I often hear the phrase "working something out from first principles". Since I am not a physicist as such, I often wondered how many first principles there are and what are they. Can every classical formula in existance be derived from these?

Can anyone give me a list?

for example, in classical nonrelativistic particle mechanics, the first principles are:

space and time are homogeneous and isotropic.

there exist intertial frames, and all the laws of physics are the same in any interial frame (the principle of relativity)

the trajectory of any particle is uniquely determined by its position and velocity at some time (Newtonian determinism).

from these first principles, all of classical mechanics can be derived.

i could easily add Maxwells equations, the lorentz force law, and Newtons law of gravitation as some more first principles, and describe successfully many useful systems.

OK I suppose what I really wanted to know was how many formulas are there to successfully derive every existing formula in classical physics today? There probably isnt that many.

If its a lot to write down can anyone provide a good website that has them listed?

Originally posted by John Connellan
OK I suppose what I really wanted to know was how many formulas are there to successfully derive every existing formula in classical physics today? There probably isnt that many.

If its a lot to write down can anyone provide a good website that has them listed?

every existing formula? i guess i am not really sure what you are looking for, or even that your question makes sense.

my immediate answer is that there is only one formula, or there is an infinite number of them, depending on what you mean.

in some sense, the only formula in classical particle physics is F=ma. all other facts about the trajectory can be discovered by solving that equation.

on the other hand, the exact form of this equation and its solutions depends on the system you are trying to solve. there are an infinite number of possible phase spaces and an infinite number of possible dynamics in those phase spaces.

what kind of a list did you want to see?

Originally posted by John Connellan
I often hear the phrase "working something out from first principles". Since I am not a physicist as such, I often wondered how many first principles there are and what are they. Can every classical formula in existance be derived from these?

Can anyone give me a list?

The problem here is one of langauage.

In physics "working from first principles" roughly means "deriving results from basic assumptions". Usually it is stated after making a small number of assumptions then seeing where a logical train of thoughts leads you. If the result roughly matches reality you are onto a winner.

As such there are a very large number of "first principles" often up for revision as more and more is learned.

th "assuming a spherical horse" ed

OK I see, so first principles are to physics, what axioms are to mathmatics in a way? Is that right? They are merely things which for the moment are assumed and cannot be proven.

Originally posted by John Connellan
OK I see, so first principles are to physics, what axioms are to mathmatics in a way? Is that right? They are merely things which for the moment are assumed and cannot be proven.

That's my take on it, yes.

I suppose, in a way, the principles have been largely shown to be true but are not unassailable. The difference between this and an axiom is I suppose, subtle. A mathematical axiom really is unaissable as it does not relate to physical reality. A physicist deals with reality so uses a different set of starting assumptions. I am not having a dig at mathematicians, BTW.