studiot

Thank you for you points migL The point I was making is that A point, a line, a plane, a ball surface or its topological equivalent are all proper subsets (or subspaces) of Rn. With the exception of a point each of these have proper sub-subsets of their own. A point has no proper subsets. Curvature is defined by a calculus on a set, but you cannot have a calculus without proper subsets, so a(n isolated) point has no curvature of its own. For instance the Kappa you are talking about in plane curves or the Kappa and Tau I referred to (though not by name) in space curves.

Gentlemen, Surely all this quantum / historical stuff is over the top for someone who is just starting to learn Ohm's Law? Welcome to ScienceForums, physics is hard. OK so here is a rough guide to electrics. First and foremost you need to know that there are two viewpoints, just like with other subjects. A practical man's overview and the underlying science. It is good to get a bit of the practical overview before plunging into the underlying science. Then you will have some familiar material to work with. This is a bit like knowing that white powder A (sugar) will dissolve when you stir it into your tea, but white powder B (chalk) will not before studying the underlying scientific reasons for this. So in electric circuits we have two kinds of elements or components. Those that supply electrical energy (batteries, the mains and so on) Those that dissipate or utilise electric energy (light bulbs, heaters and so on) We measure the amount of electricity as the current in amperes or 'amps' for short. The voltage or volts for short does double duty. For sources of supply of electrical energy it is a measure of the driving force or electromotive force. For dissipators and users of electricity it is the 'voltage drop' you asked about. In order to get or force a particular dissipating element to pass a particular amount of current you have to impress a particular driving voltage across it from a electrical source. We say the dissipating element 'drops' that amount of voltage. Ohm's Law is the simplest relationship between voltage and current. Notice I haven't (needed to) gone into the more detailed physics behind this. Some diagrams would be helpful at this stage. If you want to continue perhaps sensei or I can draw some.

Since no one is interested in my contribution perhaps I should bow out of this thread. However on the way I would ask you to consider exactly what is meant by intrinsic and extrinsic and explain how a universe with the same laws as ours, but comprising a single point can support an intrinsic curvature. Furthermore it is worth observing that a single expression of curvature is only appropriate in 2 dimensions. In 3 dimensions there are two independent curvature expressions involved. Can you extrapolate to 4 dimensions?

With respect, this sounds like a rather rote response. I did not say we could use theodolites etc to measure the curvature, in fact I said the opposite. You can always regard a mathematical structure from different viewpoints, so you can always mathematically establish a dimension to set the radius in if you wish. Alternatively you can use the point to point properties in the working dimensions, as Feynman is proposing in his measurement of the Earth's radius. The plain fact is that space, in that direction, is non linear.

Capiert, if your way of thinking and presentation can help Frank to understanding, well done. So +1 for encouragement - these are the sort of posts we like to see. However I do not necessarily agree with quite everything you said and personally found it a bit rambling, though mostly along the right lines. Perhaps a little bit at a time might be better in future?

