Severian

That makes sense to me. As you become richer, you stop needing money to survive or even to significantly increase your standard of living. Material gains become less important, so your priorities change towards living in a 'better' society. That makes you more likely to vote for the person who you think will make society as a whole more pleasant to live in, rather than for the guy who will make you richer.

Sorry, but that is such bollocks. 1. The discovery of supersymmetry at the LHC says nothing about the plausibility of string theory. 2. The non-discovery of supersymmetry at the LHC says nothing about the plausibility of String Theory. So not much to do with string theory then....

Paul Lewis Ashley Carpenter. He sounds like the members of a rock group! (Your myspace friends look really creepy...)

Yes, I agree with that. The position of the centre-of-mass with respect to (say) the nose tip will change. But it is a bit of a semantic dispute. I would say that the rocket's position is defined by its centre-of-mass, so from this viewpoint the internal movement of fuel does not change the trajectory of the rocket. If you define the position of the rocket by its outer shell, then it can, simply by moving around its centre-of-mass within the structure. Similarly, the centre-of-mass of the hopper (including the fluid) does not move, but the hopper shell may move because of the shift of the centre-of-mass.

The key to understanding this is that it is the centre-of-mass which obeys the Newtonian equations. So for example, if you have an ensemble of n particles with position vectors [math]\vec{r}_i[/math] and mass [math]m_i[/math] each, then the centre-of-mass is [math]\vec{r}_{\rm cm} = \frac{\sum_{i=1}^n m_i \vec{r}_i}{\sum_{i=1}^n m_i}[/math] Differentiating this with respect to time twice: [math]\vec{a}_{\rm cm} = \frac{\sum_{i=1}^n m_i \vec{a}_i}{\sum_{i=1}^n m_i}[/math] Notice the masses [math]m_i[/math] do not depend on time because they are fixed (I am not allowing mass->energy conversion). This is also true in a rocket - the mass of rocket+fuel doesn't change - the mass only appears to change because we stop counting ejected fuel as part of the rocket. But if each particle feels a force [math]\vec{F}_i[/math], then by Newton's second law, [math]m_i \vec{a}_i = \vec{F}_i[/math], so [math]\vec{a}_{\rm cm} = \frac{\sum_{i=1}^n \vec{F}_i}{\sum_{i=1}^n m_i}[/math] So the acceleration of the centre-of-mass frame can only come from a total net force on the constituent particles. Since Newtons first law tells us that internal force will be balanced, any net force must be external. The centre-of-mass does not accelerate unless there is an external force. Note, that this is not saying that the rocket can't accelerate - it does, because it is not the entire ensemble. One can also make the rocket wiggle or turn by transfering angular momentum between the rocket and the ejected fuel. However, if we consider that we only fire the fuel straight out the back, then the rocket (and its centre-of-mass) must exactly balance the momentum loss from the fuel. The 'external force' in this case is just the rate of change of momenta lost in the ejected fuel. If you want to consider the remaining fuel as part of the rocket (and you should) then it doesn't matter how much it moves about, it will not change the motion of the centre-of-mass of the rocket, because it is itself included in the centre-of-mass calculation.

I am just bitter that I just had every single exam question that I set sent back with the complaint that they are "too hard".

It all depends where it is from. Most BSc's are not worth the paper they are printed on. I certainly wouldn't hire anyone who had a BSc from my University. Some are very good though.

Your real name is Cynthia?

Yes, that was partly my point. The electron is also a wave. It only behaves like a particle because its wave is highly localised. In fact, in Quantum Field Theory everything is a wave (or more precisely a field). We only continue to use the word 'particle' to distinguish between different types of field because the fields are quantised.

I disagree with most of what had been said so far. The difficulty is really the use of the word 'particle' which comes with it too much baggage. The word 'wave' is much better - much more accurate. People have a bad habit of only thinking of a wave as a plane wave, spread out over all space. While this is a wave, waves can also be very localised. A wave can look and behave exactly how we percieve a particle would if it is sufficiently localised. Indeed, since our measurements of position are never 100% accurate, we will never know exactly where a 'particle' is, so it is really a superposition of the position eigenstates, i.e. even after measurements, it is still a wave, albeit a localised one. I think we confuse people when first talking about quantum mechanics with this wave/particle duality business. We should be just calling them waves and leave it at that.

Could you provide an example of what you are refering to? I think our experts answer questions on their subject with a lot of patience and I have never seen anyone called an idiot for asking a reasonable question. Since this is a science site it would be nice for you to provide evidence of your assertion. Perhaps a link or two?

I am not sure even of that. I would hope that we would try and answer 'stupid' questions too, because then maybe we have added a bit of insight into someone's life. I have no problem with answering basic questions. What I do object to is when someone clearly doesn't read your response to their question and then rambles on at length about how this must be a end of quantum mechanics or some such. That is just annoying. I also confess that I get bored answering the same question over and over, so I tend to avoid answering questions which have been asked reasonably recently. To be honest, this is just laziness on my part - I am not one of these people who think posters should perform a comprehensive search for info before posting a simple question.

