Transcript 文學中的科學觀察

宇宙的特質
余海禮
97年3/15日
真實與直覺間的芧貭與慌繆
例子:
(1)
(2)
(3)
(4)
(5)
為甚麽世界會存在固體
Zeno paradox
晚上天空為什麼會變黑？
為什麼需要牛頓第三定律
何謂存在?
真實與經驗相差異
『事實』和『理論』孿生子
尼彩:「沒有真理，只有詮釋」
沒有純粹的事實，只有理論觀照下的事實！
柏拉圖:「即使有物存在，人也無法認識它」
任何『觀察』、『解釋現象』的理論都無可
避免地牽涉到一些有關該事實預設的先驗
觀念的框架!
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
牛頓力學沒有尺度 (scale)的慨唸
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，
神秘又難懂。
牛頓明白問題所在，但採取簡化忽略這些問題
的態度!
愛因期坦：「牛頓連選擇不去問的問題的抉擇
都是個偉大的抉擇」
Need new ideas:
(1)Lagrangian (Scalar function, good for
symmetries studies)
(2) Hamiltonian (Phase space geometrical
characterization of problems)
世界是否「存在」!?
「存在」是什麼意思?
笛卡兒(Rene Descartos,1596~1650):
「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
世界由物體組成的觀點及概念只是一個幻覺
世界是一個過程的歷史，運動與變化的因果關
係才是世界的本質。沒有東西「存在」，
「存在」只有非常短暫的近似意義。
原子論的基礎
「一尺之棰，曰取其半，萬世不竭」
無法解決Zeno Paradox之飛矢不動
F=ma：東西躺在無限延伸的絕對靜止時空中，
神秘又難懂。
牛頓明白問題所在，但採取簡化忽略這些問題
的態度!
愛因期坦：「牛頓連選擇不去問的問題的抉擇
都是個偉大的抉擇」
重要的教訓：
如果牛頓和萊布尼玆知道連續
函不見得有導數，微分學就不會誕生。
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.
近代物理的特質
從伽利畧開始,開始放棄物理解釋,
轉而尋求數學的描一述方法;
物理解釋是亞里士多德心目中科學的真正目標,近代科學
不在於找出原因,而在於量化
例如:
亞里士多德會試圖解釋物體墜落的原因,
伽利畧則描述成
d=16t2
完全未提及物體為何墜落
伽利畧專注描述,是科學方法上最深刻,
成果最豐碩的創新。
我們怎麼保證邏輯原理可以使用到如
無窮集合的數學呢？
如果邏輯只是人類經驗的產物，那麼我們
是否將邏輯擴展到沒有經驗基礎的心靈構
造上呢？
Karl Popper:
科學是:可以被証偽(Falsifiable)
Hilbert 的夢想(1900 年元旦):
一個非平庸(significant)
且具一致性(consistency)的
數學體系(formal system)是可以
完備地(completely)建立起來的.
就是說,像歐氏幾何一樣一定可以窮盡所有的定理.
Kurt Gödel(哥德爾), 1931年的震撼
不完備性定理
ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED
SYSTEMS 1 (1931)
公設系統是永遠不會完備的
所謂不完全定理就是說, 不論在什麼公設系統之內,
總會有個看起來很合理的敘述,而無法在系統內被
證明
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
語言是人類乞今最偉大的發明，
掌握了語言的等於掌握了世界