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Among the important and useful properties of entropy as it is currently defined, entropy is extensive. If I have two systems $A$ and $B$ with entropies $S_A$ and $S_B$, the total entropy of the combined system is $S_\text{total} = S_A + S_B$. Were you to define "orderedness" as $\eta = 1/S$, that quantity would be neither extensive nor intensive. The ...

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The reason we say entropy is a measure of disorder is because of Boltzman's famous statement: $S = k_B \ln\Omega$ where $\Omega$ is the number of different microstates of the system. Ignore the pop culture ideas of entropy (being an artifact of nature) as evil. It simply "is". It is not evil or good. In fact, it is also used as the measure of the amount of ...

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Disclaimer: i understand you didnt ask about gauge invariance but gauge invariance and vector potentials are connected and so ill discuss both in my answer below. Schwartz "quantum field theory and the standard model" has a good, albeit very brief, accessible discussion of the utility of gauge invariance, in particular the vector potential. Gauge ...

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First, give an illustration of a linear system. You know you have to eat healthy, so you are prepared to pay 50 cents for an apple. But the next day, if apple prices double, you will forget the health benefits. Now a non linear system, because it's based on people's reaction to supply and demand. An everyday example based on the Uber taxis system. Uber ...

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Google mathematical methods in the physical sciences pdf and you will be able to download an ebook by Mary Boas, which was written for people like yourself. As Jacob says above, calculus is a must learn, and lots of websites give you examples of different levels of calculus problems. Conceptually, a good textbook is Halliday and Resnicks Physics, which sets ...

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1) Usually special relativity is taught at the end of the semester, after the class got through rotations, which they, on average, don't understand; torques, which are pseudo vectors and for this reason blow their minds up... By the time they get to relativity they are done! If you teach the same kind of course, it is unavoidable, that they will get confused....

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If you really want to learn Quantum Gravity it is never too late to introduce yourself to General Relativity as well as Quantum Field Theory. First one is crucial for understanding Quantum Gravity because it is based on both QM and GR. So for more advanced studying I recommend this book http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

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