Why do things like protons and neutrons have specific values. Also speed of light is a speed in which even if you go towards it, the speed does not vary. But why does light have to travel at speed?
Suppose you were given a book written in a language that you do not know. The analogy holds with unknown languages which are alphabetic. You start by seeing that a certain number of shapes repeat, you give them names as letters: you get an alphabet.
Charge, mass, spin and other distinguishing characteristics allow physicists to classify particles as A,B,C etc, because they have identical distinguishing characteristics. Actually when elementary particles were first seen in cosmic rays they were classified according to the greek alphabet: alpha rays, beta rays, gamma rays etc. The classification simplified the data and allowed for further observations. In the language analogy, words will be distinguished, grammar, then syntax, etc.
Edit since it was brought up again: so the answer to the question:
Why do things like protons and neutrons have specific values.
Because we have observed experimentally that they do, and these specific values allow for our distinguishing particles from each other. Only a Theory Of Everything could possibly answer with a cause for these values derived from principle, and theory is not there yet.
and the answer to the next query
But why does light have to travel at speed?
Is similar. Light travels at a specific speed irrespective of the framework system because it has been experimentally observed that it does both, it has a speed which is independent of framework.
Further experimental observations allowed classification of all particles in what is the Standard Model, a model that encapsulates the observational data up to now, and that is why it is important for any theory that is advanced about the way the world works: it has to be incorporated or come out of any theoretical model advanced as the Theory of Everything. Similarly for light, further studies established the Lorenz invariance system which also has to be incorporated into any TOE.
As the constant values are theoretically (with mathematical derivations) and also practically proves the assertions in resembling theories regardless different physical situations like in any inertial frame of reference and despite major/minute change in temperature, pressure in surrounding medium and also there will be no or negligible change in the constant value we consider is happen during this situations. Constants must has same value no matter they are being used in other theories and should give expected results.
Well, part of it is an experimental fact.
For particles, the definition of a type of particle (ie protons, neutrons, electrons) could be written 'a class of bodies with the same intrinsic properties'. So, all protons have the same properties. If each proton had a different charge, then we cannot call them all protons. We would have to call each of them a separate type of particle. So protons are all the same. Intrinsic roperties like mass, spin, charge, baryon number, etc. care the same. Note that properties like momentum need not be the same.
In fact, Wheeler, suggested that all electrons are the same electron. This comes from the notion that a positron can be thought of as an electron going backwards in time. So you can view an electron zigzagging through time, giving rise to multiple electrons at a point in time. There's a flaw with this:it require there to be equal numbers of electrons and positrons in the universe, which is as far as we know untrue.
Someone else may also post an answer showing how the masses and charges blossom from group theory, if they do at all (not sure of this).
The speed of light is more of an experimental fact. It can be thought to come from making Maxwell's laws more aesthetically pleasing. In the end, these laws are experimental facts as well, so it all comes from experimental evidence.
Light has to travel at a speed, otherwise it won't go anywhere. Yes, there's no issue with it going at infinite speed AFAICT, except for experimental evidence. I guess an alternate universe following the same laws could have infinite speed of light. Then again, such a universe would be overclassical; and magnetism wouldn't work (or electric forces would be infinitely large). But it would be much more like our everyday world. No wierd black holes, no wierd time issues.