Gravity

[tommac]

Well to take some of the great advice that I have recieved from this board.

I am considering focussing my research efforts on one topic.
The topic I have chose is gravity. So here comes my question. If there was an undergrad degree in gravity ignoring the core liberal arts stuff, what would the courses look like?

In other words if I wanted to start to study gravity what are the topics I need to study and what is the recommended order.

Also what are the topics that allow me to graduate?

[Tim Thompson]

If there was an undergrad degree in gravity ignoring the core liberal arts stuff, what would the courses look like?

It would look like a B.S. degree in physics, with additional courses in general relativity (because gravity is general relativity) & astrophysics (because this is the primary practical application of gravity). But in fact, you would need an undergraduate degree in physics, and a graduate degree in gravity. At Cal State LA we had only one course in general relativity.

A B.S. Degree in Astrophysics from UCLA probably looks more to the point than a general physics degree (which is what I have). But they don't have specific courses in general relativity. Rather, GR shows up in the various other courses.

One of the best places to specifically study gravity might be Caltech, where they do have a graduate course in general relativity, and another in gravitational radiation.

[Amber Robot]

When I was at University of Michigan they did have an undergraduate course in Gravitational Physics. The professor was quite good, though his name escapes me at the moment. I actually understood tensors. At least for a month or so.

[alainprice]

Surprisingly, Einstein's own "Relativity" is a great start. It's a lot of thought without much math that lays the basic concepts for Lorentz transforms in Special Relativity and the basics of General Relativity.

Available for free on a few sites, www.bartleby.com being one of them.

[astromark]

The first requirement for understanding what things you should equip yourself with for the undertaking of understanding the laws of, and the mechanics of... GRAVITY, would be a generous proportion of 'COMMON SENSE' Understanding that as I have little understanding of higher mathematics am myself disqualified...Good luck to you my friend. Experience has taught me that all the education and diplomas avail little to understanding. Nobody likes a know all.
Mark.

[Neverfly]

Nobody likes a know all.
Mark.

SHOOT!
People should adore me then...

I don't know anything!

Yet, I seem to inspire the opposite effect...


But then, this may be because knowing that you know nothing is considered wisdom...

Aww screw it. I just hurt my brain...

[astromark]

No. Neverfly., as I see it, your brain is fine.

Tommac... I am honestly attempting to advise you not to narrow your research efforts onto a single subject. A broad understanding of all is a much better goal than a narrow subject study case.
The subject 'GRAVITY' is entwined into most of astrophysics. Astronomy has many important areas of understanding. Understanding gravity is a huge ask.

[Michael Noonan]

No. Neverfly., as I see it, your brain is fine.

Tommac... I am honestly attempting to advise you not to narrow your research efforts onto a single subject. A broad understanding of all is a much better goal than a narrow subject study case.
The subject 'GRAVITY' is entwined into most of astrophysics. Astronomy has many important areas of understanding. Understanding gravity is a huge ask.

Understanding gravity is definitely high on the what we would like to know more about list along with time and consciousness and other very high order things. On a look at what questions you have been asking it is a great choice.

Understanding gravity is a huge ask, astromark is spot on with that and someone is going to have to do it someday. There is so much choice.

All the very best to you Tommac in your studies and don't forget BAUT when you discover all the answers, cheers

[tommac]

I mean I would like to skip all of the quantum stuff ... or any part of the classes that are not relevant to gravity.

It would look like a B.S. degree in physics, with additional courses in general relativity (because gravity is general relativity) & astrophysics (because this is the primary practical application of gravity). But in fact, you would need an undergraduate degree in physics, and a graduate degree in gravity. At Cal State LA we had only one course in general relativity.

A B.S. Degree in Astrophysics from UCLA probably looks more to the point than a general physics degree (which is what I have). But they don't have specific courses in general relativity. Rather, GR shows up in the various other courses.

One of the best places to specifically study gravity might be Caltech, where they do have a graduate course in general relativity, and another in gravitational radiation.

[tommac]

I am not looking for a degree ...

What I am looking for is a list of 20 topics or so that would be the best gravity related topics. I will then start to read papers and research each of these topics and treat it like I was going to school for it ( I am kind of against formal education as I feel it is too money driven ).

I can work on my own and study ( don't worry I will still stick around with questions ). But I want to learn everything about gravity that I can. So again I am asking all of you what is a list of all gravity related topics that I can use as a checklist for my study.

[NEOWatcher]

What I am looking for is a list of 20 topics or so that would be the best gravity related topics....

I would doubt you could narrow it down that far. Maybe you can pick out the topics you want, but, watch out, they may be interrelated.

