studiot

Fred Champion The point was (is) that the state of an object provides no link to any sort of deduction about time. The formal statement of Pauli that I have seen does not include "at the same time", or any other reference to time, because a reference to time is neither necessary nor proper. In order for the state of an object to link to time it would have to include the recognition of some sort of change (velocity, momentum,etc) and change is recognized only over two or more states. A correct description of state will include only one state (the one described) and not others. The state of an object is much like the photo of a clock. While a series of such photos may imply an intelligence (with the necessary memory) capable of recognizing change, it does not imply any phenomenon beyond that, and a single photo of a clock provides no indication of change at all. You have not addressed my question, which was quite specific. The complete wavefunction describing a many particle state is antisymmetric under the exchange of any pair of identical fermions and symmetric under the exchange of any pair of identical bosons. So first of all only fermions follow the Pauli exclusion principle, which follows directly from the above statement. Secondly, the Exclusion Principle that no two identical fermions (from the same system) can have the same set of quantum numbers, applies throughout time. That is why time is not mentioned. Because it can never happen. None of the foregoing prevents interpenetration, which is another name for quantum tunnelling, upon which the computer I am writing this depends for its action.

This is like saying, "If I had a pocket cold fusion device I could make a lot of cheap electricity" and concentrating on the easy bit - the design of the electricity generator part. Try this estimate. Take a simple harmonic oscillator and calculate the maximum particle velocity at a range of frequencies, perhaps on a spreadsheet. Since the vibrating molecule is an object with mass, relativity provides an upper limite of this vibrational speed and therefore velocity. I think, however, that for all known materials, the vibrational energy would exceed the bond energy long before this limit was reached, so you would also have to postulate a super material where this was not so.

I don't know. To have a capability to excite a wave of a given frequency you have to have a viable (in theory) mechanism for excitation. I can't think of one can you?

The velocity of sound in a given material is largely independent of frequency. Further, whilst the frequencies attainable in ultrasonics have some overlap with the lower end of EM radiation frequencies, they do not reach that of gamma radiation.

This is the first time I have ever seen a formula that includes a registered trade mark! But I agree that is way too complicated to start off with. But I was not asking for this, I was asking about the mechanics of your diagram. Your diagram should be a free body diagram or rather set of diagrams since it is a 3 dimensional situation. You are asking about forces and moments on the tyres so I would suggest the free body should be the wheel/tyre assembly. Given this, the answer to my question where does Fsr act is "Fsr acts on the hub" assuming it the the froce applied by the forks to the wheel. From what I can see (if you are saying Fc is the frictional force) Fc acts perpendicular to the plane of your diagram not in it. Also as you have drawn it the velocity is perpendicular to the plane of your diagram. If you have been taught Newton you need to introduce the centripetal acceleration, which is in the plane of your diagram. You did not answer my first question about equilibrium analyses. Incidentally I cannot see whatever you have linked to in the first post. Please post the necessary information in the thread, this is also forum policy.

Fair, if very brief, comment.

Did Pauli claim this? It is not part of quantum theory, in fact it is contrary to quantum theory, which permits interpenetration of 'object', subject to Pauli's rules.

You have some good ideas and keen perceptions. Unfortunately you have jumbled some of these up where they do not run together. I am trying to help you separate them, as it will help see things more clearly. Alven's work has nothing to do with terrestrial conductivity. Terrestrial conductivity is not a simple subject, because of the size of earth relative to any electrical connection. Strangely Coulomb was the first to investigate the mathematics of this, although he did not do so in relation to electricity. The shape of the conductivity isobars is the same as Coulombs solution to the bulb of pressure (ie the pressure distribution) under foundations, which he did study. The conductivity plots are 3 dimensional, by the way. It is just plain wrong to think that any significant current flows through insulating rocks such as granite. The resistance of such rocks is enormous in any direction. I did not say that anything attached to the Earth is the same as the Earth I said it has the same motion. So any phenomenon due to that motion will be common to both. Both are affected by the magnetic field of the Sun (which is much weaker than the Earth's at the Earth's orbit) as both are in motion through it. It was this effect Alven was describing.

