(Posted on the Science forum as well but it seems many on there don't come here or vice versa)
The following is a list of most conservation laws (both classical and quantum) and the reason they exist (i.e. the root cause for the observed conservation in terms of symmetry or invariance.)
(I think this list is from a paper by Victor Stenger but I don't have the paper or reference any more.)
Many people (especially Creationists) seem to get especially confused when applying energy conservation (1st Law of Thermodynamics) and the 2nd Law of Thermodynamics. How many times do you here the 'Big Bang cannot happen because it violates energy conservation' or 'the Big Bang violates the order-disorder nature of the 2nd Law'.
Note that we don't have energy conservation without time translational symmetry - thus the Big Bang having a time singularity (t=0) can make no statement as to whether total energy is conserved. On top of this General Relativity cannot even calculate the total energy of the Universe anyway. Also note that the arrow of time cannot be defined in quantum gravity regime such as when we approach t=0. Therefore to make any 2nd Law statements is invalid.
The net result is that Thermodynamics DOES NOT APPLY at the Big Bang in any form we know of. So to make carte blanche statements that the Big Bang cannot happen because it violates Thermodynamics is just a typical ill thought out Creationist argument from people who don't know any theoretical physics.
Conservation of momentum ------------ Space translation symmetry
Conservation of angular momentum ------------Space rotation symmetry
Conservation of energy (First law of thermodynamics)------------ Time translation symmetry
Newton's 1st Law of Motion Conservation of momentum -----------(space translation symmetry)
Newton's 2nd Law of Motion ------------Definition of force
Newton's 3rd Law of Motion Conservation of momentum------------(space translation symmetry)
Second law of thermodynamics -----------Statistical definition of the arrow of time
Special relativity -----------Space-time rotation symmetry
Invariance of speed of light -----------Space-time rotation symmetry
General relativity -----------Principle of covariance
Quantum time evolution (time-dependent Schrödinger equation) ---------Global gauge invariance
Quantum operator differential forms ----------Global gauge invariance
Quantum operator commutation rules---------- Global gauge invariance
Quantization of action -----------Global gauge invariance
Quantization rules for angular momenta ----------Global gauge invariance
Maxwell's equations of electromagnetism ---------Local gauge invariance under U(1)
Quantum Lagrangians for particles in presence of electromagnetic field ------------Local gauge invariance under U(1)
Conservation of electric charge------------ Global gauge invariance under U(1)
Masslessness of photon ------------Local gauge invariance under U(1)
Conservation of weak isospin -----------Global gauge invariance under SU(2)
Electroweak Lagrangian ------------Mixing of U(1) and S(2) local gauge symmetries (spontaneous symmetry breaking)
Conservation of color charge ---------Global gauge invariance under SU(3)
Strong interaction Lagrangian -----------Local gauge invariance under SU(3)
Masslessness of gluon ----------Local gauge invariance under SU(3)
Structure of the vacuum (Higgs particles) --------Spontaneous symmetry breaking
Doublet structure of quarks and leptons -------------Conservation of weak isospin (global gauge invariance under SU(2))
Masses of particles -----------Higgs mechanism (spontaneous symmetry breaking)
The following is a list of most conservation laws (both classical and quantum) and the reason they exist (i.e. the root cause for the observed conservation in terms of symmetry or invariance.)
(I think this list is from a paper by Victor Stenger but I don't have the paper or reference any more.)
Many people (especially Creationists) seem to get especially confused when applying energy conservation (1st Law of Thermodynamics) and the 2nd Law of Thermodynamics. How many times do you here the 'Big Bang cannot happen because it violates energy conservation' or 'the Big Bang violates the order-disorder nature of the 2nd Law'.
Note that we don't have energy conservation without time translational symmetry - thus the Big Bang having a time singularity (t=0) can make no statement as to whether total energy is conserved. On top of this General Relativity cannot even calculate the total energy of the Universe anyway. Also note that the arrow of time cannot be defined in quantum gravity regime such as when we approach t=0. Therefore to make any 2nd Law statements is invalid.
The net result is that Thermodynamics DOES NOT APPLY at the Big Bang in any form we know of. So to make carte blanche statements that the Big Bang cannot happen because it violates Thermodynamics is just a typical ill thought out Creationist argument from people who don't know any theoretical physics.
Conservation of momentum ------------ Space translation symmetry
Conservation of angular momentum ------------Space rotation symmetry
Conservation of energy (First law of thermodynamics)------------ Time translation symmetry
Newton's 1st Law of Motion Conservation of momentum -----------(space translation symmetry)
Newton's 2nd Law of Motion ------------Definition of force
Newton's 3rd Law of Motion Conservation of momentum------------(space translation symmetry)
Second law of thermodynamics -----------Statistical definition of the arrow of time
Special relativity -----------Space-time rotation symmetry
Invariance of speed of light -----------Space-time rotation symmetry
General relativity -----------Principle of covariance
Quantum time evolution (time-dependent Schrödinger equation) ---------Global gauge invariance
Quantum operator differential forms ----------Global gauge invariance
Quantum operator commutation rules---------- Global gauge invariance
Quantization of action -----------Global gauge invariance
Quantization rules for angular momenta ----------Global gauge invariance
Maxwell's equations of electromagnetism ---------Local gauge invariance under U(1)
Quantum Lagrangians for particles in presence of electromagnetic field ------------Local gauge invariance under U(1)
Conservation of electric charge------------ Global gauge invariance under U(1)
Masslessness of photon ------------Local gauge invariance under U(1)
Conservation of weak isospin -----------Global gauge invariance under SU(2)
Electroweak Lagrangian ------------Mixing of U(1) and S(2) local gauge symmetries (spontaneous symmetry breaking)
Conservation of color charge ---------Global gauge invariance under SU(3)
Strong interaction Lagrangian -----------Local gauge invariance under SU(3)
Masslessness of gluon ----------Local gauge invariance under SU(3)
Structure of the vacuum (Higgs particles) --------Spontaneous symmetry breaking
Doublet structure of quarks and leptons -------------Conservation of weak isospin (global gauge invariance under SU(2))
Masses of particles -----------Higgs mechanism (spontaneous symmetry breaking)