Saturday, December 1, 2012

More on the Arrow of Time, Neutrinos, and Dark Matter/Energy

There is only one arrow of time.

This post is a continuation on a previous post on the Arrow of Time. The goal in this post is to expand on the themes from the last post as well as to point out recent additional experimental evidence for time reversal asymmetry.

"One Ring to Rule them All"
The arrow of time associated with the weak nuclear force is the same as the entropic arrow of time (i.e the 2nd Law of Thermo), which is the same as the cosmological arrow of time (i.e. the expanding universe.) All of these arrows of time are caused by the fact that there is one (and only one) parameter in the Standard Model Langrangian of particles that allows for CP violations (i.e. T asymmetry.) This parameter is due to interactions between Fermi particles via the weak nuclear force, and the parameter is within what’s called the CKM matrix. Every other interaction between particles (both fermions and bosons) is time reflection symmetric. In other words, there would be no such thing as the "arrow of time" unless there were this one parameter. And since there is only one parameter that violates time reflection symmetry, there's only one arrow of time (that we are aware of so far.)

So, let's go back to the beginning of time (as far as we can discern.) Right after the Big Bang, the weak nuclear force allowed heavy quarks to convert into lower energy quarks and a slew of other particles. This process is described by the CKM matrix and is time (T) reflection asymmetric, as well as charge (C) and parity (P) reflection asymmetric. This asymmetric process is likely also why there are more electrons than anti-electrons, and likely why the universe is not perfectly left-right symmetric. (Though, it should be noted that this asymmetry could also be due to asymmetric starting conditions.) This increase in the number of particles led to an increase in the exchange symmetries between similar particles (i.e. entropy). This ‘finite’ and ‘digital’ value of entropy is likely embedded into a ‘finite’ and ‘digital’ space-time causing this ‘finite’ and ‘digital’ space-time to increase in size…i.e. the expansion of the universe after the Big Bang. So, we already have an explanation for why the universe increased in size after the Big Bang (i.e. the weak nuclear force increases the number of Fermi particles and this increases the entropy, which is encoded in space-time.) The question is: can this explanation also account for the continued expansion of space-time into the present?

The answer to this question is likely to be yes, but this depends greatly on knowing what is the density, mass and kinetic energy of neutrinos in the universe. Interactions between neutrinos and other fermions via the weak nuclear could be the cause of the continued expansion of expansion of space-time; though, this is still speculation because we still need to know crucial experimental information to make this calculation. It is also possible that weak interactions electrons could be a source of time asymmetry.
Let's go back to what we know, so I'll discuss with recent updates from the BaBar experiment on decay fragments from massive B mesons. This research group recently measured direct experimental evidence for time (T) asymmetry in the decay of these mesons. The big news (even though the news is not shocking in the least bit) is that prior work on T asymmetry had come from deriving T asymmetry from CP violations and assuming CPT symmetry was valid. This time, the group was able to direct calculations of T asymmetry. Here's a quote from a recent news release on the discovery. "Thus the long wait for an unequivocal time-reversal violation in particle physics is finally over."
While this news is quite exciting, the reason I mentioned that this news was not shocking is that there are text books on CP violations that are now in their second or third publication releases. CP violations are decades old, and we’ve know for awhile that CP violations imply T asymmetry provided that CPT is a valid symmetry of the laws of the physics.

A fairly readable textbook on the subject of CP violations is "Discrete Symmetries and CP Violation" by Marco Sozzi (First edition 2008, Second edition 2012.) I'll be quoting from the 2008 edition because (a) sections of only the 2008 edition are on Google Books, and (b) I only have the 2008 edition. Below are some interesting quotes regarding CP violations and how CP violations fit into the Standard Model of particle physics. I've included these quotes in this post so that people not intimately familiar with CP violations have some perspective on the relationship between space-time parity violation, Higgs Bosons, and the weak nuclear force.

"At present  we have no real 'explanation' of CP violation...the Standard Model has enough complexity to be able also to incorporate CP violation. Still, while the current theoretical framework has room for a single CP-violating phase and is consistent with all the observed manifestations of such phenomenon, the value of such phase is not better understood than, say, the value of the muon mass, and the physical origin of CP violation remains a mystery." (pg 385)

CP violation only occurs in weak nuclear interactions, and of the four components of the weak nuclear force Langrangian, "[only] the interaction of quarks and leptons with the Higgs field, introduced to give masses to them and to the gauge bosons, ... can support CP violation."

