I want to know something about special relativity.

I want to know something about special relativity.
I want to know something about special relativity.

I want to know something about special relativity.
If the observer in S sees an object moving along the x axis at velocity u,then the observer in the S' system,a frame of reference moving at velocity v in the x direction with respect to S,will see the object moving with velocity u' where
This equation can be derived from the space and time transformations above.
Notice that if the object were moving at the speed of light in the S system (i.e.),then it would also be moving at the speed of light in the S' system.Also,if both u and v are small with respect to the speed of light,we will recover the intuitive Galilean transformation of velocities:.
The usual example given is that of a train (call it system ) traveling due east with a velocity with respect to the tracks (system ).A child inside the train throws a baseball due east with a velocity with respect to the train.In classical physics,an observer at rest on the tracks will measure the velocity of the baseball as .In special relativity,this is no longer true.Instead,an observer on the tracks will measure the velocity of the baseball as .If and are small compared to ,then the above expression approaches the classical sum .
More generally,the baseball need not travel in the same direction as the train.To obtain the general formula for Einstein velocity addition,suppose an observer at rest in system measures the velocity of an object as .Let be an inertial system such that the relative velocity of to is ,where and are now vectors in .An observer at rest in will then measure the velocity of the object as[17]
where and are the components of parallel and perpendicular,respectively,to ,and .
Einstein's addition of colinear velocities is consistent with the Fizeau experiment which determined the speed of light in a fluid moving parallel to the light,but no experiment has ever tested the formula for the general case of non-parallel velocities.
[edit]Relativistic mechanics
Further information:Mass in special relativity and Conservation of energy
In addition to modifying notions of space and time,special relativity forces one to reconsider the concepts of mass,momentum,and energy,all of which are important constructs in Newtonian mechanics.Special relativity shows,in fact,that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated.
There are a couple of (equivalent) ways to define momentum and energy in SR.One method uses conservation laws.If these laws are to remain valid in SR they must be true in every possible reference frame.However,if one does some simple thought experiments using the Newtonian definitions of momentum and energy,one sees that these quantities are not conserved in SR.One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities.It is these new definitions which are taken as the correct ones for momentum and energy in SR.
The energy and momentum of an object with invariant mass m (also called rest mass in the case of a single particle),moving with velocity v with respect to a given frame of reference,are given by
respectively,where 纬 (the Lorentz factor) is given by
The quantity 纬m is often called the relativistic mass of the object in the given frame of reference,[41] although recently this concept is falling into disuse,and Lev B.Okun suggested that "this terminology [...] has no rational justification today",and should no longer be taught.[42] Other physicists,including Wolfgang Rindler and T.R.Sandin,have argued that relativistic mass is a useful concept and there is little reason to stop using it.[43] See Mass in special relativity for more information on this debate.Some authors use the symbol m to refer to relativistic mass,and the symbol m0 to refer to rest mass.[44]
The energy and momentum of an object with invariant mass m are related by the formulas
The first is referred to as the relativistic energy-momentum equation.While the energy E and the momentum p depend on the frame of reference in which they are measured,the quantity E2 − (pc)2 is invariant,being equal to the squared invariant mass of the object (up to the multiplicative constant c4).
It should be noted that the invariant mass of a system
is greater than the sum of the rest masses of the particles it is composed of (unless they are all stationary with respect to the center of mass of the system,and hence to each other).The sum of rest masses is not even always conserved in isolated systems,since rest mass may be converted to particles which individually have no mass,such as photons.Invariant mass,however,is conserved and invariant for all observers,so long as the system remains isolated (closed to all matter and energy).This is because even massless particles contribute invariant mass to systems,as also does the kinetic energy of particles.Thus,even under transformations of rest mass to photons or kinetic energy,the invariant mass of a system which contains these energies still reflects the invariant mass associated with them.

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