studiot

This is the unaswered question. +1 Consider a system of molecules in some volume. Unless both molecules have the same velocity they do not have the same kinetic energy and therefore the internal energy is not evenly distributed between the molecules (maximum entropy). So the famous 'hot death' of the universe must be a static (as in unchanging) situation from the point of view of maximum entropy. But this view ignores the fact there are twin drivers in the thermodynamic world that often pull in opposite directions. The principle of minimum energy can be used to devise a system that will oscillate indefinitely at fixed (maximum) entropy.

Thank you for considering my comments. I'm sorry my analogy was not clear enough for you to understand. So try this one instead. Both chess and draughts are played on the same board. But they are very different games with very different rules, and different end results. Events can happen in chess that cannot happen in draughts and vice versa. The same can be said of the partitions of your master set. This carries over to the other part of your answer. There are umpteen relationships in physics where something is proportional to something else. And very often the contant of proportionality carries the units as in strain (a dimensionless quantity) is proportional to stress. But that does not mean we can disregard the constant and say therefore stress and strain are the same as thermodynamic entropies. Otherwise you could model one on the other, but if you tried you would obtain conflicting results, just as if you tried to play chess with a draughts set or vice versa. Information entropy and Thermodynamic entropy are not the same, or subject to the same laws (as in the rules of chess and draughts).

Didn't you miss something out here? Thermodynamic entropy has to have units of energy per degree of temperature. Other entropies, such as your runinations (pun intended) will have different units. In a block of flats there is (or should be) a one-to-one between the pigeonhole letter boxes at the entrance and the flats and their organisational structure. But would you rather live in a pigeonhole or flat? They are not the same.

If you are interested the extract was taken from Professor Frankel's book "The Geometry of Physics" : Cambridge University Press This is a large encyclopedic tome that covers a huge amount of ground from the topology of Kirchoff's laws to the most modern versions of GR. Back along, Proff Frankel also wrote a much smaller book "Gravitational Curvature an Introduction to Einstein's Theory" : Freeman Publishing. Here he develops a lot of this, with and without tensors. He also notes and describes the several different fashions in the mathematical presentation of GR. These may be of interest.

Again thank you for your response. It is most interesting that you think to know all about my version of layers (especially when I haven't yet posted them) but fail to answer when I point out a contrdiction in the implementation of yours.

Thank you for this and your previous reply. However I was really looking for specifics wbout your system we could discuss but you made no refernce to it. As to my chinese problem, I was suggesting running the solution in your layer logic scenario and what I understand by layers for comparison purposes. But you have not doen this you you now assert that your method cannot solve those three simultaneous equations? Note the chinese wrapped the problem up in many words; I have just posted the core math of it in modern algebra.

Leading up to Marcus' comment I have marked the relevant result on the third page. @rjbeery I don't know how deeply you want to go but this is a simple derivation with one static source of gravitational potential. Your theory must predict/reproduce what happens with multiple sources. I don't know if anyone has considered time dilation at lagrange points and lines where there are at least two such potentials.

I'm not sure it's 'layer' relevant but it's a good point. +1

Thank you for your replies. Unfortunately although they have shed some light, they leave me more puzzled than ever. Both the quoted examples assert ( in different ways) the independence of one 'layer' from another. So how is it possible to establish the 'truth value' of any succeeding or preceeding layer, given the truth value in a particular layer. This must be so since with your simple example of the truth value of any layer immediately succeeding the given one must be opposite to the given value. So there must be more to it than this Since you like quoting Chinese philosophers, here is a problem that is solved in 12 'layers' posed sometime between 200 BC and 10 AD in the Ancient Chinese test "Nine Chapters on the Art of Calculation" In modern parlance it is 3x + 2y +z = 39 5y + z = 24 4y + 8 z = 39 Perhaps you would like to look at it from the points of view of your layers and my 12 layers, for comparison?

Thank you for the response. I did not say they were the same but I did (and still do) see some common features. I was really trying to establish some point to your 'layer logic' as I cannot see a 'whole' to understand and appreciate. There is a very clear reason for the 'layer model' and subsequent benefit from it, as exemplified in computing but which appears in many guises in most technical subjects. If you don't wish to discuss that further, that's fine by me. I will leave you to your musing.

Well I understood that rather impressive explanation. +1 Only one cooment. Marcus is talking 'field' in the mathematical sense, not the Physical sense. They can be slightly different.