I can only speak from my own experience. I have lived in the UK, France and Switzerland. Of these, the best healthcare was Switzerland, which was the least socialized, while the worst was the UK, which is pretty much completely socialized. Basically it really doesn't get much worse that the UK's National Health Service.

The residual strong force, that holds together the nucleus of atoms is mediated by pions. These pions are quite massive, so travel considerably slower than light.

I am not convinced. The lack of incentives in socialized medicine lead to a lot of waste.

Whereas in the UK, everyone gets screwed. We are a much more egalitarian society.

Judging by how bad the UK' Nation Health Service is, socialized medicaine does not seem like a good idea.

Supersymmetry is an extention of space-time to include fermionic dimensions. We have known for a long time that particles come in 2 types: bosons and fermions. For example, an electron is a fermion and a photon is a boson. The distinction is a bit technical, but essential it comes down to what happens to the quantum mechanical wavefunction when you exchange two identical particles. Exchange two identical bosons and nothing much happens, but exchange two fermions and you have to multiply the wavefunction by -1. (At first sight this doesn't change anything since probabilities are the modulus squared of the wavefunction, but it does affect the interference between different contributions.) Now, for a long time it was thought that the Poincarre algebra was the maximal symmetry of space-time (the Coleman-Mandulla theorem). By that I mean that the laws of physics are invariant under Lorentz boosts and translations. However, in the 80s it was realised that this isn't true. Our 4 space-time dimesnions with which we are familiar as bosonic. If I take 2 steps forward and 2 steps to the right I would end up in the same place as if I went 2 steps to the right and two steps forward. The operations commute, and the dimensions are bosonic. But what if this were not the case - what if I could go in some other directions and pick up minus signs by doing things in a different order? What if there were fermionic dimensions? So space-time can be extended by adding in fermionic dimensions, and then a rotation between bosonic and fermionic dimensions would extend the symmetry. The laws of physics would be invariant under this new enlarged symmetry. This new symmetry is called supersymmetry and it is now thought that it is mathematically the largest symmetry group any space-time can have. But surely this is rubbish - wouldn't we see the extra fermionic dimesnions (new route to the pub anyone?). Actually no, because something weird happens when you work out how this would manifest in the real world. All your fields become functions of not only your bosonic coordinate [math]x^\mu[/math] ([math]\mu=0...3[/math]) but also the fermionic coordinates [math]\theta[/math] and [math] \bar \theta[/math] (I won't go into why there are two). Each of these fermionic coordinates is actually a 2-d vector, so for example [math]\theta = \left( \begin{array}{c} \theta_1 \\\theta_2 \end{array} \right) [/math], so altogether there are four fermionic coordinates just like there were four bosonic ones (although one can imagine including more if you like). But since these coordinates are anticommute, [math]\theta_1 \theta_2 = -\theta_2 \theta_1[/math] and more significantly [math]\theta_1 \theta_1 = -\theta_1 \theta_1 = 0[/math]. So whenever we make a Taylor exansion of the 'superfield' in these new fermionic coordinates, the series will be cut off as soon as we have two identical fermionic components in one term. For example [math]f(x,\theta) = a(x)+b(x)\theta_1 +c(x) \theta_2+d©\theta_1 \theta_2[/math] with no extra terms. The objects a(x) and d(x) look like bosons, while b(x) and c(x) look like a fermions. So suppersymmetry predicts that for even bosonic particle there must be a fermionic particle and vice versa. Fermions are really just projections of this superfield onto the fermionic direction, while bosons are projections onto the bosonic (ie usual) directions.

Saying "New measurements have failed to show clear evidence that the [Gulf Stream] current is weakening" is not the same as saying it won't switch off. In fact, if it were to switch off, I would expect it to be very sudden. I think we need to be very careful how the media reports and (most importantly) interprets scientific reports. Global warming is a problem that would be very dangerous to ignore.

How many web sites do you run?

Hey Bettina, good to see you back. I thought we had frightened you away!

If you are not going to take any action, then it is a pretty pointless exercise, isn't it? Section 9 of the Official Forum policy says:

I think that is abuse of your admin status. Nevermind whether or not it is public information, or part of whatever agreement we clicked yes to when signing up, it is wrong to pass information about SFN users' IP addresses to a third party. And before you get personal, not it was not me....

I realise that that was a joke, but I think it is in very poor taste.

Clearly it must have a charge. If an electron-positron pair is created out of the vacuum, and the electron is sucked in while the positron escapes, then the black hole will gain -e in charge. (Also, because U(1) electromagnetic is a local symmetry, one cannot violate charge conservation.) However, this is in the formal sense. Since positrons are just as likely to be sucked in as electrons, and (traditional astrophysical) black holes are made up of lots of particles, you would expect them to be approximately neutral. It is just that they will most likely not be exactly neutral, so they have charge.