Severian

I am not sure what you are getting at. I could very easily write down a wavefunction for a superposition of spin up and spin down particles, in whatever basis you choose. The wavefuction in QM is simply the coefficient sitting in front of the basis vectors in the decomposition of the state in terms of the the basis, e.g. [math] |\psi \rangle = \int dx \psi(x) |x \rangle[/math] where [math]|x \rangle[/math] is the position eigenbasis and [math]\psi(x)[/math] is the position space wavefunction. In other words, [math] \psi(x) = \langle x | \psi \rangle[/math], so in the example you gave the (position space) wavefunction is [math] \psi(x) = a\langle x|+ \rangle + b \langle x|- \rangle[/math]. My objection to the name Quantum Mechnics is that the 'quantum' nature of QM, i.e. that energy, for example, comes in discrete lumps, comes from the wave properties of matter. Not only that, classical field theories also exhibit the same discretisation without being labled as 'quantum'. For example, a guitar string can only produce notes with particular frequencies (or energies) because of it's boundary conditions at the end of the string. This is really no different to the quantisation of the electron's energy in the hydrogen atom, where the boundary conditions only allow certain Laguerre function to be solutions, and since each one has a different energy, energy is quantised. This is generally true - all quantisation effects in QM are a consequence of describing particles as waves with boundary conditions. The thing which distinguishes QM from classical physics is allowing the operators to effect the system. After measurement of a quantity, the system jumps into that corresponding operator's eigenstate. Notice that simply the presence of operators isn't enough - the classical heat equation, for example, contains operators. Not even commutation relations are enough, since the "operators" in classical mechanics don't commute either.

In my view, the Lagrangian is more fundamental than the Hamiltonian. The Hamiltonian is basically just the energy operator, while it is the Lagrangian which tells you the physical behaviour of the system. Remember too that the identification of H = T + U and L = T - U is a special case and is not necessarily true. The fact that people think T+U is more fundamental is because of the way we teach physics - we look at systems where this is a constant, which gives the Hamiltonian a special significance. I would also disagree with Klaynos that the Lagrangian is not physical. While in some sense, only observables are physical, since they are the only things we can measure (and thus the Hamiltonian corresponds to a physical observable, the energy), when building theories of fundamental physics, we think in terms of Lagrangians, not Hamiltonians. The usual way people construct theories nowadays is to think up when particle content they want or need, decide on the symmetries they want to impose, and write down every term that they can think of using the particles which obeys the symmetries. The resulting Lagrangian is then the most general that it can be, but still provides physical laws which respect the symmetries. For example, making the Lagrangian invariant under time translations makes the Hamiltonian a conserved quantity (energy conservation). As for Hamiltonian mechanics more generally, one normally thinks of it as a consequence of Lagrangian mechanics and defines the Hamiltonian as the Legendre transform of the Lagrangian: [math]{\cal H} = p \dot x - {\cal L}[/math] While this isn't necessary (strictly speaking you can define Hamiltonian mechanics independently) it is how most people think of it. Indeed, this is where the U+V thing comes from: e.g. if p = mv, then [math]p \dot x = mv^2 = 2T[/math] so [math]H = 2T - T + U = T+U[/math].

Apparently it was violent enough to move the multi-tonne magnets by 30cm.

It is best to keep it clean. Use a plain white background, with black text, and maybe dark blue text for titles and red text to highlight important words.

I tried it but I didn't really like it.

When they can make a testable prediction, I will start to take them seriously.

Yes - if you exchange a charged particle (like a W+) you will change the charge. Many exchange particles will also change the mass. The exchange particles are constantly being emitted to and absorbed by all the other particles round about.

Well, there are scruples and there are scruples. If the government took the speculators who made millions out of the collapse of AIG, put them against a wall and shot them, I wouldn't complain too loudly.