The other issue I can see is what they consider prerequisites. You may have to follow a tree back to see what background information you may need to understand the topic at hand. I haven't scoured the links to see if they mention pre-reqs. Maybe somebody here can help you outline this.

... I will then start to read papers and research each of these topics and treat it like I was going to school for it ( I am kind of against formal education as I feel it is too money driven )...

While it may be money driven, I do think that the course studies have evolved to a program that does work. So; while you may be able to self study, I think you should pay attention to some of the paths that they provide.

[cosmocrazy]

Well to take some of the great advice that I have received from this board.

I am considering focusing my research efforts on one topic.
The topic I have chose is gravity. So here comes my question. If there was an undergrad degree in gravity ignoring the core liberal arts stuff, what would the courses look like?

In other words if I wanted to start to study gravity what are the topics I need to study and what is the recommended order.

Also what are the topics that allow me to graduate?

Nice to see you are taking note from many of the very intelligent folks on this forum! I think you are choosing a good subject to study. I will see what turns up on the web, i would appreciate any information or links you come across too. Good luck m8

[tommac]

Well maybe the top 20 gravity subjects. I will work on the pre-requisites myself.

I would doubt you could narrow it down that far. Maybe you can pick out the topics you want, but, watch out, they may be interrelated.

The other issue I can see is what they consider prerequisites. You may have to follow a tree back to see what background information you may need to understand the topic at hand. I haven't scoured the links to see if they mention pre-reqs. Maybe somebody here can help you outline this.


While it may be money driven, I do think that the course studies have evolved to a program that does work. So; while you may be able to self study, I think you should pay attention to some of the paths that they provide.

[Tim Thompson]

I mean I would like to skip all of the quantum stuff ... or any part of the classes that are not relevant to gravity.

This only works in popular imagination. You can't just pick some part of physics, like gravity, and study it all by itself, as if the rest of physics does not even exist. That would be a complete waste of effort, and contrary to your intuition on the matter, you would not learn about gravity as much as you think. Gravity exists in the context of physics. So you know gravity, but never study thermodynamics. So you don't know that a collapsing gas cloud forming stars has to simultaneously obey the laws of gravity and the laws of thermodynamics, and you wind up not knowing what you are doing despite your knowledge of gravity. Remember the title of Tolman's book Relativity, Thermodynamics and Gravity. Tolman realized that the universe has to obey the laws of physics, all of them at once. He laid the theoretical basis for the later prediction of the later observed CMB. You simply cannot pick & choose which part of physics you want to study. It doesn't work.

[John Mendenhall]

I am not looking for a degree ...

Mistake. If you're going to forth the effort, make it count. Go for the degree.

Ask any systems analyst with over 10 years experience. Put your intellectual effort into what will pay off the most in the long term. That's why we use and program for Windows (retch), despite its shortcomings, and why there are still COBOL (shudder) programmers, and why object oriented programming (shiver) is so pursued.

Take the math. Be very introspective about how you are doing. You need A's for what you want. If you aren't doing that well in a course, bail. Try again later.

Keep in mind that physics is a lot more fun than computers. Good luck, and remember that luck favors the well prepared.

[tommac]

Dude I am way to old to actually take this stuff seriously ... I do this just for the enjoyment of it. There is no way I would sign up for school and if I did I would do something within my field but I think i have even past the point where I dont have enough years left in my career to have it pay off more than the cost of the degree.

Mistake. If you're going to forth the effort, make it count. Go for the degree.

Ask any systems analyst with over 10 years experience. Put your intellectual effort into what will pay off the most in the long term. That's why we use and program for Windows (retch), despite its shortcomings, and why there are still COBOL (shudder) programmers, and why object oriented programming (shiver) is so pursued.

Take the math. Be very introspective about how you are doing. You need A's for what you want. If you aren't doing that well in a course, bail. Try again later.

Keep in mind that physics is a lot more fun than computers. Good luck, and remember that luck favors the well prepared.

[tommac]

I am saying I will learn all of that other stuff too ... but only where it pertains to gravity. I wont ignore the other fields but really just focus on the gravity based ones.

This only works in popular imagination. You can't just pick some part of physics, like gravity, and study it all by itself, as if the rest of physics does not even exist. That would be a complete waste of effort, and contrary to your intuition on the matter, you would not learn about gravity as much as you think. Gravity exists in the context of physics. So you know gravity, but never study thermodynamics. So you don't know that a collapsing gas cloud forming stars has to simultaneously obey the laws of gravity and the laws of thermodynamics, and you wind up not knowing what you are doing despite your knowledge of gravity. Remember the title of Tolman's book Relativity, Thermodynamics and Gravity. Tolman realized that the universe has to obey the laws of physics, all of them at once. He laid the theoretical basis for the later prediction of the later observed CMB. You simply cannot pick & choose which part of physics you want to study. It doesn't work.

