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Like Klaynos, I've not heard of physics being split up like this, that's not how it's done in the UK. But I do think that unis will (and rightly should) be happier with a student who knows calculus than one who knows algebra. I'm not saying algebra isn't important, but calculus is fundemental and comes up in everything. You're suggesting that we should not teach classical physics until students are competent with calculus (which in the UK is not until 16/17 years old)? And what physics should they be taught when they're younger? Quantum!? What you're seeming to suggest is that we should not be taught something until we have the capabilites to fully understand it. But that is a near-impossible method of learning. I learned how to integrate a polynomial before I really understood what I was doing, and I could invert a matrix long before I could see any use or applications of the things. Yet without my flawed and simplistic prior knowledge, a deeper understanding would have been a lot harder to obtain. There are many flaws in our education system, but teaching physics students that F=ma and v=u+at before they know calculus is not one of the significant ones, IMHO.

Same principle. When your hollow sphere is created, the interatomic forces will make the Casimir effect insignificant. A thought trail lead me to a figure off the Wiki page on Casimir effect which says that: "In fact, at separations of 10 nm — about 100 times the typical size of an atom — the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.3 kPa)". So if you made a sphere of diameter 10nm (100 atoms - which I think we probably could) then you would get 101kPa of force trying to crush that sphere inwards. Sadly even if we really simplified the problem I don't know how to calculate what force it would take to crush a sphere, given that it is just the interatomic forces holding it together. Also remember that if the distance between atoms that enclosed the sphere were big enough then virtual particles could "go through" the wall. So you would need do have the wall of the tube/sphere being sufficiently dense to prevent that. Finally if you were to make a sphere I wonder if the force would be larger than expected, as not only are you limiting the size of the particle (or amplitude of the wave, by confining it), but you're also placing it in the 'particle in a box' configuration, thus limiting the energy levels the particle can take. Although I suppose if the virtual particle existed for a short enough time period it could poses a non-normal-mode energy level, but still, I think it possible that the number of virtual particles is further limited by the fact it is a sphere, and not an (effectively) infinte tube, or between parallel plates, which would make the Casimir effect stronger. Maybe, I'm just guessing at this!

The only tube small enough to be affected by the Casimir effect would, maybe, be a carbon nanotube (or something smaller, but I can't immediately think of anything that would fit that category). More importantly for such a small construction to be stable it must be quite strong (carbon nanotubes are a great example of this). Given the strong inter-atomic forces, the Casimir effect is so small it would be quite insignificant. In theory you could have a weak, tiny, tube that would collapse in on itself due to the Casimir effect... but I don't think you could construct such a tiny, yet weak, tube to observe this.

If a photon did the "telling"... well, that is basically hidden variable theory. Neither photon does the "telling". Instead think of it as a single wavefunction that collapses. Remember the the wavefunction collapse is instantenous. I don't especially like the idea of everything happening at the same time and instantenously, but that is what your thought experiment is. My dislike is based far more on the fact you are observing two photons at the same instant, than the fact that on top of this they're entangled. Despite our dislike, this is the nature of thought experiments! Rereading your post, Slinkey, I think if you think more of a single wavefunction collapse, and not one photon determining the other's polarisation, it may help. This won't help you visualise the situation in your head, but I think getting past the "one photon's property determines the other's" way of thinking may help.

thedarkshade: I was looking for an image showing two travelling waves combining to form a distinct wave packet. Similar to what I had in my image, but I wanted a more exagerated version, to make the point as clear as possible. When asked if something is a wave or a particle many physicists would answer both. But equally correctly you could answer neither. If something is a wave, then by the classical definitions, it cannot also be a particle. Clasically they are distincy and seperate things. Consequently saying something is "both" can be a bit confusing, sometimes. If you say it is neither a wave, nor a particle, but is in fact a third 'thing', which somehow combines both wave and particle properties in one, then you'll be getting at the right thing. And this applies to everything. Generally things on a smaller scale will display both properties. As you know photons and electrons behave like particles when they collide with things, but will both diffract through a slit like a wave. Whereas something like humans always behave like particles, you couldn't observe a human diffracting through a double slit! The reason the whole fullerene thing came up is because fullerene, which is 60 carbon atoms, is big. Yet fullerene has been observed to diffract through a double slit, just like a wave. I believe it's the biggest thing to have been diffracted through a double slit, and have the resulting dark / bright fringes observed. No. If you think of a particle's wave property as a probability wave, then a wave packet would be where the particle is most likely to be found. The travelling waves combining to form a wave packet was just an example of how a wave packet could be formed in a mathematical way.

