abskebabs

He did develop his own "nonrelativistic" version of QM, and later showed that Heisenberg's and Schrodinger's were special cases of his own formulation. (I wish I was as good at QM as I am at knowing things about its history!) This was done in 1925 and 1926, before his work on QED. Also I wasn't sure if anyone used Bohmian mechanics, so I kind of forgot about it.

Hi everybody. I know that there were 3 versions of QM developed in the 1920s, Schrodinger's, Heisenberg's and Dirac's? I am under the impression that Dirac's is supposed to be the most mathematically elegant and shows the equivalance of the other 2, is this correct? Also what do you think are the main diferences between them and which do you personally prefer? Also as a first year student I have only been introduced to Schrodinger's version in my lecture course. Is it generally perceived to be the easiest version to understand or use?

If you learn some c++, you could perhaps start using the engine in the link below to make something. It would save you starting something COMPLETELY from scratch, though you may want to use something else fr a turn based game, as that doesn't need to be 3d. Generally, I think serious videogame making is done by huge teams of ppl nowadays. Irrlicht Engine: http://irrlicht.sourceforge.net/

I know this is a bit of late reply but I think I can understand where you're coming from on this. I can only tell you what I know anecdotally, but I think collectively from what I have seen from being a student of theoretical physics is that we can become a little big headed(I do not exempt myself from this), due to the fact we consider ourselves to studying a "hard" subject. The important thing is to not accept this and to kind of arrogance, and always try to convey a kind of openmindedness and entusiasm. Similiar types of feelings I gauged when at chemical engineering, and from attending introduction courses to it that SOME engineers deem themselves to be highly practical compared to scientists(for example). Certainly the phenomenon is not isolated to ppl on certain types of courses, or ppl in general. The other bad thing this does is it reinforces stereotypes, and ppl start thinking about themselves in a kind of "set" way, and even believing themselves or theri personalities to be stereotpyes. That is why it erks me when ppl call themselves nerds, or call me a nerd(not as an insult), in fact I know ppl who think it is quite a positive thing. That itself is open to interpretation, but I think above all, ppl should not allow themselves to accept steretypes, as I feel it is damaging as it kind of discludes you from realising more things about yourself and kind of makes you close minded towards other ppl. Everybody is different and do things for different reasons, and have different aspirations, goals, passions etc in life. In fact this is what makes life and ppl interesting and ppl shouldn't dismiss it. I think it is unfortunate that your physics professors are acting the way they are, but I guess it is what happens if you let preconceived notions get to your head. It is also unfortunate that certain publications I have recently read like articles in the last few physics world magazines have only contributed to these stereotypical notions, by giving them a broader reach.

This is basically a consequence of relativity and what I am about to say may mirror what Atheist has said above but in a slightly different way. For an object with a rest mass: [math]E=\gamma mc^2[/math] Where [math]\gamma =1/\sqrt{1-v^2/c^2}[/math] Notice I can split the 1st equation into 2 components: [math]E=mc^2+(\gamma -1)mc^2[/math] This shows the total energy being equalt to the rest energy+ the kinetic energy of the object in question. Notice we get the familiar equation for rest energy [math]E=mc^2[/math] Notice from inspection what happens to gamma([math]\gamma[/math]) as we increase v? When v is zero it equals 1. When [math]v\rightarrow c; \gamma \rightarrow \infty[/math]. This causes our expressions for both total and Kinetic energy to tend towards infinity. If you button bash with the calculator a little(or even turn gamma into a geometric series approximation) you will find that when v<<<c, we get that our expression for KE to a good aprroximation becomes: [math]KE=(\gamma -1)mc^2\approx 1/2mv^2[/math] Which is our familiar expression for KE in classical mechanics which works pretty well at low velocities. The most important question though is why these relations are true, and to really find out you need to study relativity, and start from the basic postulates, reasonig their justification and why they need to be true. Having done that the consequences of those postulates need to be followed, and eventually you get down to the algebraic relations relating quantities we can measure, like energy for example. I hope that was clear as it was the main reason I posted, just try to give a clear impression of things using a little algebra(thats all this stuff is really).