[astromark]

It is apparent that your understanding is as good as any ones... Its just perhaps that you express yourself differently. Scrolling through the many postings soon shows your quest for knowledge. In a related thread (they all are.)You ask of a singlarity... all gravity related... Tommac. Do not stop asking questions for that is the only way your understanding grows more complete. BUT, do remember that this quest for knowledge can never be satisfied completely. The very rules of existence dictate that compliance with the laws of physics. Some times its enough to concede that it just is the way it is because.... Just, because.
Mark.

[John Mendenhall]

You simply cannot pick & choose which part of physics you want to study. It doesn't work.

I beat on this idea all the time on the forum. Whatever you're proposing, as in ATM, or questioning, as in Q&A, has to fit all of physics, not one narrow part. Tolman's putting thermodynamics in the title of his book certainly puts the idea as concisely as possible.

[dhd40]

This only works in popular imagination. You can't just pick some part of physics, like gravity, and study it all by itself, as if the rest of physics does not even exist. That would be a complete waste of effort, and contrary to your intuition on the matter, you would not learn about gravity as much as you think. Gravity exists in the context of physics. So you know gravity, but never study thermodynamics. So you don't know that a collapsing gas cloud forming stars has to simultaneously obey the laws of gravity and the laws of thermodynamics, and you wind up not knowing what you are doing despite your knowledge of gravity. Remember the title of Tolman's book Relativity, Thermodynamics and Gravity. Tolman realized that the universe has to obey the laws of physics, all of them at once. He laid the theoretical basis for the later prediction of the later observed CMB. You simply cannot pick & choose which part of physics you want to study. It doesn't work.

Yes, unfortunately this seems to be true. Still, there should be some way to "explain" parts of physics to physics-layman without the need of understanding "the whole picture".
Example:So you don't know that a collapsing gas cloud forming stars has to simultaneously obey the laws of gravity and the laws of thermodynamics, and you wind up not knowing what you are doing despite your knowledge of gravity
True. But do you need QED for this?
This is how I understand tommac´s question

[grav]

Well maybe the top 20 gravity subjects. I will work on the pre-requisites myself.

Well, for a casual study, I would recommend starting with this Wiki link, and then working your way through the additional links it provides.

[dcl]

tommac: In order to understand gravity, you need to be conversant with Einstein's general theory of relativity. To understand THAT, you need to understand what the field equations of general relativity say. They are a set of four tensor equations. To understand what they say, you need to undestand where they come from: what assumptions went into their derivation. To understand that, you need to be converant with tensor calculus. To understand tensor calculus, you need to understand tensors and calculus. This goes on and on. There's no way to avoid it. You can't build a skyscraper with its foundation resting on toothpicks.

If you really want to understand gravity, you need to result to study and study and study a wide range of underlying subjects that may at first seem remote from the subject at hand.

[alainprice]

I disagree. I do not need to find unique solutions to the EFE to understand GR.

Einstein himself came to the understanding based on the equivalence principal, which even Newton noted but did not study further.

[Tim Thompson]

Still, there should be some way to "explain" parts of physics to physics-layman without the need of understanding "the whole picture".

There are, and there are plenty of popular level books & articles which try. But what level of "understanding" are we talking about? tommac is talking about a "degree" in gravity. That does not indicate to me a desire for the popular level of understanding, but rather understanding at a higher level. That higher level of understanding requires real physics & real math that does not appear at the popular level.

Example: So you don't know that a collapsing gas cloud forming stars has to simultaneously obey the laws of gravity and the laws of thermodynamics, and you wind up not knowing what you are doing despite your knowledge of gravity. True. But do you need QED for this? This is how I understand tommac´s question

You don't need QED, but then again, QED is an advanced & esoteric topic that most undergraduates would probably not see at all. Look at my previous links. The B.S. degree in physics from Cal State LA (where I got mine 30 years ago) covers the basics of general physics: classical mechanics ("theoretical physics"), electromagnetism, thermodynamics, quantum mechanics and mathematical methods. Yes, you do in fact need all of that if you are going to properly appreciate the physics of gravity. Leave out any of those basic topics, and you don't learn gravity. That's why I recommended a basic general physics degree, it lays the foundation for everything else. The reason I got into astrophysics myself is specifically because you cannot understand it without applying all of basic physics to almost any problem.

tommac: In order to understand gravity, you need to be conversant with Einstein's general theory of relativity. ...

