How to Really Understand Physics - An Undergrad's Perspective

[sol66]

Well, I'm an undergrad majoring in physics and I'm going to finish pretty much all of the upper division classes by next year. All I can say is from what I've learned, it doesn't seem like very much.

I'm just wondering, of all the physicists, grad students, and Phd's the likes ... how many people actually really understand what the hell is going on? Sure velocity is equal to omega cross your r vector ... you I can find eigenvectors of some operator. I can even do a little bit of band theory for solid state.

But there is yet still so much, even the stuff that I should have learned that is so foggy to me. I can easily do all the calculations and find the values and such, but things like why the Hamiltonian works for describing a quantum particle or even the least action principle describing the trajectory of motion is so obscure to me.

The proofs for most of these rules can be wicked long, and you forget what you were trying to prove in the first place by the time you are done ... I'm usually left with the feeling like, you that makes sense and all but eh ... I don't feel to good about it still.

The type of understanding that I want is the feeling you get when you think about the really easy things in physics such as velocity or rate change.

I guess my question is ... after so long in dealing with the subject of physics, do you ever start to get that feeling that you truly understand everything that envelopes your subject of study?

I do plan on going off to grad. school and getting a Ph.d, but I'm sort of depressed because I did terrible on my E/M test, which has secured my grade as a B. Some days I feel like I totally know everything in my physics classes, then other days I feel like I'm on the tail end of the bell curve once again. Sigh...

 

[Dina1372]

were you interested in math geometry ,...such things when you went to this field ?when you were in high school did you use to get mad of math? because i try to choose physics or Aerospace engineering in tow years.

 

[InNewtonITrus]

Of course, I realize I may be WAY out of line giving "advice" here, but the thing that really strikes me is this: you WANT to understand. And you're not satisfied if you don't. You can do the stuff, but that's not enough. This reflects your personal work ethic, and i'd say you're way ahead of most other hominids that walk the Earth around you.

You say you enjoy the UNDERSTANDING that comes when you get your mind around "rate" and the like. Cool. Why don't you try sitting down, at peace, and trying to work around the rest? In your own way. Sure, you'll need to give yourself time... but that's what I do, and the kind of association you form with those topics is motive enough. Some things may seem elusive- give yourself time with them too... they'll come, for sure. The way of the world is just the way of the world- they'll make you do tons of stuff, but don't have a set of guidelines that you must follow when it comes to learning it. It's your life, your subject, your mind- be calm, and don't lose yourself worrying about all the people rushing around...

For your real question to be answered, I guess we'll have to wait for someone with a greater difference in age from you

 

[DukeofDuke]

hah, I feel the same way. Only a few teachers can take you through the summation notation all the way during a proof without losing sight of the actual physics you are doing. I've been lucky enough to have one of them.

I think he gets it. He's also really low on the totem pole, but he gets it, and can teach it, better than the higher ups. Weird eh?

 

[twofish-quant]

I guess my question is ... after so long in dealing with the subject of physics, do you ever start to get that feeling that you truly understand everything that envelopes your subject of study?

Not for me, which is a good thing, since i really did understand everything, I'd be totally, totally depressed.

Some days I feel like I totally know everything in my physics classes, then other days I feel like I'm on the tail end of the bell curve once again. Sigh...

Which is normal. As you get older, you just get used to this...

 

[twofish-quant]

But there is yet still so much, even the stuff that I should have learned that is so foggy to me. I can easily do all the calculations and find the values and such, but things like why the Hamiltonian works for describing a quantum particle or even the least action principle describing the trajectory of motion is so obscure to me.

There is something I call "spotting a unicorn in the forest." The analogy that I use is that if you subtract two squared numbers from each other, you end up with a number that is the product of two consecutive numbers. Now if you don't know algebra, this is somewhat bewildering, but after you learn algebra, you find out *why* this happens.

The other thing is that the explanation for a lot of the rules in physics is just "the world works that way."

Anyway there is this great quote by Andrew Wiles

ANDREW WILES: Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it's dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it's all illuminated. You can see exactly where you were.
----

Physics is like that. Most of the rooms you end up in someone has already been in, and if they are nice enough, they left instructions on how to turn on the light switch. But then maybe not, and you have to stumble around a bit.

The other thing is to study the history of physics. In the course of four or five years, you'll learn things that it took the greatest most brilliant minds on the planet several hundred years to figure out. So don't beat yourself up too badly if it takes you some extra time to find the light switch.

 

[presario]

You see, understanding is difficult, understanding takes time and patience, a lot of time and patience. Most people are scheduled so tightly that they are overwhelmed with work and got other things in life that time to sit and think seems hard to afford.
Keep trying though, why not try teaching it to other people ? it helps you understand better

 

[glamotte7]

I wish you the best. I'm trying hard too.

