Transcript Questions about Einstein’s Relativity Answered

STAV & AIP VCE Physics Teachers’ Conference, Feb 17 2006
Physics Oration
S: 37o 54.807’, E: 145o 07.940’
Questions about Einstein’s
Relativity
 Answered 
Prof David N. Jamieson
School of Physics
University of Melbourne
Einstein in 1905
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 thoughtexperiment 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!
S
N
Changing magnetic field makes and ELECTRIC field
Achtung!: There
does not need to be
two laws of Physics
here!
S
N
Moving charge in wires feels MAGNETIC force
What was the basic problem that Einstein was
concerned with pre 1905?
• Moving magnet is changing
flux
– Faraday Law of Induction
makes electrons move
 
d B
E.ds  

dt
loop
• Moving coil is moving
electrons
– Magnetic force makes
electrons move

 
FM  qv  B
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!
Maxwell 1873


The great treatise
of
electromagnetism
Electromagnetic
fields and waves
propagate
through the
Aether
 The Maxwell Equations do not have a place to
insert the relative motion of source and observer
Trouton Noble Experiment (1903)

FM
+

FE 
+
Or ?
+
+

FE
1
qq
rˆ
2
4o r

FE

FM
• • • •
+
+

v
+
+ 
v

v
• • Current,
• •
i

x +x x x v
B
x x x x

 
FM  qv  B
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
  q
 E.dA 
closed surface
II
Gauss’ Law for magnetism
o
 
 B.dA  0
closed surface
III
IV
Faraday’s Law of induction
 
d B
E
.d
s



dt
loop
Ampere-Maxwell Law
 
d E
loopB.ds  oi  o o dt
Predict the speed of light as an electromagnetic wave
c
1
 o o
Magnetic fields during charging of a capacitor
y
y

E  Ex ( x, y, z)xˆ  E y ( x, y, z)yˆ  Ez ( x, y, z)zˆ

v
B  Bx ( x, y, z)xˆ  By ( x, y, z)yˆ  Bz ( x, y, z)zˆ
x
x
Simulation from Maxwell
The Lorentz Transformations
• Can use Maxwell equations to find:

E  Ex ( x, y, z)xˆ  E y ( x, y, z)yˆ  Ez ( x, y, z)zˆ

B  Bx ( x, y, z)xˆ  By ( x, y, z)yˆ  Bz ( x, y, z)zˆ
• It was also found by Lorentz that the Maxwell
equations were invariant under the transformations:
x   ( x  vt) 1904: Lorentz transforms
y  y
z  z
t    (t  vx / c 2 )
  1/ 1  v2 / c2
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!
s 2  c 2t 2  x 2  c 2t 2  x2
• What is meant by the space-time interval?
x   ( x  vt) 1904: Lorentz transforms
– This is like the
“distance”
y  y
between two
events
z  z
in spacetime
t    (t  vx / c 2 )
– An analogy may
help…
  1/ 1  v2 / c2
Maps of space
N
E