Celestial Sphere

Mike Hewson
Mike Hewson
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The Weak Force = The Symmetry

The Weak Force = The Symmetry Breaker

I think the first thing to tackle about the weak force is the name 'weak'. It is fully known as the 'weak nuclear force'. That implies there is a strong nuclear force too. Quite right. We have four fundamental forces described in physics, which in order of increasing strength are :

gravity proton + electron + anti-neutrino

... this change is mediated by the weak force, nowadays we would write :

down-quark -> up-quark + W-minus

W-minus -> electron + anti-neutrino

where the W-minus is one of the three weak force bosons. We never see it per se as it only travels an extremely short distance ( even way smaller again than a nuclei's radius ) before it too decays. Wait a while and do the counts. Compare the number of electrons going toward the south pole of the magnet to the number going north. In that study about 10% more were going to the south, say 55::45 ratio. All this was repeated soon after using cobalt-58 which would emit positrons when a proton converted into a neutron within. The opposite sense of effect**** ( more positrons to the north ) was found but at around the same level ie. 55::45 ratio.

[ The extreme cold settles down any rowdy movements. The magnetic field serves to line up all the spins of all the protons and neutrons. ]

OK. Deep breath. To put these together in the simplest of wrappings ( Occam ) you have to yield on exact parity symmetry. The weak force breaks it. A bit at least. By a mild preference to produce ( or consume for the reverse occasions ) particles of one type of spin over the other. It has a handedness - hence the phrase that 'nature is a weak left-hander' - and so believe it or not this feature is a clue as why it may be that there is more matter than anti-matter in the universe, hence most of what followed. Remember that was the issue that brought us along this line of thought ? Next up :

The Sakharov Punchline

Cheers, Mike.

** Wouldn't it be nice to derive from some deeper principle(s) a 4th degree polynomial that had those as roots ? :-)

** When it was thought to be exactly 1/137 then all manner of numerology blossomed. For instance 137 is a number with many possibly interesting features eg. it is the 33rd prime number. But no, later measurement nudged it off that precise value.

*** Almost. I'll ignore the mysteries of Bell's Inequalities, quantum level entanglement and the like. While having substantial experimental backing, that area remains an enormous conceptual challenge.

**** Or if you like : with either electrons or positrons then you finish up with a nett positive amount of charge going to the northern end of the magnet compared to the southern. That does imply a nett charge separation and for that matter a differential recoil of the cobalt lattice, which is sorted out by other processes.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
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Weak Addendum ( very, very

Weak Addendum ( very, very optional )

Here's a Feynman diagram for neutron decay :

Recall that time proceeds from earlier to later going from the bottom to the top of the sketch, and all space co-ordinates are compressed horizontally. A neutron is one up-quark and two down-quarks and is coming in from the lower left. A proton is two up-quarks and one down-quark and is leaving on the upper left. One of the neutron's down-quarks becomes an up-quark while emitting the w-minus which shortly becomes an electron and an anti-neutrino. 'v' generally means neutrino, the bar over it indicates it is anti-matter, and the little subscript 'e' notes it as belonging to electrons, so it's full title here is an electron-anti-neutrino.

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I've told a little white lie too : remember that you can't/don't actually measure intrinsic spin per se. What can be observed is helicity. Helicity is the sense of a particle's spin with regard to it's direction of motion. And that must always be a relativistic comment ie. from what standpoint ( or frame ) is that being made. So the 10% difference seen in the cobalt-60 experiment is really with regard to helicity. What I've been calling intrinsic spin is technically known as chirality and is related to transformations of wave functions and similiar esoterica. As mentioned chirality very much comes into play for interference phenomena.

Hence the full phrase for the weak force is that electrons produced have preferentially a left-handed or negative helicity. Electrons have chirality which is also happens to be left-handed. Positrons are given right-handed or positive chirality. The way this is handled in the theory is to permit such particles to be in a superposition of left and right handed components, and by fiat/construction declare the weak force to only deal with the left handed components for matter, and only the right handed components for anti-matter.

While I'm in confession mode : the parity transformation referred to is technically a reversal of the sign of all position co-ordinates. But it has the effect I've mentioned, that being flipping clockwise for anti-clockwise.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
Mike Hewson
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The Sakharov

The Sakharov Punchline

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Symmetry Finale : We have done some very hard to digest parts of symmetry in physics. There is a whole lot more as it turns out, and a good deal of that relates to symmetry of transformations in abstract spaces. This is not a bad thing per se, it's just that understanding such symmetries ( or breach thereof ) requires alot of preparatory work to merely understand the context in which such regularities arise or are phrased. As a dated example : isospin or 'isotopic spin' was an early, and still occasionally used, term in nuclear physics to represent a switching from a proton to/from a neutron. You could think of it as a kind of nucleon selector with two values in 'setting space' : 'up' for proton and 'down' for neutron. But any 'spin' connection according to any usual meanings is highly tenuous both semantically and logically. Nowadays you would probably use, say, quark numbers ( nett : positive for matter and negative for anti-matter ) and be done with it.

