Theoretical physics are, quite simply, physics that remain theoretical. This covers any areas of physics in which we can not actually confirm our hypotheses. This happens for various reasons; for instance, while the notion of their existence is fairly commonly accepted, black holes remain theoretical because we cannot actually confirm their existance, a) because they are located at a mind-buggering distance from here, and b) a black hole sucks everything within its event horizon, into it, which makes detecting evidence of its existence very difficult (to complicate matters, areas in which we suspect black holes may exist have been observed to emit radiation, although a possible explanation of this has been proposed (Hawking radiation.) Also, many subatomic particles remain theoretical because we have not yet generated energy levels that are high enough to produce them. The popular end of theoretical physics are the highly unlikely but theoretical hypotheses that are the bread and butter of many science fiction writers; time travel, wormholes, ansible technology, etc.

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 learn-t 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 ;)

                      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

Theoretical physics is not limited to what is not known or unreachable by human experiment and observation. It can be as simple as understanding why the vase you just dropped is falling towards the floor. It also grapples with the more complex question of why we never see a fractured vase magically reassemble from a million pieces, why time seems to be a one-way street.

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