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I have recently made the decision to study Physics seriously. However, in the past, I've had some difficulty with the subject because of my primarily mathematical background. I find that sometimes even if my reasoning is axiomatically correct, it doesn't lead to the right answer for simple reasons like I made a wrong assumption, or I hadn't assumed something I should have. So, I have three questions:

1) Is there some system or method I can use to determine what assumptions I should be making? This is important to me because it seems the problems I've encountered traditionally seem to be open-ended in this regard when they're not simple plug-and-chug questions.

2) There's also the question of definitions. I am uncomfortable with the fact that most definitions are not rigorous enough; this usually leaves some room for interpretation and consequently, it's unclear how they may be applied to certain situations. How do I know if the interpretation I've made of the definition is accurate?

3) Thirdly, when I'm reasoning with a problem, I'm not sure if at each step, what I've concluded is accurate or would actually happen in reality. This applies especially to problems where I'm asked to make simplifying assumptions (such as, "assume the surface is friction-less" or "assume the rod supporting the beam is mass-less") which simply wouldn't be applicable in the real world. So, I'm not really sure what to model my reasoning after in these cases; how can I get around this? Also, is solving such problems really helpful as far as learning actual Physics goes?

I can only speak for classical Physics, as I haven't progressed much further. Is Modern Physics the same in this regard, or is it more axiomatic? Finally, if there really isn't any systematic approach to this, then how can we really call the process Science? Isn't the scientific method all about finding agreement?

Thanks for all the help in advance!

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closed as off topic by Manishearth Jan 10 '13 at 20:27

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This doesn't seem very focused to me... you're asking a lot of different things, and I'm not even sure whether any of them are on topic. –  David Z Jan 10 '13 at 20:06
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Does the FAQ's line "If your motivation for asking the question is “I would like to participate in a discussion about ______”, then you should not be asking here." apply here? –  dmckee Jan 10 '13 at 20:11
    
This question really is more suitable for Physics Chat. There are way too many questions here, and it's off topic, as mentioned above Interesting question, but sorry, not that good a fit for this site. –  Manishearth Jan 10 '13 at 20:27
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Doesn't it fit the education tag? I'm really just asking for strategies, not a discussion. If you agree, can you open the question again? I should probably have mentioned I'm only looking for an answer for the numbered questions. –  ThisIsNotAnId Jan 10 '13 at 20:50
    
I am not good in pulling random handwaving approximations out of my sleeve or of the blue either. The more applied a physics topic is the more approximations have to be made and the more only handwavingly motivated steps have to be applied to come to a result. This is why I like best fundamental or theoretical physics .. :-) –  Dilaton Jan 10 '13 at 21:49

2 Answers 2

up vote 4 down vote accepted

In my experience, the best way to go is to make enough simplifying assumptions that you can actually find an answer. Once you've done that, then go back and reevaluate your earlier assumptions,a nd find a way to correct your model adding those effects back in.

Alternately, figure out a regime in which your assumptions make sense. In the case of friction, for example, friction is negligible so long as it doesn't remove energy for the system, so for a system with initial energy E, we can ignore friction so long as the distances we travel are less than $\frac{E}{F_{fr}}$, since, roughly (and not assuming a model of friction), The force of friction, if acting with a constant force $F_{fr}$ will drain out an amount of energy $F_{fr}x$ over a distance x. good estimates make an assumption about what order of magnitude an effect will happen on, and then claim validity only in the regime in which that effect will have negligible impact.

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Thank you for the reply. This strategy only seems to be viable A's long A's I'm looking at the answer to begin with. And even in those cases I've found that I'm sometimes left completely in the blue as to how the author derived the answer. Also, it seems this process will vary for different people when a problem is being solved whose answer isn't already "known". –  ThisIsNotAnId Jan 14 '13 at 20:09
    
*to be viable as long as... –  ThisIsNotAnId Jan 14 '13 at 20:15
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@ThisIsNotAnId You have to know something about the problem, but you don't already have to know the answer. In my friction example, I didn't claim anything about the motion of the particle, or the model of friction, which in principle, could be varying. All I needed was an order of magnitude of the size of the friction,a nd then I could tell you how long I would be allowed to ignore friction. –  Jerry Schirmer Jan 14 '13 at 21:33
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And I should say that learning ow to do this is definitely a skill, and that you have to practice and revisit in order to figure out what the reasonable assumptions are. –  Jerry Schirmer Jan 14 '13 at 22:27

1) Is there some system or method I can use to determine what assumptions I should be making?

I presume you are thinking of working in theoretical physics. Keep in mind that physics is not a QED discipline, it is a research one. For theory, if there is an assumption that is important it is the assumption of simplicity and economy in modeling. That is why symmetries are so important in current theoretical physics. Next to it is acquiring a feeling for appropriate approximations that will lead to this simplicity in problem set up and solving, as is pointed out in another answer. This means you should be aware in depth of the data that the problem is addressing.

2) How do I know if the interpretation I've made of the definition is accurate?

You will slowly acquire an intuition by trial and error . First by the grade you will get in the set of problems and then by solving real problems against data ( research). Sometimes you will be wrong, and will have to acknowledge it. That is what research means.

3) Thirdly, when I'm reasoning with a problem, I'm not sure if at each step, what I've concluded is accurate or would actually happen in reality.

It is trial and error, checking against data that will slowly give you confidence in the applicability of your approximations.

So, I'm not really sure what to model my reasoning after in these cases; how can I get around this? Also, is solving such problems really helpful as far as learning actual Physics goes?

You will not go wrong following Jerry Schirmer's advice in his reply. You will slowly build up a data base that will allow you to make approximations within errors that describe reality/data.

Is Modern Physics the same in this regard, or is it more axiomatic?

It is similar and more challenging because one has to build up new intuitive tools.

The aim of the discipline of physics is to model the reality we observe and measure and use the model to predict new phenomena. There are laws that have to be obeyed, like conservation laws, but axioms are part of the hypothesis in finding a model for reality. If the data disagree, the axioms too will be changed.

Finally, if there really isn't any systematic approach to this, then how can we really call the process Science? Isn't the scientific method all about finding agreement?

Agreement with what? In my opinion the scientific method consists of constructing a hypothesis and using mathematical and logical reasoning testing it against data ; if it agrees, fine, if not, the hypothesis has to be changed.

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Thank you for the reply. When we're solving problems in courses there usually isn't much data, if any, to check against. It's usually just a set up, question, and maybe an answer. So it seems trial and error would be difficult to do in these cases. By agreement I mean, if there is no system dictating what isn't and is allowed as far as assumptions and moves in reasoning go, then answers could vary depending on who you ask. So, then there isn't necessarily agreement among the people who attempt the problem. –  ThisIsNotAnId Jan 14 '13 at 20:19

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