studiot

The problem with the rubber sheet is that the curvature of a rubber sheet is of the wrong sort of curvature. There are two sorts of curvature, extrinsic and intrinsic. The curvature of the manifold in GR is intrinsic. The curvature of the rubber sheet (manifold) is extrinsic. A further comment is that a single point has no curvature. A line has no intrinsic curvature but may have zero extrinsic cirvature or some value of extrinsic curvature. A surface can have no curvature, both extrinsic and intrinsic curvature or just extrinsic or intrinsic curvature. These situations can all be drawn or sculpted in our 3D world. Once we move to 3D however we cannot draw or sculpt extrinsic curvature and it is very difficult to imagine.

Stromatolites. Amongst the first living organisms on earth circa 3.5 billion years ago and still going today. They were responsible for releasing the oxygen into a toxic (to us) atmousphere and making it breathable for oxygen breathers. https://www.bushheritage.org.au/species/stromatolites https://en.wikipedia.org/wiki/Stromatolite You may have seen the BBC series The Power of the Planet, presented by Iain Stewart https://www.bbc.co.uk/programmes/p00gczg5 An interesting reverse (geological not biological) process is the 'rusting of the rocks' https://www.newswise.com/articles/how-rocks-rusted-on-earth-and-turned-red

Really ? What is n ? That leaves me still waiting for some unit free constant that couples length to any one of the other independent physical dimensions I have mentioned. Do you know what they are? If not are you not curious about my symbols ? I certainly don't agree that all forms of 'Energy' in general are proportional to temperature.

Hi Markus, I know we are always stressing there is no fabric. Have you heard of the cosmic Fabric model of gravity ? https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjM-ouXq4PzAhUKxRQKHfQwDd4QFnoECAIQAQ&url=https%3A%2F%2Fwww.worldscientific.com%2Fdoi%2F10.1142%2FS0218271819500962&usg=AOvVaw3Kqo9MvdIjk3xvl4NsgsTR

+1 to Markus for his patient conversation and explanations to Conscious Energy.

Sounds like you are already doing lots of good things for her. Hopefully you realise she will not see DNA with the sort of microscope you are talking about - That sort probably costs more than your house. Thnking and asking about abstract things she can't see at age 6. Wow. May I also suggest some horizon broadening ? Cooking with mummy helps learn how to handle materials. I don't know where you live but perhaps you could take her to a Science Centre, there are some really good ones in Europe (including the UK). Also try to link to things you can see such as plants, animals and the world around her. The changing seasons. some fresh air. Maybe visit a farm. Tell here the world is one big laboratory. But don't get to heavy. That's my advice for starters.

I'm sure you understand the point. My examples are just that. Let us just suppose that every Scot applied to do Higher Pictish Studies and the Scottish Government funded this. Where would Scotland get its future teachers, doctors, engineers, lawyers, and so on from ? And who would employ all the those with a Batchelors or Masters of Pictishness ?

Should higher education be free (a la European) ? Well no one seems to care what constitutes higher education but I see that the expected lines have been drawn so let me ask the question in thelight of the following hypothetical situation. Higher Education in Scotland is free to Scots. (not hypothetical). Suppose everyone only wanted to study higher Pictish studies. Should that also be free ? or If you prefer to consider the point of my question. Should all higher studies be free and how do we persuade folks to take up other more useful studies?

Just a short answer is needed to start with, not an entire exposition of Physics. If I can understand and agree with it I can then follow all your other long posts that have taken so much effort. As a matter of interest the MLT system is not unique, nor is it specifically SI, although yes Système International d'Unités has adopted it. But there are also other systems in use for instance one with mass replaced by force - the FLT system. The FLT system finds favour in Fluid Mechanics as it make this system easier (at least for Fluid Mechanics) as can be seen from this small table. (after Olson : Engineering Fluid Mechanics) Note at the bottom of the table the comment about temperature. I did ask and you have not said how your L system handles temperature.

What do you mean by 'higher education' ? Does hairdressing for instance count ?

Since I asked for a clear example it is only fair that I give you one showing what i mean. On a per unit basis, the molecular weight of water is 18. Superficially, that apppears to be a pure number. But that is because the the real dimensions are hidden in the per unit, which is a gramme-molecule. So a complete statement is the molecular weight of water is 18 grammes per gramme-molecule. The interesting part of this story is that the full dimensional statement is MN, although the N is usually 'understood' and not stated explicitly.