 

[Lunar_Lander]

There is another important thing about understanding: Understanding is much better than just learning things by heart. Maybe you read Feynman's account of his time in Brazil? There the students learned everything by heart and when asked for a special thing, they could not answer that. If asked to recite a certain thing, they were immediately able to do that. The thing however was, that this passage they were citing contained the answer for the original question which they were not able to answer.

One of the professors teaching theoretical physics here is also of the opinion that understanding is important.

 

[Gordianus]

Understanding demands patience and time. Once you think you know about something, go and read carefully again. Most important: "disassemble" in your mind what you´ve read. Try to see it from different angles. You´ll succeed but it takes time.

 

[sol66]

Wow, guys ... Thanks for the post, I do feel a lot better. Nobody ever said physics was an easy subject. In high school I always had low grades because I tried figuring things out on my own, especially mathematics and physics ... without reading the book. For the most part I always figured everything out, but I was always deducted points for not doing a particular problem the teachers way ... regardless if I was right. I felt back then, I had a much better understanding of everything. Unfortunately school has taught me to care not why things are the way they are and to except things at face value. If I wanted the grade, I would become withdrawn from the subject and do whatever was required to get the grade. This has happened with physics, since I need the grades to get into grad school.

I use to be a biochem major, but I switched because biochem did not sufficiently explain to me how or why things worked. Biochemist hate all that is physics and math... they survive off of using rules of thumb which of course contains many exceptions because they base most of their rules to specific rather than general cases. I found that unless you really want to understand how things work, you need the math and physics which is fundamental at all levels.

Its just extremely stressful when you have those days where you feel like you were just born yesterday with no idea on what your doing, given that you see that everyone around seems to get the big picture( which is not the case ). I don't think I ever want to do anything else in life but physics, that's what makes wanting to understand what I'm doing all the more stressful.

 

[DukeofDuke]

You're not alone. The worst part is when your peers claim to "understand" the material after glancing at it and knowing it on the most rudimentary, factual level without really soaking in it. The whole point of physics is that you can really, really soak in it...there are no true intellectual prereqs.

 

[mal4mac]

Sorry, the human mind is just not capable of understanding notions in advanced physics. Even Stephen Hawking admits he can only visualise properly in 2 1/2 dimensions, so forget about visualising the 4D curved space predicted by General Relativity, never mind the higher dimensions of string theory. Brian Greene in 'Fabric' points out that professionals, like him, visualise cosmological space using the 2d balloon & saddle models, just like Joe Bloggs, even the pros can't get visualise three dimensional surfaces curving in the fourth dimension.

Feynman says that anyone who understands quantum theory doesn't really understand it. All you can do as a professional, is plug in the numbers and chug away. And remain just as perplexed as everyone else that the quantum whatsit can be a wave and particle.

So don't expect to understand the physics. And don't expect to understand the equations, that's the job of mathematicians, you just use them, you haven't time to be a mathematician as well. So just plug and chug, and when your numbers agree with experiment, you have done better than 'understand', you have predicted what is happening in the world. That *should* earn you big bucks and lots of plaudits... and that *should* ease the pain of not understanding...

 

[Mathnomalous]

It's great to know the hours I invest in the library are worth something. The one thing I can confidently say I learned and understood is that thinking may be the hardest thing to do in life.

 

[Gordianus]

Sorry, the human mind is just not capable of understanding notions in advanced physics. Even Stephen Hawking admits he can only visualise properly in 2 1/2 dimensions, so forget about visualising the 4D curved space predicted by General Relativity, never mind the higher dimensions of string theory. Brian Greene in 'Fabric' points out that professionals, like him, visualise cosmological space using the 2d balloon & saddle models, just like Joe Bloggs, even the pros can't get visualise three dimensional surfaces curving in the fourth dimension.

Feynman says that anyone who understands quantum theory doesn't really understand it. All you can do as a professional, is plug in the numbers and chug away. And remain just as perplexed as everyone else that the quantum whatsit can be a wave and particle.

So don't expect to understand the physics. And don't expect to understand the equations, that's the job of mathematicians, you just use them, you haven't time to be a mathematician as well. So just plug and chug, and when your numbers agree with experiment, you have done better than 'understand', you have predicted what is happening in the world. That *should* earn you big bucks and lots of plaudits... and that *should* ease the pain of not understanding...

Let me disagree. I admit I don´t "understand" QM and I feel uneasy. I can do the math but I feel there´s something missing. Think of this: QM was developed a long time ago; however, people are still discussing its meaning. It seems to me we´re struggling to understand QM (in the sense of this thread)

 

[sol66]

Well going through quantum mechanics myself, I can say ... why not discuss the understanding of quantum mechanics? To me that is probably the greatest example of a particular subject that I can do, but not fully understand. There are certain things that I believe I have a great understanding of ... like how and why finding the probabilities of eigenvectors with operators and space vectors work, but the simplest question which in itself is one hell of a question .. is why do these abstract vectors and such, which in reality isn't even really a function of real space can represent physical things that are real? Its like taking something imaginary and turning it into something real, taking an imaginary wave function and manipulating it to produce observables and probabilities.

