studiot

+1 Cool links, Mike

I'll just leave this little tantrum for the mods to sort out go well

Well I don't know, I can't get any LaTex to work on this site, I use MathML. But some seem to manage, by putting it into a script window. Ask a mod.

It says the spell is too long

The statement was pithy, too the point, accurate. Agreed 110%. What more is there to say?

So can you write down the Weyl Tensor, without making any reference to a varaible t (actually partial d/dt) called time?

No. In the Millikan experiment you make two measurements on each drop individually. Calculations are then performed on each drop individually. You measure the terminal velocity (by timing its passage past a scale) without any applied electric field. Then you measure it with the field applied, or you measure the field to halt the drop falling. The first measurement is to determine the radius of the drop. The second is to determine the charge on the drop. Note that in the experiment the drop size can vary continuously over a range of values. It is only the charge that turns out to be multiples of one basic unit. The value of this basic unit is then averaged from all the individual calculations (Millikan originally made thousands).

A few corrections are in order here. @Mike SmithCosmos The corpuscular theory of light was propounded by Isaac Newton in 1660, who coined the term corpuscular. His 'corpuscles' were able to explain reflection and refraction Huygens was a contemporary of Newton who first proposed a wave theory, in 1680. Although it was known that Snell's law could distinguish between the proposals by measuring the speed of light in dense media such as water, methods were not then available to make the measurement. Foucault achieved this in 1850 and showed that, for speed at any rate, Huygens was correct. Thomas Young developed interference experiments (1800) and theory that demonstrated behaviour only available through wave motion. Following the subsequent discovery of phenomena (photelectric effect: Hallwechs 1888, Lenard 1902) only availble to corpuscular motion Einstein revived the corpuscular theory by naming the corpuscle a photon in 1905. @compernicus1234 I have 1865 in my reference. James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, Phil. Trans.Roy.Soc. London, 155:459 (1865) Here is an extract from the introduction You seem to be concerned with Faraday's and Ampere's experiments. You see from the extract above that Maxwell was happy to acknowledge the work of others, but his introduction of an equation to describe an induced magnetic field (induction) was a theoretical extension of Ampere's law, by the introduction of what Maxwell called "displacement current". Ampere [math]\oint {B.dl = \left( {\mu \int {J.ds} } \right)} [/math] Maxwell [math]\oint {B.dl = \left( {\mu \varepsilon \int {\frac{{dE}}{{dt}}.ds + \mu } \int {J.ds} } \right)} [/math] The additional term in the Maxwell equation gives the magnetic field induced by a changing electric field You should note that his was a field theory. Faraday's law of inductiuon is a current theory, as is Ampere's Law.

Well Captn Panic did ask what you are trying to do. If you can't control the pressure in the tank, the only other place you can control it is in the piping. This means that you don't take the fluid from the outlet directly, but lead it in some sort of pipe that has a flow rate controller attached. This may include a pump.

I don't think you have quite understood what Cpt Panic was trying to tell you. The flow rate depends on the pressure pushing it along and the size of the minimum cross sectional area of pipe. It does not depend directly the volume available from the reservoir tank. Your 'flow restrictor', valve, tap, or whatever you want to call it adjusts the minimum pipe area to provide the desired flow rate for a given pressure. The flow restrictor does not control the pressure. That is up to you and how you arrange your pipework and tank. My hospital example they put the tank(Bag) up a large height in relation to the size of the bag so this mounting height controls the pressure. Captn Panic offered another way - to have a large flat reservoir. There are yet other ways some mechanically quite complex. But to have constant flow you need to arrange constant pressure.

If this is a school project, go to your local hospital (possibly the medical physics dept) and ask for someone to show you how I V and syringe pump drivers work and flow contollers work. I'm sure you will find some useful practical help there.

Here are some ideas that may help you. Mathematically we collect together all the objects that have some property(ies) of interest in a set we call a 'space'. These object obey desired rules of combination. We do this because we want our maths to benefit from any useful common properties For instance 'closure' on our space means that for some operation, F, between any members (A, B and C) of this set or space F(A,B) yields another member of the set. For example the integers are closed under addition. Adding any two integers will always result in another integer, not a fraction or any other sort of number. This may seem trivial, but it is an incredibly powerful idea. It is what we use to prove the existence and uniqueness of solutions to equations. If our set contains functions, we can select functions that are solutions to an equation of interest and combine them to find other solutions. If we have a second set of constants (a, b, c etc) and our objects combine according to the rule a*A + a*B = a*(A+B), then our set is called a 'vector space' and A and B are called vectors. Actually there are about 8 or 9 rules in all for vector spaces. These are the rules of 'linear algebra' and include 'free' vectors in physics such as forces, directions, momenta, accelerations and many more. Mathematically the term vector also includes definite integrals, solutions to many kinds of equations, differential or otherwise, matrices, in fact any mathematical object that obeys the above rule. Tensors also obey this rule so they are a type of vector in this sense. Linear algebra or linear analysis is all about this type of mathematical behaviour. Hence my reference to Kreider This terminology has one unfortunate aspect, however. If we consider the straight line y=mx+C, this is a straight line, but it is not 'linear' in the above sense. The addition of the constant causes a problem that introduces a new type of mathematics we call 'affine' Now here is where the physicists view of a vector as a simple type of tensor comes into play. There are 'constant' tensors we can add to copy the affine structure of the straight line. But there are no constant 'vectors' in physics available for this. I'm sorry if this was a bit rambling but it was rather dashed off to get something down whilst you were online.

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.