i'll first answer the second part
hope u gonna understand it coz i have tried to make'em as simple as i can
What is the difference between General & Special Relativity ?
Physical laws generally accepted by scientists before the development of the theory of relativity, now called classical laws, were based on the principles of mechanics enunciated late in the 17th century by the English mathematician and physicist Isaac Newton. Newtonian mechanics and relativistic mechanics differ in fundamental assumptions and mathematical development, but in most cases do not differ appreciably in net results; the behavior of a billiard ball when struck by another billiard ball, for example, may be predicted by mathematical calculations based on either type of mechanics and produce approximately identical results. Inasmuch as the classical mathematics is enormously simpler than the relativistic, the former is the preferred basis for such a calculation. In cases of high speeds, however, assuming that one of the billiard balls was moving at a speed approaching that of light, the two theories would predict entirely different types of behavior, and scientists today are quite certain that the relativistic predictions would be verified and the classical predictions would be proved incorrect.
In general, the difference between two predictions on the behavior of any moving object involves a factor discovered by the Dutch physicist Hendrik Antoon Lorentz, and the Irish physicist George Francis FitzGerald late in the 19th century. This factor is generally represented by the Greek letter β (beta) and is determined by the velocity of the object in accordance with the following equation:
in which v is the velocity of the object and c is the velocity of light . The beta factor does not differ essentially from unity for any velocity that is ordinarily encountered; the highest velocity encountered in ordinary ballistics, for example, is about 1.6 km/sec (about 1 mi/sec), the highest velocity obtainable by a rocket propelled by ordinary chemicals is a few times that, and the velocity of the earth as it moves around the sun is about 29 km/sec (about 18 mi/sec); at the last-named speed, the value of beta differs from unity by only five billionths. Thus, for ordinary terrestrial phenomena, the relativistic corrections are of little importance. When velocities are very large, however, as is sometimes the case in astronomical phenomena, relativistic corrections become significant. Similarly, relativity is important in calculating very large distances or very large aggregations of matter. As the quantum theory applies to the very small, so the relativity theory applies to the very large.
in few words
special relativity deals with high speeds so you get time dilation and general deals with regions of space that arent flat, which cause time to run slower
special = flat space
general = curved space
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about the derivations,,,
im going to solve ony the first one coz i dont have enough time to write the rest
Photon path as measured by a light clock looks like:
/\/\/\/\/\/\/\
If the moving light clock has speed v and takes t seconds for 1 round trip (as measured by our stationary light clock) then the light clock will have travelled a distance vt in 1 round trip.
Use pythag to find the length of the diagonal path.
sqr-root [{vt/2}² + h²], h = distance between the two mirrors.
Two digonal paths have length: 2*sqr-root [{vt/2}² + h²] ok
since the speed of light, c has a constant value it takes light 2*sqr-root [{vt/2}² + h²]/c seconds to complete a ouble journey, which solved for t gives: t = 2h/[sqr-root (c²-v²]
so t_moving = 2h/[sqr-root (c²-v²] ok
The time for 1 tick on the stationary clock, t_stationary = 2h/c
This means t_moving = t_stationary/[sqr-root{1- v²/c²) ok
hope u get it till here
if u have any further Qs
refer to ur teacher
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A Physical Question
