studiot

I'm still trying to kep it simple and walk before we try to run. You have said nothing about the relative magnitudes of the proposed force interactions. You surely know that atoms of normal matter are not held together by gravity. At the scale of atoms, the force of gravity is many, many orders of magnitude weaker than the electrostatic forces which bind the particles together in to atoms. So the force of gravity plays little or no part in the internal mechanism of atoms. So why should this repulsive interaction force be strong enough to disperse dark matter particles ?

OK I agree with this but consider. What do you need to have as a minimum for a vector space ? 1) Well you need a set of vectors. 2) You need a set of rules (the vector space axioms, which are really rules of combination of the vectors and elements of the field set) 3) You need a set of objects that form an algebraic field 4) You need a set of permissible operations. Now for the minimum (4) is combined into 2 as the one and only operation specified. When more operations are specified then more rules are required and more structure is available, using member set (4). You may also then need a set of definitions. So a vector space is a set that contains at minimum 3 sets (not subsets) as members. Note that in general the rules in the rule set do not apply to the 'space' itself. Therein lies one difference from Physics.

Did he ? I wonder if the question was prompted by the cant that is so often taught to juniors near the beginning of geometry. "Parallel lines meet at infinity" MPMin did not actually ask his question in your terms; he asked if an infinite universe was an (inevitable) consequence of flatness. I don't see anywhere that he mentioned parallel lines, but if he somehow equated flatness with parallelism then it is easy to see how this is a very good question, as iNow said in his post. Nor did MPMin actually indicate if he thinks the universe is finite or infinite. Yes i fully agree and commend this approach, but how much of a beginner is MPMin ? I look back at that long thread where he was introducing Swartzchild geometry, black holes and other heady stuff, whilst (some) other members were throwing the vector calculus version of Maxwell at him and I offered a few basic comments along the lines you indicated. For my pains MPMin and I exchanged the following Yes it does thank you

No that is not what I understood you to have meant. I understood you to have meant that in order to have a mathematical space you must have both a set and also a metric specified on it (and perhaps more besides) So my comment about the spirit of the mathematical space referred to this. So I offered you a set, which is the space of positions two (a pair of) dance partners may take up and asked for a metric for this space.

So what metric would you offer that satisfies your conditions ?

Thank you for your answer. I think you have captured the spirit of what I consider to be the difference but your example is not necessarily a mathematical space. Consider the set {AB, BA} What metric would you offer on this set ?

Again and again members ask the question "what is space ?" Indeed we have at least currently active threads which include discussion of this question. So what do members consider the difference between the two uses to be ?

Thank you for your reply. However you have completely missed my point. 'Parallel lines' that do not 'remain parallel' are, by definition, not parallel. Yes lines of longitude are a good example of 'parallel lines' that intersect somewhere. (Yet lines of latitude do not intersect). 'Non intersection' has long been recognised as an inadequate definition of 'parallel', although it is often offered at primary/junior level geometry, Equally the notion of maintaining a constant separation distance is untenable. Furthermore we live in a 3 dimensional universe, where lines are either intersction or non intersecting. Non intersecting lines are either parallel or skew. Parallel lines are in a common plane, skew lines have no common plane.

Back to your clear and concise self I see. An excellent answer. +1 I would, however, like to offer a small correction. Is "Parallel lines stay parallel" not a tautology ? Further how can you say "locally flat" and say "no matter how far you compare their distance between them" ? Local means nearby, not far away.

Here's proof of the wisdom of the 5 post initial limit agains spammers. Suggest using this to explain the limit to genuine new members.

No the change is not quite arbitrary. Here is a potted history of pusating charge spheres and other non radiating distributions, originally introduced by Ehrenfest. https://skullsinthestars.com/2008/04/19/invisibility-physics-acceleration-without-radiation-part-i/ Note these are not pulsars With these, the effects observed are due to rotation. Yes there has been discussion on other forums in the last couple of years. Google has various images of the physics of the explanation, going back to 'all' will find the PhysicsForums and Stack discussions https://www.google.co.uk/search?q=EM+radiation+from+pulsating+charged+sphere&source=lnms&tbm=isch&sa=X&ved=2ahUKEwi01Kv_udHwAhUhtHEKHV5uAx0Q_AUoAXoECAEQAw

Apologies, something seems to have gone wrong with the Math tags In my last post, the second equation should read [math]g = \frac{{force}}{{mass}} = \frac{{mass*acceleration}}{{mass}} = acceleration[/math]

Thank you for that clear answer. I agree that the dimensions (in metric) of volume are m3. So you are very reasonably equating space with volume. One of our doctoral members is fond of doing this. Please forgive me for wanting to start with some basics which we can all agree on, before proceeding to your more exotic assertions. I asked for two reasons. Firstly you enjoined me to read your introductory pdf. There you state your priciple that somehow swops or interchanges volume and mass as your breakthrough insight. Is this also the basis for you suggesting ? I commented that gravitational flux is an example of Gauss' Flux Law and you seem to agree with that. Only it is not necessary to integrate over a closed surface. That is only when you can equate the total to a finite value. The total field (integral) passing through a given surface, closed or not, will always give you the flux, if you can evaluate it. However I did comment that for the field lines (flux) to pass through that surface there must be additional space on both sides of it. A surface is two dimensional and has units m2. We are dealing with three dimensional space with units of m3, as already noted. Now I also said So I think we agree on the definition of flux, ΦG as ΦG=∫Sg.dA But wait, g=Forcemass=mass∗accelerationmass=acceleration So we have a mass over mass cancelling situation Please note that there are lots of different symbols and anmes about for some of these terms so I have used the Wikipedia symbols that are available to everyone. https://en.wikipedia.org/wiki/List_of_equations_in_gravitation You download images by drag and drop (not recommended) or clicking on the 'choose files' as indicated in the image below. This will download images (jpg is best, I use greyscale where possible to save size) to thumbnails at the bottom of your input text. Click in the text to place the cursor where you want to place the image and then click on the thumbnail. The other outlined thing are the symbols for superscript and subscript in the toolbar at the top. These are really useful as you can create near scientific notation with these plus a couple of characters by using charmap.exe (part of Windows) to find the hidden characters availble from your font sets. Much easier than Latex, (you need to use MathML here) . Tex can be accessed by going to an online editor to assemble your maths and then copy pasting from there. https://www.codecogs.com/latex/eqneditor.php?latex or http://www.sciweavers.org/free-online-latex-equation-editor

