Quantum Diaries

I have readers who aren’t my relatives! asking some pretty big questions. First thing that comes to mind is the Rodgers and Hart lyric “if they asked me, I could write a book”. Indeed, regarding what we might find at the LHC there are books, but for a quick understanding for non-physicists (and a refreshing look at our world from the outside for us) I’d start with the fresh-off-the-press Scientific American articles about the LHC and Particle Physics in general. (Thanks to Dan Green for passing these on). The people who wrote these spent much more time on it than I can afford, and strove to make it accessible to the general public. My nutshell is:

• The final piece of the Standard Model is the so called Higgs Boson. The Standard Model has been proven right over and over, but there’s this piece which is used to give mass to particles in a consistent fashion, and it looks very elegant but we haven’t had any direct proof that it is true. The LHC should be able to give the definitive answer, yea or nay, on the Standard Model’s Higgs.
• Beyond the Standard Model: Even if we find a simple Higgs, there are a few problems with the Standard Model that need resolution. Turns out that with the simplest Higgs solution, there are really very large corrections both positive and negative which have to cancel out just right in order to have a consistent theory. That seems a bit too contrived to sit with many physicists, so they are looking for a way for these things to cancel out naturally by inventing a new set of fundamental particles which are symmetric to the ones we (think we) know. So wonderfully symmetric that they call the theory “super symmetry” which is commonly called SUSY. However, the problem with supersymmetry is that there is a proliferation of new particles and parameters, so our quest to come up with a elegant theory takes a bit of a left turn. It may seem aesthetic, but now we have this nice compact “twelve things which make up everything else” and it is a little disconcerting to suddenly need a bunch more which don’t do anything except fix this one theoretical problem. However, somewhere in here we stray from physics to metaphysics, so I’ll just leave it at that. If SUSY with a certain set of parameters turns out to be true, it is a contender to be the first new insight out of the LHC.
  • Non-Discovery physics: this is somewhat heretical, because the LHC is a discovery machine, but there is quite a bit of solid non-discovery physics to be done there as well. The top quark, for instance, is produced at the Tevatron, and they (I’m using the CDF collaboration results as my source, D0 of course has results too, but I worked on CDF, so I know what I’m talking about there) can measure its cross section, mass, properties, and even look for single top production. However, they do all these analyses (probably 50 or so in those pages, and 20 abstracts submitted to the American Physical Society conference recently) with only a few hundred top quark events identified. The LHC will be a “top quark factory” and be able to very quickly increase the statistics of all these analyses by orders of magnitude. Why is it important to pursue “known physics”? Two reasons
    1. Sometimes you can see the unknown by precisely measuring the known physics. The canonical example of this is the limits on the Higgs mass coming from the measuring electoweak parameters, especially the top mass and the W boson mass (not surprising, since the higgs couples to mass and these are two of the heaviest fundamental particles we know about). If you plot the W mass versus the top mass, then overlay the potential values for the Higgs mass which keep the theory consistent, you get:
       The blobs are what we can say with 68% confidence about the values of the W mass and top mass – there’s a 2/3 chance that the real values lie within the blob. The red blob is what we knew before the Tevatron from other experiments – pretty good with Ws, not so great with top. The blue is adding the Tevatron measurements and the measurements from LEP 2, which focused on W production. The dramatic reduction in area tells you that our knowledge of these two parameters increased dramatically – there are fewer possible pairs of values which make the theory hold water. More interesting is the grey band – what it is saying is “these are the possible values for the top and W mass given that the higgs mass is a certain value, where the top of the band is a Higgs mass of 114 GeV, the current lower limit, and the bottom of the band is a Higgs mass of 1 TeV. The interesting bit is that the blue blob and the grey band don’t overlap! At face value, this means with 68% confidence we say there is no pair of values of (top mass, W mass) consistent with a Higgs mass more than what we know is the lower limit. Pretty cool for just measuring non-Discovery physics.
       BUT, my fellow physicists will take me to task for being a sensationalist. First, 68% is not big at all – how many times do you roll a dice and get a 5 or a 6? So we’re not in a pickle yet. In addition, this is just the simplest Higgs model, it could be more complicated, which would modify the picture. But, it does amply demonstrate that you can learn quite a bit about the unknown from accurately measuring the known, which was the point.
    2. The other reason for pursuing better measurements of known quantities in addition to “Discovery physics” is the nature of the unknown – you don’t know it! The existence of “Dark Energy” comes to mind – noone was looking for Dark Energy, which apparently makes up 70% or the known energy in the universe, but the WMAP experiment set out to measure more accurately the Comic Microwave Background and suddenly confronted a consequence they had not anticipated-the Universe was accelerating its expansion, which was a surprise to most everyone in the field. This effect was highlighted to me in a recent talk by Professor Ting of MIT, who’s been deeply involved in the field since the mid 1960s, where he just listed several of the seminal discoveries of Particle Physics, and what they were “suppossed to do” which was almost always something quite different. The problem with “Surprise Physics” is it is by nature impossible to forsee and therefore hard to justify, especially to the public and agencies. But it is often the case that when looking for something you find something else that calls into question your fundamental assumptions, and that is where you really gain some understanding.

