Laws of Nature & the Arrow of Time

Symbreak
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The abundance of matter and antimatter implies the laws of nature are different for particles and antiparticles. This is shown in the way more b mesons than anti-b mesons decayed into kaons and pions - the weak force does not conserve charge/parity.

But if CP symmetry is not conserved, does this explain the arrow of time? Particle events, when reversed, would not be a mirror image of events in 'forward' time. Is there any explanation for why this is so?
 
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Symbreak said:
The abundance of matter and antimatter implies the laws of nature are different for particles and antiparticles. This is shown in the way more b mesons than anti-b mesons decayed into kaons and pions - the weak force does not conserve charge/parity.

But if CP symmetry is not conserved, does this explain the arrow of time? Particle events, when reversed, would not be a mirror image of events in 'forward' time. Is there any explanation for why this is so?

As I understand it, the unbrokenness of the CPT theorem means that if CP symmetry is broken then so is T symmetry. Back in the day of the original discovery of the non-P-regarding kaon decays, physicists were quick to assert that the weakly implied time asymmetry (still conditioned on C breaking) would NOT suffice to explain the overall time asymmetry of the universe. I think this is because particle theory notably does not DO the time of spacetime, but only depends on an arbitrary clock parameter and that symmetry would be what is broken.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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