studiot

This is a direct contradiction to what you said earlier in the thread (Post#21) Yes I do indeed agree that change is not necessary for the concept of time and offered a practical example of where multiple repeat obervations yielding identical outcomes leads to the conclusion that a time variable is necessary to describe the situation. But, just as when I proved your statements about quantum mechanics in general and Pauli in particular to be ill founded, you have chosen to ignore that which does not fit conveniently with your current response.

There is more to it than this. When the lead nitrate and sodium chromate dissociate in solution, there is enough lead to totally precipitate the yellow chromate ion as lead chromate, leaving only white ions in solution making it colourless. Note this still leaves lead ions in solution as nitrate. So look at the relative amounts of each ion and see what is left in solution after precipitation (if any). Also ask if there is enough of both reactants to fully precipitate the insoluble product.

Here is the derivation of your chemist's equation. Let X be the number of litres of solution B (50% water) added. This therefore contains 0.5X litres of water. Further this means that (200-X) litres of solution A (40% water) are used since 200L are made in all. This contains 0.4(200-X) litres of water Now 200 litres of final mixture contain 200 x 0.44 litres of water ie 88 litres. Thus adding the contributions from solutions A and B 0.5X + .4(200-X) = 88 removing decimals 5X + 800 - 4X = 880 X = 80 litres

Yes I agree that is so, which is why the books I recommended are not modern. You are right the system I grew up in was not directly comparable to the one you describe. Neither the terminology nor the organisation was the same. The material I am referring to used to be taught to the last year of primary school and the first two years of secondary school, ie between the ages of 10 and 13 approximately. Since that school system was tiered, similar material was also taught to older pupils, in lower tiered schools, who were operating at lower level and destined to become secretaries, shop assistants and the like. Above all it was practical. There were even books entitled Practical Maths or more likely Practical Arithmetic or similar. These books contained many little tricks and quite a lot of understanding that more formal 'High School' studies were built on. It is good that you are taking steps to recover lost ground, but I still recommend using the old ways. You will not miss out a good coverage that way. Furthermore the old ways used much repetition, which you should not need, plus you could avoid spending a year on logarithms as they are no longer required. I really am trying to help, but not just with a couple of specifics, but by pointing the way to efficiently cover the entire area.

No offence meant, but I wonder if you missed out on basic geometry, ratio and proportion as a result. It is basic geometry to prove that you can move the two indented sides out to complete the large rectangle and find the perimeter = 2(20+30) It is basic ratio & proportion to combine ingredients to form compound % of a whole without using equations (although they will also work). I suggest you get hold of a elementary algebra/arithmetic book such as Hall & Knight or Lockwood and Down and study it.

Atoms may be real but are numbers real? And What about the questions: What are atoms? What are numbers? or even What is real? or What is a thing? Backalong in this thread you referred to an earlier post#288 you made in another thread. I read that post and found it quite interesting. Although I could not agree with the conclusion at the end, I found the analysis part was perceptive, but incomplete. That is because you were accepting the common notion that time requires change, or is associated with change. Let us accept for the purposes of the following thought experiment that atoms and numbers (of atoms) exist and can be recorded as you stated in post#288. Now let us make repeated observations on a particular plutonium atom. That is to say we fix a plutonium atom into position and then confirm a number of times that it is a plutonium atom. We will find that after some N observations it is no longer a plutonium atom, and yes change has occurred. But for (N-1) observations there has been no change. If we now repeat this experiment many times for many plutonium atoms we will find many different values for N. Notice at this point, time has not been mentioned. Being intelligent, enquiring beings we wish to go further than this an explore the ramifications of this discovery. What value of N should we expect for a given random plutonium atom? What % of atoms will still be there after N experiments on N atoms? and many more questions. After a bit of head scratching and some mathematics we will be led to the inescapable conclusion that the dynamics of finding change or no change is better represented by an underlying running variable than on the number of observations or the number of atoms. Scientifically the correct procedure in this situation is to introduce a new variable and give it a name. I therefore dub this variable Time. Arise Sir Time!

