abskebabs

Just from inspection I'm not sure if that'll work. lets have a go: ................................ Ok from trying that I get something like this: [math]c=-1-ab+-\sqrt{1+a^2b^2-4a^2-4b^2}[/math] I'm starting to doubt whether my initial equation was correct. In any case I'll just display the overall equation and what I need to get. Ok, starting from: [math]\gamma_{31}=(\frac{1}{c^2})\gamma_{32}\gamma_{21}(c^2+v_{32}v_{21})[/math] Where: [math]\gamma=\frac{1}{\sqrt{1-\beta^2)}}[/math] and [math]\beta=\frac{v}{c}[/math] I need to get: [math]\beta_{31}=\frac{\beta_{32}+\beta_{21}}{1+\beta_{32}\beta_{21}}[/math] Thanks for the help anyway:-)

I would probably pick the launderer too as it includes the chores above of which I am the least inclined to do, and I am living with the results!

Hi everybody, I'm well into my relativity revision, and was just going through deriving the relativistic "velocity addition" forumula, but came across an algebraic stumbling block along the way. Basically, you could say I need to get the identity: [math]c=a+b[/math] From [math]c=1+ab-{((1-a^2)(1-b^2))}^{1/2}[/math] Any ideas? Help on this would be greatly appreciated.

I assume you are talking about what has been happenning in the Anbar province recently. I agree developments there have been positive, casualties have dropped in the past few months, but the reasons for the change of heart of the sheiks who effectively govern this area may not be for entirely benevolent reasons. I think that the dispute that tribal sheiks who originally supported Al quaeda and the general insurgency may have initially changed heart after Al Quaeda started targeting them too in order to consolidate its control over the Sunni province. Inevitably this provoked a backclash. Also with Al quaeda out of the picture, the tribals have an effective monoploly on smuggling rackets that go to Syria and Jordan. I guess with the situation the way it is they are much preferable to what was happenning before, even if they exert a kind of mafia control on throughout this region, at least there will be greater stabillity. As for this being a galvanising force for other Sunni areas, I'm not so sure. They have already been labelled as "a band of thieves and bandits" by the influential association of muslim scholars, so support on that front may not be coming. I guess actually in a way this kind of exposes the ginorance the US always had for these kind of local leaders and their job in helping provide law and order to the regions they governed and influenced. I think even under Saddam's regime they played a much larger role in governance. Also to answer Bascule's question on whether the current engagement is worthwile, I would say no, and it will not become so unless possibly heavily modified and a new strategy is well thought out and executed. Petraeus strategy I think is an ok one, and he certainly succeeded in the places he was assigned during previous tours in Iraq under more helpful circumstances(aka using the clear and hold strategy). I remember reading about him actualy back in 2004, I think he was stationed in a western province at the time. But I don't think his strategy will work with the current No of troops on the ground, and I don't think the current Iraqi security forces and even large sections of the iraqi government, regardless of its sovereignty, can be currently relied on to look after its citizens as it clearly has sectarian leaders among its ranks. Large and wholesale change would be required, there would need to be wholescale reform of the Iraqi police and even army to a certain extent. Perhaps the justice department would be better suited to helping train the police as opposed to the army? Also for the state of Iraq to survive a lot of effort needs to be taken so that it becomes and stays secular, though I am not sure how this could now be achieved. The current investment is not worthwhile, but perhaps if the right amount of resources were provided, and a sufficient amount of realistic and stategic and forward planing was employed, then positive results could be produced. A serious deal needs to be done with Iran, perhaps a backroom one to avoid either side losing face, in order to cooerce and incentivise them to stop meddling in Iraq. They Syrians too, regardless of what other grievances America has with them need to be seriously engaged on the question of border security, and the hand of cooperation needs to be extended to them. I guess change has to come from within for a lot of this to happen, the Iraqi ppl have to make a decisive shift from their current sectarian politics that will just lead them to endless bloodletting. But I guess then again its a case of catch 22. The current security climate is pathetic, so the remaining populace rely on tribal, ethnic or religious leaders for protection, contributing to the sectarian divide. In turn these types of groups gain more power, making the problem get worse. The more educated and secular part to Iraq, including its intelligentsia and some of its most potentially valuable citizens have in the process been killed, coerced into silence, and many more have fled the country, maybe to never return. I guess basically in my opinion half mesures will not work, and if America wants to have one last try or "surge" to stabillise Iraq it needs to commit itself wholeheartedly, intelligently, and on many different levels. Progress needs to be continually managed and bottlenecks identified and dealt with. Basically more of what is happenning to an extent already. I can understand though with the war having become so unpopular, why this probably will not happen. I guess if this is not done, then there is basically not much reason to remain in Iraq, after all genocide and civil war is only being delayed, not stopped. I think things will become very messy in this case, as even now Iraq still contains quite a mixed population. I guess America would then be burdened with a humiliating failure, and Al queda will readily toast its victory, and its supporters will be overwhelmingly emboldened. The consequences would be drastic, but the status quo is disasterous too, and I don't think the merican public will stand it much longer. I have to say these consequences are already starting to seem quite scary. Iraq war Al queda veterans will be much more numerous and much more dangerous than the Afghan war ones ever were. In fact we are already starting to see this in Lebanon. They have been able to put up a pretty damn good fight against the Lebanse army considering how few their numbers are. Going through this, its amazing to think how badly this entire debacle has been managed, and how now, in the effective midnight hours viale stategies are being discussed.

