Times are slow... So instead of fabricating football news and drowning ourselves in optimism, I figured I would grace this dear great forum with a little physics. For those interested, I will be expanding on a topic that came up in the comments section, that being the violation of parity. I will try my best to limit a lot of the jargon. Additionally, I am not sure of the familiarity my readers have with physics, which means I will have to guess so bear with me. Lastly, for what its worth this is my first post here. (This is a relatively lengthy post, so if people want to get to the main point you can just ignore all axial vector stuff and roughly understand how normal vectors should work)So first question: what is parity? I have heard the term tossed around here occasionally and its typical use is to mean the relative goodness amongst the teams. Having lots of parity means that teams are relatively equal as far as how good they are. I will attempt to provide an example in terms of football, but take it for what its worth (which is probably not much).
We could then define the operation (or transformation) of switching teams, and we would realize that to a large degree teams are symmetric (for example, team A beats team B, then team B beats team C, then team C beats A; this process can usually happen in any particular order so the operation of switching teams around does not really result in say a particular team going unbeaten) .Thus, parity sort of reflects a symmetry among all the teams in the sense that they are all the same under the "switching of teams" transformation.
Well, in physics parity is a transformation and is meant to illustrate a symmetry as well, and often times this symmetry is called mirror symmetry (in physics there is a very precise mathematical transformation that can operate on your coordinate variables in equations called a reflection transformation). For our purposes (there are other manifestations of parity, or other influences it can have on equations, but these are rather technical) we will talk about parity as it relates to the symmetry that exists between an object and its mirror image.
First, it is important to understand how something like a vector would change under parity. First lets imagine a vector as an arrow. A vector does hold more information but again for our purposes all we care about is what direction the vector is pointing in space. First pretend that the arrow is pointing straight at the mirror, then if we were to project the location and direction of the arrow through the mirror (imagine going from one side of the mirror to the other) we would see that the arrow is point right back at us. If we turn the arrow so that it is pointing to our right, then we will find that in the mirror image the arrow will point in the same direction. The image below illustrates this point (focus only on the top example, which is the kind of vector I am talking about).
The bottom image illustrates what happens to an "axial" vector, which is essentially a vector that describes rotation. For those of you who took freshman physics, this is where you use the infamous "right hand rule" to determine which way things are spinning based on the direction of the axial vector. Axial vectors are a little more difficult to imagine, so I have attached another illustration of axial vectors which better shows how they behave. Back to the right hand rule, to determine which way rotation occurs based on the direction of the axial vector one uses the RIGHT hand with your thumb pointed in the direction of the axial vector. Now the direction in which your fingers curl will determine the direction of rotation.For example, if your thumb points up, then rotation will be counter-clockwise, and if down, the direction will be clockwise (again make sure you use your RIGHT hand!). One critical difference to notice between an axial vector and normal (polar) vector is that if the axial vector is pointed directly at the plane of the mirror then the reflection will not point towards you but it will point away from you. This essentially means that if something is rotating in the same plane as the mirror, then its reflection about the mirror will rotate in the same direction. However if something is rotation perpendicular to the mirror, its rotation will be reversed in the mirror image.
However, since polar vectors are more intuitive and common in our world I will for the moment focus on them (we will need the concept of axial vectors later when I describe the experiment), which leads to critical and subtle point, on one side of the plane the arrow is pointing to our right, but if we jump to the other side it points to the left (note axial vectors always point the same way), and this is what it essentially means for right and left to be symmetric under parity. Whenever this ambiguity comes up, we just define ourselves to be on one particular side of the plane and work from there, though we could have just as well decided to use the other side since things should behave identically regardless of which side you pick. This seemingly obvious assumption tells us that physical processes never select one side of the plane over the other, by that I mean that there is no difference between a process that is arranged as if its on one particular side of the plane and the arrangement as if its on the other side. For example, look at the amino acids shown below. You will see that the only difference between them is that one seems to be the reflection of the other, and this is indeed the only difference. You could call L-alanine "left-handed" and you could call the other "right-handed". The interesting things is that when they are made, they are made in essentially equal numbers of each type, so this is an example of nature not caring about right-handedness or left-handedness, because if it did then one would be produced in greater quantities than the other.