I disagree. I do not need to find unique solutions to the EFE to understand GR.

I half agree. It once again depends on what level of "understanding" one seeks. Certainly, one does not actually have to work out the solutions to Einstein's equations in order to understand the equations and their meaning at a fairly high level. However, one does need to be able to read & understand the equations when they are presented. And that means at least a familiarity with the way the equations are usually written, either in tensor form or differential geometry. Modern physics is increasingly mathematical, and we need to be aware of the role of advanced mathematics in understanding advanced physics.

Remember once again that we are not talking about a popular level of understanding, but something equivalent to a "degree in gravity". That's a non trivial topic, and simply sticking to Newtonian gravity clearly will not do. It may not be necessary to be able to work out the details of general relativity on one's own. But it is necessary to be able to read & understand the equations & solutions provided, and even to be able to understand how the solutions were arrived at, when they are provided.

After all, the goal is to achieve a "degree in gravity" and an ability along with it to independently assess the role of gravity in solving astrophysical & cosmological problems. That level of understanding requires more than simply being able to understand things that are shown by someone else, but to actually think up your own solutions. That's why I stress a higher level of understanding. Alter the goal downward, and you can alter the understanding downward accordingly.

[alainprice]

Ultimately, if you seek to quantify mental problems of gravity, you will need to turn to GR. Once there, you're forced to learn the mathematics involved.

The first step is still a big one yet to be taken, embrace GR and what it means.

p.s. Why would anyone want a degree in gravity? That's heavy!

[tommac]

OK point taken. So again if there was a degree in gravity. What would the 4 year course schedule look like? Please include base math and physics , thermo and whatever else ... or can we start with the degree in cosmology or astrophysics and cut and add from there? I want to start studying but I dont have too much time so I want to get the most for my time.

There are, and there are plenty of popular level books & articles which try. But what level of "understanding" are we talking about? tommac is talking about a "degree" in gravity. That does not indicate to me a desire for the popular level of understanding, but rather understanding at a higher level. That higher level of understanding requires real physics & real math that does not appear at the popular level.


You don't need QED, but then again, QED is an advanced & esoteric topic that most undergraduates would probably not see at all. Look at my previous links. The B.S. degree in physics from Cal State LA (where I got mine 30 years ago) covers the basics of general physics: classical mechanics ("theoretical physics"), electromagnetism, thermodynamics, quantum mechanics and mathematical methods. Yes, you do in fact need all of that if you are going to properly appreciate the physics of gravity. Leave out any of those basic topics, and you don't learn gravity. That's why I recommended a basic general physics degree, it lays the foundation for everything else. The reason I got into astrophysics myself is specifically because you cannot understand it without applying all of basic physics to almost any problem.



I half agree. It once again depends on what level of "understanding" one seeks. Certainly, one does not actually have to work out the solutions to Einstein's equations in order to understand the equations and their meaning at a fairly high level. However, one does need to be able to read & understand the equations when they are presented. And that means at least a familiarity with the way the equations are usually written, either in tensor form or differential geometry. Modern physics is increasingly mathematical, and we need to be aware of the role of advanced mathematics in understanding advanced physics.

Remember once again that we are not talking about a popular level of understanding, but something equivalent to a "degree in gravity". That's a non trivial topic, and simply sticking to Newtonian gravity clearly will not do. It may not be necessary to be able to work out the details of general relativity on one's own. But it is necessary to be able to read & understand the equations & solutions provided, and even to be able to understand how the solutions were arrived at, when they are provided.

After all, the goal is to achieve a "degree in gravity" and an ability along with it to independently assess the role of gravity in solving astrophysical & cosmological problems. That level of understanding requires more than simply being able to understand things that are shown by someone else, but to actually think up your own solutions. That's why I stress a higher level of understanding. Alter the goal downward, and you can alter the understanding downward accordingly.

[tommac]

Ultimately, if you seek to quantify mental problems of gravity, you will need to turn to GR. Once there, you're forced to learn the mathematics involved.

The first step is still a big one yet to be taken, embrace GR and what it means.

p.s. Why would anyone want a degree in gravity? That's heavy!

OK so we have :

Physics I, II , III
Calc I , II, III + differential equasions
SR + GR ( how many classes of these ? )

[alainprice]

SR is easy, high school algebra. Start there if you want.

Next you need calculus and linear algebra(or vector algebra, can't remember the exact names). For calculus: derivatives, integrals, and then second order equations, then higher order. Follow that up with differential equations. Throw in some vector calculus for fun.

Now start tackling GR. Learn all about tensors. That'll get your feet wet.