What don't you understand about my question? I only asked one simple one, the rest was some background which should be easily accessible to someone with So to repeat my simple question You are the one who introduced 'dimensions', although you actually offered units.

Yes dimensional analyis is a very hand tool. I don't think that is the way Gauss' Law works, in particular your conclusion is drawn from an end result in which two quantities appear in the numerator and denominator of the defining fraction and therefore cancel. I think you should start with this statement Again, yes I agree it is an important and fundamental question so let us ask it What are the dimensions of space ? Remember that gravitational flux is defined in terms of a gaussian surface and requires 'space' either side of it.

You have not given details the object to be detected, and if it is the only object on the floor. Perhaps you should investigate graphics tablets, They can detect the presence or absence of the stylus pen by various different technologies. But a floor sized version could be quite expensive. https://www.amazon.co.uk/Huion-Graphics-Drawing-Tablet-Board/dp/B00TB0TTAC/ref=asc_df_B00TB0TTAC/?tag=googshopuk-21&linkCode=df0&hvadid=310855849579&hvpos=&hvnetw=g&hvrand=10556702321285004752&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=1007149&hvtargid=pla-379048174962&psc=1

Yes you are right, I thought about it after I shut down and went out, but it was too late then and I was rushing.

Exactly. Mixtures have a lower boiling / melting point than any pure substance they are mixed from.

I am wondering if you cooking technique has something to do with it. Although I would not waste the higher priced maris piper on roasties, occasionally we have one or two to use up and they go in with the standard 'english whites' and seem to come out the same when roasted together. Traditionally, of course, King Edwards are the premium roasting spud. In any event, I wonder if you are not using perhaps too much oil ? Oil has a lower BP/MP than traditional fat so may not let the surface of the spud reach the higher temperature that drier cooking or deep frying would. Really ? Please explain how this works.

There are lots of ways to achieve a crisp exterior to potatoes when cooking them. Results depend upon the variety, age and condition of the tuber, including its water content. If you want good results with shallow frying you are best to parboil or par microwave them first. The European method of making chips uses this method for both deep and shallow frying. I think the most important thing is that the final operation should be intense heating of the potato whether roasting, baking or frying. If you obtain the crisp external coating too soon in the cooking sequence you will either end up with a part cooked interior or have to turn the heat down and I find the crisp exterior goes soft - You often find this in restaurents that have kept roast potatoes warm (hot) too long. It should be noted that it is possible to produce the crisp exterior even if the potatoes are floating in water (gravy), this is done in the traditional Lancashire hotpot dish for instance. I find that 'scallops' are thus the best shape for shallow frying. Some commercial chips (fries) are made from extruded precooked and reconstituted potato. On the issue of supermarket supply, I find it is always worth removing vegetables from their plastic bags (even the perforated bags) as soon as possible as the seat in the bags initiating deterioration. Carrots seem particularly prone to this and also some supermarkets seem to treat them particularly harshly so they start going black on the outside within a day or two. It should be noted that the washing process also involves som form of mechanical scrubbing.

nice +1

The point is that one of Tesla's false claims relates directly to your proposition. What makes you think space has no properties ? This is just false, and Tesla of all poeple as an electrical engineer should have known better. Empty or free space has a measurable electromagnetic impedance of about 377 Ohms.

+1

Hello Timothy, I can see you have much work to do explaining your ideas since you are using different definitions for common scientific words from (the rest of) the scientific community. Radical though he may have been Einstein did not do this. In particular do you actually know what the scientific definitions of 'fractal' and 'dimension' are ? You state "Einstein's assumption of a static 3 dimensional space....." Did you know that significant investigation into the mathematics and science of multi dimensional space was started before Einstein and received an impetus when his theory of special relativity came out ? In particular various multidimensional spaces were studied intensively with the result that 2 dimensions are insufficient, 4 and more dimensions offer additional phenomenon that are not observed leaving only 3 dimensional space as being the appropriate number. Significant Mathematical material was developed by Sommerville, Eddington, Hausdorf, Abbot amongst others at this time and the work has continued to this day because it is not yet 'finished' - if it ever will be. It is worth noting that modern (and slightly earlier) mathematicians have even added significantly to Euclid's massive epic. We can discuss these comments if you like, which could save you a lot of heartache in the future. I am sorry to be so negative as you appear sincere in your efforts.

We would need sufficient information to begin to answer this question. Impedance ? Acoustic impedance ? Radiation impedance? Electromagnetic impedance ? Impedance between the surface and something else ? Yes it may be possible to detect an intervening object depending upon the details ( a lot more of them) . Capacitive coupling comes to mind. Over to you.