My approach to physics seems pointless.

[pranav_bhrdwj]

Greetings.

I completed my bachelor's in physics from the 'University of Delhi', India, an year ago and I wish to pursue a career in fundamental research. I knew that a Master's in Physics was a very serious business and thus took an year off making sure i was ready for it.

However i have been facing this issue for a long time now.

In my first year to college i was introduced to 'Special Theory Of Relativity' and i was intrigued by its beauty. I studied it (with all my devotion) from 'Berkeley Physics Course : Vol 1' , 'Lectures on Physics by Feynman' and a book on special relativity by Einstein himself. I probably spent all my time studying and trying to comprehend it ; a huge mistake as 'STR' was only a part of my Course in Mechanics. I was happy though, that i knew STR really well.
However, 6 months later into my second semester I was devastated to realize that I had forgotten all that I had gone through. The only things I remembered were general things which i think any physics enthusiast knows, stuff like length contraction, time dilation, the ultimate speed limit. I had forgotten all the proofs which i had spent a lot of time understanding and memorizing. To me the fault seemed not having solved much problems on the topic, so i went through the theory again and this time solved all problems on the topic in the textbook, 'Concepts of Modern Physics' by Arthur Beiser. I wouldn't call the problems hard but i thought at-least I had done my part.

However, an year later I found myself at the same spot. I had to look at the formulas again, go through the proofs again and found not much difference when it came to the ease of solving problems and this was really discouraging. I was almost down to tears, for, what was the point in studying it so hard, if after an year i was no better at the topic as anyone else, who gave no attention to the details and cared not a bit more than getting grades ?

After completing my bachelors, I was still not satisfied with my grasp over Mechanics. I was weak at it in high school and problems in Mechanics (pulleys,rotational motion,friction to be specefic) always scared me. I picked up the book, 'An Introduction to Mechanics' by Daniel Kleppner and under the guidance of a very good teacher, read the text and approached the problems. After around 3 months I started to feel at ease with the problems and I could solve a lot of them after a little bit of struggle, though i couldn't solve a few at all and took to my teacher to solve them.
An year later, which is now, although I feel a lot more comfortable and confident than before, at times I can't solve problems that I had solved before, let alone the ones that I had to go to my teacher to solve. I have to go through the text, revisit some concepts and textbooks examples and then spend a considerable time,

10-20 mins for a 'relatively' easy problem : not those plug into the formula ones.
40-45 for the hard ones
and there still are problems that I cannot solve.

And thus after 4 years, I am yet again surrounded with the same question in my head : Isn't it pointless ? Why go on if I am to forget things after an year or so, when I take roughly the same amount of time to solve problems as i did firsthand ? At times I begin to lose my zeal for the subject and begin to question my interest in physics and whether or not i will be able to do research in the subject. :-/ I remember how enthusiastic I was when I entered college and had so many concepts buzzing around in my head and now i hardly spend time thinking of new things :/
Same is the story with : 'Electricity and Magnetism' and 'Quantum Mechanics', studied from textbooks by D.J Griffiths.

What am i doing wrong ? Should i be able to solve proofs on my own by now ? I know it is really late for getting this fixed up but i do not wish this problem to follow me when i do my Master's. How should i approach physics in my Master's program ?

I apologize for such a long post and I thank you all from the core of my heart for taking the time to read it. I really appreciate it. I'd be really grateful if you all can help me get out of this :)

 

[quantum_smile]

So, the process you've described is learning something really, really well and in depth and doing lots of problems...and then finding out that a year later that you don't remember any of it (without careful review). This is coming from an undergrad physics major, but I've done really well in multiple graduate physics courses, so I think this really applies to your worries about a Master's program: this is TOTALLY normal. It used to worry me before I started to realize that just because you can't go back and immediately solve problems in an old textbook does NOT mean that your knowledge is gone. Somehow, in the time period spent learning and forgetting physics...it just stays with you. I don't remember definitions or proofs or how I solved past problems, for the most part. But if you really work to get back into a topic you once learned, you WILL find that it's still with you and that you relearn more and more quickly and deeply each time. Physics professors have to prepare a lot for each lecture and carry their lecture notes with them and often reread the class textbook, even though it's probably remedial to them. It's normal.
In the end, the question is - what do you want from your knowledge? If you want to do research, I don't think you have anything to worry about. You're deep enough into one particular topic that everything relevant will come back to you. If you want to do well in classes, again, no problem right? You just relearn the basics you need to relearn, but anyways, you just need to focus on the one (or couple) class textbooks and lectures.
I guess I just rambled a lot, but I guess I was a little surprised that you're worried about something that I've accepted as normal.

