studiot

That would be a good start +1 But for 'ordinary' fluids and pipe sizes, not very thick liquids like concrete or very fine pipes like blood capilliaries. Sriman, since you introduced it, you might like to find a link for the OP?

So at the start of the reaction, what is the volume of the mixture ? An how many moles of hydrogen bromide does it contain? An how many moles of ammonia? So what are the concentrations of each?

So where did this come from?

It hasn't slipped from anything. I asked the moderators to split discussion about global gravitational geophysics from the local discussion about a local survey at Lake Balaton, because it is quite irrelevant to that survey. And they agreed. I did indeed say that since the lake is very shallow, the surface can never be more than a small amount different from the bottom. So if the bottom is flat and therefore deviates from the Earth's curvature, the water surface cannot be different from flat by more than the depth. I also supplied details of geological investigations by the Hungarian technical institutes which suggest a flat bottom to the lake and a proposed geological mechanism for this measured result. All this was fully referenced in the post in which it appeared so please stop claiming I do not supply references, where appropriate. This is particularly poignant as you have completely failed to provide any reference whatsoever in the last "quote" in your post # 24! Nevertheless I will answer the question you asked there, since you cannot work this out for yourself. Here is a quote from my copy of reference 2 in the Wikipedia article linked to by Mordred (Fowler : The Solid Earth (an introduction to global geophysics) : Cambridge University Press Look again at the list of influences on a reading of gravity. They fall into three categories. 1) Those which are permanent and can be readily calculated (estimated by calculation) 2) Those which are permanent but of unknown cause and magnitude (until the measurement) 3) Those which are transitory and depend on the prevailing conditions at the time of measurement Factors included in (1) form the basis of the calculation of the geoid, which is the 'expected' shape at any place. These are principally the gravitational force and the rotation of the Earth. Factors included in (3) are such as those mentioned in the above quotes, such as tide heights, the marching of men and so forth are removed by making auxiliary measurements Factors included in (2) are principally mass deficit and mass excess and form the basis for reporting the gravitational anomaly. That is the anomaly is the difference between the measured gravity in, after correction for transitory effects in (3) and the calculated gravity in (1). Gravitational anomaly is a small fraction of the total gravitational force so it is not practicable to plot both gravitational equipotentials and anomaly variation contours on the same map, their scales are too many orders of magnitude apart. This is why gravity maps usually show a plot of the anomaly itself, measured in milligals (standard gravity is 10,000 milligals) or in metres at sea level since the variation results in an elevation or depression of sea level by about 3 metres per milligal.

This article might interest some. Reference at bottom of page

+1, Michel for listening, we can move on and try to answer your worries. Indeed this is so. I did say, at the outset of this discussion, that my preferred order of business was to deal with the geometry first and the geophysics second. So let us consider sufficient geometry to develop an understanding of the situation. What are the observables? Traditionally distances and angles on the ground or water surface and angles on the celestial sphere and more recently distances to satellites (GPS). So we are measuring on an a surface of unknown shape (that is why we are measuring ) But we want to record and display the results in a consistent way and until the hollywood holographic projectors as seen in Star Wars and the latest Hunger Games become reality, we are stuck with flat surfaces like scraped animal skins, paper etc. In other words we want to make maps. All this started with cartography. Now the problem is that we live on irregularly shaped a 3D world that is not conformable with flat surfaces. (The correct term for a 3D surface that can be perfectly represented or mapped to a plane is a developable surface.) And we do not have a direct transformation from our unknown irregular surface that we are measuring to our flat map. So what was done traditionally was to invent or create more or less suitable regular or near regular shapes as an intermediate. The plots on the intermediate are then mapped to the flat sheet. The raw data is thus subject to two transformations, firstly from the real 3D surface to the artificial one and then from the artificial surface to the flat map. Both the spheroid (ellipsoid) and the geoid are such intermediate artificial constructs. Modern satellite technology has allowed another method to be employed, that of direct measurement in 3D, dispensing with the artificial intermediate and one transformation. But this comes with the penalty or cost of widespread loss of understanding since GPS is just a black box' that performs all the corrections and calculations for you so you have to take the results on trust. I appreciate and admire that you want to know more. I think that is enough rambling for this post, but , like the other Hollywood man said, "I'll be back" P.S. The answer to my question is that a the geoid for a perfectly spherical, isotropic and homogeneous Earth is an oblate spheroid. I'll explain next time, along with a proper explanation of why the gravity anomaly map you show (that is its corrrect name) is the way it is.

