Scientific Philosophy : Popper’s Falsificationism

Now I want to talk about some theories about scientific philosophy. I want to introduce a great scientific philosopher Karl Popper(1902-1994) and his theory.

Popper’s theory is called “Falsificationism”(否證論), which means the nature of science is to prove a theory to be false. Every single theory is facing the challenge of experiment. We should derive propositions from theories or hypothesizes waiting to be tested. A scientific theory should have the ability to give a testable statement or prediction. This property is called “Falsifiability”(可證偽性). Therefore we can do experiments to test this theory. These experiments are called “crucial experiment”(決斷實驗). If a theory doesn’t satisfy the demand of falsifiability, it is not a “scientific” theory.

Does a theory pass the test of crucial experiment a correct theory? No! Crucial experiment only prove other theories are wrong. For example, the tests of Einstein’s theory of relativity didn’t prove relativity is correct, but prove Newton’s mechanics are wrong! Relativity is corroborated(被認可) temporarily.

Falsifiability as a definition of science is widely accepted by scientific community. But I cannot totally agree the original definition of falsifiability. In that case, mathematics and string theory are no longer science because they couldn’t give crucial experiment! Maybe we can expand the definition or falsifiability.

Next week I want to introduce another great philosopher Kuhn and his theory. 

We are living in a 11-dimensional world?-String theory and M-theory

　　

　　We are all composed of particles,quarks(夸克) and electrons,which we called elementary particles. In physical theories, we always think these particles as points. Is this idea true? Although this idea had made great contributions, it still has limitation.(Because general relativity cannot combined with quantum mechanics)

　　String theory(弦論)thought all elementary particles are strings. The vibration modes(震動模式) form different kind of particles. In order to make string theory possible, it demand the world has 10 dimensions! We know that we have 3 space dimensions and 1 time dimensions. String theory contains another 6 space dimensions.

　　Where are the 6 space dimensions? They all curled up like small circle(called Calabi-Yau manifold(卡拉比-丘流形)). They are so small that we couldn’t see them.

 

　

　  There are five different string theories before 1995.(In fact,six,the other one called Supergravity(超重力)) Great physicist and mathematician Edward Witten(I think he is the greatest physicist nowadays!) connect these theories by a great idea called duality(對偶性). The five theories are all bases of a bigger theory called M-theory. The theory promote string to brane(膜,2-d),which means the world has 11 dimensions!

　String theory is a very beautiful and difficult physical theory.(perhaps the most difficult one) The ideas are abstract but simple. My introduction is oversimplified, but I hope you will like it. In fact, I want to dedicate my life to study string theory.

Schrödinger's Cat and Many-Worlds Interpretation

　　One of the founder of quantum mechanics, Schrödinger didn’t believe Bohr’s Copenhagen interpretation(哥本哈根詮釋). He issued a thought experiment(思想實驗) called Schrödinger's Cat(薛丁格的貓) in 1935.

　　The details of this experiment are as below:we put a cat, a flask with hydrogen cyanide(氰化氫,毒氣) and a radioactive matter into a box. Within one hour, the decay probablity of the matter is 50％. Once the decay happen, the detector will break the flask and then the cat will die. 

 

　　

　　According to Copenhagen interpretation, after an hour the cat will be in superposition states(疊加態), alive and dead. This is ridiculous because cat cannot be alive and dead simultaneously! If you open the box then the state of cat will collapse to a single state, alive or dead.

　　Another alternative interpretation is Many-worlds interpretation(多世界詮釋), which is well-known as parallel universes(平行宇宙). It is actually a physical theory! The cat is both alive and dead before the observation, but the alive and dead cats are in different branches of universes.

　　MWI indicates that every time we make a decision, there is another “me” in parallel universe chooseing another choice! But the point I want to say is “cat is wretched(可憐的).”, maybe rabbit is a good alternative!

A Brief History of Quantum Mechanics

　　Two of the biggest revolutions of physics are relativity and quantum mechanics(量子力學). What is quantum mechanics? It is the rule governing the microscopic world and they are all come from the wave-particle duality(波粒二象性).

Newton

Huygens

　　 What is light? Newton thought light as particles. But another physicist Huygens(惠更斯) thought light as wave. In 1801, physicist Thomas Young’s experiment(double-silt experiment) showed that light is wave. Is it true? In fact, light has wave-particle duality(after Einstein’ photoelectric effect theory in 1905 confirmed it).

de Broglie

Schrödinger

　　
        Light can have the property of wave, can electron be wave? Physicist de Broglie(德布羅意) published this idea in 1924(proofed in 1927). He got Nobel prize in 1929 because of this paper(this is his Ph.D paper).

　　In 1926, Schrödinger (薛丁格) published his theory of quantum mechanics to describe electrons. He write down a beautiful equation called “Schrödinger’s equation”(薛丁格方程式). There is a wave functionψ(波函數) to represent the state of electron. But how to explainφis a big problem. This is because the strange property ofψ. In 1927, Born(波恩) explain it as probability distribution(機率分布).

