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Beauty as a Guiding Principle Beauty as a Guiding Principle In Search of Scientific TruthIn Search of Scientific Truth
Avshalom C. ElitzurAvshalom C. Elitzur
© © Everyone 2007Everyone 2007Permission is granted to everyone to copy and/or use this work or any part of itPermission is granted to everyone to copy and/or use this work or any part of it ..
Contents
2 .Classical Physics:Two Harmonies give rise to Disharmony
3. Special and General Relativity:Less Assumptions, More Explanations
4. Quantum Theory:Opposites Unite
5. A New DisharmonyWhat Comes Next?
1. Preface: The Scientific Ideal of Harmony
Pythagoras of Samos (ca. 560 – ca. 480 BC(
Are Truth and Beauty Related?
Mathematical BeautyTheorem: Every sum of consecutive odd numbers beginning with 1 is quadratic. 1+3=4=22
1+3+5=9=32
1+3+5+7=16=42 1+3+5+7+9=25=52 …
Human Beauty
Plato, 427-347 BC
Come on!
Ideas existed prior to objects!
Euclides, 365-300 AC
The Beauty in the Axiomatic System:Simplicity, Parsimony, Unity
Assumptions
Explanations
Euclides, 365-300 AC
The Beauty in the Axiomatic System:Simplicity, Parsimony, Unity
Unity Underlying Plurality
J. Kepler, 1571-1630
God must be a harmony freak…
Heliocentric(Copernicus, 1473-1543 )
Geocentric(Ptolemy, 85-165)
TWO WORLD VIEWS
Tetrahedron
Octahedron
Cube
Dodecahedron
Icosahedron
The Insight:
There are 6 planets
Hence 5 spaces between their spheres
There are also 5 perfect solids!
r1/r2 = 1/2
Mysterium Cosmographicum
I’m a genius alright!!!
T. Brahe (1546-1601)
O yeah ?
Mars deviates in 8 minutes!
?
I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
A=+B=Constant
II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.
III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.
Newton Simplifies
“To this purpose the philosophers say, that Nature does nothing in vain, and more is in vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”
Philosophiae Naturalis Principia Mathematica (1687) Book III, Rule I
First LawAn object at rest tends to stay in rest and an object in motion tends to stay in motion in a straight line at constant speed unless acted upon by an external, unbalanced force.
Second LawThe rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.
Third LawTo every action (force applied) there is an equal and opposite reaction (equal force applied in the opposite direction).
I. Newton, 1643-1727
Newton Unifies
Newton Unifies
Revealing the underlying unity
Predicting new Phenomena
Analyzing
A Scientific Theory is Beautifulwhen its Laws are
• Few • Simple• Invariant• Comprehensive• Reveal Order beneath Randomness• Unify Different and even Opposite Phenomena• Incorporate the laws of Earlier Theories• Predict New Phenomena
“It’s the simple things thattake your breath away”
R. Descartes, 1596-1650
I. Newton, 1643-1727
G. Galilei, 1564-1642
J. C. Maxwell, 1831-1879
J. Kepler, 1571-1630
M. Faraday , 1791-1867
Classical Physics:Observational Data gives rise to Mathematical Formalism
Contents
2 .Classical Physics:Two Harmonies give rise to Disharmony
3. Special and General Relativity:Less Assumptions, More Explanations
4. Quantum Theory:Opposites Unite
5. A New DisharmonyWhat Comes Next?
1. Preface: The Scientific Ideal of Harmony
MechanicsElectromagnetism
Galilean Invariance: Natural Lawshould appear the Same for every Observer
Galilean Invariance: Natural Lawshould appear the Same for every Observer
Galilean Invariance: Natural Lawshould appear the Same for every Observer
As long as motion is inertial, David can• Build a house of cards• Perform a brain surgery• Drink tea with old English ladies• Etc.
Galilean Invariance: Natural Lawshould appear the Same for every Observer
J. C. Maxwell, 1831-1879
Maxwell gets more than he bargained for
electricitymagnetismlight
electromagnetism
radiation 300,000 Km/sec
Maxwell gets more than he bargained for
“What would you say have you been told that the man you go out with has discovered the nature of the light coming from these stars?”
• The velocity of sound can be derived from the properties of air
• The velocity of water waves can be derived from the properties of water
• The velocity of light can be derived from the properties of
• But no one knows what are the properties of aether!
aether?
E=elasticity, ρ=viscosity
What’s so special about the speed of light?
A. Einstein, 1879-1955
Einstein demands harmony (& gets it)
If Maxwell’s equations are always valid, What about Galilean invariance?
And if Galilean invariance is always valid,would Maxwell’s equation lose their validity?
Contents
2 .Classical Physics:Two Harmonies give rise to Disharmony
3. Special and General Relativity:Less Assumptions, More Explanations
4. Quantum Theory:Opposites Unite
5. A New DisharmonyWhat Comes Next?
1. Preface: The Scientific Ideal of Harmony
Einstein asks (at 16):
• What happens if David, in the moving room, will play with a light ray rather than with a rock?
• What will I see if I ride on a light ray?
In our case:
Space is absolute Time is absolute The speed of light is absolute
Let’s replace two assumptions with one:
Einstein replies (at 26):
How can any speed be absolute for all observers?!
Galileo’s velocity addition rule: V1+V2
Galileo’s velocity addition rule: V1+V2
Galileo’s velocity addition rule: V1+V2
Galileo’s velocity addition rule: V1+V2
How can any speed be absolute for all observers?!
When a frame moves at a near-light velocity, its rulers contract and its clocks slow down relative to one another, such that light velocity remains 300,000 km/sec.
Assumption: Light velocity is constant for all observers
Conclusion: rulers’ length and clock rates are not equal for all observers
Galileo’s velocity addition rule:
Einstein’s velocity addition rule:2
21
21
1cvvvv
v1+v2
When an accelerated body approaches light velocity, the addition of energy cannot turn into velocity, hence it turns into mass.
E=Mc2
Assumption: Light velocity is constant for all observers
Conclusion: Nothing can go faster than light
How can any speed be absolute for all observers?!
Why is Einstein unhappy?
I want my relativity theory to hold also for non-inertial frames!
(please, pleeeaaase…)
A few years later…
“The happiest thought of my life…”
The Equivalence Principle
David in space
David freely falling
The Equivalence Principle
Mere coincidence of profound principle?
David resisting gravity
The Equivalence Principle
David accelerates upwards in space
The Equivalence Principle
Free fall = no gravity
Resisting gravity = acceleration
The Equivalence Principle
An incoming rock draws a parabola
Acceleration=Gravity
David accelerates upwards in space
An incoming rock draws a parabola
The Equivalence Principle
David resisting gravity
Einstein’s new question:
• What would David find if he studies the acceleration=gravity equivalence with a light ray rather than with a rock? Would the principle then turn invalid?
An incoming rock draws a parabola
David accelerates upwards in space
The Equivalence Principle
An incoming light draws a Parabola! ?_______
David resisting gravity
The Equivalence Principle:Einstein’s new prediction
The Equivalence Principle:Einstein’s new prediction
"Raffiniert ist der Hergott, aber boshaft ist er nicht !"
Subtle is the Lord, but not vicious!
פיקח הוא אלוהים, אבל לא מניאק!
Spacetime
H. Minkowski, 1864-1909
x
y
t
inertia
Gravitational curvature
Gravity=InertiaSpace=Time
Mass=Energy
Pygmalion (2002) Mark Dennis
Canzone di Leonardo.mp3
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