studiot

Yes it looks like it the first move should have been b7 to c8. I thought I was too quick.

Is the bishop at g5 sleeping?

So queen takes pawn?

Seems to work OK to me in two moves. The black king can't move on his first move and the black bishop prevents mate in 1 so removing it seems a good option. But thank you for the references.

To help you complete your research into this question and work towards a better answer, here is some history. De Broglie's hypothesis (1924) was originally proposed to explain the photoelectric effect. Now the proposal followed Planck using the equation E = hf where f is the frequency of the light concerned and h is Planck's constant. Of course there is no relative speed issue with light. It has a constant speed c for all observers and sources. So using the equation c = fL where L is the wavelength, it was possible to arrive at an expression for the momentum of a photon. Relativity gave one expression for the 'apparent mass' of the photon and the momentum another, equating these eliminates division by zero mass and produces a relationship between p = hf/c = H/L = Hk where p is the momentum, H the reduced Planck's constant and k the reciprocal of wavelength or wavenumber. De Broglie further proposed that this be extended to all particles ie including massive ones and the same calculation be done, but this time including not cancelling the mass to yield a wavelength for such particles equal to h/mv. Now the velocity input to these particles will be relative to the medium the particle is travelling in. So for electrons orbiting the nucleus in its electrostatic field this will be the tangential velocity associated with that rotation. For particles passing through a cloud chamber or other matter it will be relative to that matter and so on. There there is no problem with the 'relativity' of the motion. Incidentally these associated 'matter waves' were experimentally confirmed by Davisson and Germer (1927) and Thompson (1928)

I would still not rule out river flood transport. Near where I live, there is an ancient clapper bridge across the river Barle on Exmoor. Winter floods have shifted/transported large stones weighing several tonnes, downstream from the structure again. The river Barle is an inconsequential trickle compared to your american rivers in question. http://www.bbc.co.uk/news/uk-england-somerset-38844162

I used to enjoy chess problems, they are hard to find these days but this one was too quick so I probably missed something. But isn't the first move B7 x H1 (Bishop takes Bishop) ? +1

Sometimes its good to bring some simple sanity to a thread. +1

I had always understood that Roemer was the first to measure this. https://en.wikipedia.org/wiki/R%C3%B8mer's_determination_of_the_speed_of_light

Thank you Mordred for that large list of net references. Since I normally go with books, here are a couple to complement them. Firstly The Standard classic for the heavier mathematics you refer to from the founder of this sort of theory, O,D, Kellogg Foundations of Potential Theory O D Kellogg Kellogg not only develops the mathematical theory necessary for those fields that are amenable to Potential Theory (ie have Scalar, Vector or Tensor Field Potentials) but also offers much insight into the connections with some of the more esoteric pure maths behind it such as The Heine Borel Theorem. It is strictly an analytical approach in the mathematical analysis sense. Secondly this delightful tome from the Engineering sector for those using the techniques rather than developing them Engineering Field Theory A J Baden Fuller Probably more appropriate here, this book offers not only practical insights into using the theory and solving the equations both analytically and numerically since engineers need to use equations rather than study their pedigree. It covers a wide range if Fields used in practice and includes a large table of the relevant formulae from all the different chapters about different sorts of Fields. I offer the following brief extracts that may be of help here. First the chapter list Then two pages from the introduction that all here can read and hopefully draw something from

What exactly is a kinetic energy field? You have a potential energy field because a massive ( massive = possessing mass) body exerts a gravitational effect on every point in the region around it. There is something called 'complementary energy' in continuum mechanics but it is not really a mirror image.

Since you ask, try The Boundary Element Method Brebbia. Yes, the one defines the other. The point is that it can be easier to perform the calculations over a few boundary elements than many internal mesh points. Integration over a closed surface or loop is often computationally easier than a volume integral. Do you need references for this stuff? The angular momentum remains constant but the components change. That is as the radius decreases the rotational speed increases. This is not an energy phenomenon. Moving a particle from point A to B removes potential energy from the particle or changes it to kinetic energy. A good example would be the drop hammer on a piledriver. The gravitational energy lost by the hammer in dropping is transferred to the pile. This is replaced when the cycle is completed by raising the hammer back to drop height.

I was not going to, but, Xerxes, since you bring it up A field in Physics can entail two quite distinct and different coordinate systems and usually does. No transformation exists between these coordinate systems. I do think such discussion is way beyond the basics suitable for this thread, but I will elaborate if you wish.

