuff is by reading through the recommended university physics textbooks. Just google a couple of universities and have a look at their reading lists.

 

[WannabeNewton]

This is a true point, but even if one understands the Newtonian formulation, L&L is not the best place to start learning Lagrangians and Hamiltonians. It's very terse, which I can see giving a lot of students (ESPECIALLY self-studying ones) a very difficult time. Something like Thornton & Marion, Goldstein, or Taylor would be better in my opinion.

Oh yeah I agree I just stated Landau because the other poster mentioned it. Taylor is an awesome text not to mention it has a great cover haha.

 

[chiro]

Hey Looh and welcome to the forums.

I'd actually suggest reading the Feynman lectures if you want some physics intuition. It's a three volume set and covers a lot of stuff. It's not complete with regards to todays thinking, and knowledge but it's really good for getting the intuition.

 

[twofish-quant]

As the topic says, I want to understand the universe. My current goal is a complete understanding of both the special and general theories of relativity; and as I want to truly understand it, I assume knowing the maths behind it is essential.

One bit of advance. Start with Newtonian mechanics. It's critical that you have a firm understanding how Newtonian mechanics works before doing anything else. One thing is that quantum mechanics and GR is in fact not more complicated then Newtonian mechanics. The difference is that people have "inituition" with Newtonian mechanics that doesn't exist in GR or QM.

Another bit of advance, is give up trying to understand everything. There's just too much for one human being to understand. You'll be doing great if you just find one bit of knowledge that interests you and work on that. One mental picture that I have is one of "mining truth". You just find a tiny bit of ground, and then start digging to see if you can find bits of diamond there.

With your current background, special relativity shouldn't be a problem. To understand special relativity completely takes some algebra, and nothing more.

General relativity is a bit trickier. To understand how to come up with the basic equations, you can get there with a few months of work. Now to understand the full *consequences* of these equations is something no one does. What people usually do is to work with simplications of the full GR equations.

I'm also very interested in uncertainty and quantum mechanics, but I know close to nothing about those subjects.

You are about two years away from developing a "working knowledge" of quantum mechanics. The critical bit of mathematics is partial differential equations and a little linear algebra.

For "complete knowledge", no one has that. With about five years of work, you can understand everything that is known about QM, and end up on the frontier of knowledge at which point, you have to figure something out. Or you can use "basic knowledge" of QM and go off in a different direction.

Nor do I know about string theory, but it does indeed look interesting as it, as far as I understand, could very well turn out to be a complete theory of everything.

Or it could be a waste of time. If you mine the same patch of dirt for two decades and come up with nothing, it could be that there is nothing there.

One thing is that there is this philosophy called "reductionism" which is that if you understand the basic processes of the universe, you understand everything. Personally, I think that's nonsense, which means that there is a whole bunch of other things to understand. Statistic mechanics for example.

So I'm basically asking for help here; where do I start? Are there any good e-books or online courses that you can recommend? Am I in need of an education at a university, or could I find enough material on the internet or in the library? I won't be able to attend courses that costs money, but I'll check the library for books that could help me reach my goal.

The easy thing to do is to enroll in the local university, become a physics major, and then go to graduate school. A lot of the knowledge that is there is "tacit knowledge" which isn't something that you can easily get by reading books. One knowledge is "knife skills". Something that's very important in being a chef is to be able to use a knife to very quickly chop vegetables. This is somethng that you just have to practice at. There are similar bits of knowledge in doing physics.

A lot of physics involves problem solving. Someone gives you a problem, you break it up and solve it. The important thing is to be able to do it quickly and efficiently, and to do that, you just need practice.

The interesting thing is that I do believe that there is enough stuff on the internet now so that someone that is *extremely* motivated and unable to attend university for whatever reasons could self-teach themselves undergraduate physics. But no one has yet packaged that together. Someone will...

 

[twofish-quant]

They are very heavy on (abstract) mathematics, which isn't really the core of physics. Sure, many of us find it interesting in its own right, or as a means to an end, but if you just start out reading Boas, Strang, Apostol, etc. you don't really see where the material is applicable to the real world. I'd say this is a way to get demotivated fast.

A lot depends on the personality of the person looking at the books. Personally, I find looking at those sorts of books to be quite *motivating*. It's a "I don't have a clue what these greek symbols mean but I'll ram my head against the wall until I find out". After about two months of this, the book comes from 100% incomprehensible to 95% incomprehensible, at which point i feel good.

One thing I did when I was in high school was that I took out a book on general relativity, and started crashing my head against it. I took me about five years before I was able to finally make sense of it. The cool thing was that when I finally understood what a Christoffel symbol was, and the difference between covariant and contravariant vectors, and how tensors work, I figured out how I would have explained it to a 16 year old me. I also found that GR isn't terribly useful in the types of physics I was interested in. :-) :-) :-)

But people are different. One important thing that's missing is the "social aspect" of learning physics. It's important to get yourself in some sort of community in which you can learn the "psychology of physics" from someone else.

So, for example, if you want a book for an introduction to quantum mechanics, search in this forum and you'll see dozens of threads with people asking the same question. There are also some free books online if you're unable or unwilling to get texts from the library. I'm not too familiar with them, but Ben Crowell who posts here at PF has his own set of free books you might be interested in checking out: http://www.lightandmatter.com/books.html

Also it's a good idea to look at multiple textbooks. One cool thing is to look at different textbooks and figure out that the authors are approaching the topic from completely different angles.

The other thing is that there is a huge missing step in textbooks. There are textbooks for graduate students. There is "popular literature." There isn't much in between.

 

[twofish-quant]

I also like Peter Szerkes "A Course in Modern Mathematical Physics"

It's not a great book for directly learning the material, but I think it's good as something of an "checklist" of the material that you should learn.

The other must read if you are into numerical stuff is "Numerial Recipes for C++". It's a cookbook. One thing to note is that the text is great, but the code examples are *terrible*.

