Emerging Complexity inPhysicsHow does Physical Complexity arise from Basic Particles and Simple Principles?

Ronald WestraDep. MathematicsMaastricht University November, 2005

Part 2a

The Character of Physical Laws and the Structure of Space and Time

Emergent Complexity in Physics UCM Course LS213 –2005/2006

Course outline

1. Lectures from Syllabus ‘Emergent Complexity in Physics’

2. Focus project: Life as emergent property: the physics of the abiotic processes en route to evolution

The History of Modern Physics

Thomas Kuhn (1922-1996 )

The Structure of Scientific Revolutions (~1962 )

Thomas Kuhn (1922-1996 )

The Structure of Scientific Revolutions (SSR) (1962)

Central idea :

Science does not evolve gradually toward truth, but instead undergoes periodic revolutions which he calls "paradigm shifts."

The role of Observations

and Experiments

St. Augustinus

All truth follows directly from the Holy Scriptures.

(De Civitate Dei, 5th century a.D.)

René Descartes1596-1650

Meditationes de Prima Philosophia (1641):

The exist Unchanceable Laws of Nature in space and time that govern all elementary building stones of Nature.

René Descartes1596-1650

These natural laws are completely rational and can be induced by logical reasoning using the language of mathematics

Therefore it is not necessary to validate these laws experimentally.

René Descartes1596-1650

Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and instead admitting only deduction as a method.

Blaise Pascal1623 - 1662

The first formulation

Of the

scientific methode:

Blaise Pascal

“In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity.”

Communication with Estienne Noel (1648)

Blaise Pascal

His insistence on the existence of the vacuum also led to conflict with a number of other prominent scientists, including Descartes.

The Scientific Method

The Scientific Method

Experiment / Observation

(Mathematical) Theory

Isaac Newton (1642-1727) 

Example: Gravity

Observations celestial orbits

(Mathematical) Theory

Experiments pendulum, falling apples

Newton sets the standard T * Absolute space and time

* derived quantities: velocity, accelaration, momentum (=impuls)

·   * abstraction of the point mass* abstract quantities: force, energy

             * dependance on position in space and time

Newton sets the standard T * The law of Nature as principle:

[1] the rate of change of the momentum of a point mass equals the resultant

force acting on it              [2] the force of gravity of a mass M acting on a point mass of mass m is proportional to the inverse of the square of their relative distance

 

According to NewtonT time t

place xmomentum pforce F

 

),( txFdt

pd

dt

xdmp

2),(

r

MmGtxF

According to NewtonT

N After Newton T * mathematisation of Physics·   * Extention of abstract quantities:             * E.g.: Electro-Magentism : Maxwell

N James Clerk Maxwell (1831-1879) 

T Electro-Magentism

NMichael Faraday(1791-1867) 

T Experimental findings and

principles: the law of Faraday

N James Clerk Maxwell The laws of Electro-Magnetisme

HHendrik Lorentz

Max Planck( 

Towards the end of the 19th Century Lord Kelvin had warned of two small clouds on the horizon of Newtonian Physics:

1. Ultraviolet catastrophe, photo-electric effect  

2. Michelson-Morley and aether-theory

(3. Brownian Motion)

Ultraviolet catastrophe TThe ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power. As observation showed this to be clearly false, it was one of the first clear indications of problems with classical physics.

Michelson-Morley experiment

Velocity of light does not depend on own velocity

Michelson-Morley experiment

Brownian MotionMolecules wiggle in fluid

Albert Einstein  Special Relativity (1905) solves MM’exp

Photoelectrisch effect (1905) QM

Brownian Motion (1905) Chaos Theory

 

EINSTEIN

and

RELATIVITY

EINSTEINs Blackboard in 1905:

How Einstein

REALY

discovered

relativity:

Michelson-Morley experiment

Velocity of light does not depend on own velocity

Michelson-Morley experiment

Special Relativity  In all inertial frames the velocity of light has the same value.

Direct mathematical consequences:

•time-intervals and lengths differ fordifferent observers

•Energy and mass are related as: E = mc2

Special Relativity 

E E = mc2

TThis is probably the most-well known equation in Physics

LLet us here take a simple course towards special relativity only involving the law of Pythagoras:

Special Relativity 

SSpecial Relativity 

BASIC PRINCIPLE: The Postulates of special relativity

1. First postulate (principle of relativity)

The laws of electrodynamics and optics will be valid for all frames of reference in which the laws of mechanics hold good (non-accelerating frames). In other words: Every physical theory should look the same mathematically to every inertial observer; the laws of physics are independent of the state of inertial motion.

SSpecial Relativity 

2. Second postulate (invariance of c)

Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body; here the velocity of light c is defined as the two-way velocity, determined with a single clock.

In other words: The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, and does not depend on the velocity of the object emitting the light.

Special Relativity 

in rest moving

Speciale Relativity 

Length of path according to fixed observer:

This also equals the velocity of light times the duration

Special Relativity 

This is the well-known expression of Einstein for time dilatation:

A moving clock ticks slower than a fixed clock. How much faster depends on the velocity v. If v increases towards the velocity of light c, than T becomes infinitely large.

When v = c the time of the moving clock is observed to be stopped … … has time stopped also?

Special Relativity - Dali

Einstein By Train

Special Relativity 

Consider a light flash of duration T in a train moving with velocity v.

How long this flash last for a fixed observer? - Call his observed duration: t.

Therefore the fixed observer measures the length of the pulse as:

Relativistic Four-Vectors  space: x + time: ict form:   Lorentz-transformation:

 

ict

xξ

1Ti

iIA

with : , and: c

v

21

1

space and time mix into one 4-dimensional entity:

spacetime

spacetime transforms as:

ξξ A'

space: x

time: t

time: t’

space: x’

event

TThe Cone

oof Light

 

The Twin Paradox 

The Twin Paradox 

The Twin Paradox 

The Twin Paradox 

The End