Severian

Or better yet, a War on War.

An analogy with fluids is a good place to start I think. A scalar field is a just a number for every point in space and time. For example temperature is a scalar field, since there is a temperature (a single number) depending in where and when you are. A vector field is a number and a direction, a bit like a fluid flowing. Imagine a river; at every point in the river, the water is flowing with a certain speed in a certain direction. It is a vector field, just like the electric and magnetic fields are. The divergence of a field, e.g. [math]\vec{\nabla} \cdot \vec{E}[/math] is a measure of how much of the field (or fluid flow) is coming out of a (infinitesimally small) volume minus the amount to going in. So in a fluid analogy, a negative divergence means there is more going in that coming out, as we have a sink; a positive divergence is a source. So [math]\vec{\nabla} \cdot \vec{E}= \rho/\epsilon_0[/math] is telling us that charge density is a source for an electric field (it is spewing an electric field out) and [math]\vec{\nabla} \cdot \vec{B}= 0[/math] is telling us that there are no magnetic sources (no magnetic monopoles). The curl is basically telling you how much the field curls around on itself (hence the name) a bit like a whirlpool in the water. Maxwell's equations are telling us that if the magnetic field changes very suddenly then it will make the electric field swirl around. The curl of the magnetic field is similarly dependent on how quickly the electric field changes, but also on the electric current passing (which is why an electric current forms a magnetic field swirling around it).

He got it: http://nobelprize.org/nobel_prizes/peace/laureates/2007/

That is an intersting take on things. I think if you asked the average European, they would regard Europe as being less likely to infinge the civil liberties of their citizens than the US is. Would you say there is the opposite perception in the US? If so, where do you think it comes from?

This is Zeno's paradox. Not exactly original.... http://en.wikipedia.org/wiki/Zeno's_paradoxes Edit: bah - that will teach me to open a thread, so away for a few minutes and them reply without rechecking the thread to see if anyone has posted.

It depends on what you count as physics, and which continent you live on. It is definitely not Hawking under any measure. If you count String Theory as physics, then I think it is Witten. If not, then I would probably say Weinberg. To answer Martin's rephrasing of the question, I would probably say John Ellis or possibly Nima Arkhani-Hamed. (ajb's post reminded me that I am supposed to be having dinner with Atiyah in a couple of weeks.)

It depends what they are going to do to the hand. Usually, they are orthopaedic surgeons.

When they say "it doesn't make a difference to me" they are not necessarily saying they don't care who governs them. They may be saying that they see no practical difference between the candidates, i.e. they dislike them all. I must admit if there was a general election this week (I am in the UK) I wouldn't know who to vote for because they are all crap. I nearly didn't vote last time because of this.

Well, this was a hypothetical situation. One can imagine other setups which would be disadvantageous. For example, imagine that there were a shortage of fields, so production was not increased, and the food was only distributed to the people who worked for it. Then 40% of your population will starve while 60% have plenty. I would not regard this as an advantage over the first example. So one has to be careful to consider all the factors.

I don't think I am understanding your economy. Who decides who gets the food? Is it just divided among everyone equally (whether they work or not)? If it is, then only 20% go hungry in the second example, since you produce exactly the same amount of food as in example 1. Or are you saying that only those who work get food, so 40% (who don't work) go hungry while the 60% (who do work) have an excess. In fact, the rational thing to happen in example 2 (assuming an infinite supply of ploughs and fields) is that you would scale up production to keep everyone employed. 100% employment would then mean that you produce 100/60=1.66 times as much food, so you are then capable of feeding 100*80/60 %=133% of the population. Then you can either store the extra grain or allow population growth.

The 'opinion' statement was intended to be for the entire paragraph. But anyway, this was in the context of a teacher in front of a class - not a web forum.

I think it is silly to try and second-guess what the teacher did or did not say or do. We don't have enough information, and until we do we cannot make any reasonable statement. However, it is valid to state your opinion on what behaviours are or are not reasonable for a teacher and what would constitute a sacking offense. In my opinion, stating a personal opinion (and stating that it is such) on a religious matter is perfectly fine. Stating something as undeniable fact when it is not is wrong but not seriously so. Insulting and degrading students because of their beliefs, no matter what they are, is a sacking offense.

That was actually one of their main proposals. We have known that light slows down when passing through various materials (that is how a lens works) and that is due to interaction with the particles in the medium. One normally presumes the vacuum of space to be empty, so they are instead suggesting that there is an interaction with the 'quantum foam' which is a hypothesised breaking up of space-time on very small distance scales. This seems a little exotic to me. I would have thought you would get a larger effect just from hitting the odd particle in the 'vacuum' in deep space. Every vacuum has some sort of particles. There would even be a possibility of self-scatter, having light scatter off itself; for a very small fraction of time during light by light scattering, the photon is converted to a fermion-antifermion pair which have mass and don't travel at c. I presume they have thought about all these things though. Also, I suspect that most of these would conflict with the very tight mass bounds we have on the photon from other experiments. As a side point, it is something similar that it thought to cause the masses of ordinary particles. The vacuum is not empty but filled with the Higgs field. The particles interact with this background field and are slowed down, giving them an effective mass. (The photon doesn't couple to the Higgs boson, so remains massless.)