 

[Nabeshin]

The other thing is that there is a huge missing step in textbooks. There are textbooks for graduate students. There is "popular literature." There isn't much in between.

What exactly do you mean? What would you call undergraduate level books, if not 'something in between'?

 

[Karimspencer]

I suggest starting over with physics. Even revise some of the things that you already know about. Go through some of the physics books given above and start with really basic calculus or even go over all of algebra again for it'll help. Get a good understanding about the history of physics(Greek Philosophers to the modern researchers of today) Read some published books written physics and math professors. Take some tutoring by honor students in your class. Try getting a complete understanding of basic physics so you can go up the ladder with a great understanding of out universe.

 

[phinds]

I suggest starting over with physics. Even revise some of the things that you already know about. Go through some of the physics books given above and start with really basic calculus or even go over all of algebra again for it'll help. Get a good understanding about the history of physics(Greek Philosophers to the modern researchers of today) Read some published books written physics and math professors. Take some tutoring by honor students in your class. Try getting a complete understanding of basic physics so you can go up the ladder with a great understanding of out universe.

This is a really nice ideal scenario but it posits a degree of patience that I think is unrealistic. Much more reasonable would be to do what you suggest IN PARALLEL with learning new stuff to keep the juices flowing.

 

[Looh]

Wonderful, I was close to completing my answer to the thread when I accidently closed down the tab and lost all my text. A less elaborate answer will have to suffice, I'm sorry.

Depending on how quickly you want to jump into the math, or rather, I should say, if you want to AVOID jumping into the math too quickly but get a broad perspective on the subjects you name, I'd suggest you start out with the more accessible popularizations that are light on math.

I actually wouldn't mind learning maths - but I generally feel that the more advanced concepts are, I don't know, scary. However, I think that acquiring a general overview over the subjects is a pretty good idea. As twofish-quant wrote, it's pointless in trying to understand every subject to the fullest. My best bet would probably be to get an overview and then start digging in the subject I find most interesting.
As for the book you suggested, I'll definitely check it out. Hopefully I can find it in my local library. Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

Thank you for your answer.

Anyway, here's a book list:

Looks like a wonderful compilation, thanks! I'll see if I can get a hold of some of the books.

One bit of advance. Start with Newtonian mechanics. It's critical that you have a firm understanding how Newtonian mechanics works before doing anything else. One thing is that quantum mechanics and GR is in fact not more complicated then Newtonian mechanics. The difference is that people have "inituition" with Newtonian mechanics that doesn't exist in GR or QM.

Yes, I was thinking of starting with classic mechanics. I did have a book about it, but unfortunately I've lost it.

The easy thing to do is to enroll in the local university, become a physics major, and then go to graduate school. A lot of the knowledge that is there is "tacit knowledge" which isn't something that you can easily get by reading books. One knowledge is "knife skills". Something that's very important in being a chef is to be able to use a knife to very quickly chop vegetables. This is somethng that you just have to practice at. There are similar bits of knowledge in doing physics.

Yes, the best thing is probably to just enroll in a university. But there are some problems.
First, I'm not done with high school yet. And as such, I don't have enough grades to enroll. Secondly, there is no university in the city I live in. I'm not sure if I have the luxury of choosing, so I don't know where I might end up (I live in Sweden, by the way).

I was actually going to enroll for some courses now during the summer (distance), but I needed my final grades from high school so I couldn't do it.

The other must read if you are into numerical stuff is "Numerial Recipes for C++". It's a cookbook. One thing to note is that the text is great, but the code examples are *terrible*.

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?


Thank you all for the help! I really appreciate it.

 

[Karimspencer]

This is a really nice ideal scenario but it posits a degree of patience that I think is unrealistic. Much more reasonable would be to do what you suggest IN PARALLEL with learning new stuff to keep the juices flowing.

:) Well of course he is going to learn new stuff + the basics.

 

[BruceW]

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?

algorithms. Computers have the kind of processing power that is often useful. If you think about it, lots of physics research requires programs to be written. e.g. astronomical data, data from particle detecting equipment, data from most sophisticated equipment really. And then there's also the ability to run a model of some physical situation and see what happens, and maybe make predictions about what would happen in the real-life physical situation.

 

[kloptok]

Now I don't know how good you are in maths but I would suggest starting with Introductory Linear Algebra and Calculus, as every physics university student would. Sure you've learned some stuff in high school (=gymnasium?) but there's a LOT more to learn out there. Which takes me to my second piece of advice: patience and stubbornness! You will not learn physics in a couple of months or a year. It takes years of studying to get to the advanced topics you are interested in, string theory is something you usually don't begin to study until master's level at university or even later. And general relativity is also quite advanced, tensors are tricky and require a mathematical "maturity" as people call it. Although you could very well grasp the basics if you first study special relativity.

A normal physics bachelor's curriculum starts with about two years of basic mathematics and physics courses, the first year contains a lot of maths (linear algebra, single- and multivariable calculus, probability/statistics). After this you are ready to tackle quantum mechanics and relativity (actually special relativity is not that difficult and can be done with high school algebra, but you will understand it better the more physics and maths you know). So if you do not have the patience to go through the basics before diving into relativity and quantum physics, I would not suggest studying physics at university. However, from your recent posts it sounds like you have an interest in the things encountered along the way and are interested in maths and physics in a more general sense. Then physics might just be for you.

Brian Greene is quite good, but as with all popularizations things soon gets very loosely described and there is sometimes a tradeoff between accuracy and "understandability". I do not say that you should avoid these books, they are still a fun read, especially at your level, and can give you a feeling for the ideas involved and if you like them. But to understand the maths behind string theory you will have to study many years. There are some books by Hans-Uno Bengtsson which introduce a bit more mathematics which you might be able to find in your local library ("Kvarken och universum", "Bengtsson om ..."-serien) . I would recommend you to take a look at the science shelf there and see what you find, there are sometimes also university textbooks available.

By the way, I'm also from Sweden (the Hans-Uno Bengtsson reference was a bit of a giveaway I guess =P ). I'll happily give more advice if you want!

