Ibliss: ?A new theory could lead to new concepts because new, previously unknown, phenomena are discovered. So, I was considering just the known phenomena.?
I am not so sure that you can do that. But in a way, you are supporting my view that the more fundamental the theory, the more the complexity increases.
Ibliss: ?Also, I would say that old concepts are in fact used in newer theories, even if they are strictly speaking redundant. E.g. mass and energy where two completely different concepts that have turned out to be the same thing (although when I was a first year physics student, the physics professor and his teaching assistant didn't agree on this).?
One more argument in support of the ?more fundamental means more complex?, i.e. more basic concepts/quantities. The redundancy, while it exists sometime, does not reduce significantly the number of concepts. Principially, redundancy can at the very best make a more fundamental theory have the same complexity with a less fundamental theory, and we already know this is not the case in fact. Also, you may want to think about say, topological field theory, there depending on the topology of the manifolds you end up with different sets of topological invariant quantities that you need to specify your system.
But I think that we can solve this issue of fundamentality/complexity for the theories we know by simply establishing a hierarchy of such theories, something like classical mechanics->quantum mechanics->quantum field theory, or classical mechanics->special relativity->general relativity->quantum gravitation, and then simply count the fundamental concepts involved.
As for the example you gave regarding mass and energy, personally I am more inclined to agree with the one saying that in fact they are not the same (I guess this would be the physics professor). Mass is still a measure of inertia (you cannot disregard the marticles with rest mass), while energy is significant in conservation laws. Sure, there is a definite relation between them, but they are principially not the same, in my oppinion. They describe different concepts, in spite of the traditional ?equivalence between mass and energy.
Iblisss: ?Now, I don't really see how general relativity contains more fundamental concepts than classical mechnics. Space and time did exist for Newton! They are just fixed quantities, but still fundamental (unexplainable) within classical mechanics. Moreover you have gravitational mass and inertial mass in classical mechanics. I already mentioned energy and mass above.?
I guess we disagree here. Sure, the concepts exist in Newtonian theory, as fundamental concepts, though I would not put it quite this way. In newtonian theory, geometry is just a background, and the fundamental concepts are related to absolute and relative postions and times. It is not part of the dynamics. In GR, while it retains space and time as fundamental issues, geometry itself becomes a dynamical variable . Sure, you can have GR on a fixed background, but you can also view GR as a background independent theory.
Ibliss: ?Also you could say that particles have all sorts of charges, hypercharges etc. which were not present in classical mechanics. But then classical mechanics doesn't say anything about particles. Every particle could have a different mass, charge etc. We know now that every electron has the same mass and charge. So you have far less free parameters.?
True, but in he more complex theory there are also more particles so to speak. And while in the more complex theory quantities as hypercharge, etc. occur naturally, in the less complex theory they don?t. Sure, you can introduce them ad-hoc in the less complex theory, but they don?t have any meaning. And you cget back to the old issue of superimposing theories (mechanics and say electromagnetism) versus unified theories.
Ibliss: ?It could explain why we find ourselves in this particular universe, rather than in some other.?
I don?t think that you are asking the right question at this time. In a sense I agree with Dan, although for slightly different reasons. At this moment in our history we know very little about the underlying complexity of our universe. The fact that we can describe mathematically in a more or less cumbersome manner the interaction between two very odd particles is only one face of the issue. Heck, at this time we are only toying with a form of inorganic chemistry so to speak. And I think we are eons away from having a consistent model describing say, the amoeba as a living organism. And by this I don?t just mean a that we need to extend physics in the realm of biology. What I also imply is that at this time in history we are not even able to construct a living cell from ?spare parts? although we know what they are, and although we have started to actually play a bit with modifying such parts in a living cell. But we still cannot ?frankenstein? to life a living cell. And by this argument, we are not privy to a lot of the ?surrounding? complexity that could beused somehow to answer your question.
Of course, we can use what we have as partial arguments for partial conclusions, but in my opinion at least, our partial knowledge at this time is far to puny to develop any significant conclusions. And for the time being, and even though this does not give me any pleasure, the anthropic principle is the best we have, even if we may or may not agree with it.
Ibliss: ?? you need to define a measure over the set of all possible universes first?.In fact, one can argue on purely physical grounds that the measure of a universe has to decay at least exponentially with the size of the algorithm that specifies it??
You have lost me here, I am simply not familiar with the measure arguments. So before I am able to give a more or less cogent answer, I would appreciate if you could provide me with some refs.