Hello janaki, I see you are a Medical Doctor. Congratulations. That is difficult. Back to the matter in hand, the PE of a system of N charges. I am not sure how much Physics you know or quite what your interest is in this calculation. Do you, for instance know how to calculate the PE for a system of two charges only? Would you like me to expand on the calculation procedure I outlined in post#8, perhaps from 'first principles'?

This is not right. and I am not thinking about test charges. A single charge has a defined potential around it, with spherical symmetry, of potential inversely proportional to the distance from the charge. However, re-reading the OP you are correct, she did ask for electric potential energy. This is indeed different from the electric potential, which is measured in volts, not joules. So this is a good point. And yes, to assess the electric potential energy you bring each charge in turn from infinity to its location and consider the work you do for each added charge. So yes introducing the first charge will take zero work,. Work will be done against the electric field of this first charge when adding the second. This work may be positive or negative depending upon the signs of the charges. The third charge added will require work against the superposed fields of the first two and so on. It is important to note that you need to modify your formula to a double summation to achieve this. Also is is usual to change the 1/4 to 1/8 to offset the effect of counting each pair twice, although I see you have used the condition i<j instead.

Well, for the benefit of janaki, who asked this question, would you agree with me that my formula is correct if we consider the test point for the potential to be at the origin, and placed charge q at distance +r along the x axis? sorry it's nearly 1am here so I can't wait any longer. Look here you will see my formula http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html Good night all.

I don't think so, that would be contrary to superposition. Electric potential is an additive scalar that obeys superposition. Are you sure you are not thinking of electric flux?

Superposition. Note the field is conservative. The potential V is therfore given by summing the individual contributions over all n. [math]V = \frac{1}{{4\pi \varepsilon }}\sum\limits_1^n {\frac{{{q_i}}}{{{r_i}}}} [/math]

You have a PM

StringJunky did not mention Pauli. I don't think he has actually returned to this thread, but I'm pretty sure he has an understanding of Quantum Mechanics. He actually said Now this statement is is correct in classical physics and in relativistic physics. We can set aside the issue of time for this. But I have already pointed out that is is not applicable in Quantum Mechanics, which does allow interpenetration of objects. Since SJ is not here to speak for himself I cannot say for certain what he meant, but both swansont and I have been saying the statement is inapplicable to QM and therefore Pauli. You assert that time does not exist. I am calling that a scientific assertion. You can call it something else if you wish. It is certainly the main assertion attributable to yourself in this thread.

You haven't labelled the regions in the diagram, so I am assuming they refer to the standard solid/liquid/gas states and there are no alternative forms shown. Since the 1 atm is above the triple point there is no direct sublimation at normal pressure and you would be correct in deducing 90C from the diagram. so either this is the wrong diagram or there is something else wrong with the question. I see John Cutherber got in first.

Is the following quote not true? You are clearly stating that you do not understand Pauli, or know what he actually said, yet you introduce hearsay to support your (scientific?) assertions in this thread. This is, of course, not accepted by any of the many models in mainstream physics. If you had a Maxwellian Daemon that could effect a switch of the two atoms, you (or anyone else) would not be able to tell the difference. That tenet is one of the most fundamental in physics.

You are still avoiding the issues that you yourself raised. Unique? In what way? Take an atom of copper in Rio de Janeiro and compare with another one in Adelaide. Are they unique? Does Pauli make them unique or prohibit them from having the same 'state'? Observation? What observation?