 

[phinds]

As for the book you suggested, I'll definitely check it out. Hopefully I can find it in my local library. Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

Yeah, I'd say Green is a good intro on string theory BUT I would caution you to put string theory at the bottom of your list. It MAY turnout to be the be-all and end-all, but right now it's been worked on by a LOT of very bright people for over 20 years and it really hasn't produced anything despite all the promise that was seen about 25 years ago. I recommend cosmology (including SR and GR) and quantum mechanics as being QUITE enough to bite off for a while.

I agree w/ kloptok about the need to be wary about the details in popularizations. Even Weinberg, for example, makes the EGREGIOUS mistake of referring to the big bang as a POINT when he really does know better. Also, be wary of INTERPRETATIONS. Quantum mechanics has several of them, each contradictory and yet each with its own covey of adherents.

BUT ... I still say that several such popularizations will give you a good broad picture and help you decide where you might want to focus your energies.

THere is some tension between what I just said and the very correct fact that you won't undersand much of any of it in detail without the math (which leads some people to insist that you HAVE to start with the math) ... BUT ... here's the real point: the math for some areas will appear more difficult than that for others, but that's a distraction. What is IMPORTANT is that you first figure out what you love to do and go there. If you do it that way, the degree of difficulty of the math will be irrelevant.

 

[Nabeshin]

Regarding reading Brian Greene, I agree more or less with what phinds has said above. Two points I think are worth making (or restating). The first is that a book like The Elegant Universe actually has some decent descriptions of established physics (chiefly relativity and quantum mechanics) for the first ~100 pages or so. So even though it's about string theory, you can learn these more fundamental pillars as well. Secondly, you really do have to caution against taking what is written in a book like this at face value. I suspect that if you were to just read this in a vacuum, you would assume from Greene's language that string theory is the only thing in theoretical physics that anyone is working on, that we're right around the corner from a breakthrough, and that everyone agrees this is the correct direction. Of course, none of these are really true. So while it's fine to read about these things, try not to lose context of what they are.

Another general note about popular science books is that if this is all you read, you have to resign yourself to taking a lot of things at face value. For example, you could 'understand' the expansion of the universe via the ants on the surface of an expanding balloon analogy. You might even be able to talk about some predictions and outcomes of this as it relates to our physical universe. But as far as why this is a somewhat accurate description of reality, essentially all you can say is 'because someone told me so'. It's not a terrible state of affairs though, it's one in which essentially you are not ignorant, but also not intelligent on the subject matter.

 

[Nano-Passion]

General relativity is a bit trickier. To understand how to come up with the basic equations, you can get there with a few months of work. Now to understand the full *consequences* of these equations is something no one does. What people usually do is to work with simplications of the full GR equations.

Can you elaborate on this statement.

 

[twofish-quant]

What exactly do you mean? What would you call undergraduate level books, if not 'something in between'?

Undergraduate level physics books typically assume the ability to do partial differential equations. For GR and cosmology, they are typically aimed at juniors and seniors.

The thing about popular books is that the usually assume zero mathematical ability. If you have someone that can do algebra, or better yet basic calculus, you can do lots of explanations that wouldn't otherwise be available.

This wouldn't be that much use for physics majors, but the target audience would be say a civil engineering major that is interested in general relativity.

 

[twofish-quant]

My best bet would probably be to get an overview and then start digging in the subject I find most interesting.

Something that you might be interested in galaxy formation, turbulence, statistical mechanics, and magnetic fields. Personally, I find those things more interesting than string theory.

Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

I'm actually pretty negative about string theory because we've dumped twenty years of effort into it, and gotten nada. The reason I'm more interested in galaxy formation is that it's likely that we'll know more about galaxy formation in 2015 than we do today. This isn't necessarily true for string theory.

String theory has some interesting mathematics, but there's very little useful physics.

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?

Templates. It turns out that you can write extremely efficient numerical code in C++. Also, a lot of physics code turn out to be huge CS projects with millions of lines of code.

Something that you might want look at is lattice gauge theory or numerical relativity.

 

[twofish-quant]

Can you elaborate on this statement.

Sure. You write the equations of GR, you get ten non-linear partial differential equations. No one fully understands the properties of those equations. What people do in practice is to take those PDE's and the make approximations and simplifications to get you something that you can calculate.

However, if you write those 10 equations in their full glory, there are some basic mathematical questions that are not answers. For example, can you have a wormhole or can you have a "realistic" naked singularity? No one really knows.

It turns out that GR is too complex to handle fully. What people do is to write approximations to actually solve problems. The simplest approximation is Newtonian gravity. If it turns out that this won't work, then you go for simple extensions.

The same turns out to be true for quantum mechanics. Except for the hydrogen atom, the equations are not fully solvable, so a lot of getting numbers involves making approximations.

 

[Feodalherren]

I don't know if anybody already mentioned it but Khan Academy is an excellent resource if you want to catch up on physics and/or mathematics.

You're pursing a noble goal. Although physics is far too wide for you to specialize in all of the mentioned fields, expertise in anyone of them should give you sufficient understanding to satisfy your curiosity (although the theoretical physicists specializing in relativity would sometimes argue that other physicists only THINK they understand relativity). Who knows, maybe you will be the one to finally unlock the secrets that bind the quantum and astronomical worlds together?
I wish you the best of luck on your road, it will be filled with many difficult challenges. Start training that logical part of your brain, physics = math.

 

[twofish-quant]

Although physics is far too wide for you to specialize in all of the mentioned fields, expertise in anyone of them should give you sufficient understanding to satisfy your curiosity (although the theoretical physicists specializing in relativity would sometimes argue that other physicists only THINK they understand relativity).

And by and large other physicists would agree. I just know enough general relativity to show that general relativity turns out to be unimportant in modelling supernova, and that's enough for me. It turns out that the amount of relativity that you have to know in order to do useful things in most fields of astrophysics (including black hole physics and cosmology) is pretty low.