What symmetries reflect in the real measurable world are constancies that can be ( almost ) always relied upon. Newton even proposed some of these. He said that if you don't fiddle with a system of particles ( no external force applied ) then their total momentum never changes. We could translate that into modern quantum mechanical speak as "the commutator of the momentum and energy operators vanishes", and then rely on a mathematical and interpretive structure to weasel out the same conclusion as for classical language. When the commutator isn't zero is when you are doing work on the system, or the system is working on something else ie. energy exchanges with the Universe external to the system as defined. Emily Noether's thereom about continuous symmetries would phrase conservation of linear momentum as due to invariance of physical laws under ( linear ) translation of coordinates. They are all correct as stated. Any system of mutually consistent propositions, with any one derivable from the others, may be re-arranged in some axiomatic hierarchy with a free choice as to which is considered the 'deepest'.

Also for instance I could state that I have arbitrary precision on simultaneous energy and momentum measurements, but with the subsequent downside of hence then not knowing where in the Universe the particle is nor when/whether it will turn up in the lab again ! So even the Heisenberg uncertainty relationships reflect a constancy of sorts as you can always rely upon such rules, which in turn depend on whether or not one can re-order measurements and get the same system state ( ie. a sort of symmetry ).

The intrinsic spin of the electron is known as 'a good quantum number' because it never varies. It is a 'constant of the motion'. You'd be looking at the properties of wave functions within Hilbert Space here.


OK, so where did the matter come from in the Universe? Given that we see so little antimatter I mean. Thinking very generally now, let's throw in some obvious replies :

- the Universe just started with a whole load of matter. Period. No further explanation required. This is not wrong. It does fit the observations very well and is also a simple answer. Many would view this as a non-answer though.

- there is no matter excess over antimatter. It is just that we can't find where/when all the antimatter is. For example, inflationary theories could place huge wads of antimatter well out of our horizons. It's out there but yet to throw any light upon us. Or it could be somewhere about 'hidden in plain sight' - antimatter black holes, as a random guess - but not interacting/annihilating in a typical sense that we would deduce it's presence from.

I'll regurgitate here the 'Sakharov Conditions' which try to define the circumstances where the universe did begin with equal amounts of matter and antimatter, but this has not persisted. If you have followed the symmetry discussion then this would imply that 'something broke' to produce this.

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Andrei Sakharov. What a guy. A first rate intellect of the modern era. Put him up there with Einstein and Feynman for instance. With regard to wider issues I see him as he saw himself : a Russian version of Robert Oppenheimer. They both worked on nuclear weapons and were both shafted by their political masters for subsequently speaking out in recoil/horror of them. While definitely guilty as midwives of The Bomb, they did an outrageously hard thing at the time which is to denounce the legitimacy of their own roles and hence the military programs. They held basically the same views on that, but : Oppenheimer was a communist to the capitalists, and Sakharov a capitalist traitor to communism.


The Sakharov Conditions

(1) Baryon number violation.

(2) C- and CP-violation.

(3) Interactions outside of thermal equilibrium.

In detail :

(1) Baryon or B number is a positive count for matter and a negative count for antimatter. Baryons are the 'heavy' particles eg. protons and neutrons to distinguish from the leptons or 'light' particles ( light as in opposite of heavy, not referring to photons here ). So in this language you would state that a nett baryon number of zero indicates equal amounts of matter vs. antimatter. Thus far we have discussed baryon number conservation with any/all interactions. If it occurs for every interaction then any totals will follow likewise. Thus we need some reaction along the lines of :

X -> Y + B

where whatever X and Y are they have baryon number zero. So a B pops up outside of our usual accounting rules per vertex on our Feynman diagrams. This is a necessary condition but not sufficient.

(2) You will recall that C-symmetry swapped Charge, or matter for antimatter. If obeyed then the above reaction would have a dual ( or C-conjugate ) :

X-bar -> Y-bar + B-bar

( I try to suggest a bar over the symbols here, so Something-bar is the antimatter particle corresponding to a Something ). This barred interaction would have the same physics, particularly quantum probability amplitudes for outcomes, as the unbarred case with C-symmetry adhered to. So we have to violate C-symmetry to get the unbarred interaction to run at a faster rate compared to the barred one, thus getting an excess of B's over B-bars even though both reactions are occurring.

Recall that P-symmetry swaps left for right handedness ( in the context of our discussions as to what that 'really means' ). We have to break combined CP-symmetry too. The reason ? Without writing out a confusing lump of equations like the above ( annotated with specific handedness ), let me summarise thus : one could have differential production rates of the B's over that B-bars but still have a nett B count of zero IF we allow an excess of left vs right handedness in the conjugate cases. So we have to breach combined CP symmetry to get any excess B production ie. more matter than antimatter.

[ Careful with the wording here. It is not enough to state that CP-symmetry is violated. It is an error to think that must imply C and P symmetries will be violated separately if so. You have to have C-symmetry violation separately marked. ]

(3) Now the hidden caveat/phrase with the discussions of (1) and (2) is energy dependence of those differential rates. So for ( pretty arcane but ) possibly true reasons the excess baryon production may only significantly occur in some really high energy regime. We either don't see such reactions today, or if we do we then can't noticeably measure any asymmetries. Generally speaking earlier in the Universe means hotter in temperature and thus higher average energy per particle involved. If you like the question to be put is whether our force laws have an energy dependence. I think most or all particle physicists would say definitely yes here. Even though they will disagree about the specific form of the dependency ie. what exact mathematical rule is to be applied.

