studiot

Aye Captain Kirk, but The Enterprise still needs a heading to get to the Final Frontier. And how, pray, do you specify the volume? This sounds more like the volume a free body diagram or a thermodynamic system than a frame of reference. This is just one more instance where you are stating as fact non mainstream definitions or interpretations for the benefit (?) of those who are trying to learn mainstream physics. That is confusing for them. I have already noted that some of your ideas have merit and would be very happy to discuss them with you in the proper place. Science Forums is benevolent in that it dos not demand only mainstream comments but allows genuine debate on opinions. But it must be clear they are personal opinions and it is best if you can back them up with a chain of reasoning/logic and/or references.

+1

No, sorry if I wasn't clear, the grounding is the algebra of linear spaces. The other things refer to the fact that this algebra spreads far and wide to many different (and important) branches of applied mathematics. Theoretical physicists learn tensors as an exercise in formality. I learned them from the practical viewpoint of stress and strain. This approach gives the student something tangible to grab hold of. Not only did I know what and why I needed something more than vectors. but I also knew what the results of the manipulation would bring before I started. But linear algebra is used in diverse applications as the solutions of large sets of simultaneous equations, including differential ones. Laplace transforms. Approximation theory and curve fitting. Fourier series A good modern book to have on your shelves is An intorduction to Linear Analysis by Kreider, Kuller, Ostberg and Perkins Addison Wesley. Tensors are not mentioned, but it is a good precursor. A digestible introduction to tensor and associated methods is to be found in Advanced Mathematical Methods for Engineering and Science Students Stephenson & Radmore Cambridge University Press The traditional tensor is best introduced in Coordinate Geometry with Vectors and Tensors E A Maxwell Oxford University Press

This is not a satisfactory reference in that it is not specific. Nor have you actually answered my question What do you mean by a frame of reference? It is your answer I am interested in, although of course it adds weight to your definition if it is backed up by authoritative reference(s).

You do indeed miss something. Frequency is not a term applicable to pulses. Pulses are much more complicated than simple waves, consequently pulse theory has many more terms to describe the various elements of a pulse train. Furthermore the interval between pulses is just exactly that. The interval between pulses.

I suggest it would be a good idea if you were to explain what exactly you mean by a frame of reference. I don't think you are using the conventional definition.

Tensors are quite intimidating at first since they were essentially developed as 'shorthand' for something the authors already knew in 'longhand'. A good way to approach any part of maths is to (laboriously) write out the longhand until your own mind says to you "Can we shorten this?" Then you are ready for the more compact notation. Tensors also suffer from their relationship to vectors, since they are also a type of general mathematical vector, but are often introduced as an extension to 'vectors', where it is not made clear that the vector system being extended is a particular type of vector. You need a good grounding in the algebra of linear spaces to cope with tensors ( and many other things besides). Modern theory is tending towards the use of differential forms and you might find these easier to study than tensors. (You also need some linear algebra for this). go well

No you don't need EM to start quantum mechanics. I am sorry if I was not clear in post 2. I am trying to say that you need to learn a little bit of one, then a lttle bit of another and then a little bit of another. And then learn a little bit more of the first, the second, the third..... And then learn a little bit more of the first, the second, the third..... And then learn a little bit more of the first, the second, the third..... Each time round the cycle you will get a bit further in physics. But you need to make mechanics the first one. Remember there are a lot of branches of mechanics - particle motion -force -energy-mass-wavemotion-and much more. These play an important role in every other part of physics.

Do I look old? I don't feel old. I don't feel anything till noon. Then it's time for my nap.

It varies with Reynolds No. Here is a graph, dividing the regimes into three after Acheson.

What you should know is that there are similar classification schemes, for different purposes, for the mixed loose material lying above the bedrock. Agricultural Scientists use one for soils for farming purposes. There is a United States and a United Nations standard for this. Civil Engineers use another version for classification of this material for it's strength and bearing capacity. This is supporting roads and buildings and other structures. It is also for predicting its performance in earth structures such as embankments cuttings and slopes. Finally their classification is used to describe the natural material for the purposes of extracting wanted material such as sand and aggregate or clay for making bricks. Geologists use yet another one for recording what is there. They also use their classification for understanding natural slope processes, weathering, erosion and so on.

When I was your age, after mechanics we divided physics into four. Heat, Light, Sound, Electricity & Magnetism. Nowadays we would add Particle Physics and Quantum Theory. Again, after mechanics these could be studied in any order.

Hello, Manstein and welcome. All of the different branches of Physics support each other. And all are supported by (applied) Mathematics. So there is no one perfect order to learn. What you have to do is learn some of each branch. And then go back and learn some more for each branch. You will find that results learned in one branch appear again in others. Most physics comes back to mechanics and most branches are developed from mechanics. For example force, work and energy are defined in mechanics. Then they are used to define amperes in electricity. Other mechanics properties are used to introduce quantum mechanics and particle physics. So learn a little bit of everything, but a lot of mechanics. Then learn some more of everything. Remember you can stop almost anywhere in each branch and come back later. Go well in your future studies.

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