In classical mechanics there is Noether's theorem: If a system has a certain symmetry there is a related conserved quantity. Energy conservation is a result of a system being time invariant. This is what I have learned in my classical physics and also quantum mechanics courses.

In Electroweak theory there is $CP$ violation which also means that time reversal $T$ is violated as $CPT = I$. Does this mean that energy conservation is violated in electroweak theory? If this would be true and since electroweak theory holds above the Planck (length) scale is it possible to create energy in a closed system?

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    $\begingroup$ electroweak theory holds above the Planck (length) scale. The relevant energy scale for the electroweak interaction is the ~1 TeV electroweak scale, not the Planck scale. $\endgroup$ – Ben Crowell Aug 15 '13 at 13:43

Noether's theorem does not apply to discrete symmetries like C, P, and T. Only continuous symmetries generate local conservation laws. For discrete symmetries you get multiplicate rather than additive conservation laws so they are somewhat less useful. Also note that T is an anti-unitary transformation so it is a little more subtle than the others.

On the other hand energy is a much nicer story. It is the Noether charge of time translations, a continuous symmetry, rather than time reversal. The standard model and all of its approximations and limits are time translation invariant and energy conservation holds perfectly well. In fact this is true for all non-cosmological theories in particle physics.

The one subtlety is cosmology. The expansion of the universe breaks time translation invariance (obviously) so you no longer have conservation of energy in the usual sense. This is a subtle point and debates about semantics abound (what exactly do you mean by energy is not a trivial question in general relativity). Local conservation of energy definitely holds, but... well it gets tricky at cosmological scales. If you search this site you will find a few questions related to all that.


No. Conservation of energy is generated by the continuous time translation symmetry $t \rightarrow t + \epsilon$. This is a differenty symmetry than the discrete time reversal symmetry $t \rightarrow -t$. Violating the latter symmetry does not mean that you violate the former symmetry.


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