By Jayant V. Narlikar
Normal relativity is now an important a part of undergraduate and graduate classes in physics, astrophysics and utilized arithmetic. this easy, straight forward advent to relativity is perfect for a primary direction within the topic. starting with a entire yet uncomplicated assessment of targeted relativity, the e-book creates a framework from which to release the information of basic relativity. After describing the fundamental thought, it strikes directly to describe very important functions to astrophysics, black gap physics, and cosmology. numerous labored examples, and various figures and photographs, support scholars take pleasure in the underlying options. There also are a hundred and eighty routines which attempt and boost students' figuring out of the topic. The textbook offers all of the worthwhile info and dialogue for an undemanding method of relativity. Password-protected options to the workouts can be found to teachers at www.cambridge.org/9780521735612.
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Extra resources for An Introduction to Relativity
47), we have finally the relation 1 1 h − = (1 − cos φ). ν2 ν1 m0 That is, in terms of wavelengths, λ2 − λ 1 = h (1 − cos φ). m0 This is known as Compton scattering because the change of wavelength of the photon on scattering was first measured by A. H. Compton in 1923. The signature of the effect is that the change in wavelength does not depend on the initial wavelength of the photon. It is dependent only on the angle of scattering. The quantity h/(m 0 c) is usually referred to as the Compton wavelength of the electron.
So his 4-velocity is γ (1, u), where γ −1 = 1 − u 2 . We therefore have p2 + m 20 × γ − γ p · u. Therefore the energy measured by the Pi u i = observer is E = γ ( p02 + m 20 − p · u). 4 Problem. A particle of rest mass m 0 moving with velocity v collides with a stationery particle of rest mass M and is absorbed by it. Given that energy and momentum are conserved in the collision, find the rest mass and velocity of the composite particle. Solution. The 4-momentum of the moving particle is [m 0 γ , m 0 γ v, 0, 0], √ where the direction of motion is chosen as the x-axis; γ −1 = 1 − v 2 .
We begin with the simplest physical notion. A scalar or an invariant does not change under any change of coordinates. Thus if φ (x i ) is a function of coordinates, then it is invariant provided that it retains its value under a transformation from x i to new coordinates x i : φ(x i ) = φ[x i (x k )] = φ (x k ). 11) Note that the form of the function may change, but its value does not. 6) is a scalar quantity. In our example of vectors in two dimensions, we had 45 46 P A i Vectors and tensors encountered the property that the magnitude of a vector does not change under the coordinate transformation representing rotation of axes.
An Introduction to Relativity by Jayant V. Narlikar