bei48482_FM

Integrating by parts ( x dyxy y dx), KE m  0  mc^2  1 ^2 c^2  0 mc^2 Kinetic energy KE mc^2 mc^2 (1)mc^2 ( ...

It is worth emphasizing the difference between a conservedquantity, such as total energy, and an invariantquantity, such as prop ...

Relativity 29 Kinetic Energy at Low Speeds When the relative speed is small compared with c, the formula for kinetic energy mus ...

a moving object varies with its speed according to both classical and relativistic mechanics. The degree of accuracy required is ...

Hence E^2  (mc^2 )^2  p^2 c^2 (1.24) which is the formula we want. We note that, because mc^2 is invariant, so is E^2 p^2 c^2 ...

a massless particle—the photon—indeed exists and its behavior is as expected, as we shall find in Chap. 2. Electronvolts In atom ...

Solution (a) From Eq. (1.24) the electron’s total energy is E m^2 c^4 p^2 c^2 (0.511MeVc^2 )^2 c^4 (2.000MeVc)^2 ...

Gravity and Light It follows from the principle of equivalence that light should be subject to gravity. If a light beam is direc ...

Other Findings of General Relativity A further success of general relativity was the clearing up of a long-standing puzzle in as ...

inside that of Mercury. When gravity is weak, general relativity gives very nearly the same results as Newton’s formula FGm 1 m ...

The Lorentz Transformation 37 Appendix I to Chapter 1 The Lorentz Transformation S uppose we are in an inertial frame of referen ...

38 Appendix to Chapter 1 z z (1.28) In the absence of any indication to the contrary in our everyday experience, we fur- ther ...

Because the equations of physics must have the same form in both Sand S , we need only change the sign of (in order to take int ...

This expression for xwill be the same as that given by Eq. (1.38), namely, xct, provided that the quantity in the brackets equa ...

The Lorentz Transformation 41 y y (1.42) z z (1.43) t  (1.44) These equations comprise the Lorentz transformation.They ...

In order to find Lx 2 x 1 , the length of the rod as measured in the stationary frame Sat the time t, we make use of Eq. (1.41 ...

The Lorentz Transformation 43 The observer in S, however, measures the end of the same time interval to be t 2  so to her the d ...

Vx (1.49) Similarly, Vy (1.50) Vz (1.51) If V (^) xc,that is, if light is emitted in the moving frame S in its direction of ...

The Lorentz Transformation 45 t 1  according to Eq. (1.44), while the flare at x 2 and t 0 appears at the time t 2  Hence ...

Appendix II to Chapter 1 Spacetime A s we have seen, the concepts of space and time are inextricably mixed in nature. A length t ...