Who knows, maybe you will be the one to finally unlock the secrets that bind the quantum and astronomical worlds together?

Something that you quickly learn is that there isn't one secret. There are thousands of secrets out there, and it's not hard to find a niche in which you can discover something useful. One thing that I'm trying to get the OP to avoid doing is to get so focused on string theory, than you lose sight of other "mysteries of the universe." (Such as the fact that we don't know how globular clusters, type II supernova, type Ia supernova, galaxies, or black jets work.)

The other thing is that "binding quantum physics and astrophysics" is "just an ordinary day in the office". If you do anything in astrophysics, then you'll constantly be thinking in terms of quantum mechanics.

I wish you the best of luck on your road, it will be filled with many difficult challenges. Start training that logical part of your brain, physics = math.

In fact, physics *isn't* math. Physics uses math, but it's not the same thing. A physicist is to a mathematician what a novelist is to a linguist.

 

[Feodalherren]

And by and large other physicists would agree. I just know enough general relativity to show that general relativity turns out to be unimportant in modelling supernova, and that's enough for me. It turns out that the amount of relativity that you have to know in order to do useful things in most fields of astrophysics (including black hole physics and cosmology) is pretty low.

Then you know much more than I do and I will take your word for it :).

Something that you quickly learn is that there isn't one secret. There are thousands of secrets out there, and it's not hard to find a niche in which you can discover something useful. One thing that I'm trying to get the OP to avoid doing is to get so focused on string theory, than you lose sight of other "mysteries of the universe." (Such as the fact that we don't know how globular clusters, type II supernova, type Ia supernova, galaxies, or black jets work.)

Aren't those the kinds of things that you bump into along the road anyway? People in general don't start out knowing what a black jet even is (I sure don't).

In fact, physics *isn't* math. Physics uses math, but it's not the same thing. A physicist is to a mathematician what a novelist is to a linguist.

What I was getting at was that you need to be an excellent linguist in order to be a good novelist. If you're not good at math you're going to be crippled physicist.

 

[chiro]

I'm actually pretty negative about string theory because we've dumped twenty years of effort into it, and gotten nada. The reason I'm more interested in galaxy formation is that it's likely that we'll know more about galaxy formation in 2015 than we do today. This isn't necessarily true for string theory.

You can knock things like string theory, but IMO I see string theory as a very important experiment in terms of human endeavors.

The primary reason is that these kinds of approaches in some respects take a deductive viewpoint rather than an inductive viewpoint, where instead of trying to make inductive and extrapolative statements about something, you start from something that is a lot more general and work backwards.

I think that we need both approaches: we need inductive approaches and paradigms based on looking at very specific things, but we also need the deductive approaches which are really complex, taxing on the minds of the theorists, with no gaurantee or real promise of producing anything that brings anything useful for a long time to come, but still in all respects, something that moves towards the same goal.

The benefits of deductive approaches are at least two-fold.

The first is that the deductive approach has a logical impetus as well as an explanatory mechanism for choosing one particular set of constraints over another and this is absolutely critical when it comes to understanding.

Having a way to give some kind of logical argument over why you prefer one set of constraints over another, whether its geometrically, algebraically, or even materially motivated is something that should not be overlooked.

The second reason is that it forces people really to stretch their minds and be able to deal with systems of increasingly higher-complexity so that people can train themselves to see the kinds of context that they would not see if they tried to base all reasoning on pure deductive and extrapolative approaches.

Taking such an abstract view will tend to generate results and a kind of contextual understanding that will be bound to produce new mathematics, and as a consequence new ways to look at any general abstract system.

The context generated from the attempt of trying to understand the most general allowable form of a system in comparison to one or two specific realizations is going to be much richer in understanding, even if it takes a century to make sense of it all and I'm afraid some physicists don't get this.

For these reasons, I personally think that both approaches (the general most abstract highly mathematically driven view, and the specific experimental view) are required, but I'd go further and say that the deductive viewpoint offers a lot more in the long run than the highly narrow specific viewpoint does primarily for its explanatory power alone.

 

[twofish-quant]

Aren't those the kinds of things that you bump into along the road anyway? People in general don't start out knowing what a black jet even is (I sure don't).

Sure. This is one problem. The more that you know, the more you know that the less you know. After a few years, you give up trying to understand everything, and you are lucky if you understand anything.

What I was getting at was that you need to be an excellent linguist in order to be a good novelist. If you're not good at math you're going to be crippled physicist.

1) You really don't. The skills that linguists have, and the skills that novelists have are different. For example, mathematicians live in a world that is very strongly proof-based. Physicists usually don't care about proofs.

2) There are different levels of good. If you take an average physicist, his math skills are likely to be much. much better than those of the general population, but one thing that you'll quickly find is if you go into physics is that you'll be coming into contact with people whose math skills are blindingly better than anything you have.

For most physics, it's necessary to be proficient at linear algebra and PDE's.

 

[twofish-quant]

The primary reason is that these kinds of approaches in some respects take a deductive viewpoint rather than an inductive viewpoint, where instead of trying to make inductive and extrapolative statements about something, you start from something that is a lot more general and work backwards.

The trouble is that there are a lot of possible principles to start off with, and if it turns out that the universe just doesn't work according to string theory, then it just doesn't work according to string theory. Personally, if you had someone that was interested in fundamental physics, I'd point him in the directions of the various approaches that are different than string theory. Loop quantum gravity or entropic gravity for example.

we also need the deductive approaches which are really complex, taxing on the minds of the theorists, with no gurantee or real promise of producing anything that brings anything useful for a long time to come, but still in all respects, something that moves towards the same goal.

No problem with that, but how many decades do you want to work on something before looking for another path? If it turns out that the universe just doesn't work according to string theory, then it doesn't matter how much effort you put in, it's not going to work.

The context generated from the attempt of trying to understand the most general allowable form of a system in comparison to one or two specific realizations is going to be much richer in understanding, even if it takes a century to make sense of it all and I'm afraid some physicists don't get this.

