Physics 55 Friday, December 2, 2005 1.Quiz 7 (last quiz) 2.Relativistic mass, momentum, energy...

Physics 55Friday, December 2, 2005

1. Quiz 7 (last quiz)2. Relativistic mass, momentum, energy3. Introduction to General Relativity4. Einstein’s equivalence principle

Discussion Question

How would our world be different if the speed of light were 35 miles per hour?

Graphical Summary of Relativity Formulas

Will show this on the white board: sketches of how time, length, mass, energy, momentum vary with speed v when v becomes close to c.

An important point: the Newtonian formula for momentum, mv, needs to be corrected near the speed of light. The momentum does not become bounded with the value mc but can increase arbitrarily as v approaches c.

Relativistic momentum formula also shows that a particle at the speed of light (photon, graviton) can have finite momentum with zero mass.

Implications of Relativity: Design of 21st Century Research Devices like LHC

Large Hadron Collider (LHC)27 km (17 miles) long ring on Swiss-French border.

Neat Relativistic Optical Effectshttp://www.anu.edu.au/Physics/Searle/

The 1915 General Theory of Relativity: Gravity as a Distortion of Spacetime

Predictions:1. Space and time are not independent but form a single entity called

“spacetime”.2. Orbits of masses are shortest pathways (geodesics) in spacetime.3. Gravity is a geometrical distortion of spacetime, explains why inertial

mass (m in F=ma) same as gravitational mass (m in F=GmM/r2.4. Time slows down when clock is in stronger gravitational field.5. Additional precession of elliptical planetary orbits 6. Black holes can exist.7. Black holes must have singular point in their interior.8. Accelerating masses generate gravitational waves that propagate at

speed of light.9. Many predictions about cosmology such as possibility for space to

expand or contract, explains Hubble’s law.

Einstein’s Equivalence Principle

In any sufficiently small region of space, the effects of gravity can not be distinguished by any experiments from a constant acceleration.

PRS Question

A balloon full of He gas tied to a string is floating inside a car when the driver hits the accelerator and the car speeds up to the right. Then the He balloon will:

1. stay where it is. 2. move toward the back of the car. 3. move toward the front of the car.

Effect of Gravity on Clocks

The Gravitational RedshiftThe frequency of light is like an internal clock and so we might expect, and experiments confirm, that light “beats slower” and therefore has a longer wavelength in stronger gravitational fields compared to the same light in weak gravitational fields.

We can estimate the magnitude of this effect if we boldly try to use energy conservation on light with the quantum formula E=hf. Thus consider a monochromatic laser with wavelength =500 nm pointed upwards toward the ceiling H=4 m away. What wavelength and frequency is the light at the top of the room? Equate change in gravitational potential energy E=mgH (with m=E/c2=hf/c2) to change in photon energy E=hf. We get:

2

216

22 8

f 10 m/s 4 mor 4 10

f 3 10 m/s

hfmgH gH h f

c

gH

c

This is a tiny effect, wasn’t until 1960s that experimentalists could figure out how tomeasure such a small shift in frequency or wavelength. Note how Planck’s constant divided out and disappeared, indicating that quantum mechanics not involved here.

Implication of Special and General Relativity: Synchronizing Accurate Clocks for the Global

Position System (GPS)

Atomic clock, size of rice grain.