bei48482_FM

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 c^2

(0.511MeV)^2 (2.000 MeV)^2 2.064 MeV

(b) From Eq. (1.25) the photon’s total energy is

E pc (2.000 MeVc)c 2.000 MeV

1.10 GENERAL RELATIVITY

Gravity is a warping of spacetime

Special relativity is concerned only with inertial frames of reference, that is, frames that

are not accelerated. Einstein’s 1916 general theory of relativitygoes further by in-

cluding the effects of accelerations on what we observe. Its essential conclusion is that

the force of gravity arises from a warping of spacetime around a body of matter

(Fig. 1.17). As a result, an object moving through such a region of space in general

follows a curved path rather than a straight one, and may even be trapped there.

The principle of equivalenceis central to general relativity:

An observer in a closed laboratory cannot distinguish between the effects pro-

duced by a gravitational field and those produced by an acceleration of the

laboratory.

This principle follows from the experimental observation (to better than 1 part in 10^12 )

that the inertial mass of an object, which governs the object’s acceleration when a force

acts on it, is always equal to its gravitational mass, which governs the gravitational

force another object exerts on it. (The two masses are actually proportional; the con-

stant of proportionality is set equal to 1 by an appropriate choice of the constant of

gravitation G.)

Relativity 33

Figure 1.17General relativity pictures gravity as a warping of spacetime due to the presence of a body

of matter. An object nearby experiences an attractive force as a result of this distortion, much as a

marble rolls toward the bottom of a depression in a rubber sheet. To paraphrase J. A. Wheeler, space-

time tells mass how to move, and mass tells spacetime how to curve.

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