studiot

Here is an easy experiment you can try. Equipment 1 sink of water 4 dinner plates 1 washing up brush Immerse the stack of plates in the sink of water, make sure they are completely submerged. Take the washing up brush and make a swirl in the water above the plates. Report what happens when you go faster and faster. Where did the force come from ?

The discharge pipe went straight up from the airing cupboard containing the tank into the attic and curved over the header tank to discharge into it. Straight into the block of ice at the top of that tank.

Not quite, if I understand the mechanism of your thrust correctly. Since you have drawn a circular boat ( ie a coracle) I have also indicated one. Fixed on the edge is a stator', in my case with the North pole facing inwards, As the centre rotor rotates the axis of its magnet always points along the radius, with its south pole at the put end of the rotating arm or rotor. As the rotating arm approaches the stator. the stator (and therfor the boat) will experience an increasing sideways pull towards the end of the rotor. When the rotor passes the stator the pull direction will reverse. This induces a left - right wiggling to the stator. However the vector of the force has a component along the line between the wiggles as shown. ~This is your thrust. So there is a polarity ( in direction) reversal involved.

I'm glad you understand that your are trying to create a model. However you are relying on two features, present in the model, but not present in gravity. Firstly polarity, as I have already said. Your vibration relies on alternate attraction and repulsion to work Gravity has only attraction, but never has repulsion. Secondly, again as I have already said and you have now ignored twice, the distances over which gravity acts effectively are very different from the distances in your model. So your model is inappropriate.

Polarity means positive and negative, as with electricity and magnetism, (though we call magnetic polarity north seeking and south seeking) Gravitational attraction is always positive. Please note that the force of electrostatic attraction is vastly stronger than gravity at atomic and molecular distances. Please note that most substances (matter) occur as molecules not individual atoms. You have drawn the typical 'miniature solar system' representation of two atoms with several or many electrons, also called the Bohr atom. This is perfectly adequate for this discussion. You can consider the electrons as little balls moving round so fast that they can be considered 'smeared out', over the shell and take an average. But I also commented Hence my offering about shielding.

My comments only take into account the effects of rotations of not the direct effects on quantities (differential or otherwise) as projections or components. Rotations by themselves do not lead to the cross products involved.

Indeed the electrons in both the Bohr orbital model and qhantum models suffer the opposite effect, which has significant consequency in the chemistry of atoms and molecules. It is called the electrostatic screening or shielding effect. https://en.wikipedia.org/wiki/Shielding_effect Folks so often forget the effect of the other electrons in an atom or molecule when considering the actions of one single electron.

Interesting, you have taught me something. +1 It the dangers rather depend on where the freeze up is. Some years ago, when we had colder winters, we were away for a holiday and when we came back there was no water coming out of the hot taps, except for an initial flow. These taps were fed from a DHW copper cylinder, with an attic header tank and gravity inlet feed. The attic tank had frozen, blocking its outlet to the DHW tank, causing a vacuum to prevent water exiting the hot tank. I found this when I heard a crumpling sound and investigated. The DHW tank had crumpled inwards because of the vacuum. I was so relieved when the soft copper popped back to shape, but remained watertight. after the attic tank was thawed.

There is no polarity involved in gravity.

This contains a fundamnetal inaccuracy mixed up with correct statements. exchemist is correct about the principle of induction heating conductive material. You are correct that this is not the cause of melting deep within a planet. Solid materials from ice to carbon dioxide to methane to iron can melt if the pressure is high enough. The pressure can be high enough due to gravity. If, only only if the resulting liquid is electrically conductive, convective currents within the liquid will generate electric curents according to Faraday's Laws. These curents will in turn generate magnetic fields. Even within the Earth the exact circulatory pattern has yet to be resolved.

Thawing pipes containing frozen water can have unwanted consequences; how to go aout the job needs careful consideration. Also a hair drier or other hot air blower is better since you won't have wet pipes to cope with. If you must use hot water, soak a cloth in the water and wrap it round the pipe. Rinse and repeat.

Obviously not well enough known to be noted here. The issue is a practical one, that both GR and QM share since both assume infinite divisibility of space. The issue is that the smallest particles we have identified are about 15 orders of magnitude greater in size than the planck length and 20 orders of magnitude greater than we have successfully been able to probe. ( note I am measuring size by L units, not M units ie diameter not mass). If you want to probe the mathematics of the region between this sizes I recommend this book which take you from Brirkhoff and Von Neuman (1936) through Segal (1947) to Kakutani(1948) and Gleason (1953) and Bogachev (1998) for mathematical models of what happens with Borel sets in (possibly infinite Hilbert spaces (manifolds). The question of the meaning and existance of A*B and A + B and A-B and commutators is examined in great detail leading to Segals axiomatic statement of QM. It is how ever admitted that (axiom VII) the justification is 'that it works'. As my last reference indicated work has proceed since Mackay's 1963 original.

That is true for finite rotations. However the calculus and for instance KJW's presentation is based on the fact that infinitesimals in the limit rotations do commute and differential geometry works at all. And GR is based on diff geom. That is why partials form linear combinations. Also the discussion seems to be being dragged further and further away from the OP, which was about what happens in that limit. And there is a fundamental issue between GR and particle physics that no one has thus far brought up.

Good summary +1

Work it out for yourself. Gravitational potential times Mass Density ML2T-2 x ML-3 = ? Actually I must own up to a definition error here I gave the dimensions for gravitational potential energy, not gravitational potential (which is potentential energy per kg) so the multiplication is Gravitational potential energy times Mass Density ML2T-2 x ML-3 = ? Gravitational potential times Mass Density L2T-2 x ML-3 = ? neither of which work out to ML2T-1

Good insights getting straight to the heart of the matter. +1 Work it out for yourself. Gravitational potential times Mass Density ML2T-2 x ML-3 = ?