Thus the non-zero mass of the weak bosons (W±, Z) and the CP violations of the weak force are both related to the fact that there is a Higgs field. The mass of the zero-spin boson particle found at CERN with a mass of 125.3 GeV has nearly exactly half the mass of the sum of the three weak bosons, which is clear evidence that this particle is likely the Higgs boson that gives rise to the mass of the weak bosons (W±, Z). This means that we have likely found the field that gives rise to massive force carriers as well as the time asymmetry of the universe. While we still have a lot more research to do in this area, I think that it's important to step back and delight in the fact that we are that much closer to understanding the cause of the arrow of time. Though, of course, we are left with the nagging questions about why is there only one parameter that leads to time asymmetry and why is this parameter in the Langragian for the weak nuclear force but not in the Langragian for the strong nuclear force. My guess is that this has something to do with the algebra of the quaternions (weak nuclear force), compared with the algebra of the real numbers (gravity), the algebra of the complex numbers (E&M), and the algebra of the octonions (strong nuclear force.) But I don’t know what is special about the quaternions compared with the other three algebras. (The big question is why the strong nuclear force don't violate CP symmetry.)

Now, I'll continue quoting Marco Sozzi:

"A non-trivial unitary matrix appears, called the Cabibo-Kobayashi-Maskawa (CKM) matrix, which measures the mismatch between the matrices which diagonalize the U and D quark mass terms. ... The appearance of the CKM matrix with complex elements opens the possibility of having CP violation."  (p392)

The following are some general requirements on the quark side for CP violations: (1) there must be at least three families of quarks (note that we have found 3 families of quarks and leptons so far); (2) there can be no degenerate masses for the quarks; and (3) there can be no zero mixing angle. Using our current understanding of the number of quarks, the CKM matrix is a 3x3 matrix, but however you write the matrix, the matrix only has one free parameter that allows for CP violating interactions.

Note also that "if neutrinos were massless (degenerate), CP violation would not be possible [for leptons]." (P398). "With massive neutrinos, the leptonic sector can this introduce a second source of CP violation, arising via the same kind of mechanism as for the quark sector." (p399)

So, massive neutrinos can also provide a source of CP violation, but it appears that the source of the CP violation is the same ‘source’ as the CP violations for quarks. In other words, there’s only one arrow of time. So, neutrinos could be source for continued time asymmetry now that the original source of time asymmetry occurs much less often (i.e. most heavy quarks have already decayed into lighter quarks.) In addition, with the death of supersymmetry, neutrinos are the main dark matter candidate. (provided that there are neutrinos with masses near 1 keV.)

So, if neutrinos have mass, if interactions between Fermi particles via the weak nuclear force causes space-time to expand, and if there are enough neutrinos that they could be the source of dark matter, then we have the possibility that neutrinos could be both the main source of dark matter (i.e. the invisible mass in the universe) and the main source of dark energy (i.e. the expansion of space-time) after the universe settled down into mostly up and down quarks.

There is a term for this theory: Neutrino Minimal Standard Model

There are a number of physicists trying to prove that neutrinos are the main source of dark matter and that dark energy is really just the expansion of space-time due to increased entropy. What's interesting about the the weak nuclear force (and the reason why I think that it's the cause of the expansion of space-time) is that it's the only force involving collisions between 3 or more particles and it's the only force in which anything really can be said to happen. For gravity, E&M, and the strong nuclear force, fermions exchange bosons (such as photons or gluons), but nothing really happens to the fermions. They can be attracted to or repelled by other fermions, but they don't change into other particles. (Nothing really happens…even for the case of gluon-gluon interactions via the strong nuclear force.) This is just the opposite for the weak nuclear force. Here, we have the creation of new particles, such as when a down quark simultaneously turns into (a) an up quark, (b) an electron and (c) anti-neutrino. This interaction can increase the entropy of the universe because there are more particles afterwards, and my speculation is that this “weak” interaction causes space-time to expand.

So, let me now point out some basic statements about our current knowledge of the arrow of time and discuss reasons why we absolutely need an asymmetric force to explore the arrow of time.

(1) Knowing that the Big Bang was a point of low entropy does not imply that entropy automatically increases with time. Some physicists like to think that it's more probably for the universe to be in certain states than others, and this is the sole reason for the 'arrow of time.' But this begs a number of questions, such as: What the heck is ‘time’? And why didn't universe start in its most probably state to begin with? We don't know how such a state of low entropy is possible.  In fact, a state of low entropy appears to violate the second law of thermodynamics, unless of course the universe somehow started in a very low entropy state. We have no clue why the universe likely started in a state of low entropy.