 

[pranav_bhrdwj]

I can't thank you enough :)
It really is reassuring in the sense that i am not the only one. But then what benchmark do you set, which helps you figure out you are getting better ? And if learning and forgetting is a part of the process what exactly do we gain out of it ?
Thanks again, you read through really long post :P

 

[STEMucator]

You should be focusing on retaining ideas conceptually. You should not be memorizing proofs and expecting your understanding to be retained over long periods of time. The brain is a physical thing, and it will deteriorate whether you like it or not.

The idea is what you want to grasp, not the 1000 problems relating to the idea.

Don't be afraid if you remember the concept, but not how to apply it. The internet is there for you, and when you are doing research, no one really expects you to have memorized every problem. You will have time to re-learn how to apply the the concept, but without prior knowledge of the concept, this may prove difficult and take longer than it should.

So as long as you know gravity pulls down, you should be okay.

 

[pranav_bhrdwj]

You should be focusing on retaining ideas conceptually. You should not be memorizing proofs and expecting your understanding to be retained over long periods of time. The brain is a physical thing, and it will deteriorate whether you like it or not.

The idea is what you want to grasp, not the 1000 problems relating to the idea.

Don't be afraid if you remember the concept, but not how to apply it. The internet is there for you, and when you are doing research, no one really expects you to have memorized every problem. You will have time to re-learn how to apply the the concept, but without prior knowledge of the concept, this may prove difficult and take longer than it should.

So as long as you know gravity pulls down, you should be okay.

Thank you for your reply. However i beg to differ. Gravity pulls down is something everyone is aware of. And as far as i am able to understand your post you've emphasized on retaining the concepts, however this is something anyone with an interest in physics may follow. There ought to be a difference between a physics grad and someone going through popular-science books and that is what i am trying to comprehend. As to what exactly is the point in all this if at the end of the day, I remember things which are quite general (as i mentioned,stuff like length contraction, time dilation, the ultimate speed limit). I agree i have an in-depth knowledge of the working of physics but is it really enough ? How do i get better and what benchmark should i set ?
You've also mentioned that memorizing proofs shouldn't be a priority, however do you think i should be able to work my way around them by now ? I mean should i be able to prove things on my own ?

P.s : Thanks for taking the time to reply, i really appreciate it :)

 

[micromass]

Thank you for your reply. However i beg to differ. Gravity pulls down is something everyone is aware of. And as far as i am able to understand your post you've emphasized on retaining the concepts, however this is something anyone with an interest in physics may follow. There ought to be a difference between a physics grad and someone going through popular-science books and that is what i am trying to comprehend. As to what exactly is the point in all this if at the end of the day, I remember things which are quite general (as i mentioned,stuff like length contraction, time dilation, the ultimate speed limit). I agree i have an in-depth knowledge of the working of physics but is it really enough ? How do i get better and what benchmark should i set ?
You've also mentioned that memorizing proofs shouldn't be a priority, however do you think i should be able to work my way around them by now ? I mean should i be able to prove things on my own ?

P.s : Thanks for taking the time to reply, i really appreciate it :)

The goal is indeed to find proofs and derivations yourself if you need it. Of course, there are some hard and tricky derivations out there. But most of the things you should be able to find yourself. But don't memorize the proofs! Instead, look at the different methods the proofs use and try to internalize the methods. Forgetting is natural, certainly if you never use the things you studied. Cold facts disappear from memory fastest. But the methods and the how-to should stay for longer.

 

[pranav_bhrdwj]

The goal is indeed to find proofs and derivations yourself if you need it. Of course, there are some hard and tricky derivations out there. But most of the things you should be able to find yourself. But don't memorize the proofs! Instead, look at the different methods the proofs use and try to internalize the methods. Forgetting is natural, certainly if you never use the things you studied. Cold facts disappear from memory fastest. But the methods and the how-to should stay for longer.

