RELATIVITY_PART 2_RELATIVITY(Lorentz Transformations, Doppler Effect, Relative Momentum).pptx

RELATIVITY(Lorentz Transformations, Doppler Effect, Relative Momentum)

1. RELATIVITY The Lorentz transformations The Doppler effect for electromagnetic waves Relativistic momentum and energy

2. The Lorentz transformations The Lorentz coordinate transformations relate the coordinates and time of an event in an inertial frame S to the coordinates and time of the same event as observed in a second inertial frame S ¿ moving at velocity u relative to the first. For one- dimensional motion, a particle’s velocities v x in S and v x œ in S ¿ are related by the Lorentz velocity transformation. (See Examples 37.6 and 37.7.)

3. The Lorentz Transformations

4. Overview of Special Relativity 1905, Albert Einstein revolutionized physics by introducing this theory, which proposes that the laws of physics are the same for all observers in uniform motion relative to each other.

5. Postulates of Special Relativity The laws of physics are invariant (unchanged) in all inertial frames of reference. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or the observer.

6. The Need for Lorentz Transformations These postulates lead to consequences that challenge our classical notions of space and time. As objects move close to the speed of light, our intuitive understanding of simultaneity and the passage of time breaks down. This necessitates a new mathematical framework to describe how measurements of space and time vary between different inertial frames.

7. Lorentz Transformations - Key Concepts The Lorentz transformations provide this mathematical framework. They describe how coordinates of an event in space and time transform between two inertial frames moving relative to each other at a constant velocity.

8. Lorentz Factor The Lorentz transformations provide this mathematical framework. They describe how coordinates of an event in space and time transform between two inertial frames moving relative to each other at a constant velocity.

9. The Doppler effect for electromagnetic waves The Doppler effect is the frequency shift in light from a source due to the relative motion of source and observer. For a source moving toward the observer with speed u , Eq. (37.25) gives the received frequency ƒ in terms of the emitted frequency ƒ0. (See Example 37.8.)

10. Relativistic momentum and energy For a particle of rest mass m moving with velocity v , the relativistic momentum p is given by Eq. (37.27) or (37.31) and the relativistic kinetic energy K is given by Eq. (37.36). The total energy E is the sum of the kinetic energy and the rest energy mc 2. The total energy can also be expressed in terms of the magnitude of momentum p and rest mass m . (See Examples 37.9–37.11.)