Whew – so much for the nutshell. Ok, Ken asks about SPIN with capital letters. First, I must say this looks a little crazy. The LHC itself will not rotate, no. However, spin is a tricky subject. First, there’s the normal meaning: a spinning top, or the canonical figure skater, or the Black Hole, is undergoing a rotation about an axis. When they spin that big wheel on The Price is Right (I am a child of the 70s), the $1.00 spot changes its orientation, first on the left, then up, the on the right, then down, but never changes its distance from the center of the wheel. That is the canonical understanding of spin, and I believe applies to Spinning Black Holes, although I am not the expert there.

Particle spin is completely foreign to common notions, however. It’s not easy to grasp even with a physics background, but I’ll give the explanation a shot. Consider that we treat an electron as a point particle with no extent, and completely featureless – so if something has no extent, and no “$1.00 marker” to distinguish its orientation, how can we say it has “spin”? What we really mean by “spin” is that we can distinguish apparently two identical particles by an intrinsic quantity having nothing to do with its position or velocity or any given axis but behaves like spin, or more specifically angular momentum. Wait, what does “behave” mean? Well, if I look at the Price is Right wheel from the other side, instead of seeing the $1.00 marker do “left, up, right, down” I see it go “right, up, left, down”. The thing is doing the same motion, but how I describe it depends on how I look at it, and it changes in a specific way. That’s what we mean by “behave”. So Angular Momentum behaves in a certain way under transformations, and interacts in certain specified ways with for example magnetic fields, and experimentally this other quantity behaves like angular momentum, so we call it a type of angular momentum and label it “spin”.

But wait, it gets more strange. Quantum mechanics here jumps in and tells us that particles can only have certain allowed values of spin, and we divide them up into two groups – those with “half integer” spin, like spin =1/2, 3/2, 5/2, … are called fermions (for Mr. Fermi), and those with integer spin, like spin= 0,1,2,3…are called bosons (for Mr. Bose). But there isn’t any particle with spin = 3/4 for instance. So it isn’t a continuous variable, but it is quantized. Now, for some reason known as the “Pauli exclusion principle” (a principle is something we know is true but don’t know why) fermions cannot share the same state, i.e. two electrons cannot be in exactly the same spin and orbit around a nucleus, whereas two bosons can. Is this important? As my Mom would say, “you bet your boots”. It is exactly this principle which gives us the Periodic table structure. Here’s a picture:

Hydrogen has one proton and one electron, Helium has two protons and two electrons in the same orbit but with opposite spin states. But an electron only has 2 possible spin states, so you couldn’t put another electron in that orbit. That means you have to open a new “shell”, which means next row in the periodic table. In the new shell you continue building with Lithium and Berryllium, one electron in each state for this orbit (as well as for the previous shell) but now you can introduce a new “suborbit” which has 3 potential configurations times two electons for each configuration, giving you 6 new possibilites – that would be Boron, Carbon, Nitrogen, Oxygen, Fluourine, and Neon. This pattern repeats for Sodium through Argon, but in the next level you open up yet another suborbit for Scandium through Zinc, etc. Spin gives you the Periodic table, which gives you Chemisty, which leads to Biology…at least that’s the way we Physicists like to think of it!

Which brings us back to SUSY, from above. The hypothesis behind SUSY is that for every type of fundamental fermion (leptons and quarks) there is a supersymmetric partner which has integer spin, i.e a boson, and for every known type of fundamental boson there is a supersymmetric partner with half integer spin. Given what spin has done for science, something like this could rock the world pretty significantly. So while we won’t spin the LHC, the LHC may very well have something to say about spin.

PS: in true blog fashion, this is stream of consciousness pretty much, so fellow physicists please pardon perceived lapses of reason or explication, or at least try it yourself before you complain!