Lol indeed, the answer is also stated in the article you linked to, though no proper explanation/analysis is provided.

This article gives some facts and figures on the early attempts https://en.wikipedia.org/wiki/ZETA_(fusion_reactor) You should also look up sceptre tokamak

Hello, maximillian, I think the Wikipedia link I provided to seasat and subsequent satellites was in the other thread in post#202. I did post further information from another (fully referenced) textbook here in this thread in post #12 which described the calculation used by seasat and subsequent satellites to determine the distance from the satellite to the water surface. The original Seasat information I provided was in post#197 of the other thread http://www.scienceforums.net/topic/98386-laser-curvature-test-on-lake-balaton/page-10 and took the form of a measured (by seasat) world ocean surface relief map showing the measured surface which clearly shows the bottom features reflected in the surface topography. This is a public domain image produced by the seasat team, which I took from another textbook, "Image Interpretation in Geology" by Drury, along with some other explanatory text which Michel seems to object to. Because many are confused by the nature of the geoid I provided a simpler newtonian mechanics explanation of why there is a dip in the cente of a large enough lake and why a hump in the water surface tends to spread out sideways or level itself out, in post#2 here. The usual explanation involves vector calculus on potential surfaces and spherical hamonic theory. It is also important to note what is meant by a 'gravity map' Most are not absolute values but show deviations from some theoretical shape, which is why the scales run from +100m to -100m in Michel's references. I have also fully answered his query in the post immediately preceding yours with reference to the Wikipedia article in post#12 by Mordred where it states explicitly what I have said. Have you thought about my question posed at the end of post#17 If the Earth were perfectly spherical, homogeneous and isotropic, what would be the shape of the geoid? Here is a hint. The geoid is not completely governed by gravity.

Gosh, Mordred, those last two posts were from the heart not the head? I can only council the warning about this greatest scientific error of doctrine "The latest theories are superb and absolutely correct. All previous theories are bunkum." Many a great scientist has suffered at least a red face when following this doctrine. I can best refer you to Sir Harold Jeffreys's Book Scientific Inference, chapter VIII in my second edition, Cambridge University Press. The mathematics and mathematical philosophy are discussed in great detail, in particular where, why and how you need second order effects to eliminate older, more obvious explanations for the observed phenomena. I also refer you to the most current, bang up to date, text Dynamics and Relativity, W D McComb - Oxford University Press, pages 222 to 225 Where Mccomb discusses what he calls four-space in terms of my (Minkowski) offering. He dubs this" the older version" where he treats the Lorenz transformations in terms of rotations and what he dubs" the modern version" where he treats four-space in terms of constructing a vector space with a suitable inner product. Now Tim has asked for some tangible model (I think) and I would say that the Minkowski approach treating four-space as an extension of what went before provides this, Whereas a totally artificial mathematical construct of a particular vector space equipped with specific inner and exterior products is less 'tangible'

I understand Minkowski (though I don't have original references) originally proposed his 4D world in Argand format since there are only 3 (known) spatial axes not four, so a fourth one must be imaginary. Using tau = ict allows the standard metric and works well when moving from relativistic kinematics to relativistic mechanics.

The issue of 'equal footing' is interesting since whilst you can directly plot distance, you cannot plot time. The method of overcoming this is, of course, to multiply time by a velocity to obtain a distance. Thus we get to 'ct' as the fourth axis. However this has some disadvantages, not the least being that there are now two versions of 'spacetime' one with four distance axes and one with three distance axes and one time axis. Another disadvantage is that euclidian distance is no longer the sum of the squares of the projections on the axes but has a negative sign in the equation. This latter can be overcome by the Argand view of the world and multiplying time by ic instead of c and considering the the fourth axis as a rotation from the others. What implications this has for separation of time and space I'm not sure.

OK so you don't want another model when offered, despite asking for one. But you cannot keep claiming that other models do not exist. Over and out.

I don't suppose your visits overlapped. I think formal study is difficult in India and the OP is trying his best with the English language, so I took it to mean to angle I'm glad it was a small quibble since inclinometers (I have several) measure angle. https://en.wikipedia.org/wiki/Inclinometer They were much used in the survey of India.

But hopefully you have gained something from our little exchange of pleasantries ? I know I have and have just awarded myself a whisky in honour of a successful conversation.

Sorry but I can't access this link, it seems to want more money or something in the meter.