70 posts, some of them have involved a lot of work and I still don't understand the basis of what you are saying about dimensions. Most of what you have posted assumes the reader understands and agrees with your basic statement about dimensions. I don't understand or agree. You mention unit analysis and also Tesla. There is a form of analysis in electrical power engineering called 'per unit' analysis. I don't know if you are trying to emulate this. The problem with 'unit analysis' is that the dimensions are hidden in the 'units' employed. They haven't really gone away. So can I respectfully suggest you put some of this effort into developing (proving) your underlying claim once and for all? Perhaps showing one simple example developed from start to fininsh, but involving as many as possible of the seven basic quantities in the LMTAθIN system. For your information here are two free websites where you build mathematical formulae and copy/paste into ScienceForums. http://www.sciweavers.org/free-online-latex-equation-editor https://www.codecogs.com/latex/eqneditor.php

Yes of course the business of Physics is to examine the interactions of its laws and the resulting structures in excruciatingly fine detail, as well as discovering and enunciating the laws themselves. But my point is that it is not the laws that can be scale dependent but the results of their interactions. Some are some are equally definitely not and some vary as scale varies. I gave some examples, but I am surprised considering one I have not mentioned, that cosmologists do not accept this since the spectra resulting from electron transitions and molecular vibrations are held to be that same at either end of the universe as on Earth. How's that for scale ? I do agree with your comment abour Reg/Davy/...? although it would have been nice if he knew when to call time on antics.

No I don't think you did answer either my questions, nor those of swansont. Anyway the OP picture 1 is purely Newtonian. GR is not involved. The curvatature is in the values of Newtonian gravitational potential. It is a depiction of a Newtonian gravity well. There is a similar picture of the Schwarzchild solution in GR which with which it should not be confused. @pmourad This New Zealand teaching website offers a really good explanation and some interesting material to play with. https://www.sciencelearn.org.nz/image_maps/76-exploring-physics-concepts-with-a-gravity-well

L-12 does not equal L-6L-5

Hi Markus, thanks for your reply. I'm sorry but that's too one sided. It's not true to say that the laws of Physics are scale dependant per se. It would be better to say that physical structures formed from interactions and combinations of these laws may be scale dependant. Some structures may only form at certain 'scales', such as colloidal suspensions, critical fission masses and black holes. It is true to say that different laws obey different variation relations with distance and/or or time This results in different laws predominating at different distance or time separations. I define 'local' as within a given region of space containing the subject(s) of interest. So clearly different physical structures can arise depending upon the size or extent of the 'locality' Exceptions to this might be regions with a huge extent in one dimension,but a minute extent in other dimensions. So shape is also significant.

Everyone is entitled to thir opinion, including those that can't or won't back up their assertions with detail.

Yes of course a marble would roll down the fabric of the trampoline. But the fabric of the trampoline is woven so there is a mesh with fine holes. This is fine so long as the holes are much smaller than the marble. But what would happen if we rolled successively smaller and smaller marbles until the marble was smaller than the holes ? If this is so then you can sketch the real curvature of space in the 1D and 2D cases. I look forward to your sketches. Again let us see a sketch, employing only a single axis. It is only possible if you have a non linear function that maps points on one (part of) the x axis to another part of the x axis. This is exactly the type of relation I described to those new philosophers who have recently joined. Which is why it is a bad analogy. It is allegedly gravity that gauses the 'curvature' in both cases. Nothing else. Just gravity. Yet your description of the rolling marble has normal reactive forces acting. It's not the stress - energy tensor you need but the Riemann tensor, if you must use tensors. But nobody mentioned them. In another thread Markus mentioned an alternative to curvature - torsion. This model (analogy) does not suffer from the difficulties of R . But these are way above the level this thread is pitched at. @pmourad Do you understand the idea of 'length of arc' of a curved line, that is distance as measured along the line (not the mathematical formulae involved) ? This is the same as what I meant by land surveyors' through chainage.

Simple but really cool. +1

These misunderstandings show why I dislike this analogy. 1) If it is meant to represent paths of objects (which is a very vague and ill defined statement) not the curvature of the fabric of space why is the picture so named the curvature of (the fabric of) space ? It can't be spacetime as there is no time axis. 2) If it is a representation of a path of a real object then why does that object not follow the direct line towards the COG of the Earth ? 3) The top picture implies that we start with an two dimensional model grid (whatever the grid represents), flat and empty of matter. We then place some matter (eg the Earth) onto this grid and it is displaced somehow into the third dimension by 'bending of a grid', whether the one in the picture or another grid. Now extend that up one dimension so we have a 3D grid, that implies, of necessity a 4D universe for this displacement to occur. 4) if you prefer start with a one dimensional line. If this line is one dimensional it cannot be curved, the term cannot be invoked and maintain the one dimensionality of the universe containing that line. In differential geometry in order to give rho and kappa maning you must invoke further orthoganal derivatives. Land surveyors are familiar with this one dimensional version under the name 'through chainage', which works basically as I have tried to describe it for pmourad as I seem to recall said they have only basic high school algebra. 5) We are talking about 'distortion' due to gravity alone. Surely you are not suggesting some additional force ?