It's ok I never mind talking about myself(who does mind tho really? ). I'm studying theoretical physics at the University of Birmingham, but you could surely have found that out by looking at my profile? I guess I must be one of the few that ever looks at those... Back on the subject, I'm still worried about the confusion I have over this and may consult either my lecturer or my tutor about this. The above identity which Tom mattson has refuted in the case of velocity is crucial for what follows, concerning the unit tangent, it's derivatives and the orthonomal triad of unit vectors is it is perpendicular to. I guess one thing I should clarify is t does not necessarily represent time, but is just a general parameter. I don't think this really chnages the situation much though. I guess I'm much more likely to get questions on differential equations(these were like 1/3 or 1/2 of my 2nd semester maths) tho, than the more awkward apects of this part of the course.

Hiya! Hmm... really these are all "physical" properties, but from the perspective of chemistry, I agree with the other posters' comments. I make one addition, that I would have said 7. bitter taste is a chemical property. I don't think the mechanism behind taste, or certainly smell is that well understood though, so it's a little bit open. My gut reaction would be to go with chemical, as there is no phase or "state" where things are bitter but certain substances will have a taste due to their elemenatary composition.

If the statement is false then why is it in my lecturer's online maths notes(I am doing a physics course btw)! Could it be true for certain cases, but not generally? I'm confused now...

Indeed, I have not refrained from asking questions but have been considering joining forum more specialised in maths or mathematical sciences, on which I can ask more advanced questions and hopefully get more responses. I think this forum is filled with ppl who have abillity in maths, but I am not sure who, if anyone would be expert material...

I already understand what s means, as I have already said, I understand it to equal |r|. What I guess I am struggling with is the idea that modulus of the rate of change in a vector necessarily equals the rate of change of the modulus of a vector(the same thing in words). I guess its just the rate of change thing that pickles me a little. IFor example I have no problem with your above statement, basially that the modulus of change in a vector quantity equals s. Indeed this is what I have already stated too above. I guess, I just have to think a bit on this one, n maybe I'm being a bit slow...

From my maths notes, I have come to a point in the section concerning paremtric differentiation on curves and have a query concerning it. I will label the change in x, y or z using a vector quantity [math]\vec{r}[/math] Basically the tangent of any curve can be represented using the following equation: [math]T=d\vec{r}/dt[/math] With which we can define a "unit tangent" whereby: [math]\hat{T}=|d\vec{r}/dt[/math] But another quantity is established: [math]ds=|d\vec{r}|=(dx^2+dy^2+dz^2)[/math] The following equality is then established: [math]ds/dt=|d\vec{r}/dt|[/math] Although it seems highly suggestible, the final statement still erks me a little. Can anyone show why it has to be true? In my mathematical cosncience I feel it may not necessarily be a trivial connection. Thanks for the help

Thanks for the reply Dave. I read the conditions for a saddle point, and indeed a stationary point of inflection is a kind of saddle point. I still have an enquiry though. I read in the vector calculus section of my electrodynamics book that there was another type of stationary point described as a "shoulder" I could imagine this in 3d to be in a way either a max or minimium transposed orthognally on a pointo of inflection to produce a surface. Am I right in guessing this? Also is this also generally classified as just being another type of saddle point? Related to this, how does the situation change when we start talking in terms of 2nd rank tensors, and represent functions using them, I mean do we get increased complexity in the behaviour or types of stationary points observed? I think I can kind of figure why General Relativity therefore is a nonlinear theory, from observing how tensors are represented and appear to be. Also, I'm afraid I must confess my lack of knowledge of terminology; What is a Hessian?

lol. I think I should try that. I once tried doing my physics homework at the pub, but unfortunately it didn't turn out to be as productive as initially intended!

