Severian

I'm sure they would use them if they had them. That would make them just as evil as the Americans.... This reminds me of: http://www.theonion.com/content/node/43012

I have already given you the correct technical definition (seriously!). For a particle of mass m travelling with velocity [math]\vec{v}[/math], this becomes [math]\vec{p} = \frac{1}{\sqrt{1-v^2/c^2}} m \vec{v}[/math]. If you want to link it to force, then force is the rate of change of momentum.

The conserved current associated with a translation symmetry

Not really. In Lattice Guage theory it is used to regulate infinities which crop up in the theory, but they always take the 'continuum limit' at the end of a calculation. They have a quantity called the 'lattice spacing', usually denoted 'a', which is the minimum distance between allowed space-time points. At the end of the calculation they extrapolate their results to a=0.

Lattice Gauge Theory has been using discrete time (and space) for years.

They would, or rather could, still annihilate as long as they are not orthogonal. The vertex where they annihilate would project the 'mass eigenstate' (a state of definite mass in which the neutrino propagates) onto the 'flavor eigenstate' which is either electron, muon or tau neutrino. If neutrino 1 is 100% electron-neutrino and neutrino 2 is 100% muon-neutrino, then they would not be able to annihilate. But if neutrino 1 is a fraction x of electron-neutrino and neutrino 2 is a fraction y of muon-neutrino, then the probability of annihilation would be x2y2 times the probability of two pure electron-nuetrinos annihilating. (The probabilities come about because it is quantum mechanical. The interaction vertex is like a measurement in that it collapses the neutrinos into definite flavour states. If it is in a state of 100% e-neutrino then it can't collapse any further, but if it is 50% electron and 50% muon neutrinos, then 50% of the time it will collapse into a pure electron neutrino and 50% of the time inot a pur muon neutrino.)

What are tubesocks?

We understand the CMBR reasonably well now. For a while after the big bang, the energy density of the universe was so big that it was very easy to create particle-antiparticle pairs from photons. In essence this made the universe opaque to photons. If a photon was emitted, it would react with omething else or turn into particle-antiparticle pairs very quickly, so the light was not abe to travel far. After a while, the universe had expanded enough to lower the energy density so that collision with other particles became rarer and there was not enough energy in the photon to produce the (massive) particle-antiparticle pairs. This meant that all of a sudden the universe became transparent to photons - they could travel very far without interacting. The CMBR is the radiation emitted by this 'surface of last scattering'. The photons have been travelling for billions of years. This model predicts the temperature and power spectrum of the CMBR really rather well.

To answer the original question, yes - they would, but you would need 1 trillion years to pass a signal between them (which is rather a long time considering the univers is about 13.7 billion years old). In other words the electromagnetic force has infinite range. the same is true for gravity. The strong force, on the other hand does not have infinite range, and will be cut off at distances of order 1/GeV (with appropriate factors of c which I can't remember off-hand).

I would dispute that. While it is true that phenomenology is more active in Europe (particularly Germany), string theory is much bigger in the US. In fact, they don't do much phenomenology in the US at all.

Each possible trajectory for a particle between two fixed points is a 'path'. To make an analogy, if you fly from New York to Tokyo you could fly to LA and the to Tokyo, or fly to Europe and then on to Tokyo. Each of these is a possible path. Now, of course, for a single particle with no interaction, the path which will be taken is obviously a straight line between the two points, which is pretty trivial. But it becomes more interesting when you have mutiple particles which scatter off one another. Then the 'path' is really the particular movement of all the particles from their initial to final points. So, what is this sum over paths? Feynman's theory assigns a complex number to each path. Technically, it is the exponential of [math]i=\sqrt{-1}[/math] times the "action". In turn, the action is the integral of the Lagraingian over the path (or if you prefer to remain covariant, the Lagrange density integrated over space-time): i.e. [math]e^{i \int d^4x {\cal L}}[/math] The Lagrainagian is defined by the theory you are looking at - for example, for a non-interating electron of mass m, it would be: [math] {\cal L} = \bar \psi \left( i \gamma^\mu \partial_\mu -m \right) \psi [/math] (Notice the similarity to the Dirac Equation - the Dirac Equation is the Euler-Lagrange equation for this Lagrangian.) Then you add up all the paths, weighted by this exponential. Most of the contributions will cancel against each other, and the one which is dominant will be the one for which the action is minimised. This is known as "the principle of least action".

It is hard to see how a society founded on terrorism can ever expect terrorism against them to stop. The existence of Israel itself is a demonstration that terrorism works, so is an encouragement to the arab extremists. I never liked Sharon, but the direction he has taken recently has been an improvement. I am worried that with his death the shit will hit the fan....

To answer the original question, symmetry already has told us plenty of things about cosmology. GR is based on a symmetry, the Big Bang model is based on symmetry, the interactions of particles in the early universe are based on symmetry. Almost all of physics is based on symmetry. And all of physics requires causality, so that is clearly used in cosmology too. However, a universe which is a 4-d sphere would be just as symmetric as a 4d open sheet (which is what you seem o be proposing).

It is still being debated. In fact, there is no evidence for the creation of space and time at the Big Bang whatsoever. There is evidence for the pattern of events a tiny fraction of a second after the 'big bang' but what happens before this is still unknown (and probably always will be).

This is correct. In fact it is the basis of a whole slew of eperiments, and is know as deep inelastic scattering. As search fr 'deep inelastic scattering' on google throws up a few links, inlcuding: http://www.physics.ox.ac.uk/documents/PUS/dis/ http://www.nikhef.nl/pub/experiments/zeus/theses/wouter_verkerke/latex2html/node4.html http://en.wikipedia.org/wiki/Deep_inelastic_scattering

It terms of people I know, I think it would have to be Dick Roberts. He is the UK's most cited particle physicist (last time I looked) but is incredibly modest and doesn't shout about his very significant contribution to particle physics (like a lot of people do). He is an incredibly nice guy and a good friend. If I could be just a 1/10th of the person he is, I would be very happy. Here is his publication list: http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=ea+Roberts,+R+G

The iron bar is held together by electromagnetism - not gravity. The very fact that gravity can't pull the iron bar apart (try holding just one end of the bar) shows that it is much weaker than electromagnetism.

'One dimensionaa' just means that you need one number to tell someone how far along the string you are (just the distance from one end). If you were on a sheet of paper, you would need 2 numbers, so it would be two-dimensional.

You're kidding right? Are you meaning the Lisa Randall of particle physics (eg Randall-Sundrum model), or is there some other Lisa Randall? If that is who you do mean, why?

Johnnie Walker tastes like methanol normally, so no need to worry. Try a single malt and you will notice the difference (I recommend MacAllen, Rosebank or Glenmorangie).

When people say 'one dimensional' they are not including time. Just like you would say that a photograph is 'two dimesional' but an object is 'three dimensioal'. You don't say a TV picture is 3d just because it changes with time, do you? Strings have one space dimension, but do change wit time.

QFT is not contained in QM. In QM only the operators (the things you measure) such as energy, position etc are quantised. In QFT the fields themselves are quantised. Your understanding was pretty reasonable, apart from the bit about gravity. We don't have a consistant QFT for gravity yet, but even if we did, the graviton would couple to energy, not mass. The Higgs mechanism is generating mass.

That is actually a very good comment. This is currently one of the suggestions, that gravity is diluted by leaking into the extra dimensions. It works out that it is not a factor of 1/d (where d is the number of dimensions) but is highly dependent on how tightly the extra dimensions are curled up. Potentially one can put limits on this at the LHC.