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25

Can I make GR my starting point, and look at SR later as a special case of GR? This would be like making differential geometry your starting point and then learning linear algebra as a special case --- or learning calculus as your starting point and then learning about straight lines as a special case. In other words, it's insane.


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The concept of infinity as used in calculus arises mathematically as an equivalence class of divergent series to compactify the reals (or complex numbers), so infinities are, even in a purely mathematical (calculus) setting, in some way approximations of large numbers. There are rich theories of other concepts related to infinity not directly related to the ...


5

Before learning general relativity you need to learn special relativity,classical mechanics,electromagnetism,fluid mechanics,tensors,differential geometry first. this is the way we physics majors learn general relativity. We learn ofcourse quantum mechanics,statistical mechanics,optics too,but these are not directly necessary as far as I know ,but to ...


4

Instead of explaining how the weak and electromagentic interactions unify (a bottom-up approach), I will try to showcase this from the other direction, explaining how the electroweak interaction gives rise to the weak and electromagetic ones after symmetry breaking. I will include some minor technicalities, but try to render them as insubstatial to the ...


3

Are there other things that in theory thought to be impossible but are not anymore? It is said that the field of Chemistry came about from the desire of Alchemists to turn lead (or other "base metals") into gold (achieving transmutation of elements). When the periodic table of elements was discovered and chemical reactions started to become well ...


3

I would like to add to DanielSank's fantastic answer, as I've just had a thought on another way to state his brilliant passage: Consider a violin string which has a set of vibrational modes. If you want to specify the state of the string, you enumerate the modes and specify the amplitude of each one, eg with a Fourier series $$\text{string ...


2

Yes, escape velocity should really be escape speed. The Wikipedia article on escape velocity states this explicitly. I doubt there is any logical reason for using the term escape velocity and I suspect it is an accident of history. You might want to ask on the History of Science SE how the term originated - a quick Google failed to retrieve any information ...


2

Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics: Introduction to Special Relativity, 2nd ed. W. H. Freeman & Company, 1992. In print, ISBN 0-7167-2326-3, list price $26.00 (hardcover) Simply the best introduction you could get. You want to start with SR. Make sure you have a good grounding in Classical "Newtownian" Physics first, as well ...


1

A recent and famous example is the accelerated universe. https://en.wikipedia.org/wiki/Accelerating_universe Along the history of mankind people didn't know how big is the universe and what governs it's evolution. Until the very beginning of the 20th century the scientific consensus was that the universe is static (even Einstein thought so, a fact which ...


1

Yes, especially in research-level topics. There are several research groups that work with finding ways to apply differential geometry concepts to solid state systems (although condensed matter seems to be the preferred term nowadays). See for example the book by Altland and Simons, Condensed Matter Field Theory, Chapter 9 "Topology". This book is suitable ...


1

I came across this one recently. It had a good chapter on stress and strain with a lot of derivation. Coming from Physics, not Engineering, it was a good primer. Lots of equations, derivations and prose. Polymer Engineering Science and Viscoelasticity: An Introduction By Hal F. Brinson, L. Catherine Brinson http://www.springer.com/us/book/9781489974846 ...


1

Elementary particle physics is an outgrowth of what was high energy physics, historically at the time. X-rays were high energy physics when first discovered, they are part of the tools of solid state physics now. Alpha particles and gamma rays were high energy physics at their time, they are nuclear physics now. Mesons discovered in cosmic rays started ...


1

As an alternative to Anna's nice historical discourse a heuristic that covers modern uses of the phrase would be that energies are "high" when the QCD can be treated as perturbative. That regime sets in considerably above the nucleon mass scale, say 10s of GeV. So LHC physics is in, JLAB physics is out (even with the 12 GeV upgrade).


1

The meaning of infinity in an equation is always contextual. One example is the Lorentz factor, which shows the strength of relativistic effects $$ \gamma = \frac{1}{\sqrt{1-v^2/c^2}} $$ If we set the speed in the equation to the speed of light, then the Lorentz factor goes to infinity. This isn't a problem, because objects can only approach, but never ...


1

Mathematical approximation of physical models is one reason. Take for example the spring mass oscillator where damping, assumed to be negligible is entirely discounted. A linear systems model in terms of a Laplace transfer function relating displacement of the mass relative to applied force is $$\frac{x(s)}{F(s)}=\frac{k}{s^2+\omega^2}$$ The roots of the ...


1

Some years ago, Gerard 't Hooft posted "How to Become a Good Theoretical Physicist", which is more inclusive than just string theory but which you'll probably still find a valuable list. Here's what he recommends for mathematics: "Primary Mathematics": Natural numbers: 1, 2, 3, … Integers: …, -3, -2, -1, 0, 1, 2, … Rational numbers (fractions): ...



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