Saturday, September 21, 2013

Experimental updates on the Weak Nuclear Force (and predictions for time irreversible dynamics)

This week, the Q-weak experiment at the Jefferson Lab published some initial results from an experiment in which they scattered electrons off of protons in the form of liquid hydrogen. The experiment involved sending in electrons of one spin, measuring the scattering angles, and then sending in electrons of opposite spin to measure the different in the scattering angles due to the difference spin of the electrons. The weak nuclear force caused differences in the scattering of electrons off of protons depending on the spin of the electrons because the weak nuclear force is parity asymmetric. From this difference in scattering, the researchers were able to measure the weak nuclear coupling constant for electrons and protons. This was the first time that researchers have isolated the weak charge of the proton at low collision energies. The value of this coupling constant is in good agreement with the Standard Model of physics. The figure below (Figure 2 from their paper) shows the asymmetry of scattering (due to the weak nuclear force) as a function of the scattering energy squared. Notice in this figure that the value for the asymmetry at zero energy (i.e. near room temperature energies) is not zero. This means that the weak nuclear force has a non-zero effect at room temperature for electron-proton scattering.

 In addition, by combining their results above with results from other groups who have measured the weak coupling constant of large nuclei, they were able to estimate the weak nuclear coupling constant for electrons and neutrons. By comparing the difference in coupling between electrons-protons & electrons-neutrons, they were able to estimate the weak nuclear coupling constant between electrons and up/down quarks. All of the values obtained are in agreement (within experimental error) with the Standard model of physics. [It should be noted that the group has analyzed only 4% of their total data set so far, so it's important to highlight that firm conclusions from this experiment should wait until the entire data set has been analyzed.]

This research is a major achievement, and it also can be used to constrain non-Standard Model physics. It will be interesting to see what this research (when coupled with other experimental results) says about supersymmetry and string theory. But since the researchers did not expand on these topic in their paper, I'll leave it for others to figure out how these results constrain possible supersymemtric theories and string theories.

The goal for the rest of this post to is expand upon the implication of these results to everyday macroscopic phenomena. As mentioned above, the asymmetric coupling term is non-zero at low temperature. This means that the parity-asymmetric (and hence time-asymmetric) interactions between electrons and quarks is non-zero at room temperature. Notice what this is saying. This means that when we include the weak nuclear force into the Hamilitonian for dynamics, there is a term in the Liouville equation that is time asymmetric (as well as parity-asymmetric.) This means that the weak nuclear force (alone) can explain the cause of time asymmetry in macroscopic systems. In other words, without the weak nuclear force, you can't derive collision term in Boltzmann's equation from the Liousville equation. (Remember Boltzmann cheated in his derivation by assuming "molecular chaos.") With the weak nuclear force, one doesn't need to "cheat."

Let me expand more on this. There is a well known, standing problem in thermodynamics that goes by the name the Loschmidt Paradox. This paradox states that it's not possible to derive macroscopic time asymmetric laws of motion from underlying time reversible laws of fundamental physics. This paradox holds even for the case when there are time-symmetric fluctuations because the Fluctuation Theorem suggests that the entropy of the universe in both the past and future should be higher than the entropy of the present moment. This clearly violates real-world experimental results, which show that the entropy of the universe only increases with increasing time.

In order to derive time-asymmetric macroscopic laws (such as Ohm's law of electrical conduction or Fourier's law of heat conduction), we need time-asymmetric laws of fundamental physics. As I mentioned above, one can derive Ohm's law and Fourier's law using the Fluctuation Theorem and time reversible laws of physics; however, this derivation of the laws has incorrect predictions if one changes the sign of the direction of time. The Fluctuation Theorem would predict that the entropy would increase backwards in time. This is clearly wrong, which means that the Fluctuation Theorem is only an approximation of the correction derivation of Ohm's law or Fourier's law. On the other hand, one can derive the correction predictions (in both the forward and backward time directions) if one includes the weak nuclear force in the Hamiltonian because this term in the Hamilitonian is time-asymmetric and non-zero. In fact, when there are 10^23 particles in a volume, this term can be quite large, even though it is small for any single electron-electron or electron-quark collision. The term in the Hamilitonian due to weak nuclear force coupling between fermions allows the overall equation to be time-asymmetric, and allows for the "phase-space" volume to increase with time. Without this term or the assumption of molecular chaos, the "phase-space volume" would remain constant with time.

The second problem with the Fluctuation Theorem (as originally derived in the ~1950s) is that it didn't predict/explain superconductivity or superfluidity, or for that matter, it doesn't explain why photons don't spontaneously split into grouping of lower energy photons (which would increase the entropy of the universe, but would mean that studying distant objects would be very difficult to accomplish.) Superconductivity, superfluidity, and photon non-splitting (i.e. superfluidity of photons in a vacuum) can only be explained by the fact that the weak nuclear force only applies to fermions, and not to bosons. (To paraphrase Roger Penrose in Ch25 of "The Road to Reality", the weak nuclear force only occurs when fermion particles are the "zig" state or when fermion anti-particles are in the 'zag" state.) The clear conclusion that must be drawn from all of the experimental results (both macroscopic and microscopic) is that it is the weak nuclear force that is the cause of macroscopic time asymmetry. There is no other known means for the entropy (or phase-space volume) of the past to be lower than the entropy of the future. (In relativistically-invariant notation, the last statement can be rephrased as follows: the entropy of smaller values of space-time is less than the entropy of larger values of space-time because of the weak nuclear force.)

Let me summarize as follows:   the gravitational force, the electro-magnetic force, and the strong nuclear force can not increase the phase-state volume of the universe. These forces conserve the phase-space volume of an isolated system. The weak nuclear force can increase the phase-state volume of an isolated system, such as the universe. Another way of stating this is that the weak nuclear force is a 'bit' (i.e. information) generator that causes the phase-state volume of the universe to increase.

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