damn i suck at that game! My best so far is 2448! I probably shoudlnt admit that outright...

Interestingly how did maxwell himself interpret the speed of light predicted from the permitivity and permeabillity of free space? Did he think that the so called predicted speed was relative to the vacuum, or not at all? I guess if he lived a bit longer, he could have himself realised what this predicted speed meant and beat Einstein to being the founder of relativity by a few decades:D ! I remember my lecturer saying that one time.

Tbh im not sure, but I could give you an answer to the question though I doubt its correctness. I do not understand fully understand what all the terms in the tensor mean, indeed I have only recently acquired a vague notion of what a tensor actually is. Nevertheless, to answer your question; I would go with no, because it doesn't matter what velocity you are travelling with respect to a charge/electric field, you always need an electric field for there to be a magnetic field, and that electric field needs to be in relative motion to whatever is measuring the magnetic field. Therefore as you cannot have the latter without the former, how could you have a purely magnetic field?

Interestng question. I feel there should be another question that should be asked alongside with this that may be on a more personal level with ppl. Do we need to feel we are better than other ppl at something or in some way to feel better about ourselves. Do we need a hierarchy where we can see we are not at the bottom, so we can safely say to ourselves, "it could be worse". I can see how these ideas in regard wth racist ideas, regardless of how delusional they are could yield similiar feelings in ppl if this were the case.

Thanks for your responses, I understand now, and feel I should have thought a little harder about the question before posting it; it would have been more rewarding to reach the conclusion myself. It's interesting how there seems to be a certain kind of symmetry here, in the case that we only need to relate observables we see in our own frame to accuarately work out other relative quantities, and again this is in line with the postulate that the laws of physics are the same in all inertial reference frames! I should have realised that if a magnetic field were to be detected moving alongside a moving charge, this would real an "absolute velocity" which shouldn't be allowed by principles of relativity. We can calculate quantities in this way with the minimium amount of available information about "observables." Wonderful:-)

Hi everybody. This may have been mentioned before, and I apologise if it had, but this has been puzzling me just now. I know that a moving charge generates a magentic field, but all motion is relative, so if I was moving at the speed of the charge parallel to it, would I still detect a magnetic field? In the framework of relativity how can we answer this question?