Yes, but they never behave as a wave and a particle at the same time. Mind, I once read of an experiment which claimed to show something acting as a wave and a particle at the same point. Although I think the commonly accepted view is that a "thing" is either a wave or a particle, it behaves as one or the other, but never both at the same instant. Travelling waves can be combined in any way, one combination results in wave packets being produced, see:http://hyperphysics.phy-astr.gsu.edu/hbase/waves/wpack.html I couldn't find a better image online, but here is an example of the above: two travelling waves combine to form a wave packet. Now imagine if the wave packets were smaller, the distance between them bigger etc. (or if you were looking at the image from a long way away) it would seem like dense areas of wave, with spaces inbetween, i.e. it would look like particles. Does that help you to understand how a particle can be expressed as a wave packet? [edit] See here: http://dspace.mit.edu/html/1721.1/35749/1-138JFall-2000/OcwWeb/Civil-and-Environmental-Engineering/1-138JWave-PropagationFall2000/Simulations/detail/groupvel.htm (wait for the image to load)

I think your method of detection here is of critical importance. I also think there are two relevant questions. The first, of whether the cat will die, seems a simple one. You must have some sort of polarising filter (or some way to measure the polarisation), which will then result in a signal, say 1 or 0, being sent to the poision vial, thus killing or not killing the cat. In this scenario, assuming both photons reach the polarisation detection circuit at the same instant, both a 1 and a 0 will be sent. The reason I said it were simple is because in a digital electronic system 1+0-->1... i.e. the signal which says "keep the cat alive" cannot undo the signal saying "kill the cat". As the signals come at exactly the same instant you cannot seperate or prioritise one signal or the other, both signals must be processed equally, a signal and a lack of a signal is simply a signal. However if, instead of 1 and 0, your polarisation detector results in a 1 or -1 signal, then the two signals will combine to form 0, i.e. no action will be taken. It is a simple question of how the "kill" and "not-kill" signals merge, when both sent through the same circuit at the same instant. As for how the entanglement collapsing works, if both photons are truly detected at the same instant, then they'll both go from a superposition to a definitive state in that instant. Remember with QE the wavefunction collapse is instantaneous. Everything happens in a instant, it's not so nice to think of that happening in reality, but this is a thought experiment and so I can't see a problem.

Are you asking if so-called "hidden variables" could be residing in higher dimensions? If so I believe the answer is no, based on Bell's theorem (and the Aspect experiment that verified it). Bell's theorem said that if any hidden variable exist (and the assumption I'm making here is this includes your theoretical higher dimensional hidden variables, which, if they do exist, I think is a safe assumption to make) then Bell's inequality would be correct. Whilst if QM is correct (that is to say, the universe truly is indeterministic) then Bell's inequality would be violated - as was shown to happen in Aspect's experiment (and many more that have been carried out since). Basically what I'm saying is that once Bell's theorem was verified it was proved that there are no hidden variables, full stop, i.e. including in other dimensions.

Radians are dimensionless, you don't have to include it (no?). Besides, I don't lose marks for missing rads, therefore rads aren't required. QED. I've heard all this rubbish about using and abusing ZPE, but I suppose I just didn't realise there was 10^5J of energy around us. Although of course it's ZPE, and not just "energy", and this is the critical difference that I didn't fully appreciate. Cheers guys! [edit] ˉ¹, hmm, didn't know there was a superscript minus sign, useful!

They slow them down. From what I know about what CERN did they had to produce the antiprotons themselves, and then transfer them into, and slow them down using, an antiproton decelerator. They did this so they could study them at lower energies.

Ahh, so it is me misunderstanding ZPE. I just looked at 10^5J and thought it were a massively high amount of energy to just be around us. But what you're saying, if I'm correct, is that yes there really is this massive amount of energy around us, and that it must stay around us because, well, it's ZPE, you cannot remove a fundamental lower limit of energy from a system. Am I talking along the right lines? I guess this is what happens when you do questions ahead of when you get taught how to do them! [edit] ah, me/Atheist posted at the same time. I just knew someone would comment on the no units for omega! Grr you! s^-1 looks messy when you're not using Latex!