Schrödinger’s equation

　　Great physicist Niels Bohr(尼爾斯．波耳) summarized and epitomized(集大成) the interpretations of quantum mechanics and issued his “complementarity principle”(互補原理) in 1927. These interpretations are called “Copenhagen interpretation”(哥本哈根詮釋) and therefore become standard explanation of quantum mechanics.

Niels Bohr

　　
   




     What is the strange property of ψ? Because of the wave-particle duality, electron has the property of wave called superposition(疊加). It allows electron in “any” place before we do an observation. After the observation, electron’s wave function ψ“collapse”(波函數塌陷) to a single state.

　　 These are brief history and theory of quantum mechanics. In next article,I want to talk how such theory lead to ridiculous conclusions.

Newton v.s. Einstein:The Theory of General Relativity

　　The problem of special relativity is that it cannot cover accelerating particles. In 1915, Einstein finished his theory of general relativity(廣義相對論) by equivalence principle(等效原理).Einstein once said:”I was…in the patent office at Bern(in 1907) when all of a sudden a thought occurred to me:’If a person falls freely, he will not feel his own weight.’I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.” This is equivalence principle,which connects acceleration with gravity. Therefore, Newton’s gravitational theory is just a approximation.

Equivalence principle

 

Einstein and Tagore

　　After a long time of try and error, Einstein finally write down the”Einstein gravitational field equation.”(愛因斯坦重力場方程式) It tells us gravity is just the curvature(曲率) of spacetime. Perhaps the diagrams are the best explanations.

Einstein gravitational field equation

　　The best interpretation of general relativity is by a great physicist John Wheeler:”spacetime tells matter how to move;matter tells spacetime how to curve”

　　The most important tests of general relativity are the curved light(光的彎曲) and precession of Mercury(水星的進動),especially the test of curved light in 1919. After that, Einstein become a world-famous person.

　　Strangely, Einstein didn’t get Nobel prize by relativity but by photoelectric effect(光電效應). This is because the theory of relativity is too controversial then.

　　For further applications of general relativity, you can search some keywords:cosmological constant(宇宙常數), gravitational wave(重力波),dark matter and dark energy(暗物質與暗能量).

　God particle:the origin of mass

　　The Nobel prize in physics of this year is for the discovery of Higgs boson(希格斯玻色子).There were a long history and stories about the “God particle”(上帝粒子).

　　We are all composed of particles.But why particles have mass? This is a big problem among physics community in early 1960s. Higgs particle(accurately, Higgs field) is the solution! In simple, there are a lot of Higgs particles filled up the space. Once we move, Higgs particle will collide with you. You wil feel a “resistance” and their potential energy will be absorbed by you. Therefore, you have mass!

potential energy of Higgs boson

　　Last year, on July 4,LHC(大型強子對撞機)told everyone that they have found a new particle. This year, on March 14,CERN(歐洲核子研究組織)issued a release that the previously detected new particles are Higgs boson.

  

Higgs

　　There are over six people have contributions on Higgs boson,but only Englert and Higgs got 2013 Nobel prize. This is because they are two of the first three people(one died in 2011) to publish their papers(1964 published).

　

Englert

　　The explanations and stories above are oversimplifications. So if there are some concepts seems confused and you want to know the details,you can ask me in private.

　　

　　If you want to know more by yourselves,here are some key words that you can google:boson(玻色子),spontaneous　symmetry breaking(自發對稱破缺), Nambu-Goldstone theorem(南部-戈德斯通定理),electroweak unified theory(電弱統一理論),standard model(標準模型)

I recommend this book!

This article is great! But may be a little difficult to you.http://case.ntu.edu.tw/blog/?p=14336

The Theory of Special Relativity

　　In 1905, the miraculous year of Albert Einstein. He was just a patent officer(專利員) in Bern.but he published 5 papers that changed the world. Two of them are about the theory of special relativity(狹義相對論).

　　In special relativity, Einstein proposed two important basic principles.The most crucial one is the principle of invariant light speed(光速不變原理): light in vacuum(真空) propagates with the speed c,which is independent of observers. That is,everyone observe the same speed of light no matter what your motion is. The principle leads to an interesting phenomenon called time dilation(時間膨脹). In short and simple, the faster you travel(but there is no acceleration, because you must in  inertial frame of reference(慣性座標系),the speed of you must be a constant or at rest), the slower time flow in other people’s observations on you.

　　There are a lot of paradoxes about special relativity because of time dilation, but the most interesting and famous paradox is the twin paradox(雙胞胎悖論). There are a pair of twin brothers, one aboard a spacecraft for long-distance space travel(the speed is close to the speed of light), while the other is left in the Earth. Results When the traveler returns to Earth, he found himself younger than his brothers(means you are in the “future”).But motion is relative, the person in spacecraft observe his brother in the earth is also very fast. Who will be the younger one? The answer is still the person in spacecraft. Solution is that the person must return to the earth, the process must have acceleration, we can therefore judge who is in motion.

　　The big problem of special relativity is that it is just for inertial frame of reference, I will tell you how Einstein promote his theory to general relativity(廣義相對論) to describe the accelerating particles in next article.