1) I imagine it is stored in a bug shed at CERN, for historical reasons if nothing else. The old bubble chambers they used to use are now museum pieces. 2) The nominal LHC energy is 14TeV. At that energy the peak of the gluon spectrum (the proton is mainly gluons) is about 600GeV, so really it has a reach of a few TeV or so (> 1TeV due to the tails in the distribution). Most likely the Higgs is < 190GeV and it is certainly < 700 GeV, so this is plenty of energy. 3) There are two proposed upgrades, the VLHC (Very Large Hadron Collider) and the SLHC (the Super LHC). The VLHC is a proposed upgrade on the energy while the SLHC is a proposed upgrade of luminosity. Most people think the SLHC would be better, but it really depends on what the LHC finds. 4) Yes it would, but it is more likely that the next machine will be a linear collider. Since there are no bends, no sychrotron radiation. 5) Already answered. I personally know lots of good Russian physicists working on the LHC, but I am not sure how much they government has contributed. 6) The protons are injected from the previous High energy rings (the SPS - Super Proton Sychrotron). This in turn is injected from smaller rings. At the source, the protons come from Hydrogen gas. 7) Hawking is a cosmologist. What does he know? 8) The economic feasibility of the next collider after the LHC depends entirely on what they find.

The Standard Model has no action at a distance. Everything is mediated by the exchange of particles. So electrons which move apart due to electromagnetism are transferring momentum by exchanging a photon, just like two ice skaters moving apart when one throws a ball at the other.

It probably would have been better in fact, because you wouldn't have had all the jet fuel to melt the building supports. It would of course, depend on the design, but I can see no objection in principle. It might be infeasible simply because the reactor would be too heavy.

The Marshall plan didn't really help all of Europe. The UK got some money to rebuild from the US but in fact we only finished paying off our war debt to the US reasonably recently, and the debt was larger than the money we got. This is one of the reasons why the UK was much much worse economically than Germany (ironically) in the post war period.

It is quite constrained (mainly the prediction for S and T), but there are ways around most of the obstacles. The problem is that a previously aesthetically pleasing idea becomes less pleasing when you have to contort it wildly to avoid constraints. There are also composite Higgs models (eg. the BHL model where the Higgs is a top-antitop bound state - iirc this also needs susy otherwise the top quark needs to be too heavy) and Higgless models (togther with extra dimensions, where the KK states solve the WW scattering unitarity violation).

I once got into trouble in the US for using the phrase "smoke a fag" (iirc I was suggesting it as a method of stress relief).

My next door neighbour is in his sixties and just took up the saxophone. And my God is it annoying! Please please please, for the sake of your neighbours, leave it alone.

I have never hit my daughter and I can't imagine ever hitting her. I don't even shout at her. If she does something bad she is punished in a way which is quantifiable for her, with a clear explanation of why she is being punished. I have in the past used restraining force though, when for example I was changing her nappy, she grabbed the old nappy full of shit and made as if to throw it.

"Mate" and "piss-off" are said quite a lot, but "blimey" went out with the war. Also, "mate" is very regional - they only say that in certain areas. Where I come from it would be "pal".

If anyone is interested in looking to see what is going on with the LHC, here is a link to a nice resource which displays the webcams which are online right now: http://www.cyriak.co.uk/lhc/lhc-webcams.html Edit: I should have said - these are CMS only

Hell, why stop there? Why not Annex Mexico too, and maybe the rest of central America?

No, in the same sense that QCD doesn't. In principle Technicolor could just be another QCD at higher scales, and the W and Z are then composite particles. (This model, and technicolor models generally, have many other problems though.)

Of course. In fact, we have already seen another mechanism for creating mass. The masses of hadrons are not just the sum of the masses of the constituent quarks. QCD provides the extra mass - the strength of the interaction forced condensates to form. The high energy equivalent of this would be Technicolor. The elctroweak precision tests give: MH = 76+33-24GeV, or in other words MH < 144 GeV with 95% confidence. If you fold in the LEP constraint this becomes MH < 182 GeV with 95% confidence.

I am fairly sure we will find a Higgs Boson. I am not sure it will be fundamental, but there will be some sort of propagating state which fills the role of a Higgs. We need one simply to construct SU(2) invariant mass terms for the quarks and leptons.

This one looks impressive too: http://arxiv.org/abs/0806.3390

Yes. The probability goes down with the square of the energy. This is because you are moving away from the photon's mass-shell which is at zero (since the photons have zero mass).

Which annihilations are you talking about? If you go to really high energies, the mass difference between the photon and Z become negligible, so the extra mass of the W/Z doesn't matter and all that will determine the decay is the couplings of the particles. At low energies, significantly below the W and Z mass you will not produce the W and Z mass much because you just don't have enough energy to make their mass (they have to be very off-shell). However, if the annihilation happens at around the energy of the W or Z mass, then you have what is called resonant production. In essence you have hit the resonant frequency for creating the W or Z, so you make a lot of them.