fredag 2 maj 2014

The Principal Difference Between Laws and Principles of Physics

There are laws of physics and there are principles of physics. Examples of principles are:
  • Principle of Relativity: Physical laws take the same form in all systems of reference (Einstein).
  • Principle of Special Relativity: The speed of light is the same for all observers (Einstein).
  • Principle of Equivalence:  Inertial and gravitational mass are equal (Einstein).
  • Pauli's Exclusion Principle: No two particles with the same quantum numbers can be at the same position in space and time.
  • Principle of CPT Symmetry: Physical laws are invariant under charge conjugation, parity transformation and time reversal.
Examples of laws are:
  • Newton's 2nd Law: $F = am$.
  • Hooke's Law: $\sigma = E\epsilon$. 
  • Gauss' Law: $\nabla E =\rho$.
  • Faraday's Law: $\frac{\partial B}{\partial t}+\nabla\times E =0$.
  • Ampere's Law: $\frac{\partial E}{\partial t}-\nabla\times B =J$.
To seek to identify the difference between laws and principles, if any, recall how Einstein introduces the Special Theory of Relativity in his 1905 annus mirabilis article On the Electrodynamics of Moving Bodies: 
  • The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.
  • We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. 
We see here how Einstein introduces principle as synonomous to postulate as stipulation or regulation or rule or dictate telling physicists how to view certain aspects of physics.

On the other hand, a physical law expresses a quantitative relation between different physical entities like the stress-strain relation of Hooke's law. 

We conclude:
  • Principles belong to modern physics.
  • Laws belong to classical physics (mechanics and electromagnetics). 
  • Laws are expressed in quantitative mathematical formulas. 
  • Principles are expressed in words.
  • Laws are statements about physical reality (which may or may not be true).
  • Principles express stipulations which are to be respected by physicists, which are not statements about physical reality which can be true or false, but definitions which are true by construction. 
  • Principles are man-made and need no justification.
  • Laws relate to physical reality and require justification.
  • A principle should be viewed with critical suspicion.
  • A law may be viewed with admiration. 
One may wonder why physics as principle as judiciary law as regulation as dictate, has become the trademark of modern physics, when modern society is democracy and not dictatorship. 

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