Fine, but why string theory as opposed to say lattice gauge theory or high temperature superconductivity? Also if you want general, there is a *lot* of interesting work in complex systems and statistical mechanics, that's not only general but also useful.

If you want to understand *general* systems, I think you are much better off doing something like catastrophe theory or information theory. Also sometimes, you can stumble onto something without realizing it. For example, there are some very fundamental connections between general relativity and C++ classes (i.e. people talk about covariant functions). It turns out that there is a connection because of category theory, which I stumbled onto. Something that I've been thinking about is how to put some "meat" (i.e. metric space) into category theory. If you look at category theory, you see lots of arrows, but I've been thinking about how to put some flesh onto the skeleton.

And if you want to get really general, you might want to study like foreign exchange options. It's possible to do gauge theory on those.

For these reasons, I personally think that both approaches (the general most abstract highly mathematically driven view, and the specific experimental view) are required, but I'd go further and say that the deductive viewpoint offers a lot more in the long run than the highly narrow specific viewpoint does primarily for its explanatory power alone.

I don't necessarily disagree, but I don't see the connection with string theory. Connecting "general deductive view" with "string theory" would make sense only if string theory was the only game in town, and it's not.

 

[chiro]

String theory is one framework of doing deductive science from very abstract foundations. I concede that it's not the only game town, but that point wasn't brought up and I would defend any serious deductive framework endeavor that has enough support.

I also agree that information theory and statistical mechanics are excellent ways to study the system, and the idea of using liquidation in economic terms to model physical interactions would be a great avenue to pursue since the analog makes some kind of sense and also that there is actually a lot of real world data that can be analyzed.

Even if people don't see results in their lifetime, i don't think it's worth not pursuing. This happens all the time anyway where people think they will solve it all and end up realizing that it's probably a little early after a lifetime of dedication. Doesn't mean its all wasted though.

 

[chiro]

The trouble is that there are a lot of possible principles to start off with, and if it turns out that the universe just doesn't work according to string theory, then it just doesn't work according to string theory. Personally, if you had someone that was interested in fundamental physics, I'd point him in the directions of the various approaches that are different than string theory. Loop quantum gravity or entropic gravity for example.

Well that's the thing about deductive thinking: figuring out the right principles.

If we just ignore actual physics for a second we know that it would be sensible to rule out inconsistent illogical systems, systems that have divergence, blow-up and instability, and systems that don't settle (converge to some unrecoverable static state).

Doing these alone greatly reduces the scope and allows people to develop some context in both microscopic and macroscopic levels.

Now on top of this you add more specific examples like entropy constraints and evolution constraints of various kinds. This again greatly reduces the scope again.

Now the mathematical ones above irrespective of the domain are very easy to explain: consistency is required so that the whole description is non-ambigous and mathematically proper. You don't have to go as far as set theory axioms, but just enough to show that its a proper system definition.

The stability makes sure things don't go crazy: that's easy to understand. The staticity condition means that things don't 'get stuck': that's easy to understand. Divergence is easy to understand, not only in terms of stability but also for the most important thing in physics which is measurability.

These things are easy to understand by anyone even if they have never done a physics or maths course in their life! You can explain it to them using analogues and it would make sense to them.

 

[twofish-quant]

I concede that it's not the only game town, but that point wasn't brought up and I would defend any serious deductive framework endeavor that has enough support.

Sure, and after 20 years of trying the experimental support of string theory is ?

Even if people don't see results in their lifetime, i don't think it's worth not pursuing.

Ph.D. committees want you to produce something after five to seven years. You may not (and you aren't expected) to come up with the answer to life, the universe, and everything, but it's a bad sign if you come up with nothing useful.

Even figuring out that it's the wrong approach is useful. One problem I have with string theory is that it's difficult to know when you are even wrong. Working on something for two decades and then having it be totally obvious that it was the wrong approach and that it's time to work on something else would be useful, but it doesn't seem to me that string theory has even gotten to that point...

This happens all the time anyway where people think they will solve it all and end up realizing that it's probably a little early after a lifetime of dedication. Doesn't mean its all wasted though.

You aren't going to solve everything in a lifetime, but I think it's reasonable to ask after X years if you've been able to solve *anything*.

 

[twofish-quant]

If we just ignore actual physics for a second we know that it would be sensible to rule out inconsistent illogical systems, systems that have divergence, blow-up and instability, and systems that don't settle (converge to some unrecoverable static state).

No we don't know this. We do know that the Rules of Quantum Mechanics follow a different set of logical rules than classical aristolean logic, and there are perfectly good logical systems that allow for inconsistent statements.

As far as divergence, blow-up, and instability, there's no reason to automatically assume that the laws of physics at extremely high energy are stable and non-divergent.

Now the mathematical ones above irrespective of the domain are very easy to explain: consistency is required so that the whole description is non-ambigous and mathematically proper. You don't have to go as far as set theory axioms, but just enough to show that its a proper system definition.

On the other hand, we have been able to get places with theories that are mathematically bad. Quantum field theory is mathematically inconsistent, but it's inconsistent in ways that we can "work around" at energies we are interested in.

These things are easy to understand by anyone even if they have never done a physics or maths course in their life! You can explain it to them using analogues and it would make sense to them.

Which is precisely why I think they are suspect.

Essentially what happens is that people go out and see their own little tiny bit of the universe and then assume that everything has to be a certain way. I've seen really weird stuff, so when someone starts putting constraints because the universe has to act in a certain way, I'm suspicious of that.

One reason that I think physics is "hard" is not so much that the things that we are studying are difficult to understand, but it's because our senses are limited. Here is an example. Take a cup of tea, and try to explain what it looks like to someone that has been blind since birth. Try to explain "red" and "yellow" and describe the color of the liquid. It's hard. It's going to take some effort to "see red" and if someone who is blind just uses the concepts that they are familiar with, they are going see something, but they are also going to be missing other things.