As I have pretty much wasted today doing absolutely nothing useful apart from briefly browsing the section on vector calculus and electrostatics in my electrodynamics book today, I thought I'd shed some light on what ocurred during my own investigation into the problem I had earlier mentioned here. Who knows I may even be able to focus my mind in the process and then get some revision done:-p !(I even make myself laugh sometimes) Ok, 1st of all I will go through my solution of the 8 pint 5 pint problem for you. My aim will not be to show you how to get 1 pint though, but to show you what happens if you keep cycling through. Hopefully if you're reading this you've already made a good attempt at solving the problem yourself so I'm not giving away any "spoilers". I will use the LHS bracket of the expression I write down to represent the amount in a 5 pint glass, and the RHS to represent the amount in the 3 pint glass(In hindsight I should have originally given simpler examples with a difference in volume different to 3 pints, but hell with it). By convention(unless mentioned otherwise) from here on you will see the glass that is recognised as holding a larger amount to be the one on the left. You should be able to figure out from the steps when I empty the contents of one glass into another and when I just empty a glass on to the hypothetical floor. I will begin with both glasses empty and will fill the 8 and use that to try and fill the 5. I will proceed from here henceforth: [math](0,0)\rightarrow(5,0)\rightarrow(2,3)\rightarrow(2,0)\rightarrow(0,2) \rightarrow(5,2)\rightarrow(4,3)\rightarrow(4,0)\rightarrow(1,3)\rightarrow(1,0)[/math] [math](1,0)\rightarrow(0,1)\rightarrow(5,1)\rightarrow(3,3)\rightarrow(3,0)\rightarrow(0,3) \rightarrow(5,3)[/math] Notice we reach the end of our cycle(or just before the beginning depending o n your perspective), because if we carry out the same procedure again, we loop back to the conditions we had at the beginning. The No of stages it takes to get to this point is important(also notice, just before completion the amount in the large glass is always the same as the max amount in the small glass, tho I know thats kinda obvious! ) and something to keep in mind when attempting to see what happens generally. I think also if you keep in mind the answer you have for the following question, it may help you when investigating the general problem: Would the No of stages it takes to solve the above problem differ if we had a 6 pint glass and a 2 pint glass, and carried out a similiar procedure? For that matter would the No of stages differ if we had any multiple of the above ratio between the sizes of the glasses? When tackling the general problem, which I urge you to try, I would recommend laying out your work in the form shown above or in some similiar clear way. You may notice you have to make "choices" along the way concerning possible relative magnitudes between quantities involved(I am referring to more than the obvious initial choice of whether unknown quantity A is larger than B). I may be back to ask some slightly more advanced questions on this problem a little later when I have further advanced my own investigation and noticed patterns within the problem. Happy hunting!

I must say I am pleasantly surprised at the reception this thread is receiving. If only the other thread I placed in the maths part of this forum got this much attention:rolleyes: . Anyway, John F seems to have done this puzzle the same way I did, and kudos to him for working it out. YT I think I see what you and the Grifter are getting at in terms of multiplying the original difference in volume of the 10 pints by the No of times the 7 pint glass is filled using the 10 pint glass, though I have had difficulties relating the differences observed in the quantities as you go through dividing 10 pints between the 2 glasses to what you have stated. Nevertheless the rule Grifter has stated is of limited scope, and is not general. In the case mentioned above it only works if you refill the 7 pint glass 3 times, i.e. when the amount in the is 9. If I was to rely on your formula, then the 4th time I fill the 10 pint glass and tip it over to the 7 pint I would get 12 pints, which is clearly nonsense as I can't even get this amount into the 10 pint glass. Also the rules states that this is true for any values A and B. This is not true, and it can be seen that the number 3 written is just the difference between 10 and 7 in the specific case where A=10 and B=7. Therefore your statement is really just: [math]X(A-B)=X(A-B)=R[/math] Where I have put R to represent the remaining amount in the 10 pint glass after every "step". To illustrate, I will rewrite your formula: [math]3X=X(A-B)[/math] You said this was valid regardless of the values of A and B, but it cannot be general, as it doesn't work with any other values of A-B! In case I may have jumped to conclusions I will provide further commentary in a little while.