No, you are overthinking this. There's nothing 'mental' about traffic lights (Unless you got that question wrong in your driving test?) State diagrams feature importantly in digital electronics, though it's true man can't match the speeds attainable by quantum processes. These are idealised human constructs.

Emblazoned in the title of this thread is the word model. We construct models to obtain desired information about the thing we are modelling. You say that you want to keep it simple (basic stuff) and I come from a generation where this approach was a watchword. To this end geometric models were once much in vogue. A feature of a model is that we can "ask it a question" . So for instance we can easily calculate the (invariant) interval given the time and distance between two events A and B in the same frame, using the standard formulae. But we can also do this geometrically (and very simply) and assign meaning to the drawing. 1) With centre A draw a circle equal to the distance light travels in the elapsed time, to some suitable scale. 2) Draw line AB equal to the distance between the events, to the same scale. 3) Erect a perpendicular at B to cut the circle in C 4) Length BC is equal to the interval to the same scale Would such a model be of interest? Say for a more difficult problem, based on this method. A station inspector, A stands on a station platform and is passed by a passenger B on a train at t=0 Some time later A see a flash of lightning strike the train at a point he knows to be be distance d ahead and he notes the time on his watch. Thus knowing the time and distance he wishes to find the time the passenger thinks the flash occurred and how far away it was from him (the passenger)

It doesn't have to be quantum. For traffic lights showing red is a state as is showing green. The traffic light state vector is a list of all such states. Red Red and amber green amber (red)

I assume this is an admission of being wrong. Radioactivity is usually the first example brought up to demonstrate time without motion, but there are others. You agreed with me that traffic lights 'do not go anywhere' i.e. they do not exhibit motion. Yet they are cyclic in time (arguing whether they are a wave or not is pointless) and knowledge of that cycle would allow an observer to measure time by the state of the lights. Admittedly it would be a crude clock, but a motionless clock nonetheless.

There are four possibilities conforming to your description. For the first 3 wtf has told you how to find PX by solving the triangle PCX. Note that PX does not need to be a tangent it may cut the circle. In the fourth possibility PCX are colinear so PX = PC + r and a = 180o Note that for case 1 the triangle is a right angled triangle so a simple formula is used case 2 and case 3 uses the cosine rule. Note that for acute angles ( a<90) cos(a) is edit (oops beware the double negative) negative positive so the last term is negative, but for obtuse angles (a>90) cos(a) is negative so the last term is positive. Note also that since we are using the cosine rule there are no positions of P that cannot be solved, unlike for a sine rule problem. case 4 is again a simpler equation.

Gosh, Tim you are so difficult to help. Here is the simplified version with annotation. Below My reply He already did Below My reference to where swansont already told you. Quote Below My further helpful example explaining state vectors. Consider standard traffic lights The 'state vector' cycles, but the lights do not go anywhere. My encouraging comment. I will leave you and swansont to argue whether my word cycle or oscillate is more appropriate for a discrete state vector

Some questions. The integers are countable (by definition) but they do not possess the property that between every pair of integers there exists another integer. For example there is no integer between 2 and 3. So if you line up the integers you can reasonably state there are 'holes' in the line. The rational numbers are made by ratios of the integers and do posses the property that between every pair of rationals there exists another rational. In fact this means that between every pair of rationals there is an unending sequence of rationals. So you must prove the assertion there are holes in the rational lineup.

I'm still at a bit of a disadvantage or loss to know exactly what you are seeking in this thread. You say you are aware of two physical models (whatever physical models means). Are you asking for more? You have confined your remarks to a very small part of physics - that of the purely mechanical and only one corner of mechanics at that. What about the relativity of charge or fields or continuous (elastic) media, Hamiltonian-Lagrangian mechanics or......? The problems with transformations in Minkowski 4D is that whilst they work well in the corner of mechanics you have discussed (dynamics) different formulations have to be introduced to discuss very physical matters such as charge, momentum, energy, Lagrangians, and so forth. Such matters are discussed in elementary form in famous texts such as Goldstein - Classical Mechanics Grant and Phillips - Electromagnetism Eisberg - Fundamentals of Modern Physics Newman and Searle - General Properties of Matter and in greater detail Moller - The Theory of Relativity and no doubt in many more.

Here is a very cogent discussion, also relevant to the thread on whether spacetime is a real or just a mathematical construct, from Modern Physics by Wilson published as part of the Blackie Student Physics series.