String Theory, Black Holes and the Fundamental Laws of Nature

来源:数学科学研究中心

String Theory, Black Holes and the Fundamental Laws of Nature
Andy Strominger
Center for Mathematical Schiences, Zhejiang University, Hangzhou
And
Harvard University, Cambridge MA, USA
Mar 30, 2005

  First I would like to thank Prof. Li Song for the opportunity to speak today. I’d also like to thank Prof. Yau Shing-Tung, Prof. Xu Hongwei and Prof. Liu Kefeng for the opportunity to spend the semester at wonderful Hangzhou, Zheda Center for Mathematical Sciences.
  I know that many in the audience are mathematicians. String theory has influenced mathematics. I would like to explain how physicists think about string theory.
  The scienctific quest to understand the basic laws of nature has been ongoing for centuries. This lecture will describe what may be the next major step, string theory.
  (the following picture describes the situation, people on earth wants to know how the nature works. They can see the sun. They conjectured that there are black holes. They also conjectured that everything is made of strings.)
Picture 1
  In the pursuit of knowledge, a contradiction or puzzle is our best friend. In 1905, Einstein puzzled about his image in a mirror moving faster than light speed, as in the figure below:
Picture 2
  Resolving this contradiction led to a shocking conclusion:
Nothing can travel faster than the speed of light
And transformed our view of space, time and the universe around us.

All such major revolutions in physics have been seeded by contradictions. As the diagram below shows the history:
Picture 3,4,
In the appearance of contradictions, experiments are also essential. The key experiments contradicting the old theory but supporting the new idea are shown in red in the picture above,

Einstein’s 1915 general theory of relativity says that the force of gravity is an illusion caused by the curvature of space and time. As in the picture below, the earth moved in a straight line in a curved space, whose curvature is caused by the sun.
Picture 5
The uncertainty principle of quantum mechanics says that all positions are uncertain. Andy Strominger could not tell where he is due to this uncertainty. It is not know what we will get if the uncertainty principle is combined with space-time curvature, so called the problem of quantum gravity.
Picture 6
Quantum mechanics has combined with electro-magnetism to give quantum electrodynamics, via quantum field theory. This quantum electrodynamics works for strong, weak and electromagnetic forces, tested to one part in 10 billion, which is the most accurate theory ever known.
Picture 7
When people try to combine quantum mechanics and general relativity via quantum field theory, it leads to divergence, as noted by Pauli in 50’s.
Picture 8
There are further puzzles when one attempts to apply the laws of quantum mechanics to black holes, as discovered by Hawking in the early 70’s.

For both of these reasons, the laws of physics as taught in Harvard University physics course 15-253 are inconsistent!

A second problem in modern physics is UNIFICATION. The known laws are a laundry list: strong force, weak force, space-time, electro-magnetism, gravity, quamtum mechanics, leptons, etc. People wants to have a unified theory to describe all these theories together, a hopeful candidate is string theory. Einstein spent the last half of his life on this unification problem, but he didn’t have enough pieces of physics theories to solve the problem.
Picture 9
What is string theory?

In string theory formulation, all particles are really strings under closer (10-33 cm) inspection. For example, a photon, an electron and a quark are described by a string as shown in the following picture:
Picture 10
There are infinite more particles which are heavy and unobservable but crucial for consistency. String theory unifies all forces and particles of nature, as different modes of the string, including gravity!

String theory is like a delicious soup in which mixed ideas from last 20 years combined in harmony, Kaluza-Klein, branes, super-symmetry, duality, gauge theories, etc.
Picture 11
String theory has been fruitful so far. For physics’ problem, it is related to confinement and black holes, which is the focus of this talk. String theory also produces unprecedented math-physics interaction such as mirror symmetry, Donaldson theory, knot theory, etc.
Picture 12
A Brief History of String theory is as follows:
~ 1950 Pauli notes the problem of quantum gravity.
~ 1970 String theory, the only known mathematical resolution, is discovered. But it is believed in capable of describing our universe because electrons and quarks are missing.
~ 1984 String theories using Calabi-Yau spaces are discovered which described universe remarkably like our own. Interest in the subject increases greatly.
~ 1995 – present Quantum jump in our understanding of string theory. The many “different” theories are found to be phases of a single theory, much as ice, water and vapor are phases of H2O. These developments lead to important insights into:
1) Quantum field theory.
2) Mathematics: algebraic geometry, Donaldson theory.
3) Quantum properties of black holes (this talk).
~ 20?? – String theory is proven correct.

Sadly, we don’t know when we will be able to prove or disprove the theory. However, indirect evidence for string theory has been obtained from Hawking’s contradiction involving quantum mechanics and black holes.

What is a black hole? As we know, due to gravity, moving objects need to exceed a certain speed limit in order not to fall back onto the planet, which is called the escape speed. The escape speed increases with the mass of the planet, on the moon the escape speed is about 2km/sec while on the earth it is about 11km/sec. If a celestial body has such a large mass that its escape speed exceeds the speed of light, then nothing can gets out of it and it is invisible to us . This is a black hole.
Picture 13
Black holes are the most mysterious objects in the universe and there is likely a huge one in our own galaxy. It is a hole in space with nothing on the other side.
Picture 14
If you really want to be rid of something, throw it in a black hole and it dissolves into the nothingness.

Stephen Hawking’s 1974 contradiction: When the effects of quantum mechanics are included, radiation boils off and the hole closes off, leaving no trace of what was thrown in. Hawking argues that information is lost forever.
Picture 15
But this contradicts quantum mechanics, which says that information is never lost. Hawking argued that quantum mechanics is wrong and needs to be corrected. A proper calculation requires a full theory that reconciles quantum mechanics and gravity. So let’s try string theory:
Picture 16
Instead of nothing we find strings!!! The contradiction is resolved. Quantum mechanics is restored. New insights are gained into other problems in math and physics.

Behind these words are precise and beautiful equations, which have both used and inspired modern developments in mathematics. Describing without equations is like trying to convey the beauty of Xi Hu with words but no photos.
Picture 17
But it is the best I can do in one hour! If you wants more, come to our center of Math Science workshop.

Conclusions:
Picture 18
String theory is a promising steppingstone to a better understanding of nature. We don’t know hwo far we have to go, but we seem to be moving forward.