Thursday, May 24, 2007

Quantum Gravity

I just read Three Roads to Quantum Gravity by Lee Smolin. I was surprised at what he had to say. He made several points that gave me much food for thought:
  1. General relativity implies there is no such thing as space and time without objects. Space and time are not independent entities. I knew space were not absolute, but had never thought of this extreme position before. Related to this there are no objects, only processes.
  2. Quantum theory disagrees with relativity on precisely this point. Quantum theory assumes a static space-time background and so directly disagrees with relativity. This is why the two theories cannot be merged.
  3. String theory is also based on a static background. According to Smolin this means it cannot be the correct theory. However, it may be a useful tool just as Newton's mechanics are very useful even though they are wrong when relativistic speeds and gravity are involved. String theory methods have produced a lot of interesting results.
  4. Smolin and loop quantum gravity theorists propose that space and time are not continuous but discrete. In the 19th century materials were thought to be continuous. We now know they are discrete -- they have molecules and atoms. Smolin compares this situation to space. His main line of argument is that black holes appear to have a finite amount of information (proportional to the area!). If space were continuous black holes should be able to contain an infinite amount of information. This is mostly theoretical but it is testable.
My thoughts:
  1. Despite these ideas being new to me, they seem to make a lot of sense. My feeling is that they are good. They do require a lot of re-thinking.
  2. Does #4 mean real numbers and real analysis do not really apply to our universe? Do we only need integers and number theory?
  3. Likewise do #1 and #4 mean that the universe is finite? Or at least that we cannot ever know if it is infinite? Smolin presented an idea I have heard before about how we can only know so much of our universe because of the speed-of-light limit. Basically we cannot know anything that happened too far away and too recently for light to have reached us. For example, we cannot know what happened yesterday on a star 100 light years away from us until 100 light-years from now. Since the universe is less than 14 billion years old, we cannot know about anything over 14 billion light-years away.
  4. If the universe is finite must there be a first cause? Here I move away from science into philosophy. I've always liked Aristotle's first-cause argument. If the universe has infinities it is not clear his argument works. Without infinities it seems like his argument is more valid. Quantum physics also argues against strict cause and effect and there are probably physicists (including Smolin) who could explain why this is still a weak argument.
Needless to say, I really liked his book and am tempted to read it again. It's been a long time since I've run into so many good new ideas. I was also impressed by how well he explained many physics topics that have until now been rather hazy to me.