Nice Article on CERN's LHC

[Pangloss]

Yahoo (via Reuter's) has a nice article up about the Large Hadron Collector at CERN, due to begin operations in 2007. Nothing really earth-shattering in the story, but I just thought I'd pass it along since things are kinda quiet in here.

 

http://story.news.yahoo.com/news?tmpl=story&cid=585&e=1&u=/nm/20041018/sc_nm/science_cern_dc

[Severian]

Aymar says foremost among those achievements was providing proof in 1973 for the so-called electroweak model -- that two of the four forces of nature, the weak and the electromagnetic force, had been unified at the outset of the universe.

 

It always annoys me that this claim is made. They are not unified at all - just explained under the same framework. They are still quite distinct forces.

[Ophiolite]

Aymar says foremost among those achievements was providing proof in 1973 for the so-called electroweak model -- that two of the four forces of nature' date=' the weak and the electromagnetic force, had been unified at the outset of the universe.[/i']

 

It always annoys me that this claim is made. They are not unified at all - just explained under the same framework. They are still quite distinct forces.

I understood that under the conditions early in the big bang the two forces were effectively indistibguishable, they were the same force. As conditions ameliorated they took on distinctive characters. I understand you are saying this is not so. Could you clarify please.

[Severian]

Certainly! As I have explained elsewhere on this forum, the four forces of nature are probably all a consequence of symmetry in the universe. (I say 'probably' because gravity is still not understood, but will most likely be the same.) The laws of physics are symmetric under certain transformations, and as a result we have a force.

 

For example, the strong nuclear force is described by Quantum Chromo-Dynamics (QCD), which is a consequence of an SU(3) symmetry. 'SU(3)' is just a technical description of a symmetry - but think of it as being like a rotation (in 'color-space') - we make the rotation and the laws don't change.

 

Electromagnetism was found to be explained by Quantum Electro-Dynamics (QED) which is caused by a U(1) symmetry, which is just changing the wavefunction by a phase.

 

Both of these forces are mediated by massless particles: QED has the photon, QCD has the gluon. The fact that they are massless is a consequence of the symmetry. Each of these forces have a number (a 'gauge coupling') which tells us how strong they are, ie. how strongly the photon or gluon interacts with matter. These numbers are parameters of the theory.

 

The problem is the weak interaction. It is weak because the force mediators are heavy. To transfer momentum between particles via the weak interaction, we have to create one of these heavy particles and send it from one to the other. This is difficult to do, so the force is weak. It seems that since they are heavy they cannot be coming from a symmetry.

 

This is where the Higgs boson comes in. It is postulated that without the Higgs mechanism, the weak interaction would be a consequnce of SU(2) symmetry, which is very similar to SU(3) of QCD. The symmetry would give massless particles which would mediate the weak interaction (which wouldn't be weak of course) and the strength of the interaction would be given by another gauge coupling.

 

The Higgs mechanism 'breaks the symmetry' - it picks out a direction in SU(2) space so that the laws of physics do change under an SU(2) rotation. (Think of a table tennis or ping-pong ball: if I rotate it, it looks just the same, and you can't tell how much I have rotated it by. But if I draw a cross on at at one point, it will look different when I rotate it - the cross will move. The Higgs mechanism is like drawing a cross on a ping-pong ball.) This mechanism means that although the underlying laws of nature are SU(2) symmetric, their manifestation is not, and the weak mediating particles need not be massless. They become heavy and the force becomes weak.

 

Now at the moment, this description has three forces in it. The forces are described by SU(3), SU(2) and U(1). However, it is not quite correct. The photon is not a result of the fundamental U(1) symmetry after all. This is because the particle resulting from the U(1), normally called 'B', and one of the particles coming from the SU(2), called W3, have the same quantum numbers. We cannot in principle tell one from the other, and when the Higgs mechanism breaks SU(2), it is not W3 which is given a mass, but some combination of W3 and B (which is then called the 'Z boson'). The orthogonal combination of W3 and B remains massless and is the photon.

 

So the only link between the weak interaction and electromagnetism is that their force mediating particles mix with each other. This is not unification! If we want to unify the force, they must be explained by the same principle, and will have one common parameter which determines their strengths. In the Standard Model, we still have two separate strengths for the SU(2) interactions and U(1) interactions, so they are not unified.

 

This is not to say that they won't be in the future. A Grand unified Theory (GUT) seeks to describe all three forces as a consequnce of a bigger symmetry group, eg. SU(5) or SO(10). Going back to our ping-pong ball, if I had drawn a circle rather than a cross and rotated the ball about the centre of the circle, keeping the circle at the north pole so to speak, you still wouldn't be able to see the rotation, so it still has a symmetry. It is thought that some large symmetry group may be broken down to SU(3)xSU(2)xU(1) giving us three forces. Before this breaking the three forces would all be described by one force, a consequnce of the bigger symmetry. But this is still speculation, and has definitely not been proven.