Fundamental Proofs in General Physics?

[CollinsArg]

Hello, I'm a freshman and I'm struggling with some questions. I'm trying to relate all I'm learning from my Physics classes to the real world (that is the mathematical connection and its expanations with the real world). I have some especifics questions but also a general answer I think could be given to me as a freshman.

Science sees the world with critical reasoning and logic. That's the way I try to learn Physics as it is a science. The problem is that some books lack of fundamental proofs, is there a book or a field of Physics which tries as hard to verify and give concise proofs of it, as Funamental Mathematics like Logic M, does? An example: My book says: "...it is confirmed by experiments that forces acts as vectors...", and then goes on expaining Newton's Laws. Now, I'd like to see and be sure myself it is so, and I think this way I would understand more and be more able to think a way to solve a physics problem.

PD: English is my second language, sorry if I have grammar mistakes. Thanks!.

 

[fresh_42]

Hello, I'm a freshman and I'm struggling with some questions. I'm trying to relate all I'm learning from my Physics classes to the real world (that is the mathematical connection and its expanations with the real world). I have some especifics questions but also a general answer I think could be given to me as a freshman.

Science sees the world with critical reasoning and logic. That's the way I try to learn Physics as it is a science. The problem is that some books lack of fundamental proofs, is there a book or a field of Physics which tries as hard to verify and give concise proofs of it, as Funamental Mathematics like Logic M, does? An example: My book says: "...it is confirmed by experiments that forces acts as vectors...", and then goes on expaining Newton's Laws. Now, I'd like to see and be sure myself it is so, and I think this way I would understand more and be more able to think a way to solve a physics problem.

PD: English is my second language, sorry if I have grammar mistakes. Thanks!.

You can probably check why forces behave like vectors on your own, e.g. pulling a heavy weight at different angles. In general, however, you won't be able to run all experiments that have led to the laws of physics. Usually a lot of them are in courses like "experimental physics" but of course never all of them. So how should an answer look like? The laws of physics try to establish some fundamental principles like Newton's laws in classical mechanics, or symmetry properties in particle physics and deduce subsequent relations from it. If they pass the test by experiments, they will find their way into textbooks in which they are called theories or laws, and will be forgotten otherwise. But how would you "prove" that there are such things as neutrinos or which rules they obey?

 

[CollinsArg]

But how would you "prove" that there are such things as neutrinos or which rules they obey?

This is exactly why I'm pondering about. Shoudn't I re-prove it so I could understand it? I mean, not experimentaly, but like some paper that tells me how it was found and why do they reach to that conclution, or should I just to believe what the book says? Thank you.

 

[Dale]

I mean, not experimentaly, but like some paper that tells me how it was found and why do they reach to that conclution, or should I just to believe what the book says?

Many good textbooks include a list of references to the original experiments. If you don't want to trust the book then you should read the references.

 

[fresh_42]

This is exactly why I'm pondering about. Shoudn't I re-prove it so I could understand it? I mean, not experimentaly, but like some paper that tells me how it was found and why do they reach to that conclution, or should I just to believe what the book says? Thank you.

This depends on the amount of time you have available. In my opinion it is hard enough to learn the what and how. Once you are firm in a matter you almost automatically get interested in historical contexts and at least partially will learn them out of pure interest. Also standard texts as "why is there such a thing as a neutrino" will certainly be part of any introduction to the subject. But do we really need to know how Archimedes found his laws, except for an interesting note in the margin? Or whether Galileo really threw stuff down this tower? Or why bicycles are stable while riding them, but not at rest? The latter, e.g. will surely be part of an introductory course in experimental physics. So many of the things you mentioned will be part of a study, simply not necessarily at the same spot in the same book.

 

[ZapperZ]

This is exactly why I'm pondering about. Shoudn't I re-prove it so I could understand it? I mean, not experimentaly, but like some paper that tells me how it was found and why do they reach to that conclution, or should I just to believe what the book says? Thank you.

You are confusing "science" with the "characteristics of science". You argue that it "... sees the world with critical reasoning and logic ... " but you missed one very CRUCIAL and important distinction of science that separates it from religion - that must have empirical verification, i.e. it must be falsifiable. String theory "... sees the world with critical reasoning and logic.. ", but many people still do not accept it as valid science because it lacks experimental verification. So sure, "logic" is a necessary criteria, but it is NOT a sufficient criteria!

There are many aspect of physics that can't be derived or "proven". CPT symmetry, conservation of mass-energy, conservation of momentum, etc.. all our fundamental symmetries and constants are there not because someone derived or proved it, but because they are what we observed! Many of our theories come from a set of starting postulates, and then a logical sequence of derivation is made from those postulates to see if those theories match physical observations. Only when they do do we finally accept those theories as valid. Being logical and looked at with critical reasoning do NOT guarantee its validity, as there are many theories that have fallen to the wayside.

We designate force as a vector, for instance, because we can clearly see that not only does it matter that there is a magnitude to it, but also that the direction that it is acting matters in a system. It requires no mathematical proof. Instead, we use the principle of "What if...?". So what if we consider force as a vector, and apply all the mathematical rules of vectors on it? Will it produce results that match what we observe? That last part is what MANY people, especially the public, do not appreciate. This is where the rubber meets the road, i.e. our initial starting point (Force is a vector) has many consequences that must be tested and verified empirically..

If Mother Nature tells us that, yes, the results match, then we accept our starting point as being valid within the boundary of what we can test or understand. If the results fail spectacularly, we throw it out. If parts of it match, but parts of it do not, then we go back and figure out if what we started with isn't entirely right and it isn't entirely wrong either. Maybe it needs tweaking, etc.

Experimental verification is why science has such a stringent level of what it accepts to be valid. It should not be ignored as an important criteria. And from my personal experience, it should be THE most important criteria! And strangely enough, it is often ignored by many.

Zz.