(2) The fact that the universe started in a state of incredibly low entropy is called the Past Hypothesis. It is still a controversial topic in physics and the philosophy of science, because the Past Hypothesis begs the questions: What was before the Big Bang?  And how can the laws of physics get turned on or off at the start of the Big Bang? Even knowing what is the source of the arrow of time is unlikely to tell us anything about what happened before the Big Bang. There is likely (though this is only my speculation) no such things as ‘before the Big Bang.’ As I’ve mentioned before “We live on the wrinkled 3D surface of a 4D sphere…in which the radius of that 4D sphere is what we call time. The radius from the center of the sphere to the surface of the sphere is not the same everywhere because the surface is wrinkled by mass/energy of particles.” Since ‘time’ is just a radius of this expanding 4D sphere (which is likely expanding due to weak nuclear force interactions), then there is no such things as negative radius, and hence no such things as ‘before the Big Bang.’  There would have to be an additional, non-radial space-time dimensions in order for us to speak of ‘before the Big Bang.’  (Additionally, once the radius of the 4D sphere hits a maximum, there is no more 'time.' There isn't an infinite amount of time spent into this state of thermal equilibrium. Time is finite just like space.)

(3) Some physicists say that it's more probable for the universe to be in a state of high entropy than a state of low entropy, and therefore the arrow of time is simply probabilistic in nature, and that all of the underlying laws of physics of time-symmetric reversible (except for those ‘rare’ beta decays.) I think that something is missing here. We can build isolated experiments where there are only time-symmetric laws, such that there is no change in entropy in these systems  (such as superfluids, superconductors or photons travelling through space.) It is more probable for the star-light to be in a state of many low energy photons than a few high energy photons, but this doesn't happen. Entropy doesn't seem to change for systems when only bosons interact, and this should give us a clue as to the problem with the logic from these physicists. Why does entropy only increase in systems with fermions? And why does the rate of increase in entropy in such systems seem to depend on the rate of collisions? What is it about collisions that creates pseudo-randomization?  (in collisions involving purely gravitational or E&M forces, there is not randomization provided that you know the stating entropy doesn't include in classical collisions. But for real world collisions, entropy does seem to require collisions.)

(4) What we need is a means of calculating exactly how the entropy of a system will increase. If you don't have a force of nature that asymmetric with respect to time, then there is no way to calculate entropy production from first principles. Sure, engineers can calculate entropy production by using experimentally derived rate constants, but we have no means of estimating entropy production from first principles without either having a time asymmetric force (i.e. the weak nuclear force) or by violating one of the time symmetric forces (gravity, E&M, and strong nuclear force) and introducing a random fluctuation into the system (i.e Boltzmann's assumption of molecular chaos.)

(5) CPT symmetry states that the motion of an anti-particle that has been reflected in a mirror and that is going backwards in time will have the same equations of motion compared with a particle moving forward in time. Assuming that the weak nuclear force is symmetric with respect to CPT symmetry, does this mean that the weak nuclear force is not the source of the arrow of time?  The answer is no. Assuming that the weak nuclear force is symmetric with respect to CPT symmetry does not imply that the weak nuclear force is not the source of the arrow of time. The reason is that there would still be an arrow of time if the universe were made of space-reversed, anti-particles…it’s just that, in this scenario, the universe would start out large and shrink in size. The source of the arrow of time, and hence the decreasing space-time 4D would be the same term in the CKM matrix. The universe would still be time irreversible because you couldn't time-reflect these space-reflected, anti-particles. If you were to run this ‘decreasing universe’ backwards in time, it would look qualitatively the same as the increasing 3D wrinkled surface we currently inhabit. Whether the ‘movie’ of backwards, reflected, anti-particles looks exactly the same depends on whether there are any truly random forces in nature. Random forces would violate CPT symmetry because you couldn’t predict the outcome of the CPT reflected system, knowing the outcome of the non-CPT reflected system. It should be noted that physicists have found no evidence of CPT violation, and hence no evidence for randomness in nature.

So, CPT symmetry is a profound symmetry, and if true (as is likely the case given recent evidence), then it means that the fundamental interactions (even those obeying the CP-violating weak nuclear force) are not probabilistic. But it should be reiterated that CPT symmetry does not imply that there is no arrow of time. The arrow of time comes from the CKM matrix in the weak nuclear interaction between Fermi particles and the Higgs field. This is a very ‘weak’ interaction. If this had been a ‘strong’ interaction, then the universe would reach equilibrium very quickly and the world would have been entirely different. Let me end by reiterating the key themes from this series of posts on the arrow of time:  (1) The macroscopic arrow of time (i.e. increased entropy) and the microscopic arrow of time (i.e. time asymmetry of the weak nuclear force) are the same thing;  (2)  the increase in entropy is likely caused by the weak nuclear force; and (3) neutrinos (with energies around 1 keV) are the likely dark matter candidates.

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