Theoretical physics (
IMHO)
Theoretical physics attempts to
gain knowledge about the world by
abstracting the physically important information
in a system and then playing with
the abstraction. Any system has
a huge amount of information associated with it
and it is beyond our ability to deal with all of
this information so we try to simplify
and idealise the system. If we are looking
at a ball rolling down a hill then
the colour of the ball will usually
not be important, perhaps we will
neglect the air resistance, treat the ball as a point like
particle. This is the process
of making a model, later we may find that
we wish to refine our model
our throw it out in favor of some radically different model. Having deep physical insight
is often connected with the ability to
find the important parts of a system
to model or understanding the weaknesses
and strengths of different models.
Richard P. Feynman had superb physical insight,
he said that he would make a little
picture in his head and he would keep
adding to it and eventually he would know how
a system ought to behave.
Through trial and error
it seems that the universe likes to behave
in a mathematical way, light intensity falls of as
the inverse of the square of the distance, this is
a mathematical relation that always holds.
As theoretical physics has evolved
it has been found that the
physics of the every day is rooted in
deeply mathematical objects, vectors,
tensors, geometric forms. The world
of these mathematical creatures is very broad,
much broader than the physics we may wish
to represent with them.
One of the deepest questions in physics is why do some
mathematical objects seem to correspond
to reality and not others? (I can't
give an answer to that one, well not yet)
Once we abstract two different physical
systems sometimes the underlying
mathematical structure is found to be the same and working
backwards from there
a new and exciting connection is found
between the two apparently different
physical systems. We have learnt something new
about the world around us. The greatest example of
this in my mind is the connection Newton
made between the moon and an apple falling in his back yard.
In one sweep he connected the
celestial to the mundane. Other equally deep
connections have been found in recent years,
the unification of the strong weak and
electromagentic forces is the best modern example.
The extent to which one can play with one's model
is restricted by what is mathematically allowed
and by experimental evidence. There have been
many nice theories, but if they don't agree with
what we see it's bye bye.
Einstein was always drawn by the elegance of
a theory. He believed that the beautiful theory
must be the correct one. The arbitrary nature
of quantum mechanics seemed so ugly to him
that he never believed in it.
The flow chart below is a summary of these
ideas.
So are those mathematical structures,
atoms, quarks, strings, are they real?
I guess that depends on which shadows you
like to look at ;)
transformation
governed by
experiment and
formal mathematics

mathematical  new allowed
construct  construct
^ 
 
 
(abstraction period of
through interpretation
modeling) 
 
 (previously unknown relation) V
physical world  new/simpler
picture