Well geometry is a very wide subject that has developed considerably in the nearly two and half thousand years since Euclid. It is this development that has muddied the waters somewhat in the distinction, since in Euclid's day there was only one sort of geometry, some of which we no longer include in modern definitions of 'Euclidian Geometry'. To distinguish I offer a description of modern Euclidian Geometry. Any other sort of Geometry is non-Euclidian. The main characteristic feature of modern Euclidian Geometry is the idea that the distance between two points is given by the square root of the sum of the squares of the coordinate distances between them. In other words the scale factor is the same in all directions at all points in the region of interest. This is not true for instance in Projective Geometry used by artists for perspective and cartographers for mapping, and draftsmen for some aspects of engineering drawing. It is also not true in the Geometry of most surfaces, particularly spheres. One consequence of this property of Euclidian Geometry is that it aligns with what we now call Vector Geometry. That is we can prove theorems in Vector Geometry by Euclid or vice versa. Vector Geometry is itself a development of Coordinate Geometry. So Coordinate Geometry is Euclidian. We now identify Euclidian Geometry with what we call linear algebra and vector spaces. Another form of Geometry involves the application of the Calculus to Geometry. Euclid did not know about the calculus and this sort, called Differential Geometry, has some Euclidian and some non Euclidian aspects.

So what is the question?

So I'm wasting my time discussing with you then? You are the one who introduced the Pauli Exclusion Principle to this thread. (post#14) The PEP concerns some quantites that include time in their definition. Period. You cannot have it both ways.

I agree that that on first reading something appears amiss. What is a lake? That is does it include the container for the water or is it just the water? A good way to be clear is to specify "the water in the lake is likely to suffer.........."

@ Fred Champion A gently nudge towards post#39

For those who think they know what would happen to something travelling faster than light it is instructive to put v>c into the equations. The problem occurs at v=c since relativistic expressions involving the ratio [math]\left( {\frac{v}{c}} \right)[/math] result in an attempt to divide by zero. This is not the case when v<c or v>c, although the results of the latter calculations are interesting.

From what you say, this is not really a homework question. So I can post a more complete answer. I think you are trying to make the issue too complicated by concentrating on the patch of contact between the tyre and the road. The crux of the analysis is that the reaction between the tyre and the road has to pass through the centre of gravity of the bike or it would fall over. Consider a bike plus rider, of weight W, travelling around a horizontal curve or radius r as shown with velocity v. It is subject to a centripetal acceleration v2/r There is one point (or line) of contact with the road, so the total reaction here R, is comprised of the vertical reaction, Q and the frictional force F. F is the only force that can supply the horizontal centripetal force necessary to exert the centripetal acceleration, thus [math]F = \frac{W}{g}\frac{{{v^2}}}{r}[/math] If the cyclist leans over at an angle theta the line from the point of contact with the road must pass through the centre of gravity, so R must pass through the centre of gravity, G. (W passes through G and also has no moment about it) Further since there is zero vertical movement [math]Q = W[/math] So [math]\tan (\theta ) = \frac{Q}{F} = \frac{W}{F}[/math] The analysis of four wheeled vehicles is different.

No I don't think you do now either. I was and still am (gently) challenging your understanding of the Pauli exclusion principle, I offered further detail by noting that the PEP only applies to fermions. The above was extracted from http://en.wikipedia.org/wiki/Boson Why not? If what do you understand by state? I understand it to be a list of parameters, some of which are a function of a physical variable we call time. Without this variable the parameters themselves would not exist so how could the state based on them exist? For instance two of the parameters in Pauli's list are angular momentuma and spin. Both are the time rate of change of something.

Yeah, that's true. I was trying to establish some context before answering your 3 specific questions. I don't know how much you know but the subject of wave motion takes up whole chapters of physics or applied maths texts at every level from elementary to postgraduate. There are even complete books about it. The particles do not form the wave. Notice I said that the elements or particles 'carry' the wave. A wave is not like traffic on a road. The traffic is made up (formed) from lots of individual vehicles. This is the first and most fundamental thing to know about waves, nothing else will make sense until you have understood this point. Imagine a single weight hung on a spring bouncing up and down. That is a single oscillator or vibrating element or 'particle'. It is not a wave, and not executing wave motion. Now suppose we have a bunch of similar weights on springs. They could be made to bounce up and down completely randomly, with no connection to each other. That is still not a wave. But suppose that they have a mechanical connection so each weight will nudge its neighbour and impart some of its motion. A wave is then formed that passes down the line of weights as the motion is handed on from weight to weight, like a chain of buckets. But the weights themselves do not move along the line. I can draw a sketch later if that helps.