Hi everybody, I found this in a book full of mathematical puzzles and I thought it would be enjoyable for people to have a go at it. Ok now imagine you have a 10 pint glass, a 7 pint glass a tap and nothing else which you could use as a container. Do not worry how much fluid the tap can give you, for the purposes of this question I will say it is water and there is a potentially infinite amount of it, but you can deem it to be whatever you're imagine sees fit;) . Can you obtain exactly 9 pints of water using only the 3 things available to you? It is possible to empty the glasses, fill them using the tap, or by pouring the contents of one into the other. However, the puzzle cannot be solved by pouring only partial amounts of water into the 10 pint glass and trying to measure 9 pints, as you are required to get EXACTLY 9 pints, and this would be an unreliable form of measurement as these glasses have no scales on them. If you can do that then try to get 8 pints. If you can do that, see if you get either of the 2 results by employing different methods. Can you try getting other amounts with different glasses, like say 1 pint from an 8 pint glass, 5 pint glass and a tap? Are you beginning to see a pattern emerging? Now once you have done all that you can get to the most interesting part of this thread. It is an investigation into the general problem. I would advise tackling the above part of this post before before attempting this. So imagine now that you have a glass of A pints and another glass of B pints( so both of these are unknowns).Now imagine that the only thing you know is that the A pint glass is larger than the B pint glass. This is a condition I am setting. Now investigate what happens if you try to fill one with the other, and continue to do this. What do you observe? Can you comment on this? Do you have to set certain conditions to decide on what outcomes are possible? When you do this please relay the results of your investigation. In the mean time I will be attempting to tackle this general problem myself. Have fun!

Would these many of these stationary points just be differen types of saddle points though? I have been told that the conditions for there being a minima or maxima, which depends on the sign of the determinants made up from an array of all the partial 2nd derivatives of a function. If all determinats from 1*1 to n*n are +ve we have a minimium. If we have the 1*1 -ve, 2*2 +ve, 3*3-ve etc... we have a maxmium. If otherwise I have been told we have a saddle point. My main point in posting was to verify whether this was correct, as I wasn't sure if it was necessarily. By no means do the 2ndary derivatives even have to be +ve r _ve(they could be zero). If so what do we have, and how can we determine this? Also 3 dimensionally, wouldn't it be possible to have stationary points of inflection. To be specific I mean a 2 variable function with x and y as variables plotted on the z axis displaying a stationary point of inflection along one cartesian cross section(meaning perpendicular to either x or y axis), and another point of inflection observed from looking at another the other cross section? If this occurs, isn't it another type of stationary point in "ordinary" cartesian axes?

Hi everybody, this is a question that popped into my head while revising some maths. I have just covered the section describing stationary points for multple variable functions. So for example if we have a function of 2 variables we can imagine in 3 dimensional cartesian axes that the variables are described by the x and y axes and the value of the function is represented by the z axes. The subsequent stationary points for the resulting shape can be found when the partial derivatives for both variables equal zero. All this is fairly trivial, but we have been told that the 3 types of stationary points possible for this kind of function. These are maxima, minima and saddle points(kinda shaped like pringles:-) ). Also for a 2 variabled function we were told the conditions for each of these concerning one of the partia 2nd derivtivesl derivatives and a determinant made of the possible partial 2nd derivatives. We were then shown how this extends to 3 variabled functions and then how it generalises to n variable functions and the resulting condtions for these types of stationary points for these functions. What I was wondering was, we know that the saddle points we observe in cartesian axes cannot exist 2 dimensionally and this is an inherent characteristic. Geometrically though we can intuitively picture what one of these looks like 3 dimensionally(mmmm... pringles;) ). My question is(I know, I took a long time to get to it!), couldn't there be other types of stationary points apart from the 3 I have mentioned, and inded are there? I know that once we have more than 2 variables it would be pretty much impossible to visualise these(at least with cartesian axes anyway!), but just because we cannot visualise them, that doesn't mean there isn't more does it? I suppose however that these other types of stationary points may just happen to be called saddle points when in fact they just have different Nos of variables displaying -ve and positive partial 2n derivatives. Am I off the mark in suggesting this? I would be very grateful for replies on this thread. Thanks in advance.