Well in that case I will bow out and not bother further.

I do wish you would read my short comments properly. Especially as I have collected the bits together for you. You are clearly not following the (simple) point I am making. You have not one referred to the Raman effect, have you not come across it? Meanwhile others are pushing for mathematics. Here is some mathematics connecting refractive index, permittivity and permeability, including for the vacuum. https://www.doitpoms.ac.uk/tlplib/dielectrics/dielectric_refractive_index.php

The point is that in any physically substantial environment whatsoever ( I daren't say medium though that is the usual phrase) the transmission of light leads to two beams or rays. The main beam passes through, diminishing according to the Beer Lambert or similar law. Spectrophotometers mainly use this beam. The scattered ray, off at some angle, is the basis of Raman spectroscopy, which is also used in chemical analysis. Scattering is definitely something to think about, but it occurs when there's an abrupt change in media with an associated change in refractive index. We're considering a smooth, continuous gradation so I'm not sure how optics would normally handle that. Also, the Einstein Lens apparently doesn't differentiate by wavelength so perhaps spacetime neither disperses nor scatters as a "medium". I do appreciate the input, so thank-you. There is no change in media, abrupt or otherwise, in a chemical sample in a spectrophotometer.

The point is that in any physically substantial environment whatsoever ( I daren't say medium though that is the usual phrase) the transmission of light leads to two beams or rays. The main beam passes through, diminishing according to the Beer Lambert or similar law. Spectrophotometers mainly use this beam. The scattered ray, off at some angle, is the basis of Raman spectroscopy, which is also used in chemical analysis.

I would just like to point out here that Einstein did not refer to photon's or quantum theory when he introduced relativity and light clocks. Indeed he carefully avoided the mechanism of light until he had included it in his maths where he always discussed a light pulse. The light pulse being the instantaneous 'front' of whatever constitutes a travelling light ray. 'Das lichtquant' was another paper, directed at and confined to other effects.

Hello Trestone, I see that you first posted a proposal for something called layer logic before I was a member. Today Search engines don'e sem to have given the idea much if any traction. So perhaps I can ask if the layer logic is anything like what is called the 'layer model' in computing ? I note your notation/presentation seems to be an adaptation of normal mathematics and (computer) programming. https://www.google.co.uk/search?source=hp&ei=U1nBXtulM5rAgwf3_LvIBw&q=computing+layer+model&oq=computing+layer+model&gs_lcp=CgZwc3ktYWIQAzIFCCEQoAE6AggAOgUIABCDAToGCAAQFhAeUMQLWPwnYPAsaABwAHgBgAHoBIgBliOSAQs0LjYuMi4yLjEuM5gBAKABAaoBB2d3cy13aXo&sclient=psy-ab&ved=0ahUKEwibm56qnLvpAhUa4OAKHXf-DnkQ4dUDCAg&uact=5

You're right. Well said. +1

Really? What about this?

What exactly is a 'graded time dilation field' ? Have you changed your thoughts since this? https://www.physicsforums.com/threads/gr-as-a-graded-time-dilation-field-in-euclidean-space.742809/ I'll do it for you. Marcus has just told the OP what he was told 7 years ago.

I note you use page 109 of one of Eddington's books as a supporting reference. In his later book, 'The Mathematical Theory of Relativity', Eddington refers to this page and provides the mathematical derivation of the formula shown. (pages 90 - 91) He also explains why the analog system is easier to calculate (he was a great calculator in the days before computers) and warns about the difference in coordinate systems employed in this analog and the local coordinate system of GR.

Polio is an RNA virus; more than one vaccine has been developed for it.

Obesity is a large risk factor for many medical conditions, both physical and mental. So it is surely not a surprise that a virus that attacks so many different parts of the body should be especially harmful in obese persons.

What is the ultimate beginning, middle, and inevitable destination of entities/objects/systems while in any equilibrium state as you said, also while in any type of relationship? Is there such an absolute and singular of entity/object/system that is absolutely independent of any type of relationship? Thank you for your reply. Sadly I didn't understand a word of it. Please explain to an idiot like me in simple baby steps how what you have said in any way answers my question ?

Take a pure liquid substance in a sealed container. What is the equilibrium state of the contents above the critical temperature? However I would admit that I was thinking about a ball perched on a hill top, rolling down to a bench partway down and at the valley bottom when I originally wrote that bit.