I'm asked to find the ZPE of 1m³ of air, assuming it is all nitrogen. Here's what I did: 1) use PV=nkT to find the number of particles in 1m³ P = 1.01 * 10^5 k = Boltzman's consant T = 298 K and got n = 2.5 * 10^25 per m³. 2) I am given that the "spring constant" (this is all approximate) in nitrogen is s = 2240 N/m. Atomic mass is 14, reduced mass, μ, of N-N system is 7. Converting 7 from AMU to kg and using ω=√(s/m) I get ω=4.39*10^14. 3) I'm then told E=ħω/2. I stick in ħ and my value of ω, multiply by the number of molecules in a m³ of air and get the total ZPE in 1m³ of air is ~6*10^5 J. If I made a mistake please let me know where. If I did not make a mistake then I've just said that the ZPE of 1m³ of air is sufficient to "boil" a human, and that doesn't sound right to me! Maybe I'm misunderstanding ZPE, but I can't see a mistake in my calculation. Thanks in advance!

Yes. I once read that probabilistically speaking, the chances are that there are life forms on other planets, but that we have just never found them as they are too far away from the Earth for us to detect. On this basis I advise that you go find these other life forms, hope they are more technologically advanced that us... and then hopefully you will listen to them when they tell you that you cannot make a repulsive gravity hoverboard... it is impossible! You could make a lifter, which works on ionic winds: http://jnaudin.free.fr/html/lifter1.htm here's a little about ionic wind: http://en.wikipedia.org/wiki/Ionic_wind and here's how to build one: http://jnaudin.free.fr/lifters/howto.htm although that will only lift it's own weight - a few grams. It really does hover though (by some defintions of the word "hover")! Otherwise if you place a board on a helicopter then it would "hover"... does that count? What exactly are you looking for?

I suppose you might consider the dimensions of the car if you were to need loads of people, who might not, potentially, be able to fit around the car. But this is clearly not the case. A good thing in questions like this is to single out the information you need. In this case all you need is that the car weighs 500kg and that 1 person can lift 80kg (so they're strong people!). As for the fact that the people can lift 80kg up by 1m, and you only want to raise the car by 0.2m... you can't really use that information because you can't relate lift height to lift weight (you would need more information. For example you cannot say that because it's only 1/5 as high they can lift 5x more weight or anything of the sort. As you cannot use this you cannot really account for it in the maths. Although if this is an estimation problem then maybe if it were, say, 10.3 people can lift the car up 1m, then round that down to 10 people can lift it 0.2m... but that's really iffy and you can't really justify it, so I wouldn't say it. Incidentally if it were 10.3 people needed, and obviously you can't have 0.3 people, then 10 would not be enough, so you would need to round up to 11.

YT I had exactly the same thought! Currently most of the blue laser pointers are based on dismantled BluRay players, and as such are very expensive. Increased demand for BluRay means cheaper units, meaning cheaper blue lasers!!

For example if you are on a moving train and drop a ball then you see it go down and then bounce back up. Whereas someone outside the train (on the platform) will see the ball go down/up but also along (because the train is moving). So you see the ball move like || whereas the person the platform sees \/. http://webphysics.davidson.edu/Course_Material/Py230L/relativity/relativity-ex1.htm?D1=1 look at that animation at the top (set the v/c value to say 0.5), then click Set value and play... you'll see what I mean. The point is that if you apply the up/down thing on a train to light then you get some weird effects. That is part of the basis of relativity. If you want me to explain more then just ask and I'll be happy to!

I wasn't aware of the law suit regarding Area 51, that was quite interesting to read about. I reckon it is just a development and testing lab for the latest military technology, from aircraft to crazy scifi-sounding technologies (the Tactical High Energy Laser that shoots down missiles comes to mind - I know this was not developed in Area 51, but that is what I mean by scifi-sounding technologies).