Congratulations on realising that aspect of an electrical grounding system. Most people misunderstand the action of grounding. No the Earth is not a very good conductor in that it has medium to high resistivity, and with some rocks eg granite very high resistivity. But it also has a very large cross sectional area so when we divide one large number (the resistivity) by another (the cross section) the apparent resistance is much smaller. But the real reason that the earth works as a ground is its abilty to maintain its potential, regardless of the charge flow into or out of it (for any practical charge flow we can create). I do not know if core spins at a sufficiently different rate to have a significant effect. But the strength of the field is sensibly constant over short times, at any point on the surface. It is the rate change of the field which induces the current, either by relative motion between the conductor and the magnet or by rapid change of the field. I am not sure if you quite picked up on my point about conductors attached to the Earth. Anything attached to or part of the Earth is not moving relative to the Earth's field, so no current is induced as a result. In the Early to middle part of the last century a physicist called Alven won a Nobel prize for his work on electric effects in gas plasmas. He also developed an electromagnetic theory about the electric effects in clusters of stars (which contain a lot of plasma) and the induced currents caused by spinning galaxies. The aspect of this theory is it uses simple conventional theory to explain many astonomical phenomena without a 'big bang' but it did not catch on, although it has not been disproved. https://www.google.co.uk/search?q=hannes+alven&hl=en-GB&gbv=2&oq=hannes+alven&gs_l=heirloom-serp.3..0i10l6j0i5i10i30.9047.10109.0.10812.7.7.0.0.0.1.110.734.2j5.7.0....0...1ac.1.34.heirloom-serp..1.6.609.PBpWrwbmRCQ

You need to work on your diagram before doing any calculations. Do you understand that the bike is not in equilibrium so you cannot use an equilibrium analysis directly? How is Fsr applied to the wheel? What is Fc ? Friction or circular motion forces? On the subject of the curvilinear motion, are you considering accelerations (Newton's solution) or Quasi Equilibrium (D'Alembert's solution) ?

No problem whatsoever, airing legitimate scientific thoughs and questions like yours is the purpose of this forum. Yes indeed the Earth carries its magnetic field through space around the Sun with it as it goes. It also rotates that field as it spins on its axis. In order for this moving field to create a current it must interact with a conductor, that is not moving with the Earth. In other words any conductor mounted on the Earth has the same motion as the Earth and so experiences no change in the terrestrial field due to the Earth's motion. So your pickup conductor would have to hang in space above the Earth. How would you get it up there? How would you keep it up there? How would you connect to it? Bear in mind that it could not 'hover' over one spot. Charged particles in space around the Earth are not mounted on the Earth and do not posses its motion. These are affected by the motion of the Earth's magnetic field as I indicated earlier. These are the 'winds' . Google has some very pretty pictures of the Van Allen Belts. https://www.google.co.uk/search?hl=en-GB&source=hp&q=van+allen+radiation+zones&gbv=2&oq=Van+Allen&gs_l=heirloom-hp.1.6.0l5j0i10j0l2j0i10j0.1406.6125.0.10859.10.10.0.0.0.0.125.1016.6j4.10.0....0...1ac.1.34.heirloom-hp..0.10.1016.iVBfU6UEgzo

By itself a magnetic field cannot "stimulate a current of electrons". That requires a source of energy, other than the magnetic field. The source of energy either supplies mechanical energy to move the magnet and its field through space, or It supplies electrical energy to cause the magnetic field to change in strength. The magnetic field itself is not a source of energy, just an relay transmitting energy from the source to the load. And the field can only perform this task if it is changing either by motion or by changing in strength.

Do you mean a transformer? Let us use this device as an example of how not to guess at the physics. By the way looking back, sorry about my poor spelling in the last post.

I have no objection to the namaste greeting. That is really good. I wish everyone was that polite. But your text is permeated with confusions about physics, and these are related to phenomena such as terrestrial plate techtonics, atmospheric effects and so forth. A magnetic field is generated by magnet. This filed only moves if the magent does. Solar winds are streams of charged particles emitted by the Sun. they do move and in doing so interact with the magnetic fields of the bodies of the solar system, according to Lorenz law. Does this help?

If you would like to discuss physics then let us discuss physics. If you would like to discuss far eastern religious philosophy, then surely the physics forum here is not the place. Please do not mix the two, they do not mix well. I suugest you look up the difference between a magnetic field, which is not moving, and a 'wind' which is and start your rethink from there.

