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MIDTERM: Wednesday 11/3
Consequences of Newtons Laws
1. Keplers laws follow as theorems from Newtons laws.
2. Galileos Earth-bound laws (freefall, trajectories of projectiles, periods of pendulums)
also follow as the
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Zoltan Domotor
465 Cohen Hall
Office Hours: MWF: 12-1
First reading: Frame of the Universe- Ch. 4,5
Universe, Space and Time
Universe as a whole is spherical. There is a part within it that is observable- handled by
non-invasive
Phil026 Midterm Review
P1. GEOCENTRIC COSMOLOGICAL MODELS
Pythagoras-Philolaus (500 BC)
Top-down and rationalistic model
o Top-down meaning that they cooked up the model and then explained
it/linked it to the universe. Why? They wanted to understand the
PHIL 026 Exam Review
11/4/12
Cosmological Theories
Challenges for Greeks in all cosmological systems:
Variable velocities of planets
Stationary points/retrograde motion, eclipses
Varying distances of planets from Earth (moon changes size, planets chang
Pythagoras-Philolaus model
Geocentric, with circular orbits. Center of the universe is the central fire, and the
counter-Earth blocks the Earth from the central fire.
This is true because a world created by God must be perfect, intentional, harmonious and
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Galileo and the Church
The conflict started with a letter addressed to Grand Duchess Christine. In 1616, Pope
V issues a decree that puts Copernicus on the Index. Cardinal Bellarmine notifies
Galileo about his letter
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Nicholas Copernicus (Conclusion)
Osiander edited/published Copernicuss book. Osiander wrote an unsigned preface,
changed the name of the book (without Copernicuss permission) to something that
sounded more Aristoteli
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Copernican Heliocentric Cosmological Model
The static sun is the center of the universe, with the planets (up to Saturn had been
discovered) orbiting around the sun, and the moon orbiting around the Earth, with an
en
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Ancient Cosmological Paradigms
Mini-paradigm shifts in the ancient geocentric tradition:
Pre-scientific cosmology Pythagoras-Philolaus cosm. paradigm Aristotelian strictly
geocentric cosmological paradigm Ptolemaic ge
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Ptolemaic Geocentric Cosmological Model (Conclusion)
The problem: Phenomena (data) indicate complex motions of the following kind:
Mercurys heart-like orbit from the vantage point of Earth.
1. Ptolemy saved the phenom
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I. Roots of Relativity
A world created by God.
Prominent cosmologists and philosophers of the ancient tradition:
900700 BC: Homeric period (pre-philosophy); 600 BC: Thales (starting point for
philosophy); 580 BC: *Pyt
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Reading: Frame of the Universe, Chapter 6
Aristotelian 2-Sphere Cosmological Model
Static Earth in the center of the universe. There is one sphere, on whichs surface is the
moon (so the first sphere is basically the m
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Aristotelian Strictly Geocentric 2-Sphere Model of the Universe (350 BC)
The Model
Earth is in the center of the universe (static, spherical Earth in center)
Arguments: If the Earth moved, then when you jump, you woul
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Reading: Frame of the Universe, ch. 8 (Copernican Revolution)
Ptolemaic Geocentric Cosmological Model (that saved all of the phenomena, 160
AD)
Trouble in the Aristotelian paradise
Variable distances of planets from t
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Next reading: Frame, ch. 12 Special Relativity
Newtons 4 Fundamental Theoretical Concepts
1. The notion of absolute space (infinite container conception). This notion also includes
the notion of absolute rest.
Exampl
Jeremy Cole
PHIL 026-401
Prof. Zoltan Domotor
12/15/10
1
Jeremy Cole
PHIL 026-401
Prof. Zoltan Domotor
12/15/10
Galileo and the Church
In 1632, Galileo Galilei published his lifes masterpiece, Dialogue Concerning
the Two Chief World Systems , in which he
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Term paper: 15 pages double spaced, on anything that is covered this semester.
Curved Spacetime
Minkowski spacetime and its light cone structure.
With time on the y-axis, and space coordinate on the x-axis, the light
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Confirmation of Relativity Theories
Definition: An event (phenomenon) E is said to confirm a hypothesis H in theory T just in
case the following conditions are satisfied:
Event E is observed out there.
The descriptio
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Reading: Today: Frame, ch. 13- General Relativity. Next week: Frame, ch. 14Relativistic cosmological models.
General Relativity (Einstein 1915)
Basic concepts
Inertial force arises in the presence of acceleration (fo
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Problem Areas
P1- Geometric cosmological models (Frame, Ch. 4,5,6)- Pythagoras-Philolaus, Aristotle,
Ptolemy
Pythagoras-Philolaus (580 BC)
Underlying metaphysics: Triangle with numbers at one angle (top), music at an
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Consequences of Special Relativity (cont.)
1. Relativistic composition of velocities
2. Minkowski light cone structure of spacetime
3. Nonexistence of absolute simultaneity- Time has sense only in reference to its
me
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Consequences of the Two Principles of Special Relativity
1. Nonlinear relativistic composition of velocities: V 1 V2=(V1+V2)/(1+(V1V2/c2) c.
V c=(V+c)/(1+(v/c) x c/c=(v+c)c)/(c+v)=c.
2. Minkowski light cone structure
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Newtons Laws of Motion
L1 Law of inertia- All bodies move in a straight line with constant velocity (or remain in a
state of rest) if no forces act upon them (Descartes).
Symbolically: Force(b,t)=0 velocity (b,t)=con
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Johannes Kepler (1571-1630)
Keplers laws (empirical rather than theoretical, meaning Kepler simply put down a
summary statement of his observations, he does not give explanations).
Law of ellipses- All planets move i
LECTURE 19
Consequences of Newtons Laws
Recall the second law of motion: F = m*a
and the law of gravity: F = * m*m/r2
m*a = * m*m/r2
d2x/dt2 = * m/r2(t)
This equation has 3 typical solutions:
i. collision
ii. passing each other
iii. moving in elliptical o
10/15
Next Reading: Ch. 12 in Frame
Newtons Concepts and Laws
CONCEPTS
Space (Container metaphysics)
Time:
o One-dimensional oriented continuum, with no beginning and end.
o It is not affected by any events/phenomena occurring in it.
o It flows homogene
GENERAL RELATIVITY (GR)
(Einstein 1915)
GR is based on two principles:
1. Local Principle of equivalence
2. Relativistic gravitational field equations (10 partial differential equations)
Local Principle of equivalence
At each spacetime point gravitationa
LECTURE 1
Knowledge comes in stages
Must have high degree of confidence its right BUT
Not always right -> EVOLVES
The method of paradigm shifts
Thomas Kuhn
When shifts, old paradigms are dislodged and given to history
4 paradigms
Greek paradigm
why
LECTURE 2
Four Worldviews regarding the Universe and its content (survey)
1. Greek (Aristotelian)- did not see much because did not have telescopes
2. Newtonian- fits far the best with our intuition, but its not correct
3. Relativistic- and this is not ev
LECTURE 3
I. Roots of Relativity
1. Greek Cosmological Models
1.a. Pythagorean (similar to Aristotles model)
1.b.
Pythagoras-Philolaus model
1.c. Aristotelian model
1.d.
Ptolemaic model
The Greeks assumed the premise that the universe is intelligible.
Fou