That makes sense actually, though I cannot help but ask: Why is it not coupled? Also, why is the Earth spinning in the 1st place .Is it residual angular momentum as insane suggested, and if so should the rate of the Earth's spin actually be slowing down slightly because of resistive/frictional forces it encounters from things in space?(these questions and my own possible ideas for answers I have already alluded to)

If it's geometry, then again there's a lot of choice. Basically you could pick Euclidian geometry(which is basic geometry which you will have been taught at school), or one of the Non Euclidian geometries. For your level you may find a number of the latter a considerable challenge, so that's your call. Not everything involving Non Euclidian geometry is beyond you though, if I were you I would try Taxicab geometry perhaps. Or even some basic topology. Actually some parts of fractal geometry are not too bad either, e.g. considering notions of self similiarity dimensionality etc. If you want to find out more about this then just type in google something like "middle thirds set" or "cantor dust", and you may find plenty on the subject matter. Actually self similarity dimensionality may get you quite a few too. Its your call though what you do...

Intriguing, though I doubt I have the mathematical skill yet to properly understand; but is there a reason for the breaking of these symmetries? Or is it just a failure on the part of classical physics?

During my physics tutorial session recently, I remember a girl asking a question that she said her dad asked her based on physics that seemed to make us step back a little and think. So I'm sure you may enjoy it:-) Ok basically its kinda 2 questions. What is it that causes the Earth to spin, is it some remnant of angular momentum that still exists since its creation. or is there some other explanation? Also Why is a pendulum that is stationed on the Earth's surface unnaffected by the Earth's spin? Or is this incorrect? I could imagine explanations to these questions like to a good approximation we can assume the pendulum to be within an inertial frame, or that the pendulum is "decoupled" from the frame of the centre of the Earth etc, but I would like to hear from you.

There are so many possible interesting topics you could cover in the wonderful world of mathematics. To name a few that interest me, there is geometry(both Euclidian and Non Euclidian), calculus, abstract algebra, the list goes on... I don't know what level you are at, or what you think your mathematical competency is like, but you could really do an essay on any of the major branches of mathematics. If you are at high school level though I would recommend trying to at least get the gyst of what is going on so that you can elaborate this in your essay rather than go through the entire full detail. Try and set yourself targets. The reason I am giving this kind of advice is because I did a similiar kind of essay during my A levels on Qunatum theory, and this is basically a summary of some of the lessons I learned along the way when trying to do this kind of work. Good luck with your essay:-)

I would contend that democracy though, depsite its flaws still functions better than dictatorships overall because of thechecks and balances involved. Unfortunately in democracies though, the "masses" have a disproportionate influence made on them by demagogues, like politicians, and the media in general; subsequently they are manipulated by these demagogues. I think maybe in our age though, ppl maybe starting to wise up on them as the internet is providing ppl with many ore independent sources of information, and hopefully overall ppl are starting to become more weary overall of the information they receive. The case may be slightly different in developing countries, but even there I think sometimes the media and politicians understimate the intelligence of the ppl, and then later have to pay for their ignornace in the ballot box. With reference to Military spending, notce how these departments or Ministries have the word "Defense" in them? So their primary objective is to provide "defense" from all the other countries that are also spending considerable amounts of their GDP on "Defense", oso then they have their justification to spend money on this. The military always needs a potential adversary to survive, and in most cases it will have some potential adversary. In a way it maintains and takes care of itself this way, much like the political class and elite generally do.