 

[chiro]

Sure, and after 20 years of trying the experimental support of string theory is ?

It's not going to be a total solution, but one that complements more narrow approaches and the experimental evidence.

You can't just expect a project or endeavor of that magnitude to pay off in the way that one of more modest means would: it's not a fair comparison.

Ph.D. committees want you to produce something after five to seven years. You may not (and you aren't expected) to come up with the answer to life, the universe, and everything, but it's a bad sign if you come up with nothing useful.

This is probably one contributing factor to why things are the way they are. I'm not saying for many applications it's bad, but sometimes you need to know the times when to not follow the rules.

Also the deductive way of doing things doesn't solve the whole unified thing even if a lot of the principles are worked out, because it's at a different level than that of the more specific approaches. The specifics are in a completely different context which tells us things about specific, highly-constrained things.

As you well know, we have GR but we still need supercomputers to be able to get decent results from a simulation: this doesn't mean though that it's irrelevant in terms of getting any kind of context though.

Even figuring out that it's the wrong approach is useful. One problem I have with string theory is that it's difficult to know when you are even wrong. Working on something for two decades and then having it be totally obvious that it was the wrong approach and that it's time to work on something else would be useful, but it doesn't seem to me that string theory has even gotten to that point...

You aren't going to solve everything in a lifetime, but I think it's reasonable to ask after X years if you've been able to solve *anything*.

But this is what I don't get: you don't want to take a risk?

Everything is a risk. Typically what most people want to do if they are brave enough to take risks is to take calculated ones, but even then it's still going to be risk especially when it comes to nature.

Our mathematics that we have is really not one that is suited for analysis of systems with many degrees of freedom or many interdependencies.

We have the techniques of non-euclidean geometry which allow one to look at non-orthogonal systems which model such dependence, but most people can not really grasp things more than say 30 variables.

We are talking about systems with millions upon millions of degrees of freedom, and we are trying to apply techniques that are best suited for hundreds, not many millions or billions.

I agree that we won't solve it all in a life-time, but even logically, the idea of trying to use a hammer instead of a power-saw doesn't make sense.

The techniques are going to be more complicated, and they will be non-intuitive when they are first created. They will like everything else, be refined and polished so that they do become more intuitive than they were before.

And the argument for even thinking for going in this direction, let alone actually going there is based on this idea that we can not use existing paradigms that were designed for a different kinds of problem (low number of degrees of freedom) to be used effectively and optimally to look at a different kinds of problem (high degrees of freedom).

It's going to be really hard and horrible, and it probably won't be done in anyone's single life-time, but the impetus behind it is rather simple: we are trying to understand something that needs an appropriate framework: do we try and adapt the system to our framework, or the framework to our system?

The people that work on these high-level approaches have my congratulations despite the fact that nobody really understands anything well enough to really handle it, because they are likely to be the ones that are taking a chance that people two or three or more generations later will benefit, and this is an extremely hard thing for any person without exception to do.

 

[chiro]

No we don't know this. We do know that the Rules of Quantum Mechanics follow a different set of logical rules than classical aristolean logic, and there are perfectly good logical systems that allow for inconsistent statements.

Well in order for something to be 'measureable' it has to be finite and thus not diverge. Physics is based on the principle that things be measureable.

It doesn't have to follow classical logics in any way: it just has to be measurable.

As far as divergence, blow-up, and instability, there's no reason to automatically assume that the laws of physics at extremely high energy are stable and non-divergent.

True, but we have a lot of evidence for it both theoretically and experimentally, although I agree with you that we haven't had particle accelerators for that long (but we can look at the external universe and supernovae, and cosmic rays).

The theoretical evidence can be found in theorems to do with black holes (and yes I realize it's speculative) in the form of evaporating black-holes, and results about how black-holes may grow (again speculative).

In the low-energy situations, we have a lot of data to deal with.

We also have thermodynamics which deals with entropy, and shows us how hard it is to generate situations where we get lots of energy.

These indicators give at least an initial premise behind this idea.

If the theory is wrong, then like every other theory it needs to be changed. But given theoretical speculation and experimental results (especially with thermodynamics), it does have a little support at least.

On the other hand, we have been able to get places with theories that are mathematically bad. Quantum field theory is mathematically inconsistent, but it's inconsistent in ways that we can "work around" at energies we are interested in.

You can have theories about physics that are non-deterministic and even non-continuous where the above constraints are still respected.

These constraints do not require determinism, nor do they require some kind of continuous aspect. You can represent systems primarily using number theory to model the kind of discrete behaviour where things jump or can't be modeled by continuous representations and analyzed effectively through continuous analysis (i.e. the integral and differential calculus), and you can use statistics to model things that are not in the context of a deterministic fashion.

You can also incorporate non-locality if you want to as well.

Which is precisely why I think they are suspect.

Essentially what happens is that people go out and see their own little tiny bit of the universe and then assume that everything has to be a certain way. I've seen really weird stuff, so when someone starts putting constraints because the universe has to act in a certain way, I'm suspicious of that.

One reason that I think physics is "hard" is not so much that the things that we are studying are difficult to understand, but it's because our senses are limited. Here is an example. Take a cup of tea, and try to explain what it looks like to someone that has been blind since birth. Try to explain "red" and "yellow" and describe the color of the liquid. It's hard. It's going to take some effort to "see red" and if someone who is blind just uses the concepts that they are familiar with, they are going see something, but they are also going to be missing other things.

Well this is what mathematics has primarily become: it has become a way for us blind people to see in a way that we never can with our five senses.

Mathematics has done this with every subfield including logic, algebra, probability, calculus, and so on. Probability is the most striking area because time and time again, the math makes it intuitive, but the senses always mislead us even for the most gifted mathematicians you try and use it like D'Alembert.

Mathematics also gives us a gateway to the uncountable. Through mathematics we can understand when an infinite series even converges, how to make sense of an infinite-vector space and a basis for that space.