Yes, yes, yes This is exactly what I have been looking for. And this is what scares me. I remember getting frustrated as to how I couldn't prove things on my own. Proofs in physics aren't exactly like those in mathematics in the sense that they don't always ''exactly'' follow from things that have been proved before, something I adore about mathematics (I followed a course in introduction to real analysis, from 'Bartle and Sherebert'). I cannot think of proving results following from 'Lorrentz transformation' ; as an example, I cannot derive the results of 'Lorrentz Velocity Transformation' on my own. I can look at it, understand it but cannot prove it on my own without any prior knowledge of how Sir Hendrik Lorrentz did it and as you've said 'The goal is indeed to find proofs and derivations'. At times the proofs require application of multiple concepts apart from rigorous/amazing application of mathematics. So how do i go about it ?
And if forgetting is natural what exactly am I gaining out of this process ?

Thank you, really, thanks a lot. Waiting for your reply :)

 

[micromass]

I can look at it, understand it but cannot prove it on my own without any prior knowledge of how Sir Hendrik Lorrentz did it and as you've said 'The goal is indeed to find proofs and derivations'. At times the proofs require application of multiple concepts apart from rigorous/amazing application of mathematics. So how do i go about it ?

While you are studying, you should try to find out such things. Try to find out how Lorentz did some things. This might require multiple books. But eventually, the concepts should become so clear that these kind of derivations should seem self-evident. Of course, this does not hold for the tricky long derivations. But perhaps you should try a deeper kind of studying?

And if forgetting is natural what exactly am I gaining out of this process ?

Forgetting is natural, but forgetting everything is weird. You should definitely remember some things from SR, which are usually the most important concepts and principles. And you are also learning the methodology of how things were derived (you won't necessarily remember the specifics of the derivation though).

 

[quantum_smile]

So here's one way you realize you've learned something:
Mid-freshman year winter: I've learned Griffiths quantum and a course of abstract algebra and special relativity and E+M! I have the prerequisites to learn quantum field theory according to this author. Opens-QFT-book. Gets stuck on third page.
Year later: Oh my gosh, how did I not understand this introduction before?

The real reason is probably that I took a particle physics class that covers an intro to QFT, learned more about four-vectors in special realtivity, took two more quantum classes, etc. If I really tried to learn QFT now, I'd probably find that having covered Lie algebras, advanced classical mechanics, etc. in the past would be **extremely** useful. But how much of this material can I automatically regurgitate on the spot? Could I do a single problem in Griffiths particle physics without rereading the chapter? Probably not. It's when you start building on past knowledge and keep finding that more advanced material gets easier and easier to learn after time passes that you can prove to yourself that you're learning something. Another reassurance is this satisfying feeling that all the math you learn just sticks with you, which I guess doesn't really appear for classical mechanics - more like after you take multiple QM classes and linear algebra and functional analysis.

 

[pranav_bhrdwj]

While you are studying, you should try to find out such things. Try to find out how Lorentz did some things. This might require multiple books. But eventually, the concepts should become so clear that these kind of derivations should seem self-evident. Of course, this does not hold for the tricky long derivations. But perhaps you should try a deeper kind of studying?

When studying i try to understand all the concepts that follow, create a mental picture of things and then solve problems to check how good I am. Is there more to it ? Could you please elaborate on 'deeper kind of studying' because I think I already do that :/

Forgetting is natural, but forgetting everything is weird. You should definitely remember some things from SR, which are usually the most important concepts and principles. And you are also learning the methodology of how things were derived (you won't necessarily remember the specifics of the derivation though).

Yes, what I meant was not being able to rebuild proofs the way you mentioned I should. I do remember the main principles and concepts behind the theory but as I have said in my post and previous comments, but isn't that something general ? Things like why Newtonian physics wasn't enough why length contracts, why time dilates, why traveling at the speed of light isn't possible etc ; is that what you meant when referring to main concepts and principles ? Also please elaborate on 'learning the methodology of how things were derived'.

 

[quantum_smile]

About the idea of rebuilding proofs...
If you're studying a textbook and have read all previous sections, in THEORY, a lot of the time, you should be able to "rederive" all the results in the section that follows before you even read it. Why are students not given this task? Because it would take forever. You have no idea how long it actually took Lorentz to derive the correct equations for the Lorentz transformations, and even if it took him no time at all, it's because he was old and knew a lot. Coming up with new ideas in physics with careful mathematical rigor is always very difficult and takes a lot of practice to get better at, and no professor/class will ever expect you to be able to do it easily.

