Questions about Einstein’s Relativity

Answered

Prof David N. JamiesonSchool of Physics

University of Melbourne

Einstein in 1905

STAV & AIP VCE Physics Teachers’ Conference, Feb 17 2006

Physics OrationS: 37o 54.807’, E: 145o 07.940’

Where did the Special Theory of Relativity come from?

• He seems to have been fascinated from an early age by the nature of light, a fascination that persisted throughout his life

• From an essay he wrote in 1895, (at age 16), we know that he then believed in the ether, and had heard of Hertz's experiments on the propagation of electromagnetic waves; but he does not show any knowledge of Maxwell's theory

• In much later reminiscences, he reports that during the following year (1895-1896) he conceived of a thought experiment: what would happen if an observer tried to chase a light wave? Could s/he catch up with it? If so, s/he ought to see a non-moving light wave form, which somehow seemed strange to him

• In retrospect, he called this "the first childish thought-experiment that was related to the special theory of relativity

This is from the text of "'What Song the Syrens Sang': How Did Einstein Discover Special Relativity?" as printed in John Stachel, Einstein from "B" to "Z" (Boston : Birkhäuser, 2002), pp. 157-169.

Can you catch a beam of light?

Mysterious Magnetism

How does a compass

work?

Two ways to make electricity!

NS

NS

Changing magnetic field makes and ELECTRIC field

Moving charge in wires feels MAGNETIC force

Achtung!: There does not need to be two laws of Physics here!

What was the basic problem that Einstein was concerned with pre 1905?

• Moving magnet is changing flux– Faraday Law of Induction

makes electrons move

• Moving coil is moving electrons– Magnetic force makes

electrons move

dt

d B

loop

s.dE

BvF

qM

Galileo: Can’t have a velocity

dependent force in mechanics!

The F=qvB force appeared to contradict the principle of inertia

• Comments on his apparent lack of knowledge of the Michelson-Morley experiment

– Einstein did not appear to know about it in 1905

• The implications of Maxwell’s equations

Galileo 1634 The laws of Physics do not depend on absolute motion

Does this include electromagnetism?

YES!

The Maxwell Equations do not have a place to insert the relative motion of source and observer

Maxwell 1873 The great treatise

of electromagnetism

Electromagnetic fields and waves propagate through the Aether

x x x x

x x x xB

• • • •

• • • •

Trouton Noble Experiment (1903)

rF ˆ4

12r

qq

oE

+

+

BvF

qM

++ v

+

+v v

+

Current, i

v

++

EF

EF

MF

MF

Or ?Not observed!

The (1905) paper was on the “electrodynamics of moving bodies”

• At first glance that doesn’t seem to make sense – moving bodies don’t have electromagnetic fields do they?– Yes! Even Lorentz knew matter was made of electrons and

ions (by 1904) • Does the Lorentz contraction occur in empty space?

– Yes! It arises from the relativity of simultaneity – even in empty space

• What was meant by that title?– New forces (magnetism) arise from a moving charge

• The full implications of the principle of relativity: His intuition that magnetic force was really electric force etc.“What led me more or less directly to the Special Theory of

Relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an

electric field.”

A. Einstein (1952), from a letter to the Michelson Commemorative Meeting of the Cleveland Physics Society, quoted by R.S. Shankland,

Am. J. Phys., 32, 16 (1964), p35.

How did Einstein come to the two postulates?

• Significance of Maxwell’s work, rather than MM expt. etc. – First postulate: Laws of Physics are the same in all

reference frames• This is an affirmation of Galileo now stated to apply

to all laws (mechanics and electromagnetism)– Second Postulate: Speed of light is independent of the

speed of the source and the observer• This flows directly from the Maxwell equations!

• Idea that the universe worked on ‘elegant’ principles (like relativity)– Not everyone agreed relativity was elegant!– F=ma is elegant, but not relativistically correct

The Lorentz transformations

• Why had Lorentz proposed them earlier?

– From the invariance of the Maxwell equations – see next slide!

• Was it to explain the MM expt?

– No! Fitzgerald proposed the length contraction to explain MM then appealed to Oliver Heaviside to provide a mechanism

– Heaviside’s derivation of the electric field of a moving charge particle revealed Special Relativity BEFORE Einstein but did not understand the implications.

• And why does Einstein get all (well most of) the credit?

– It was Einstein who linked the Lorentz transforms to the invariance of light and thereby uncovered the second postulate never before discovered by ANYONE else!

The Maxwell Equations

I Gauss’ Law for electrostatics

II Gauss’ Law for magnetism

III Faraday’s Law of induction

IV Ampere-Maxwell Law

Predict the speed of light as an electromagnetic wave

dt

di E

ooo

loop

s.dB

o

q

surface closed

A.dE

0surface closed

A.dB

dt

d B

loop

s.dE

oo

c1

Magnetic fields during charging of a capacitor

Simulation from Maxwell

zyxE ˆ),,(ˆ),,(ˆ),,( zyxEzyxEzyxE zyx

zyxB ˆ),,(ˆ),,(ˆ),,( zyxBzyxBzyxB zyx

y

x

v

y

x

The Lorentz Transformations

• Can use Maxwell equations to find:

• It was also found by Lorentz that the Maxwell equations were invariant under the transformations:

)( vtxx yy

zz

)/( 2cvxtt 22 /1/1 cv

1904: Lorentz transforms

zyxE ˆ),,(ˆ),,(ˆ),,( zyxEzyxEzyxE zyx

zyxB ˆ),,(ˆ),,(ˆ),,( zyxBzyxBzyxB zyx

The significance of this was unknown to 19th C Physics!

We sometimes say that relativity suggests a four dimensional world where we have 3 space and 1 time

dimensions • Are time and space in some way equivalent?

– No! They have different roles in the theory• In what way is time related to space as a dimension?

– Time and space dimensions can be exchanged be changing from one frame to another

• Is something in the 4D world invariant?– Yes!

• What is meant by the space-time interval?– This is like the

“distance”between twoeventsin spacetime

– An analogy mayhelp…

)( vtxx yy

zz

)/( 2cvxtt 22 /1/1 cv

1904: Lorentz transforms

2222222 xtcxtcs

Maps of spaceN

E