What really baffles me is what on Earth gave Heisenberg the insight to come up with the matrix mechanics representing quantum mechanics? Schrödingers representation makes more sense to me, but then again they were both awesome mathematicians and used a set of rules which they found to be experimentally true to come up with the foundation of quantum mechanics. I suppose as far as Heisenberg mechanics is concerned, he probably just used the same rules that were implemented by Schroedinger, but found it easier to formulate a mathematically equivalent form in linear algebra.

Well, I guess also a lot of the modern physics that I've delt with such as angular momentum and quantum spin, are biproducts of solving particular systems such as the hydrogen atom. Using separation of variables to solve the hydrogen atom along with the laugrenge polynomials introduced new variables such as L and M to allow us to solve the equation. Oddly enough it turns out that those variables seem to have physical qualities attached to them. Deriving something physical from a purely abstract piece of mathematics such as angular momentum of a quantum particle makes understanding that physical property impossible. You could only understand it in terms of the mathematics and the rules you set up for manipulating the math.

I suppose in that sense, it would be futile to try to classically understand something that is not a classical object. In other words its like trying to represent a Five dimensional abstract complex vector in a 3-D real world, its impossible... or more like trying to take a blue crayon and making it draw red. Its not possible, although what quantum mechanics is more likely that not is analogous to taking that 5th dimensional abstract complex vector space and using it to describe a real 3-D vector which is possible.

I'm wondering, who else agrees with my opinion of what it means to understand quantum mechanics, or even what quantum mechanics is in terms of our reality?

 

[Gordianus]

If Feynman himself told us he didn´t understand QM; who am I to deny his wisdom?
He, and other brilliant minds gave us the rules. The numbers we calculate agree with the experiments but we don´t know yet why. The possible lack of a reality bothers me a lot.
Anyway, I concur that our mind can´t grasp anything beyond classical systems and we have to resort to mathematical descriptions, but, in my opinion, pure mathematics can´t provide the answers to physical questions.

 

[Klockan3]

Most of QM isn't that strange, the strange parts are what happens during interactions and spin, the rest is well understood for the non-relativistic cases. That particles are waves isn't that strange at all really, just because you visualize them as small balls in earlier courses do not mean that it is more logical. Who said that objects in microcosm must have a definite size and edge? That just comes from applying our knowledge about our observable world and then trying to project it to other systems, it don't come from any experiment or so at all so it isn't any more physical than what the ancients Greeks thought about gravitation.

In essence you just got to accept that particles have spin and that during interactions the wave function collapses. Those have very strong support from experiments so you should take them as axioms just like F=ma, at least until you start researching it for yourself. F=ma isn't intuitive either by the way, the ancient Greeks did not believe in it for example, should we then state that classical mechanics is unintuitive?

What should be taught however is that there are no hidden variable model that is compatible with qm that is also compatible with special relativity, otherwise students starts to believe in hidden variable theories and that is bad.

 

[Klockan3]

I guess my question is ... after so long in dealing with the subject of physics, do you ever start to get that feeling that you truly understand everything that envelopes your subject of study?

I think that the rate of understanding is very different from person to person, I am sure that some physicists barely understands how the basic Newtonian relations plays out while others understands the whole axiomatization as far as it can take them.

If you want to understand you need to study in a different way than if you want to do good on courses, generally understanding takes more time for the same scholastic results but will reward you with a greater sense of satisfaction. Also the more you understand about the material the better your memory of it will be, I am convinced that in the long run everyone would benefit from trying to understand rather than just trying to pass the goals of the courses.

 

[Nabeshin]

I'll pipe in with my own two cents from my limited experience.

The way I see it, it's not so much about truly "understanding" any given subject matter, or physics as a whole, or anything like that. The important feature is that you continue learning about it all the time. For example, I look at myself a year ago and think of all the physics I was ignorant of back then and it is simply astonishing! Similarly for two years ago and so on.

The point is how much you have grown as a physicist, not to some ultimate end but simply relative to where you were in the past. If I could maintain the level of learning I mentioned above for the rest of my life (highly unlikey!), I believe I would be very happy even if I did not fundamentally "understand" something like QM.

I don't know, so if you're feeling like you don't understand much, just look at where you were just 12 short months ago and reevaluate that judgment.

 

[diazona]

The type of understanding that I want is the feeling you get when you think about the really easy things in physics such as velocity or rate change.

For me at least, as of the second year of grad school, the only things I understand as well as the easy things (velocity and rate change etc.) are those easy things themselves.
I understand your position entirely because I've had the same goal of understanding the more advanced things to the same level. Right now it looks pretty impossible.