 

[micromass]

When studying i try to understand all the concepts that follow, create a mental picture of things and then solve problems to check how good I am. Is there more to it ? Could you please elaborate on 'deeper kind of studying' because I think I already do that :/

Well, you said that you didn't know how Lorentz found his things. That is something worth looking into. It's personal of course, but I always like to read the history behind a concept. I think this will definitely help you remember it.

 

[pranav_bhrdwj]

:) that is really reassuring :)
however i agree with what @micromass said about being able to rebuild on proofs. Could you help me out here ?

Another reassurance is this satisfying feeling that all the math you learn just sticks with you, which I guess doesn't really appear for classical mechanics - more like after you take multiple QM classes and linear algebra and functional analysis.

Also could you please explain that classical mechanics bit .. :)

 

[pranav_bhrdwj]

About the idea of rebuilding proofs...
If you're studying a textbook and have read all previous sections, in THEORY, a lot of the time, you should be able to "rederive" all the results in the section that follows before you even read it. Why are students not given this task? Because it would take forever. You have no idea how long it actually took Lorentz to derive the correct equations for the Lorentz transformations, and even if it took him no time at all, it's because he was old and knew a lot. Coming up with new ideas in physics with careful mathematical rigor is always very difficult and takes a lot of practice to get better at, and no professor/class will ever expect you to be able to do it easily.

Very true, infact that was the kind of reply i got every time I approached my lecturers about this. They said i am not expected to do this. And yes infact at times just rebuilding on proofs already done consumes a lot of time let alone deriving them on my own. However this is a skill I think a physicist needs to acquire, atleast being able to do proofs when I know the concepts well, on my own. But the thing is having read a proof in a particular way really limits you in the sense that when trying to rebuild it, your mind almost sort of forces you to remember what you had done in the past and any kind of deviations seem non intuitive.

'Coming up with new ideas in physics with careful mathematical rigor is always very difficult and takes a lot of practice to get better at'
^What kind of practice ?

 

[pranav_bhrdwj]

Well, you said that you didn't know how Lorentz found his things. That is something worth looking into. It's personal of course, but I always like to read the history behind a concept. I think this will definitely help you remember it.

I wish I could have found time for this, it sure would've been enlightening but time constraints due to other courses in my semester restricted me to my texts. Are you suggesting that finding out how physicists got about their problems, deriving things could help me create an aptitude for proofs ? Would this not be a very time consuming task ?

 

[STEMucator]

Discovering new ideas in physics requires a certain ingenium. I wouldn't expect a new idea to just dawn on someone randomly, it takes years of research and conceptual understanding to formulate new concepts and to prove their validity.

You need a conceptual understanding to prove theorems, and to derive them on your own. I don't think memorizing and regurgitating someone else's proof from a book will serve you too well in the long run because chances are you're going to forget the exact symbols and mathematical procedure.

Rather, you should be focusing on why the author of the proof writes the steps they do conceptually. Understanding why the proof is valid is more important than being able to produce the proof itself. If you cannot understand the proof itself, how could you ever re-produce the idea and present it so people can understand it.

My advice: When reading through a proof, explain to yourself in English as simply as possible why each step of the proof is entirely valid. This will improve your conceptual understanding of the idea and will improve your retention so you will be able to re-produce the idea much more easily in the future.

 

[pranav_bhrdwj]

You need a conceptual understanding to prove theorems, and to derive them on your own. I don't think memorizing and regurgitating someone else's proof from a book will serve you too well in the long run because chances are you're going to forget the exact symbols and mathematical procedure.

Agreed !

Rather, you should be focusing on why the author of the proof writes the steps they do conceptually. Understanding why the proof is valid is more important than being able to produce the proof itself. If you cannot understand the proof itself, how could you ever re-produce the idea and present it so people can understand it.

I assure you, that when reading a proof, I make myself familiar and absolutely comfortable with each and every step that follows. In fact there's hardly a way to understand the proof without being certain of its validity.

My advice: When reading through a proof, explain to yourself in English as simply as possible why each step of the proof is entirely valid.

This is something I have been already doing however it still is difficult to reproduce a proof solely on this basis. As far as i understand i think what you are implying is that a strong conceptual understanding makes proofs seem self evident. However, I still find myself unable to reproduce it (after i have no memory of how the author proceeded with his proof).