[Tim Thompson]

Physics I, II , III
Calc I , II, III + differential equasions
SR + GR ( how many classes of these ? )

How you choose to number the course depends on the material in the specific course, and whether they are semester or quarter length courses. The ** degree I linked from Cal State LA includes 5 general physics courses, 1 quarter each. So, along the same lines, with one quarter courses, and using Cal State LA as a template, here is what I would say:

Physics: 20 classes
Physics 201-205 (general physics)
Physics 306 (modern physics)
Physics 311 (elements of modern astronomy)
Physics 410A-B (mathematical methods of physics)
Physics 411 (introduction to astrophysics)
Physics 425A-B (introductory theoretical physics)
Physics 426A-B (Electricity and magnetism)
Physics 427 (thermodynamics)
Physics 428 (statistical mechanics)
Physics 432A-B (introductory quantum mechanics)
Physics 444 (nuclear physics)
Physics 488 (modern topics in general relativity)
Physics 306 includes special relativity, as well as introduction to atomic physics.

Mathematics: 6 classes
Math 102 (college algebra)
Math 103 (algebra & trigonometry)
Math 206-209 (general calculus)
The math department has specialized course in linear algebra, differential equations, vector & tensor analysis, differential geometry & etc., all of which are required topics, but all of which are covered in the physics department mathematical methods courses.

I would add to all that one additional special course each in special & general relativity, as both of the courses shown here are general, survey courses. Neither is an in-depth study of the topic, but that is what you really need to appreciate gravity at an advanced level, perhaps something like the Caltech course I pointed to earlier, Physics 236 (General Relativity) and Physics 237 (Gravitational Waves). Furthermore, a class like Caltech's Physics 229 (advanced mathematical methods of physics) is really good for advanced topics in general relativity.

I also note that this set lacks in depth study of topics specific to astrophysics & cosmology. So one might supplement this list with a few classes from, say the Caltech astrophysics course list. Topics like galaxy formation or cosmology would be good supplements to a list like mine.

Well, there you have it. I think this is a good example of what you need to know of you want to understand gravity and the applications of gravity, at a reasonably advanced level. But there is no substitute for experience, and I would say that a real advanced understanding would take a course list like this, plus 10 years or so of experience. After all, in the real world, a PhD is not where you stop, it's the goal you have to achieve in order to get a start on a career in the field.

[tommac]

By any chance did you save any of your old exams?

How you choose to number the course depends on the material in the specific course, and whether they are semester or quarter length courses. The ** degree I linked from Cal State LA includes 5 general physics courses, 1 quarter each. So, along the same lines, with one quarter courses, and using Cal State LA as a template, here is what I would say:

Physics: 20 classes
Physics 201-205 (general physics)
Physics 306 (modern physics)
Physics 311 (elements of modern astronomy)
Physics 410A-B (mathematical methods of physics)
Physics 411 (introduction to astrophysics)
Physics 425A-B (introductory theoretical physics)
Physics 426A-B (Electricity and magnetism)
Physics 427 (thermodynamics)
Physics 428 (statistical mechanics)
Physics 432A-B (introductory quantum mechanics)
Physics 444 (nuclear physics)
Physics 488 (modern topics in general relativity)
Physics 306 includes special relativity, as well as introduction to atomic physics.

Mathematics: 6 classes
Math 102 (college algebra)
Math 103 (algebra & trigonometry)
Math 206-209 (general calculus)
The math department has specialized course in linear algebra, differential equations, vector & tensor analysis, differential geometry & etc., all of which are required topics, but all of which are covered in the physics department mathematical methods courses.

I would add to all that one additional special course each in special & general relativity, as both of the courses shown here are general, survey courses. Neither is an in-depth study of the topic, but that is what you really need to appreciate gravity at an advanced level, perhaps something like the Caltech course I pointed to earlier, Physics 236 (General Relativity) and Physics 237 (Gravitational Waves). Furthermore, a class like Caltech's Physics 229 (advanced mathematical methods of physics) is really good for advanced topics in general relativity.

I also note that this set lacks in depth study of topics specific to astrophysics & cosmology. So one might supplement this list with a few classes from, say the Caltech astrophysics course list. Topics like galaxy formation or cosmology would be good supplements to a list like mine.

Well, there you have it. I think this is a good example of what you need to know of you want to understand gravity and the applications of gravity, at a reasonably advanced level. But there is no substitute for experience, and I would say that a real advanced understanding would take a course list like this, plus 10 years or so of experience. After all, in the real world, a PhD is not where you stop, it's the goal you have to achieve in order to get a start on a career in the field.