OK, that is exactly what we do, only we don't call them points, lines or planes. We call them a small element dx and perform the summation on all the dx 's a small strip dxdy and perform a double summation on all the dx 's and dy 's a small section dxdydz and perform a triple summation on all the dx 's, dy 's and dz 's They do not have to be infinite sums, but if they are then the sums go over into integrals, as mathematic says. I am have tried to avoid this since I don't know your mathematical level, but the notation is A single summation becomes a single integral, which is just called an integral A double summation becomes a double integral, also called an area integral A triple summation becomes a triple integral, also called a volume integral There are some additional complications to this.

It is indeed fun and also very much a live and developing subject. The real question is where do you stop? Alongside the techniques you mentioned should perhaps be placed the calculus of variations and use of generalised coordinates. Probably the most modern developments are the applications to finite and boundary element calculations, powder and granular mechanics.

P and NOTP can only take you so far. Every designer of electronic logic circuits knows (or should know) that although logic circuits are based on the same propositional calculus as P & NOTP, there is a third option, known as tristate.

Acme, I think your Easter hangover must still be with one of us. I think you will find the text you attributed to me was actually penned by SamBridge (post#20) To continues with the geometry example I offered in post#12 Having defined a straight line in definition#4, Euclid went on to define a triangle in definition#19 as a trilateral rectilineal figure, contained within three straight lines. The theorem (he called them postulates) he developed from his axioms and definitions was that the sum of the angles adds up to two right angles. Now Euclid diod not know about spherical triangles, so if I offered a spherical triangle as a counterexample, disproving Euclid it is a good example of what ajb was talking about. Eulcid remains valid, with the terms of the definitions, but spherical triangles failure to observe the two rightangles theorem demonstrates that this theorem should not be applied to non rectilineal figures. So far as I can tell everyone is trying to tell you that the above is not so. Axioms are stated as true statements, without proof and have some independence from each other. Theorems are statements developed from these axioms in such as manner as to be true so long as the axioms are true. This process of development is called proof. A counterexample or other disproof would be of a theorem, not an axiom. You cannot disprove something you start out taking to be true, without proof. Thus a disproof would be against your development process, not the axioms. Of course you could one day find that your axiom has let you down and is indeed not true, which is why so much effort goes into testing them. But it is also possible that you could find conditions/definitions outside the original ones. This is the situation ajb and I are trying to explore here. Does this make sense?

Elsewhere I use the signature Do I look old? I don't feel old I don't feel anything till noon Then it's time for my nap. I definitely reckon that my avatar represents this statement.

imatfaal Agree entirely with your latest post but you mentioned your previous which made me go back and re-read. I cannot agree - there is no such sufficiently complicated system of axiomata that does not produce theorems that cannot be shown to be true and which must produce theorem which are not true but cannot shown to be false. This is Godels answer to Hilbert's Second (?) Question; no there is not a self consistent set of axiomata that produce all possible correct theorem but only produce true theorem. ie Anything complex enough to be interesting and useful will have self-contradictions, anything simple enough to not have problems is so boring to be of academic use only Sorry, I really cannot follow this or what you are getting at. Please explain differently.

Yes but the OP asked something slightly different. Yes, a single counterexample discredits a proof, but proofs are about theorems and the OP asked about axioms. There are no proofs involved with axioms. So all you can say is that a 'counterexample' highlights an area where the writ of one or more axioms does not run. This is what I described in my earlier post.

It's good that you understand it now.

I started this reply before ajb and imatfaal posted further, however the comments are still valid. I suggest you reread ajb's post#2. This was proved in the early part of the 20th century. But we need to go back a lot further. A system of mathematics (there are many, there is no single one) is a logically self consistent construct that builds on axioms to create theorems and other results. However it is not built on axioms alone. Axioms in isolation cannot provide sufficient information. The history of geometry is a good example. The original 5 axioms (he called them propositions) of Euclid were supported by 23 definitions and 5 what he called 'common notions', without which we could not have Euclidian Geometry today. Without definition 4 (a straight line) the rest is nonsense. If the analysis is not restricted to straight lines many of the results can be negated by a curved line as a counterexample. Exactly as ajb has indicated. In the 18 century (I think) one of the axioms was changed and projective geometry was born. (Some of) The theorems and results of projective geometry are at variance with standard Euclidian geometry, but the new system is consistent within itself and its altered axiom. In the 19th century, the fifth axiom was removed altogether to found Riemanian geometries. In the 20th century Geometry moved from discussion of figures and shapes as being the fundamental to discussion of sets, symmetries and groups.