I'm a physics student and I was once told that physicists are good at some career (can't remember what, some sort of computational something, maybe) because of their problem solving skills and how they are comfortable with the concepts of 0, infinity, points and lines etc. I couldn't appreciate why understanding what a point is could be so useful... Now I was about to say that an electron really is a point charge, i.e. that a physical entity really is zero dimesional... but then I came across this: http://scienceworld.wolfram.com/physics/ElectronRadius.html so now I'm not so sure. Reading more over here: http://en.wikipedia.org/wiki/Classical_electron_radius it says that in things like non-relativistic Thomson scattering the electron radius (a classical property) is used. But that other modern physics experiments (none actually listed) indicate that the electron really is a point charge. In fact the Wiki article is even titled classical electron radius... hmm... the electron was my example of a physical 0 dimensional entity - I think it still is, although I'm not so sure now! Back to your question, the path of a photon is 1D, but that's just a path, not a physical entity. Aww, I don't like your question! But things can exist in 0 and 1, 2, 3 etc. dimensions! (sorry for the unsatisfying, non-convincing & proof-lacking response!)

I found this trick very useful a few years ago when I was building an IR R/C circuit, I could check the remote was working using my phone!

The LHC is planned to start in May 2008. I think they have run periods during which millions of particle-particle collisions will occur every seconds, producing more terrabytes of data than you can even imagine. Most of this data is automatically removed by a computer, which labels it as "not interesting". But a huge amount of data will still be sent to scientists who have to analyse it. As for how long a run "period" is I have no idea.

Yes, but then you just encrypt a virus and then you get around your hardware string-searching AV. Routers include a fairly basic hardware firewall, although a software one is still necessary on top of the router's one. As for AVs, software is the way to go.

I check through the Services list, eliminate unnecessary background processes, do registry cleanups, defrag etc., but I still find that after a year, and certainly 2, if I were to format it would be a bit quicker.

I voted for the wrong thing by mistake! I voted that I want blu-ray. Well, when the blu-ray vs. HDDVD first started I was supporting blu-ray... but in this poll I'd say I want both, and it will remain that way until one or other wins or they become compatable with each other! Basically what I want is to be in with the majority and have the most popular technology, because in this case I believe that's the best position to be in. In reality I won't get either though! Not until there's a clear market leader (or they're compatable)... I'm but a poor student! And I like PC gaming over PS3/360, so that rules those out.

That is in fact quite wrong. But I am smiling because it reminds me of a mistake that I made, when I thought this was true. I was doing a science report on temperature and resistance (small temp -> less resistance). I was 15 at the time, I knew my teacher had done a PhD related to superconductors, so I decided to extrapolate my data to claim that at T=0 the resistance is also 0. Little did a young and innocent me know how very wrong that is! The first problem is that we can never reach T=0. Note T is temperature in Kelvin. We can get very close to 0, but it is impossible to reach it (it is against the laws of physics, it is not an experimental limitation or a problem with our technology). But this is a minor side point. The problem is that superconductivity is not explained by low temp -> little movement, it is explained by something totally different, known as BCS theory (named after the 3 people who discovered it - Bardeen, Cooper & Schrieffer). Basically it says that at low temperatures electrons pair up (to form Cooper pairs)... and because of how these electron pairs interact there is 0 resistance. The "high" temperature superconductors mentioned work at around 70 Kelvin, or -200C or -334F - so they are quite cold too! However BCS theory doesn't seem to apply to them in quite the same way; at the moment there is no definitive theory that explains how high temperature superconductors (aka Type II superconductors) work. If you want more then look up "BCS theory" and "Cooper pairs". Also a useful note if you do look this up is that Tk or critical temperature is the temperature when something interesting happens. Tk for a superconductor is the temperature at which the material starts superconducting.

Of course that's a list of the best unis. For what subject!? Also where do you plan to work and in what aspect? I would vote Cambridge over Oxford (except in some circumstances; like if you wanted to do a pure physics degree - Cambridge would have you Natural Sciences and then specialist in physics, whereas Oxford has a straight physics course). Also if you want a scientific education but are considering banking or finance as a career then Imperial College London, with it's contacts and location is probably the best choice. In this year's Times Higher Education Supplement world league table the top ten were: 1 Harvard University (US) 2 University of Cambridge (UK) = University of Oxford (UK) = Yale University (US) 5 Imperial College London (UK) 6 Princeton University (US) 7 California Institute of Technology (US) = University of Chicago (US) 9 University College London (UK) 10 Massachusetts Institute of Technology (US) All I can say is that any of them are awesome, so you need to look at other categories. Course specifics, if you visit do you like it, location, finance(?), career prospects etc. etc.