# Five or four axioms for Qm

1. May 15, 2006

### Son Goku

I've read several QM texts which list five or four axioms for Qm, from which the rest is derived.

I was wondering what might the axioms of Classical Physics be.

I'm assuming one of them is:
$$\delta{S} = 0$$
What might the others be?

2. May 15, 2006

### MathematicalPhysicist

i can't think of any other axioms besides newton's three laws of motion, there's ofcourse the theorem of conservation of work (but it's not an axiom), and also of momentum.

3. May 15, 2006

### meemoe_uk

Thermodynamics - the laws of thermodynamics
Electromagnetism - maxwell's equations
Mechanics and gravity - newtons laws
Statisical mechanics - boltzmann's laws for gases

The axioms of these physical sciences were the axioms of classical physics.

Last edited: May 15, 2006
4. May 15, 2006

### Son Goku

The Maxwell Equations are derived though. I would have thought the axioms for Electromagnetism would have been something along the lines of:

1. "Particles have a quantity associated with them called charge....."
2. "......"
e.t.c.

From which Maxwell's Equations are derived.

5. May 15, 2006

### meemoe_uk

6. May 15, 2006

### masudr

Yeah, I'd go for

$$\mbox{1. extremizing } \int L dt \mbox{ with respect to neighbouring paths}$$

I can't think of anymore... you couldn't specify L = T - V, of course, because for some systems, that won't hold.

7. May 16, 2006

### arildno

A fundamental axiom in classical mechanics is conservation of mass for the material object.
This is as fundamental as Newton's laws of motion for the material object.

Last edited: May 16, 2006
8. May 16, 2006

### dextercioby

An axiomatic basis for Classical Nonrelativistic Mechanics could be

1. Newton's first law.
2. Newton's second law.
3. The principle of independence of the action of forces.
4. Newton's third law.
5. The weak principle of equivalence (stating the equality between inertial mass and gravitational mass).

From these all classical mechanics in inertial reference frames can be derived.

In the Lagrange formulation, we only have the variational principle and the same goes for Hamilton and Hamilton-Jacobi formulations.

For electrodynamics, one could postulate the most general form of Maxwell equations for nonmoving material media.

For equilibrium thermodynamics, we have two formulations, each with its own axioms: CTPCN and neogibbsian.

For statistical physics, we have an axiomatical formulation as well.

Daniel.

9. May 16, 2006

### arildno

And add to that conservation of mass.