lol:D

The idea of the speed of light being the same in all inertial frames may seem esoteric at first, but I would urge you try and think deeply about how things would be if this was not the case. For example, whenever we learn Mechanics we always learn abut velocities being measured relative to something else, and there being no meaning to the idea of an absolute velocity. Relativity is basically a revison of this taking into account the predictions of Mazwell's Electrodynamics. In this sense you are absolutely right, there would be no logical reason to start relativity withoutthe result from maxwell's electrodynamics that predicts a speed for EM waves and light, but neglects to mention a frame with which it was measured. It was then conjectured by many physicists that there was an absloute fram with which the speed f light was measured. Experimentally it was later shown such a frame was shown not to exist. Meanwhile, Einstein who was thinking in a rather original way when approaching the problem, was willing to throw away the idea of absolute reference frames which were meerly hopeful conjectures and try to reanalyse mechanics with a different view: That the speed of light was the same in all inertial reference frames. I think it is important to realise how drastically different and original this postulate was in reference to resolving the conceptual difficulties between electrodynamics and Mechanics. But then again when you look at it again, isn't the 2nd postulate just a reaffirmation of the 1st? If there were such an absolute frame with which the speed of light , wouldn't it effectively be a preferential "ether" frame in which the laws of Mechanics including those regarding the 1st law of Newton's mechanics be contradicted, and wouldn't we effectively burying our 1st postulate that physics is the same in all inertial frames if the speed of light could only be measured correctly with respect to one of them? Think about this, and you may come to realise why the 1st and 2nd postulate of relativity go hand in hand, after interpreting the message found in electrodynamics that EM waves propogate at a constant speed, that is worked out without any reference. I think Richard Wolfson isn't wrong in what he has said, he just has neglected to mention to an audience of whom I assume are novices; the subtleties involved in interpreting the laws and equations of electrodynamics. Without an implicit understanding of this you cannot begin relativity.

I must say I admire how your enquiries are leading you to dig for the roots of theories of physics, their logical foundations, and how the rules they imply lead to consequences that can then be observed(like the unintuitive consequences of Quantum Mechanics). I think if you combined that with a ready ability to be able to earn some maths in which to properly express and investigate this, you could become a pretty decent physicist:-) . On the whole I agree with Tycho that once you start to combine the "wave" properties of matter with the "particle" properties, you begin to start seeing the consequences of what you are doing appearing(or as I said in your post on relativity "emerging"). A prudent way to lead into this is to consider experimental phenomena like blackbody radiation, the photoelectric effect, compton scattering that started to cast into doubt that light could outright be considered as a wave travelling in a medium(incidentally refuted by relativity). At the same time however, if light, traditionally thought of as a wave could be considered a particle, could the reverse be true? This leads us to de Broglie's hypothesis, that the notion that applies to waves where: [math]\lambda=h/\rho[/math] Could be extended to include "particles" such as electrons. Once wave properties of electrons were discovered this conjecture of symmetry was confirmed, and you could begin to apply differential equations similiar to the wave equation, taking into consideration the quantum properties already mentioned to things like atoms. Once we start taking wave properties into consideration though, we have to consider that it is impossible to determine the location of a wave withina ny degree of uncertainty. This leads to the Heisenberg uncertainty principle, whereby the better we know the momentum of a quantum "particle" the less well define we have its position to be(hence greater uncertainty). This may lead you to question, well what does it all mean if we have these wave and particle properties coalescing? We can rationalise them using a probablistic interpretation of Quantum Mechanics often referred to as the born interpretation whereby the square of the amlplitude of the "waves" coincides with the probability that we can detect the "particles" at a that location. I know that probably wasn't enough to clarify things, but I hope it gives you a picture with which you may be able to begin to resolve conceptual dificulties. But remember thats what makes this stuff fun;) ! It makes you think.

I must say I'm honoured to have been nominated( blushes). May I enquire by who or how the nominations were decided?

