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Lecture One

# Lecture One. Introduction “Unfortunate” Relativity

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Lecture One

Introduction

“Unfortunate” Relativity

Everything is relative.

Criticism of “Everything is relative”

• Russell: Chapter 2

• Feynman: Vol.I, Chapter 16, Section 1

• Bohm: Chapter I

B. Russell, The ABC of Relativity, Chap. 2

Feynman Lecture, Vol. I, Chap. 16, Section 1

D. Bohm, The Special Theory of Relativity, Chap. 1

“Unfortunate” Relativity

Perhaps the name is unfortunate.B. Russell

The ABC of Relativity, Chap. 2

“Unfortunate” Relativity The name relativity theory was an unfortunate c

hoice: The relativity of space and time is not the essential thing.

A. Sommerfeld

quoted by Taylor and Wheeler

in Spacetime Physics, 2nd ed., p. 53

“Unfortunate” Relativity

The principle of relativity was first stated by Newton.

R. Feynman Feynman Lectures, vol.~I, p.~15-1.

Relativity Principle(earliest statement)

The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forward in a straight line without any circular motion.

Sir Issac Newton

Principia, Corollary V.

Relativity Principle(earliest statement)

Sir Isaac Newton, Principia

quoted by Jeans, Feynman, Resnick, and maybe others.

Relativity Principle(modern statement)

Einstein, 1905

The characteristic postulateof

Special Relativityis

The Principle of the Constancy of the Speed of Light

(rather than the Principle of Relativity).

“Thus the special theory of relativity does not depart from classical mechanics through the postulate of relativity, but through the postulate of the constancy of the velocity of light in vacuo.”

A. Einstein (1916)

“Unfortunate” Relativity• 相對性原理（ Principle of Relativity ）並非相對論所特有

• 從牛頓以來的古典物理都共許相對性原理

• 時空的相對性並非核心關鍵 essential

• 不遷性（ invariance ）才是核心關鍵

The constancy of the speed of light is essential in Special Relativity.

E = mc2

E = mc2

c: 古典物理與相對論的分野m: kinematics 與 dynamics 的分野

c 299 792 458 m/sec(exact)

meter (1983)• One meter is the distance

traveled by light, in vacuum, in the fraction 1/299,792,458 of a second.

second (1967)• The second is the duration of

9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the fundamental state of the atom of cesium 133.

• frequency = 9192631770 cps

• wavelength ~ 3.26 cm (microwave) cycle per second

Phys. Rev. 137, A702 (1965)

Physical Review Letter 1, 105 (1958)

• Cesium is the best choice of atom for such a measurement because all of its 55 electrons but the outermost are confined to orbits in stable shells of electromagnetic force.

• Thus, the outermost electron is not disturbed much by the others.

• The cesium atoms are kept in a very good vacuum of about 10 trillionths of an atmosphere so that the cesium atoms are little affected by other particles.

• All this means that they radiate in a narrow spectral line whose wavelength or frequency can be accurately determined.

Classical physics fails

as the speedtends to c.

Notationv : relative velocity between inertial frames of reference

u : velocity of object

Macroscopic world

• artificial satellite （人造衛星） u 18,000 mph (miles per hour)

u/c 2.7×10 -5

• sound wave （聲波） u 300 m/sec

u/c 10 –6

Classical physics (Newtonian mechanics) works

Microscopic world

• 10 MeV electron, u = 0.9988 c• 40 MeV electron, u = 0.9999 c 2× 0.9988 c (1.9976 c)

Classical physics fails badly as u/c 1

Classical Physics

K = ½ m u ²

K 4 K, v 2 u

Microscopic world

• 10 MeV electron,

B = 2.0 weber/m ² r = 1.8 cm

0.53 cm

Classical physics fails badly as u/c 1

Classical Physics

r = m u / qB

MeV電荷 × 電位 = 能量

1 MeV = 1.6×10-13 J

MeV as mass unit 1 kg × c2

= (3.0×108) 2 J

= (3.0×108) 2 × (1.6×10-13) -1 MeV

= 5.61 × 1029 MeV

1 MeV/ c2 = 1.78 × 10-30 kg

MeV as mass unit電子質量 me = 9.11×10-31 kg

me c 2 = 9.11×10-31 × 5.61 ×1029 MeV

= 0.511 MeV 0.5 MeV

mp c 2 = 1.67×10-27 × 5.61 ×1029 MeV

= 938 MeV 1000 MeV(1Gev)

From MeV to u ？

• 何謂 10 MeV electron ？動能 K 為 10 MeV 的電子

• 但是因為古典物理不適用• 所以 K = ½ m u ² 不適用

u (2K/m) ½

Not yet！

Connection between Mechanics and Electromagnetism

• Why the validity of classical mechanics hinges upon the velocity of light？

• Because light plays a basic role in the measurements of space and time that underlie mechanics.

By critically examining the procedures used to measure length and time interval, Einstein developed the Special Theory of Relativity.

Crucial Issues•Principle of Relativity

•Speed of light (in vacuum)

Specification of an event in inertial reference frames

• Specification of an event in a reference frame by coordinates

• Comparison of the coordinates of an event with respect to different inertial frames of reference

Two ghosts in classical physics

•absolute motion

•inertial coordinate systemEinstein and Infeld: The Evolution of Physics

The ghost of absolute motion is expelled by

Special Relativity

The ghost of inertial coordinate system

is expelled by General Relativity

Homework Assignment

Chapter 1: 2, 3, 4, 7, 8.

The End

http://www.scu.edu.tw/physics/teacher/rency/