I agree with Snail that another maths expert is needed on this forum. Personally I would like it if anyone with a decent knowledge of chaos and nonlinear dynamics or geometry joined, but I keep an open mind. I recognise this will not happen overnight by any means though. On another note, it would be nice if there was less approval/classification obsessed losers here:rolleyes: . Actually as I think I've been out of the loop for a while, why does Severian not have the Physics expert text near his username anymore? Edit: Also I dislike the fact that the brainteasers part of this forum has been closed, though I don't know the reason for this.

From my brief knowledge of both causal sets and LQG so far; I must say I am finding both very intriguing. But regardless of this, I think that there should be at least some kind of observational or experimental results that are motivations for investigations in theoretical physics. Does either approach or any approach in quantum gravity for that matter stem from such motivations? Also I have a question for Martin. Why do you prefer LQG to causal sets?(sorry if that was a little blunt)

I think dietary considerations may have a lot to do with ageing differences between different populations and communities. For an example with a slightly different health issue; the incidence of Alzheimer's disease among elderly Asian(in the Uk this refers usually to south Asian not East Asian) people is pretty low. This has been attributed to the turmeric that is a regular intake in their diets(including mine, and my family's incidentally:-) ).

It is amazing from watching the video that a so called professor can so convincingly convey is his seeming lack of knowledge of the criteria that would make something a "proof". Even more shocking, amusing and alarming is the conduct of the news media who do not question anything he says, and instead of trying to verify his claims, ask for the opinions of nonscientists on this matter... It reminds me of the conversations I had with some Jehovah's witnesses recently when I told them I was studying theoretical physics and they try telling me supposed things about how the bible has science incorporated and blablabla. Nevertheless it was enjoyable for me to politely show them how the connections they were making were not logical and dependent on extreme subjectivity ignorant of context(though I admit I wasnt anywhere near this eloquent in ordinary conversation) On wikipedia it says that Frank Tipler's line of argument is based on technological progression on an exponential scale, with the propogation nanomachines throughout the universe and the amalgamation of a "super intelligence" called Omega point which is akin to "God". This is followed by a ressurection whereby this AI recreates or simulates everyhting that came before it. I think this coincides somehow with a singularity that is basically the Big crunch of the Universe tha he relies on as an assumption in his socalled theory. Interesting how wishful conjecture equates to proof:rolleyes: . Not sure even if it is possible, what an all encompassing AI would share with the christian vision of God anyway. Also Bascule, I remember you speaking of something similiar a little while back about an intelligent AI gaining the capacity to simulate the Universe, to "become God" in some sense. Do note that I am not accusing you of making the same claims as the person in the video.

I'm sorry if it seems innapropriate ressurecting this thread, but I was just having a look and realised that I failed to ask a pertinent question. Why are the values you get infinite and why is it mathematically legitimate to discard the infinities? I think this process is called renormalisation. Please could you shed some light on this?

Depending on the exam board, you can find a lot of past papers online as pdfs on the respective exam board websites. Why not try one? The major exam boards are AQA, Edexcel and OCR. You should be able to find the websites pretty easily by searching google, or whatever engine you prefer. Also I think you'll find them a doddle;)

It's been quite a while and only 2 ppl have replied to this thread at all. Is the subject matter not that interesting, or do ppl feel they do not have much to say on this as there has been quite a few views?