These are dreadfully worded. Whomever made these up needs firing. As Neonblack said, the answers they want are probably b both times, but it is difficult to know what they are trying to ask. For question 1, you are right about Pythogoras' Theorem. Your speed relative to the shore will be [math]\sqrt{(3m/s)^2+(2m/s)^2} = \sqrt{9+4}m/s=\sqrt{13}m/s \approx 3.6m/s[/math] at an angle [math]\tan^{-1} (3/2)[/math] to the south of the direction of flow of the river.

It seems a little unhelpful that they say "Ferenc cautioned that... a simpler explanation had not been ruled out", and not tell us what it is.

I did say "if they had been sufficiently well trained then they would have realized that the breadboard wasn't a problem after a quick inspection". I probably wouldn't have confiscated it since it is relatively useless in making a bomb or using as a weapon, but it is fair enough to stop her and inspect it. (And when they are done inspecting it, a nice smile and a polite 'Sorry for bothering you ma'am".) To be honest I am not sure where this thread can possibly go now. I know that I would not have mistaken the 'device' for a bomb, but I admit that it is an assumption that security personnel should also know that it wasn't a bomb. However, is it really too much to ask that they have enough training to make such a basic judgment?

But the average American should not be making the decision whether or not to arrest her. That decision should be made by security professionals, who one might hope did have "a clue what a bomb is supposed to look like". If they do not, then it is their fault (or their boss's fault) for them not being sufficiently trained to do their job in a competent manner.

To clarify my earlier statement, one can write Maxwell's equations in a covarient form as [math]\partial_\mu F^{\mu \nu} = j^{\nu}[/math] where [math]j^{\nu}[/math] is the 4-current (i.e. charge density in the time component and three-dimensional charge current in the space componenets), and [math]F^{\mu \nu}[/math] is the field strenght tensor. [math]F^{\mu \nu}[/math] can be written in terms of the Electric and Magnetic fields, according to: [math]F^{\mu \nu} \equiv \left( \begin{array}{cccc} 0 & -E_1 & -E_2 & -E_3 \\ E_1 & 0 & -B_3 & B_2 \\ E_2 & B_3 & 0 & -B_1 \\ E_3 & -B_2 & B_1 & 0 \end{array} \right)[/math] [math]F^{\mu \nu}[/math] is a second rank tensor under the Lorentz group, so if you perform a Lorentz transformation [math]\Lambda[/math] then [math]F^{\mu \nu} \to \Lambda^{\mu}_{\:\:\alpha} \Lambda^{\nu}_{\:\:\beta} F^{\alpha \beta}[/math]. Thinking in terms of matrices, this mixes the time-like and space-like parts of the matrix up (similarly to how a rotation mixes the rows and columns up) and therefore a pure electric field in one frame can look like a magnetic field in another. Notice that I never said that you could find a frame where all electric look magnetic. The point here is that magnetic fields are the relativistic completion of electric fields.

Electric fields and magnetic fields are actually the same thing - the difference is only a point of perspective. A pure electric field to one observer may be a magnetic field to a different observer.

Don't you think that security guards in airports should be given some rudimentary training on what a bomb is, what it can be made from and what is likely to be suspicious as a possible component of a bomb?

A few years ago I would certainly have labeled myself as a 'liberal'. But as I get older I am finding myself getting more conservative. Does that mean that I am a less 'critical' thinker than I was before? No, it is quite the opposite; I have become more critical. To a certain extent this is because I have seen what 'change' can do. Being in higher education, I have seen the unbelievable drive in recent years of the 'liberals' to make education more 'inclusive'. This has undeniably led to a reduction in standards which make everyone suffer. We now have much more difficulty finding students capable of doing scientific research than we did before. So conservatism is often rooted in a desire to preserve systems that work. Once something has been broken by tinkering liberals, it may never be the same again, and everyone will be worse off. I now find myself as somewhere between liberal and conservative. I would like to see change in many areas, but that shouldn't be knee-jerk 'lets have a group hug' change. It should be well thought out, reasoned and motivated change, with honest tests and safety measures put in place to ensure the change is an improvement and a facility for changing it back if it is not. Ironically enough, I am finding that some of the things I want to change most (so in some sense I am least 'conservative' about) and the things that the 'liberals' have introduced into our society in the guise of progress.

You are best to submit it to the arXiv first and then point the journal at the arXiv copy. That way it is in the public domain faster and the referee will be more tolerant of it (I am always very suspicious when refereeing a paper not on the arXiv, because they usually have something to hide). However, that will mean that you will need an arXiv endorser. I am not sure how you will go about finding one (email academics at random?). I am an endorser but I am not willing to endorse this (no offense). 40 pages isn't too long - I have written papers that long before. (They get smaller in the journal because they typeset differently.)

To be honest, I am failing to see the significance in this. For example, could someone explain to me why this discovery gives us a "greater understanding of the strong force in general"?

It is not that the equations break down. It is a postulate of the theory that electrons travel at c in all frames, so they cannot have a rest frame.

You need to be slightly careful here since photons don't have a rest frame, so it is meaningless to talk about the velocity of one as seen by the other (which I think is what you mean). If you consider a frame which is moving at 0.999999999999...c in the same direction, then relative to that frame, both photons are still moving at c. (Weird huh?)