Hi geordie, This is a very good question, however I am not convinced by the Feynman quote. Although, like Einstein and Newton he was a tremendous genius, he, like them, was not always right in hindsight. That is not to say he did not have a point, but, as ever, life is a bit more complicated. His 'experiment' was a thought experiment and I will return to it at the end of this post. Here is a real world example of curvature and its effects, that has real implications in the real world. If we set up a theodolite at each of three points, A, B and C on the surface of the Earth and measured (the sum of) the angles of the triangle ABC we would not get 180o. We would get some larger number. This has practical significance in surveying. We do not need theoretically super accurate equipment this affects ordinary theodolites and surveying and is called 'spherical excess' Nor is it to do with the fact that the Earth is not a perfect sphere. The reason is due to the fact that the surface of the Earth is a curved manifold that cannot contain a plane triangle exactly. Both a plane and the Earth's surface are 2D manifolds 'embedded' in the same 3D space. The plane triangle, whose angles do add up to 180o. 'cuts through' the underlying 3D space, in which the 'curvature' radii and centres lie. In order to calculate the correct values we have to use the more complicated equations relevant to the 2D manifold that is the surface of the Earth. The choice of sphere or more complicated figure is the realm of Geodesy. As we are 3D (or 4D in spacttime) beings we have direct access to all the dimensions concerned and can make measurements in them. So we get different measurements depending upon whether we measure in the Earth's surface manifold or the plane manifold. [sidenote] This situation is the difference between 'local' and 'global' for many phenomena in Physics and of great importance in computer graphics where the approximation to any curved surface by a plane is known as a 'Coon's patch' [/sidenote] Back to Feynman. As we have discussed before, the 'curvature' in 3D space or 4D spacetime is different in that we do not have access to another dimension where the curvature might take place. All we have are the observed equations between points in our 3 or 4 D space which are not linear or Euclidian or flat - the appropriate terms sicne we have ramped up one dimension from a plane. So Feynman was not 'wrong', but his simplification was not totally 'right' either.

Your confusion arises because you expect a single unique definition for the word real. If you look in a decent dictionary (which might be a scientific one) you will find that most words have multiple definitions. Sometimes these definitions are variations on a similar theme. Sometimes they are quite different. And just occasionally these are opposed in meaning. As English speakers we have learned to cope with this using the context. English itself has sub divisions of some words A very common difficulty with the words real and reality occurs when folks try to shoehorn into one definition. Reality for concrete nouns is quite different from reality for abstract ones.

There are two quite different and incompatible definitions of 'particle' used in Physics. This incompatibility is fine so long as you do not try to mix the domains of definition as is being done here.

Here is a statement of Boyle's Law, in relation to this problem [math]{P_{100ft}}{V_{100ft}} = {P_{surface}}{V_{surface}}[/math] Even if you did not take the next step, you need to be able to take the data and present it in this form. Doing this should get you some marks. Saying I can't do anything gets you none. So can you rearrange this to give the ratios as asked? The gas laws are taught and used in Chemistry, Physics and General Science and many other branches of technical activity.

Since I do not have the time tonight to go through relativistic velocity addition I can only suggest ask Mordred or try to reread my links and get something more out of it. Nothing is moving at superlucent speed in any inertial frame.

You can't. You have to convert to a consistent set of units. You will also have to address the fact that pressure was given to you in yet other units and convert that as well. Perhaps this question is really an exercise in unit conversion? I strongly recommend using the MKS units which are universally accepted in Science (even in the USA). How about attempting my question concerning Boyle's Law? Ask if the sentence is too long. We can return to the pressure part when we have decided what we want to calculate.

You need to add the velocities relativistically, not linearly. See here https://www.google.co.uk/search?q=relativistic+addition+of+velocities&hl=en-GB&gbv=2&oq=relativistic+addition+of+velocities&gs_l=heirloom-serp.3..0l5j0i22i30l5.613172.621609.0.626531.35.26.0.9.9.0.203.2825.13j12j1.26.0....0...1ac.1.34.heirloom-serp..0.35.3090.b6Y_aF-YHdQ

g is the acceleration due to gravity, not grams. Look here and see if you can find and explanation of my formula that you like. [math]P = \rho gh[/math] https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=pressure+in+a+column+of+fluid&gbv=2&oq=pressure+in+a+column+of+fluid&gs_l=heirloom-hp.3..0j0i22i30l2.1078.6594.0.7172.29.25.0.4.4.0.234.3016.4j18j2.24.0....0...1ac.1.34.heirloom-hp..1.28.3186.-a2Ow7pf89U Where P is the pressure, rho is the density (it is a greek letter rho), g is the acceleration due to gravity and h is the depth. What does Boyle's law tell you about the ratio of the gas volume at 100 feet depth to the gas volume at the surface compared to the ratio of the pressures at these points?

