#### Transcript 文學中的科學觀察

```宇宙的特質

97年3/15日

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『事實』和『理論』孿生子

Newton's First Law:
no Force, no Change in Motion
Law 1
Every body perseveres in its state of rest, or of uniform motion in a right
line, unless it is compelled to change that state by forces impressed
thereon.
Newton's Second Law:
Acceleration of a Body is Proportional to Force; Fnet, ext = ma
Law 2
The alteration of motion is ever proportional to the motive force
impressed; and is made in the direction of the right line in which that
force is impressed.
The unit of force is that force which causes a unit mass (one kilogram) to
accelerate with unit acceleration (one meter per second per second).
Newton's Third Law: Action and Reaction
Crucial observation: forces always arise as a mutual
interaction of two bodies, and the other body also feels the
force, but in the opposite direction.
Law 3
To every action there is always opposed an equal and
opposite reaction: or the mutual actions of two bodies upon
each other are always equal, and directed to contrary parts.
This law takes place also in attractions.
Technical Difficulties (conceptual)
concerning F=ma in solving Three
body problem(i.e. Sun, Moon, Earth
system) where analytical solution is
not possible

x  ax,
m  m/a
F = ma 保持不變
Our existence => failure of Newton
The bucket rotate with respect to:
Center of Mass of the Universe
F=ma：東西躺在無限延伸的絕對靜止時空中，

Need new ideas:
(1)Lagrangian (Scalar function, good for
symmetries studies)
(2) Hamiltonian (Phase space geometrical
characterization of problems)

「存在」是什麼意思?

「我思故我在」
Cogito ergo sum
I think therefore I am
「世界是由物體組成」只是個幻覺

「存在」只有非常短暫的近似意義。

「一尺之棰，曰取其半，萬世不竭」

F=ma：東西躺在無限延伸的絕對靜止時空中，

What are the goods and wrongs of:
F=
2
GmM/r
No time for propagation of signals
Space-Time = Matter- Energy Distribution
Space-Time becomes meaningless
without matter and vice versa
The Most important experiments of
Mankind in the next 10 to 30 years:
(1) LHC - new physics and vaccum
(2) LIGO and LISA - space and time
(3) WMAP - picture of universe
The LISA orbits are chosen to minimize changes in the distances
between spacecraft. Each spacecraft will be in an Earth-like orbit around
the Sun (shown here) with a period of one year. The spacecraft orbits will
be slightly elliptical and slightly tilted with respect to each other and with
respect to the plane of Earth's orbit.
The LISA spacecraft is based on a short cylinder 1.8 meters in diameter
and 0.5 meter high. The cylinder supports a Y-shaped tubular structure
that contains two instruments.
LISA will observe gravitational waves from several sources. One is the
coalescences of massive black holes that result from the merging of
galaxies.
LISA will observe gravitational waves from several sources. One is
stellar-mass black holes in-spiraling to massive black holes. LISA
will be probing conditions in galactic cusps, and providing precision,
high-field tests of gravitational theory.
LISA will observe gravitational waves from thousands of compact
binary star systems, including several known systems. Some will
contain black holes or neutron stars.

d=16t2

Karl Popper:

Hilbert 的夢想(1900 年元旦):

Kurt Gödel(哥德爾), 1931年的震撼

ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED
SYSTEMS 1 (1931)

Example:
(a) 無法排除自我指涉的系統, 如法律系統
(b) 宇宙(開放)可能不存在終極理, 如弦論
Implications of Godel
Godel Thm  (1) Language is richer then Mathematics
(2) Mind is richer then Mathematics
(3) Universe is richer then Mathematics

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