Yes Linda is not recorded as having returned since before I posted my original erroneous reply. And yes you are correct in assessing a difficulty with the original statement in the OP about the concentrations of A and B. That is why I started with the chemical equation AB = A + B This is what is implied in the OP It is also implied that the equation could not be for instance A2B = 2A + B. So unless there is an unknown source of A and/or B, or some further reaction involving A or B, the concentrations of A and B must be equal as the only known source is AB. Of course the OP is at variance with this so has not been properly formulated. So it may well be as you suspect since this is a biochemical reaction.

I can agree with that, except for the 'hence' since I don't agree with the premise of scale. Davy_Jones has also agreed that there is more than one 'reality' or if you prefer, two versions of reality can both be true. I will come back to Davy in a moment, but first to complete my comments about Markus' post. Consider a brick wall. In my reality the wall, the bricks and the mineral particles that make up the bricks and mortar are all simultaneously real. Indeed one could not be real without the other. But what you (and Davy) said about contextuality is spot on. Yes you must alway qualify many things about the ground in which you are working. Hmm, does not seem like a problem to me. No doubt there are difficulties with the concept; this doesn't appear to be one, though. Isn't this like saying, The coin has two sides: one heads and the other tails. Our concept of reality is a mess"? When one side of the planet is illuminated, the other is not. When it's summer in Canada, it's winter in Australia. Where's the problem? In the philosophy of language, they talk about indexicals (words such as "I", "now". "here". etc.), that is, certain statements are indexed according to the person, time, place, etc. of utterance. Therefore, taking indexicals into account, there is no contradiction between the statements "It's hot here", when uttered by yourself, and "It's cold here" when uttered simultaneously by me. Both can be true. Thank you for your reply and most importantly thank you for including this most important statement. Far more important than the squabble over reality and truth, which we all now seem to accept need further qualification to make sense. The philosophy of language. Yes indeed you have just qualified 'philosophy' , as I have said to you several times now and you have always side stepped. I repeat that both Science and Philosophy need qualifying, just as we have all noted that truth and reality need qualifying. So many needless and pointles arguments ensue when that qualification is missing.

Yes and I wish they wouldn't do that as it is a bad analogy. Yes the Earth appears sitting on the fabric pulling it down as if it were a heavy ball on a trampoline. That is the trouble, a heavy ball on a trampoline pulls the fabric down into what ? Space where there is no 'fabric' whatever that is supposed to mean. Where did that space come from ? And the pulling it down - well a heavy ball only pulls down the trampoline because the earth is 'underneath it' pulling on the ball with gravity. And the lines on the fabric are stretched and distorted. But distorted from what ? Aren't they supposed to be the correct gridlines of the fabric ? How can they be distorted ? +1 for recognising it. Here is a better one, soor no pretty dagram at the moment. Say you are a road runner that can only travel along the road. Now say you are standing at 5 West Street on a grid pattern of roads where the sides are completely built up with buildings. And say you want to get to 5 North street. Well you can't cut through the corner of the buildings, you have to go first along West street to the intersection of North Street and West Street. And then you have to go up North Street until you reach number 5. These are the 'rules' of this grid pattern of points. Furthermore this route is the shortest possible route for a road runner. This is an example in 2D, that works without invoking the 3rd dimension at all. Now suppose we scale this up to 3D. Again we have an arrangement of point, just now in 3D. And we have rules either of travel between these points or equivalently the way these points are laid out. This time there is no need to invoke a 4th dimension (ignoring time for this). The (mathematical) rules are pretty complicated, but that basically how General Relativity works.

We are agreed then. Let's go down the pub and forget it all

Was the underlined part a question ? Yes I think it is wise to explore every avenue towards an improved life for all. But I fear that neither of yours are attractive. Population control is Nature's way, using the tools of war, pestilence and famine. It's very effective but do we really want this way ? Cloud control is a drop in the ocean (excuse the mixed metaphor). We need fundamental, root and branch, changes to our society, with proper respect for and contributions from all sectors. That is certainly not happening at the moment. Which is a great pity because nearly all would benefit from such change.