So you are looking for first principles. Have you seen the equation for the pressure in a column of fluid? P = density x g x height of column

Since you have posted this in Chemistry, I take it this is a Chemistry question. Yes the number of protons determines the actual element concerned - a matter of Physics. But from the Chemist's point of view, the organisation of the 'table' into (horizontal ) octets or periods is much more interesting. This is because the chemical properties are largely determined by the electrons, not the protons and we observe recurring groups of properties. For example the first (vertical) group in the table is known as the alkali metals (Lithium, Sodium, Potassium etc) and the second (vertical) group the alkaline earths. Elements from the same group take aprt in very similar chemical reactions and can often substitute for each other. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=table+of+elements&gbv=2&oq=table+of+el&gs_l=heirloom-hp.1.0.0l10.1469.4422.0.6328.11.10.0.1.1.0.204.1391.1j7j2.10.0....0...1ac.1.34.heirloom-hp..0.11.1422.86Z3aUlIaKE

You can, of course, construct a marked straight edge, using a compass and an unmarked one. But that would be against the spirit of the game.

First where does it say in your question to use PV = nRT? Have you heard of Boyle's Law? https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=boyles+law&gbv=2&oq=boyles+law&gs_l=heirloom-hp.3..0i10l10.1109.3797.0.4047.10.10.0.0.0.0.297.1439.2j7j1.10.0....0...1ac.1.34.heirloom-hp..0.10.1439.pgJ9APDpU9M I am not sure you need the densities at all, unless you want to calculate the increase in pressure with depth from first principles. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=pressure+increases+with+depth&gbv=2&oq=pressure+increase&gs_l=heirloom-hp.1.2.0l10.1485.4485.0.8422.17.13.0.4.4.0.219.1391.2j7j1.10.0....0...1ac.1.34.heirloom-hp..3.14.1516.aGzLh9kyPPY Ask for more help if you need it.

What a rude response to all those who put their own time and effort into replying to you. Since you are already such an expert that you can dismiss my observation in so cavalier a manner I take it you are aware that we do not even know if the Second Law applies to the universe as a whole or not and why. This conundrum was known to the architects of Thermodynamics and has been pondered and debated in a much more civilized manner than your post for more than a century. There are two issues. 1) The Second Law applies to closed systems; we do not know if the universe is closed or not. 2) We do not know if the universe is finite or infinite. If it is infinite how can its (already infinite) entropy increase?

Now that St George is dealing with the trolls, I will have some time to look at this in more detail this evening. Meanwhile your expression (it is not an equation) has an incorrect number of brackets. Perhaps that is why your do my homework for me program is showing an error. Can you start by assigning a tension to each string and developing the equations of motion (you do realise that equilibrium cannot be used in this question?)

Hello Jmanm, I suggest you are boggling your mind by falling into the classic trap of extrapolating to much and too far from too little data. That is what going from local effects to the ends of time and the universe amounts to. Try to condense your question into one short paragraph and you will get a sensible answer.

Well thank you for all that. It makes it absolutely clear that not only do you you actually know more than you let on, you are misusing that knowledge for reasons of your own. Knowing this enables me to waste no more of my time on your machinations. Don't feed the trolls.

You will be better understood if you use standard language. For example If two numbers m and n, when multiplied together, yield the number N then m and n are said to be factors of N so long as m and n are not equal to N or 1. (Some people extend this to say that N is prime if the only two 'factors' of N are N and 1) There are no numbers m, or n that satisfy this for [math]N = \infty [/math] I think you mean something else and I was trying to help you find whatever it is.

So you are not going to answer my question?

Since I didn't ask that why should I care? I will repeat my question one more time. What do you understand a factor of infinity to mean, since you introduced the term and it appears contrary to common mathematical usage to me?

Well if that contains an answer to one of my questions, I don't see it. I would remind your obligations under of the rules of this forum to answer questions, fairly put, about details of your hypotheses.