Thanks, Strange, for explaining what this thread was all about. +1 I nearly missed it, so word to the OP - using a more descriptive title will encourage folks to read (and contribute to) your thread.

Like I said, I expect a block of posts was moved. I'm not even sure how far they can sort individual posts within a block. A separation line has to be drawn somewhere and sometimes things get tangled up in this. I have 'suffered' this myself so it is not personal, However I would like to say that I, and quite a few others I think, value you contributions here.

One thing that comes out of Green's / Gauss' theorems as a surprise to many is the fact that ie form and structure for many physical phenomena, in the interior of a bounded region, can be completely defined by knowledge of what is happening on the surface. The Boundary Element Method can often achieve great computation efficiency in replacing the Finite Element Method because of this.

Yes please tell us the results when available. +1

V&D Perhaps a more measured response would be to PM the moderator concerned? I have found the mods quite open and sympathetic to private discussion and quite prepared to adjust moderator action if a good case is made. You have provided some excellent and readable responses in several threads, particularly relativity, so please don't fall out with the mods, they do a super job under the circumstances. I expect that a whole block of posts were moved and if any fine adjustments become appropriate that can take a few days of quite background discussion. I don't know why relativity is one of those subjects some become over emotional about.

Multiplication and division can introduce some funny effects when applied to quantities with units. for instance multiplication can loose all the information as in frequency times period = 1 Division, on the other hand, can loose the units as in velocity ratio or mechanical advantage or many other dimensionless ratios. It is also clear that whilst multiplication / division can be modeled as repeated addition / subtraction for integers, the model suffers when we introduce non integer quantities. Physically the model is also suspect with say a hydraulic force multiplier which multiplies the input by a fixed scalar.

Actually I did, and what's more I told you that there are many different (types of) Fields with equally many different types of properties and that the properties are controlled by the field variable. Note you did not mention this field variable, I did. And yes, if you were not so determined to try to force the answers into some preconceived but inappropriate form we could certainly have a productive discussion. I could tell you that magnetic fields, electric fields and gravitational fields have a fundamental difference. I could note that neither magnets, nor currents are 'fields' themselves but are physical entities capable of interacting with a suitable field. Do you know which of these is a conservative fields and which a non conservative field - I have already introduced conservative and non conservative fields as a fundamental property? I could say look at a flowing river and note that if we place an 'arrow' at every point we get a 'direction field' which will tell us which way the water flows at every point. We could improve that by placing a vector which tells us both the strength and direction of the flow. I could say that the record of temperatures at every point in a body constitutes a temperature field, which will tell us which way the heat will flow, but doesn't refer to any mysterious 'lines of force'. Or I could say the same of a record of reagent concentrations in a mixture and note the concentration gradient field. I could also observe that one common usage of the word is not what is meant in science. A field is not the (physical) stage upon which a particular activity takes place. This usage is very common for instance the field of play for a game, the field of battle, a field of poppies etc, all of which have physical embodiment and may be specially prepared in some way for the intended action. I wonder, perhaps, if you aren't trying to make the scientific usage conform to this notion?

Actually your question was answered. Maybe my post#8 was too long or you did not understand it. It should have at least help you realise that there are many fields, each one quite different. So the question 'what is it?' is pretty meaningless I'm sorry that the definition of a field does not match your idea of one. That's life. If you would like to know more, ask for further explanation rather than railing against those trying to help you.

Think of it this way. Consider a point mass, m at point A in a potential (energy) field. Moving it to a point B of lower energy yields some energy for some purpose eg accelerating the mass. If we now complete the circle we have to re-supply that energy to the mass to return it to point A because the PE field is a conservative field. But at all time the potential is there at both points A and B and all points in between.

Yes that's exactly what geordief asked and the answer is the same. The 'Field map' of Potential energy for a 1kg test mass is the same whether the mass occupies a particular point or not. That is there is only one point where the mass actually occupies at any one instant, the rest of the map is available if and when the mass choose to be there.

When it comes to pints I find imperial measure far superior.

Yeah, right on. Even if that value is zero or null at some points. But not necessarily at every point, just in the region of space of interest. IOW Fields can have boundaries. That is why I said value or values. It does not stop at vectors, though. Tensors etc also make fields. Are you asking about Fields, mediating particles 'action at a distance' or what?