One last point to drive the uhhh... point... home is imagine trying to communicate with an alien species far away by using something akin to a phone. We could define numbers by saying "one", followed by a tick of some sort, then "two", followed by two ticks, etc... we could define our height by using the radius of the hydrogen atom (since physics is the same everywhere in our visible universe) but we immediately run into the problem of defining right and left. Since these are completely symmetric, there is no way we (nor the aliens) could differentiate one from the other, and thus there would be no way of telling our alien friends which way is right and which is left.
This symmetry in nature seemed so fundamental and so intuitive (and every time it was tested it always held) that physicists always assumed it. The reason why physicist like symmetries so much is that whenever a symmetry exists there is also a conservation law that is tied to it. These conservation laws allow us to better predict the outcome of reactions, decays, or any interactions in general. So the more conservation laws, the better we can constrain nature and the better we can predict things. Anyways, right around the mid 1950's when physicist were studying weak interactions (a type of interaction possible because of the weak nuclear force, a fundamental force of nature) they began noticing very weird behavior ( I can go into the details in the comment section if anyone is interested). Eventually a pair of young very brave Chinese physicists (working here in the US) proposed that maybe parity is violated in weak interactions. Most physicist scoffed at the idea because it just seems so ludicrous. Even the great physicist Richard Feynman wagered 50 dollars that parity wouldn't be violated. Eventually, they were able to convince a well-renowned female Chinese experimental physicist to perform an experiment to look for evidence of parity violation.
Roughly, the experiment goes as follows:
Because Cobalt 60 has a relatively strong magnetic component, one can use a very strong external magnetic field to aline the atom in any particular direction (the temperature must also be so low that the random thermal motion of atoms does not cause an atom to bump into its neighbor and disrupt its alignment). Additionally, Cobalt60 decays (through weak interactions) by emitting electrons and neutrinos. So the idea is simple (though actually running the experiment was not!) align all cobalt60 atoms in a particular direction and then count how many electrons are emitted from each side of the atom. I will now simply quote the results, here but if you want to know exactly why this is implied by the experiment keep reading. If parity was to be preserved it should be the case that the same number of electron were emitted to the right of the atom as the number that were emitted to the left. But much to the surprise of everyone more were emitted to one side than the other! Nature actually distinguished one side from the other. If we translate this phenomenon in terms of normal vectors (what we are more used to), then something going to the right on one side of the mirror would also go to the right on the other side and vice versa.
The illustration below roughly "illustrates" (forgive me) what would happen if we were to simultaneously run the experiment with everything arranged "right-handly" and "left-handedly", that is if we were to arrange the atoms one way and then arrange the atoms the way they would appear if they were reflected through a mirror (there is no virtual image like there is in a mirror, its as if there is a mirror in the middle). Again, we notice that more electrons are emitted on one side with respect to the other. This may not seem like it violates parity, but remember how axial vectors act under parity. On the left side of the mirror, if we curl our fingers in the direction of rotation, we get that the axial vector is pointing to the left. If you scroll up and look at how the axial vector behaves under parity, you will see that its direction should not be changed, and so the axial vector in the mirror image should also be pointing to the left, which means that if electrons are emitted to the right in the normal case, then they SHOULD be emitted to the right in the mirror case, but instead we find that they are emitted to the left (which is the way polar vectors work, but not axial)!
To better help convey the idea, here is another example with a different orientation. The diagram below again demonstrates what SHOULD happen if parity was conserved. In scenario described as "this world" the magnetic field aligning the atoms would be pointed in the up direction (from the right hand rule). We could create a mirror image of the arrangement by pointing the magnetic field down. Then what we would expect if parity holds is that if electrons are emitted down in real world, they should be emitted down in the mirror world (because the magnetic field is flipped in the mirror world). However, this is NOT what happens; what actually happens is that in the real world electrons are emitted downward but in the mirror world electrons are emitted upward! It is as though in both cases the electrons always pick to go in the south direction and this is indeed very unsymmetrical and violates parity.
The violation of parity is but one of many examples that shows us how weird our universe can be, and how fundamentally different things behave on very small small scales. However, this begs the question how and why does nature distinguish right from left? Is there a symmetry more fundamental than parity that is not violated? And so science marches on!
I will be more than happy to answer any questions people might have.