Now one can run all of the above reactions ( or perhaps others we don't even know of ) backwards - by time symmetry - and get a baryon number of zero from any excess of matter or anti-matter. If you like we are now invoking full CPT symmetry here. But what might be common at high energies :

X -> Y + B

may not run backwards ( much ) at lower energies because the Y's and B's cannot summon the combined energy to make an X in any specific interaction opportunity. So now there is a statistical argument ie. can there be sufficient Y's and B's with the right momentary properties and arriving in pairs at the same times and places to do this :

B + Y -> X

and thus washout any matter excess ? The hypothesis is that there was some sufficient interval of time early on so that this can't happen enough. Another way to state this is that the Universe was briefly out of thermal equilibrium while the temperature dropped and so 'froze in place' a baryon excess. But this is a special argument of sorts, as that dis-equilibrium must begin at ( almost ) the right instant/temperature when baryon number goes from being efficiently violated to being ( almost ) precisely conserved.

So folks that's a possible punchline as to why it is that we are all now here. We are a residue of distant statistical fluctuations based on energy dependent force laws and asymmetries thereof. There is a metric ton or twenty of considerations along theoretical and observational lines to decide whether any of the above is verifiable.

To polish off : sometime later the antimatter combined within the matter thus :

B + B-bar -> photon(s)

eliminating most of both. But with a wee relative excess of matter of about several parts in 10 billion. That gives a vast excess of photons per baryon ie. a few billions of photons for every baryon. Most of those photons are represented in the CMB today. So we close the loop of thinking back to So What Happened To The Photon Energy ?

My goodness we've skimmed over a huge slab of intellectual real estate ! Any questions at all ? :-) :-)

Cheers, Mike.

( edit ) Actually another good topic ( to outline in a new thread ), very relevant to the LIGO interferometers, would be the quantum mechanics of light.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
Mike Hewson
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Entropic

Entropic Afterthoughts

More on dis-equilibrium. There's an entropy angle in the

B + Y -> X

idea. An 'X' is a simpler system. A 'B + Y' is a more complicated one. There is going to an enormous ratio of ways to have a 'B + Y' compared to an 'X' alone. The B and Y go their own directions/speeds/angles/energies and combinations of etc. But how many ways can an X sit by itself ? How do you get the B and the Y to come back to the same ( or any other ) place at the same time to at least give an opportunity to re-make an X ? This is a core entropy query : how does a system ( without external assistance ) return to prior greater simplicity once the horses have bolted ?

Equilibrium is where all the elements of an isolated system are freely interacting and for sufficient time, so that a known relative distribution of energies ( Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein ) can form in the population considered. Suppose that wasn't happening. That means some subset of the population of particles was held off from interacting - or not given sufficient time to do so, giving the same effect. That implies one could account for that subset's energies on a separate sheet, so to speak, and any measurement of the remaining particles would not be relevant either way to it. So for instance one could have a scenario where :

- the vast majority of particles had equilibrated amongst themselves. With a given average then labelled as their 'temperature', plus a known correspondence b/w energy levels & the fraction of the total particle number at/around any said levels.

- a smaller subset, again with particles equilibrated amongst themselves but at a rather different average.

- so in one's mind at least there is a partition into the haves and the have-nots on an energy scale. Now that numerical partition has to have some physical basis though. Otherwise it would not form or persist. Maybe not a partition in the sense of a wall b/w two rooms, but a mechanism of sorts.

A really rapid expansion of the system could do that. What about a superluminal expansion of space ie. that inflation idea ? It could place segments of the Universe that were in causal ( sub-light speed ) contact well away from each other, and for an extraordinary long time too. Only later does light ( and thus all force influences ) catch up to the separated parts. That could be happening in the Universe now. Old news now appearing within our horizons. But by then all manner of events have happened in the subsets so at the return to causal influence we won't have prior opportunities eg. cooling has closed off certain energy dependent mechanisms as discussed.

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Carefully note that if you do examine a body, via it's emitted radiation say, and are not sure that it is equilibrated internally, then you don't know if what you have received reflects the true energetic status of said body. There could be an unsampled subset, not generally interacting, but holding either a relative excess of energy, or a relative deficiency of energy, compared to the bulk of the system. If this case predictions based upon an equilibrium assumption will screw up over some time scale for the simplest of reasons : the system being described is in reality not the one that you think it is. And no amount of fungibility will save any modelling.


After all tomorrow we could get a vast wave of gammas arriving to let us know that there was once some huge annihilation matter/anti-matter splurge !! Scientific ideas are always falsifiable and thus subject to review with new information. The best data set to re-apply inductively sought patterns from prior data sets is : future data! That's why science when properly applied works so well .... :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
Mike Hewson
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Here's a good precis of

Here's a good precis of thermodynamics. :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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