There needs to be a slight change to your statement. Einstein's special theory of relativity begins with the assertion that physics is the same in all INERTIAL frames, and following from this the speed of light needs to be the same in all inertial frames of reference. Before progressing it is important to truly understand what an inertial frame is and how it can be defined. I find thinking about subtleties like this really helps avoid confusion later on. It is basically a resolution of the "conflict" that occurs from Maxwell's electrodynamics where a constant is predicted from the equations; this was later found to be the speed of light, but what puzzled physicists was that this velocity did not have attached to it any particular frame of reference. When we take the physical principles that the speed of light is the same in all inertial frames(and so effectively is a law of physics), as well as the fact that physics is the same in all inertial reference frames; it leads us to other implications. For example this leads us to banish the notion of absolute velocity and rest frame, a notion that was actually entertained by physcists a few years before Einstein, who thought the speed of light could be measured with respect to an "ether." How all this leads to time dilation is a good question. The only sufficient answer I feel I can give is that once we start applying these notions to simple situations or thought experiments involving mechanics, we obtain resultant implications such as time dilation and length contraction. Beyond all this though we start to observe connections between space components between events and time components, that in essence reveal what could be called a an underlying spacetime geometry. This is referred to as Minowski spacetime geometry. Note that I have only talked about special relativity so far and not general relativity as I do not have any real knowledge of the latter yet. I may leave this to be handled by someone with a greater knowledge of physics than me. If you would like me to explain how the implications od special relativity are drawn in more detail, using physical examples then please tell me and I will be happy to attempt to. I think that is the great beauty about relativity actually, you just need to have a little imagination and apply these postulates to mechanical situations and the consequences of relativity emerge:cool: .

As you have now seen the rest of this thread, I think I can how summarise and clarify my difficulty. I have noticed from looking at this thread now that I have made several careless mistakes, even adter editing, so it is not surprising you may be finding difficulties if what I ave presented is so unclear! Anyway, you notice that if we have 2 roots of the auxiliary equation for the differential equation(if we take the solution to be of the form [math]y=e^{kt}[/math]) as [math]k=l[/math] or [math]k=l+e[/math]: Then I cannot understand how the independent solution to the equation for the root [math]k=l+e[/math] is [math]y=\frac{1}{f}[e^{(l+f)x}-e^{lx}][/math] (I made a typo on this originally). Once(or if) I understand this, personally I think I may feel a slight feeling of euphoria:D as I will fully understand why the solution [math]y=xe^{kx}[/math] is correct for repeated roots, rather than just relying on the notion "that it works". Sometimes I feel perhaps I am more of a mathematician at heart than a physicist as I think most physicists wouldn't really care about this and just simply be glad it works. I guess looking at it from their perspective tho I may just be acting like a pain in the a## . Thanks a lot for taking the time to look at this Tom:-)

You're right it should be: [math]y=e^{lx}[/math] and [math]xe^{lx}[/math] But I still have my difficulty with the equation that preceded the one on the right above and how it relates to the 2nd root. Or is what I have written here wrong too?

This has been bugging me so I would very much appreciate it if sum1 could clear up my difficulty ASAP. Suppose we have a general linear, homogenous ODE with constant coefficients as follows: [math]\sum_{i=0}^{n}Ai\frac{d^i}{dx^n}y(x) = 0[/math] We can propose a solution to the equation to be: [math]y=e^kx[/math] Whereby k can be one of the solutions of the resulting polynomial: [math]\sum_{i=0}^{n}Aik^n[/math] I know that if I have 2 repeated roots the independent solutions should be: [math]k=e^{lx}[/math] or [math]k=le^{lx}[/math] In my notes this is justified by saying that if we have 2 roots that are very close to each other e.g. [math]k=l[/math] and [math]k=l+f[/math], then their 2 independent solutions are: [math]k=e^{lx}[/math] and [math]k=\frac{1}{f}[e^{(l+f)x}-e^{lx}][/math] Now I can see how the 2nd solution yields the 2nd solution at the end of the previous paragraph when the limits of f tend to zero. What I cannot understand though; is how it is the independent solution of the equation for the root [math]l+f[/math]. I was under the impression that this would be just: [math]e^{(l+f)x}[/math] Thanks in advance:-) (Edit:[math]Ai[/math] doesn't represent a multiple of A and i. I didnt know how to get subscript on latex(I'm an amateur I know) so I just wanted to be clear that this represents n different coefficients from i=0 to i=n)

I just remembered.... My friend used to have a program on his computer called "Klik and play". You could make pretty simple 2d games on it without knowing any programming languages so you might wanna try it out if you wana learn the basics of videogame design(and show off to your friends too! ). The same company has made more programs like that since and the latest I think is called "Games factory 2". A link to the site is below: http://www.clickteam.com/eng/index.php