Let us start our journey of modern physics Part 3 by action principle. What is action principle? Let me first motivate the discussion of action principle by a few questions. Some of them are actually philosophical, not so physical at least at this moment, but this inspires us to think how nature should work. For example, think about the movie Matrix. Have you watched the movie series Matrix? In that movie, actually, our word is simulated by a computer program. If we think in that way, then how that computer program would be written. Now, we know relativity that a lot of things are relative, there is no absolute observer. If there is a programmer who is programming the laws of nature in our world, what would the programmer do? Would the programmer first define himself, herself as absolute observer and write down the laws of nature and add symmetries to announce that there does not exist absolute observers. Or is it possible that the ultimate code of nature that very fundamental laws of nature. Can they be written into some way which is not observer dependent, which is not relative to the motions status, to the angle or to some other preference choices physically and mathematically to the observer? Is the fundamental laws of nature relative to observer, or there is a better way, an invariant way to write down the laws of nature? The second question, what would the nature like to do? What would I like to do now? I'd like to show you how beautiful modern physics is, but what would the nature like to do? The nature appears like to tell you that the motion of an object is governed by the X double dot, the second time derivative plus the potential differentiated by X equals to 0. The equation of motion of this guy, which looks really different feeling compared to what would I like to do? I'd like to show you how beautiful physics is, this two motivations looks so different. Can we ask the question, what would the nature like to do and get a better answer? Also about the conservation laws of nature we have talked about in modern physics Part 1, that conservation laws are very important, but are they really the most fundamental laws of nature? Or they can be derived from something even more fundamental. Are the conservation laws of nature fundamental? Also we have learned some classical physics and in modern physics Part 2, we have introduced some quantum laws of nature. They looked so different. Are there any connections between the classical laws of nature and quantum laws of nature? Are they related? These questions are pretty abstract and let's also talk about a more practical question. The question is that in our physical reality, there are so many kinds of things that we'd like to describe. For example force of a particle, for example the electric and magnetic field, for example, gravity and for example, the laws inside a nucleus. For example, the inside proteins there are the quarks and what is the nature of these quarks? There are so many different aspects of laws of nature, since there are so many pieces of laws of nature and we'd like to study, for example, conservation laws, quantization, etc. we'd like to study that natures of these laws of nature altogether. We don't like to study them piece by piece. Then the relevant question is, do we have a unified description of all these laws of nature, all these questions, philosophical ones and physical ones, they can be at least in some extent, answer in one sentence. That sentence is nature is thrifty in all it's actions. What does that mean? What do I mean by an action? What do I mean by nature's thrifty in the actions? This will be the part of action principle.