This is where you should go back and read up on the HUP. I also recommend you read more carefully exactly what swansont said. (Hint "specific") Conjugate variables for the purpose of the HUP have dimensions ML2T-1 when multiplied together So Momentum times Position MLT-1 x L = ML2T-1 Energy times Time ML2T-2 x T = ML2T-1 But you also said So Pressure times Volume ML-1T-2 x L3 = ML2T-2 and Space times Time L3 x T = L3T Neither of which satisfy the HUP conditions of conjugate variables.

What I actually said was Complaining that GR is flawed is a bit like trying to put a screw in with a hammer and complaining that the hammer is flawed. When you offered this were you confusing the mathematic process of taking a limit with limitations such as the limitation on square roots "There are no real square roots of negative numbers" ?

Yes and that position is that you are unwilling to correctly read what others tell you or even to ask them what they mean by a statement. You seem to prefer immediate outright denial. If you are saying that I did claim that GR is flawed pleased post the quote . Otherwise reread what I actually said about about GR and apologise.

Go on ? And what about your misreading of my previous posting ?

Instead of shouting everybody else down how about you try listening? In particular I didn't make this an argument. That is most definitely not what I said. I will ignore the first sentence as you clearly do not know what conugate means in the context of QM. But I do agree that you can labe the axes any way you like. If you lable them as you describe in the underlined sentence, it becomes impossible to plot any points at all using those axes. That is a direct result of the uncertainty principle. On the other hand if you prefer to hold a civilized discussion then I am quite happy to expand on my explanations further.

I don't call that a flaw for the reasons I have already outlined. Yes it limits the applicability of the model, as does any form of linearisation of non linear equations.

I suppose it rather depends what you mean by fundamental flaw. GR is just a model. Reality is under no obligation to follow it exactly. In fact no model is exact. But so far as we know there is no self inconsitency. There are also several 'solutions' to the equations of GR. So in this respect the GR model has no flaw. As regards your proposal, I think you have the idea a little mixed up. What meaning do you attach to this claim and what (mathematical) proof do you have of its veracity ? Mathematically we have learned to handle the 'impossible' division by zero. For instance the point scalar density has a definite and measurable value which coincides with the scalar limit of Mass / volume as the volume approaches 0. Similarly, but in a more complicated fashion, vector flux reduces to a limit of flux over area as area approaches 0. This applies to pressure at a point (force over area), magnetic, gravitic or electric field density etc. Mass has zero dimension, force has one dimension, area has two dimensions and volume has three dimensions. If time is involved it adds at least one more dimension. When we set a quantity in a multidimensional universe of greater dimensionality, eg force divided by area we introduce at least one extra degree of freedom. With force over area the area has two dimensions curvature or rotation has one of these. But we are setting this ratio in a three dimensional universe so we immediately introduce a second degree of freedom and a second direction for the curvature. If we want to go to a GR universe we enter a four dimensional mathematical space. How many ways can curvature operate in this space ?

For the benefit of those in Europe or the UK who might also like to know their answer to this question, here are some instructions. https://www.aico.co.uk/waste-electrical-and-electronic-equipment-weee/ https://www.cornwall.gov.uk/rubbish-recycling-and-waste/recycling/recycling-items/smoke-alarms/

The Periodic Table Hmm - An interesting place to start your study of chemical bonding. To have any sort of periodic table at all it was necessary to identify enough different 'elements' to arrange. This was achieved between the late 17 hundreds and the early 18 hundreds. At that time there was no such idea as 'atomic number' (ask if you need to know what this is). Known elements were arranged by atomic weight - although this was not as easy as it seemed and the first Internation Conference in Chemistryheld in 1860 was intended to produce proper definitive definitions for 'atom', 'molecule', 'radical' and 'equivalent' but ended without achieving this. However some of the participants, including Mendeleyev, left with the the suggestion by Cannizzaro to abandon the weight order. Chemists up to that time has followed the classical mathematical connection between music (yes music in the guise of harmonic scales) and science. There was Dobereiner's triads or rule of 3 Triad 1. Lithium: Sodium: Potassium: ... Triad 2. Calcium: Strontium: Barium: ... Triad 3. Chlorine: Bromine: Iodine: ... Triad 4. Sulfur: Selenium: Tellurium: ... Triad 5. Iron: Cobalt: Nickel: and Newlands rule of rule of octaves which led to the first 'periodic table' https://byjus.com/chemistry/newlands-law-octaves/ https://www.simply.science/images/content/chemistry/structure_of_matter/dev_of_periodic_table/conceptmap/Newlands_Law.html Following the switch to 'atomic number' Mendeleyev was able to place the 63 known elements in their proper position in a table. But they did not know why or about the other 55 naturally occurring elements ( or the radioactive ones). Since that time there have been many attempts to extend the table and it has been found necesary to split the original 8 columns to incorporate new subcolumns. Different arrangements do this differently. Have you ever been to the Science Museum ? It is really worth a visit if you can get there, here is their offering on the subject. https://www.sciencemuseum.org.uk/objects-and-stories/chemistry/developing-modern-periodic-table-spirals-stars OK so where are we today ? Well we are moving away from periodic tables of chemical properties alone, bearing in mind radioactivity and what we now know about the structure of the atom. A new term 'nuclide' has entered the scene and the 'table' often now takes the form of a plot N (the number of neutrons) against Z (the number of protons) This is known as a Segre Chart https://www.radiologycafe.com/frcr-physics-notes/basic-science/atomic-structure/ https://en.wikipedia.org/wiki/Table_of_nuclides