No amount of sensory can give us this insight, and by ignoring this approach, we are always going to rely on the intuition afforded to us by our five senses, or a product thereof.

Physics is about things that can be measured: if it's not by our tongues, ears, eyes, skin, or nose, it's be the lab equipment that we design to measure things that we can't do by ourselves.

But this sense is in no way a contender with mathematics, because of a couple of reasons.

The first reason is that it is a language that everyone can agree on. This is one of the most important aspects of it because this one fact makes it possible for more than one person to study the same thing and agree on what a particular construction says and how to interpret it.

The second thing is that explores things that may potentially exist even though we may never measure them.

The reason this is important is because if we only consider the very narrow thing that we are measuring, in relative isolation with all the other stuff that is going on, then it means that again we have to extrapolate from that one point the rest of it all even when the stuff we are extrapolating from may not have actually been realized itself.

This is the thing: you are saying that we should not use procedures that are too wild like the ones proposed, but yet physics and physicists try to build models to predict what has not been already made realizable. We don't try and predict stuff that has been already realized, we try and predict stuff that has not.

Mathematics in a sense has a platonic aspect where it doesn't necessarily correspond to reality, but then again the stuff that we predict doesn't either until it becomes reality.

We can't really make sense of infinity, but what we do is we use math as well as things like art and other mediums to get one particular very narrow context of it.

You can't tell a blind man what red and yellow is and I agree with you. But what you can do is find a way to utilize what they can sense to try and build the best bridge possible to reach the best description possible, even though they can not see it.

For example, I can get a blind person and I can construct geometric figures that have solid edges. This can be used to build the idea of spatiality and geometry. From this I can go further and introduce these kinds of examples to build a language.

I won't probably be able to ever get to the clarity of yellow or red, but it doesn't mean I can't use what I have to make an inwards progression to describing it by building the best bridge to utilize the sensory capacity that already exists.

And this is precisely what we are doing with mathematics every single day, with countless numbers of mathematicians, and contributing scientists and engineers, who are creating a bridge to this higher sensory capacity.

 

[Feodalherren]

1) You really don't. The skills that linguists have, and the skills that novelists have are different. For example, mathematicians live in a world that is very strongly proof-based. Physicists usually don't care about proofs.

2) There are different levels of good. If you take an average physicist, his math skills are likely to be much. much better than those of the general population, but one thing that you'll quickly find is if you go into physics is that you'll be coming into contact with people whose math skills are blindingly better than anything you have.

For most physics, it's necessary to be proficient at linear algebra and PDE's.

I really don't understand how you can say that. I have only done the very basic Newtonian physics and to me it seemed to be more math than anything. Our tests only consisted of a couple of questions that we would manipulate in a thousand and one ways with f=ma what not.
Physicists may not be on equal footing with mathematicians on number theory but they sure as hell can manipulate equations and understand the mathematical language just as well.

 

[Nano-Passion]

I really don't understand how you can say that. I have only done the very basic Newtonian physics and to me it seemed to be more math than anything. Our tests only consisted of a couple of questions that we would manipulate in a thousand and one ways with f=ma what not.
Physicists may not be on equal footing with mathematicians on number theory but they sure as hell can manipulate equations and understand the mathematical language just as well.

You might not see it now, but there is a difference.

Physics requires a type of problem-solving and critical thinking that has little part to do with mathematics. We use mathematics yes. And yes it is our language. However, math is still very different than physics and vice-versa.

In mathematics, you have one way to progress knowledge and you can be certain that you are right given a proof.

In physics however, nature doesn't care about pretty manipulations. It is and just is. There are many ways to come to a conclusion and there are also just as many ways that they are completely wrong.

In math, we model the whole discipline among some common accepted "truths", however arbitrary they are, such as 1+1 = 2 or that you can draw a line between two points.

In physics, we model the whole discipline around how nature acts, not how we want it to act or what is a common accepted "truth." In fact, revolutions in physics happen by debunking these "truths."

 

[twofish-quant]

I really don't understand how you can say that. I have only done the very basic Newtonian physics and to me it seemed to be more math than anything.

You are using math tools, but you aren't creating those tools.

Physicists may not be on equal footing with mathematicians on number theory but they sure as hell can manipulate equations and understand the mathematical language just as well.

Different set of skills. Some mathematicians can be surprisingly bad at simple equation manipulation. The other thing is that you are doing very, very basic stuff, mathematically speaking. Once you get into really complicated stuff, then you'll likely will find people that are just much better at math than you are.

 

[twofish-quant]

You can't just expect a project or endeavor of that magnitude to pay off in the way that one of more modest means would: it's not a fair comparison.

I think you can. If you are on the right track, you should be able to find something that suggests that you are on the right track.

But this is what I don't get: you don't want to take a risk?

I want to take intelligent risks. If you are digging for gold, it makes more sense to dig somewhere that someone hasn't dug before.

Our mathematics that we have is really not one that is suited for analysis of systems with many degrees of freedom or many interdependencies.

Then develop new math. One thing about math is that there are all sorts of mathematical techniques that are useful in analysis with huge numbers of degrees of freedom, but physicists typically get very little training in those techniques.

We are talking about systems with millions upon millions of degrees of freedom, and we are trying to apply techniques that are best suited for hundreds, not many millions or billions.

If often happens that if you increase the degrees of freedom, that it vastly simplifies the problem. If you have an extremely large number of degrees of freedom, then often the system will very quickly go to equilibrium in some fixed point. For example, if you are trading Euros and Dollars, you will go insane trying to track every transaction, but because there are so many transactions, the system very quickly goes to equilibrium and the math to describe it turns out to be quite simple. Now if you start trading dollars and some third world currency, then the transactions are low, and the math gets more complex.

And the argument for even thinking for going in this direction, let alone actually going there is based on this idea that we can not use existing paradigms that were designed for a different kinds of problem (low number of degrees of freedom) to be used effectively and optimally to look at a different kinds of problem (high degrees of freedom).

A lot of physics involves systems with extremely high degrees of freedom. You can model those. The first thing that you do is to try to reduce the number of degrees of freedom by figuring what processes are important and which ones are not. You can also do time scale separations.

The people that work on these high-level approaches have my congratulations despite the fact that nobody really understands anything well enough to really handle it, because they are likely to be the ones that are taking a chance that people two or three or more generations later will benefit, and this is an extremely hard thing for any person without exception to do.

I think the emperor has no clothes. It's not that I'm against research in string theory. It's that I think we have enough people working on string theory, and that if we have someone new, then it might be a good idea to get them to work on something that has nothing to do with string theory.

 

[twofish-quant]

Well in order for something to be 'measureable' it has to be finite and thus not diverge. Physics is based on the principle that things be measureable.

You can do math with infinities. There are hyperreals, surreals, and transinfinite numbers. Also even with physics as it is, it's impossible to determine the state of a quantum system with a measurement.

The theoretical evidence can be found in theorems to do with black holes (and yes I realize it's speculative) in the form of evaporating black-holes, and results about how black-holes may grow (again speculative).

Ummmmm... You are trying to justify a theoretical results with another theoretical result.

This is the thing: you are saying that we should not use procedures that are too wild like the ones proposed, but yet physics and physicists try to build models to predict what has not been already made realizable. We don't try and predict stuff that has been already realized, we try and predict stuff that has not.

Who's we? I spent seven years trying (unsuccessfully) to predict that supernova exist. They obviously do, but we don't know how they work. There are tons of things out there that exist that we don't understand. We have no freaking clue how turbulence works.

Take a tube. Push water through it. If you push it fast enough, it will suddenly go turbulent at some critical Reynold's number. If you can tell me what they number is without actually pushing water through a tube, then that's worth a Nobel prize.

I won't probably be able to ever get to the clarity of yellow or red, but it doesn't mean I can't use what I have to make an inwards progression to describing it by building the best bridge to utilize the sensory capacity that already exists.

I think you can. A lot of physics involves training the "mind's eye" to see things that people couldn't normally see.

And this is precisely what we are doing with mathematics every single day, with countless numbers of mathematicians, and contributing scientists and engineers, who are creating a bridge to this higher sensory capacity.

But the problem I see is that people then use that capability to assume simplicity when this might not exist. For example, if I were to describe a circle to a blind person, this would be rather easy. Now if I were to describe the shape of Cheasapeake Bay to a blind person, this would be hard.

The trouble is that because it's easy to describe circles, people assume that the universe is made of circles when when we look at things, we often see a lot of complexity.

 

[deRham]

It's not that I'm against research in string theory. It's that I think we have enough people working on string theory, and that if we have someone new, then it might be a good idea to get them to work on something that has nothing to do with string theory.

As an outsider to this discussion, I'm wondering if someone can tell me why string theory does have so much activity. Perhaps it is experimentally unfounded, though I would hope that there are people who found the mathematics of an established, successful (experimentally, and theoretically pretty sound) theory of physics to strongly suggest certain string theory approaches.

 

[deRham]

I'm afraid someone will tell me "there have been 6000 threads on this topic" and start getting cranky ... I personally think this topic can't have particularly easy answers if it's still so hotly debated, so I'd be interested at least to be pointed to what some opine to be good discussions of it.

 

[Nano-Passion]

As an outsider to this discussion, I'm wondering if someone can tell me why string theory does have so much activity. Perhaps it is experimentally unfounded, though I would hope that there are people who found the mathematics of an established, successful (experimentally, and theoretically pretty sound) theory of physics to strongly suggest certain string theory approaches.

Active compared to what? I'm no expert so I'll just paraphrase what I've picked up from others.

1) String theory is really beautiful to a lot of folks.
2) String theory had a solid approach to unifying the fundamental forces, and at one point, it was the only viable one. Any further detail is beyond my scope of knowledge though.

 

[chill_factor]

I really don't understand how you can say that. I have only done the very basic Newtonian physics and to me it seemed to be more math than anything. Our tests only consisted of a couple of questions that we would manipulate in a thousand and one ways with f=ma what not.
Physicists may not be on equal footing with mathematicians on number theory but they sure as hell can manipulate equations and understand the mathematical language just as well.

What's F=ma? Adding, subtracting, multiplying, and dividing. Almost all the math in your general physics class, you've learned in 5th grade. That's just one equation, but applied in different ways.

Do you call doing different ways of adding, subtracting, multiplying and dividing "hard math"?

That's called arithmetic. Math itself is based on proofs.

 

[xdrgnh]

Sure. You write the equations of GR, you get ten non-linear partial differential equations. No one fully understands the properties of those equations. What people do in practice is to take those PDE's and the make approximations and simplifications to get you something that you can calculate.

However, if you write those 10 equations in their full glory, there are some basic mathematical questions that are not answers. For example, can you have a wormhole or can you have a "realistic" naked singularity? No one really knows.

It turns out that GR is too complex to handle fully. What people do is to write approximations to actually solve problems. The simplest approximation is Newtonian gravity. If it turns out that this won't work, then you go for simple extensions.

The same turns out to be true for quantum mechanics. Except for the hydrogen atom, the equations are not fully solvable, so a lot of getting numbers involves making approximations.

If someone could come up with actual solutions to those 10 partial differential equations would it be a big deal?. Or does the numerical solutions give enough detail that actually analytically solving them wouldn't give us any new information?

 

[Nabeshin]

If someone could come up with actual solutions to those 10 partial differential equations would it be a big deal?. Or does the numerical solutions give enough detail that actually analytically solving them wouldn't give us any new information?

It certainly would be a big deal, but it's also almost certainly impossible (I don't know of a proof of the impossibility of analytical solutions though, so I can't say it's certainly impossible). Numerical simulations take months and months, and depending on the precision required can go for much longer than that. Even after having the simulations, you have to put a non-negligible amount of effort into extracting the physically relevant physics from the numerical effects causing error and anomalies in your simulation.