studiot

Actually it is what I said. I even posted an excerpt from a renowned textbook describing such a situation, the coincidence two spaces viz momentum space and position space at a particle.(post#88).

A few notes. Firstly Xerxes had confirmed what I said elsewhere, that there is more than one space associated with some fields. He refers to the tensor space and the dual space, although I sis not mean that particular combination for my purposes, I think it proves the point. Secondly all the tensors you will meet can be represented as square matrices, but not all square matrices are tensors. For instance the matrix 0 1 0 0 0 1 1 0 0 is not a tensor. Second order tensors produce square matrices like the above, third order tensors produce cubical matrices and so on. I see a sixth order one was noted.

Pity you dismissed my comment so summarily. On the Lochee Road in Dundee there is an 'environmental monitoring' station, which records weather data and sends it back over the same grid the street lights and houses are connected to. I still think you had a mains borne false triggering from such a device. Perhaps your neighbour has a remote weather station or home automation gadget? Your timescale is a bit vague, and you have not said if the computer is still working and misbehaving?

Put it in a 'spoiler (There is one in the 'special BB code drop down - third icon from the left top row on the input box)

Reminds me of an elecrtical repairman's story I once heard. He had installed an automatic security light outside a property. Shortly after hed was called out because the light kept coming on and staying on during the night. Several tests later there were no faults to be found with the installation. So in desperation he kept watch one night. When the light came on he found a semicircle of local cats sitting facing the light. In your case I would look again (if you can remember it) at the geography. Some street lights are light operated, some are operated from a remote timeclock control signal, sent along the mains. Even early computers had various 'wake on' settings in BIOS. They are never truly off, and can be activated by a suitable remote signal. Perhaps you pc was picking up such a signal from a street lighting or other remote station.

Here is an authoritative reference on the history of Field theory (advertising suppressed) Berkson : Fields of Force: The Development of a World View from Faraday to Einstein. Original hardback 1974

Congratulations, you actually asked a question instead of proclaiming your gospel. And wow, swansont quickly gave you a helpful answer +1 Let me offer you two pieces of advice. Firstly Einstein's clocks and thought experiments all refer to perfect or ideal clocks and other apparatus and perfect observers. Nevertheless secondly, you need to distinguish between practical difficulties and theoretical ones. It is the practicalities that cause difficulties with simple pendulum clocks. However this thread is about the measurement of G and perhaps g, not the measurement of time. I suggest starting another thread if you want to discuss that. Now that you have found out how to get help from swansont ask plenty of questions, he is a real expert in the area of time measurement.

Very good reference Eise. +1 However a word of warning about it. The preferred reference in the page on electronics is to Tony Kuphaldt's monumental work. Unfortunately Tony uses the reverse polarity convention from the rest of the world in his circuit theory. This is not technically incorrect but can make for many difficulties when reading what the rest of the world writes.

Well Xerxes has certainly spelled it out for you in gory detail (What he said is true), But one word of warning. Xerxes has not been lazy, he has been kind to you and written out all the summation signs. (he has actually put a lot of work in) Tensor addicts have a secret convention that they do not bother with the giant sigma sign, they regard it as 'understood' whenever you see the double suffix. Let me know if you need a translation to rough guide English.

I think the original proposal has now been disproved by many good counterexamples. However the subject of pattern, symmetry and symmetry-breaking is interesting and worthy of more discussion. Here are a couple of extracts from Philip Ball The Self-Made Tapestry, Pattern formation in nature. The interesting idea is that patterns form as a result of symmetry breaking or reduction of symmetry and that the most symmetrical patterns are the most boring. He gives many examples. So the circle has the greatest symmetry of any plane figure, a snowflake is the result in the reduction of symmetry. A uniform gas is 'randomly symmetrical'; apply a symmetry breaking force and the structure becomes more complex and more interesting.

Nice counterexamples +1

Be careful what you wish for, lest it comes true. H+ is only a bookkeeping quantity in relation to water. Look here https://en.wikipedia.org/wiki/Hydronium (also calleed hydroxonium and here https://en.wikipedia.org/wiki/Hydrogen_ion Safety note Passage of electric current will only get you hydrogen and oxygen gas and a large bang if you are not careful. Specify your needs more thoroughly.

I am not an expert in astro work, although I have carried out both gravimetric and astro surveys. Thus I asked a real expert. Are you such an expert ? If not, why did you presume to lecture me as though you were? It is fairly obvious to anyone who has done gravimetric work why swinging pendulum clocks are fine for measuring little g, but inappropriate for measuring big G. It is also obvious to anyone who has ever set up or moved a grandfather clock. If you don't know the answer to this, why don't you simply ask? I'm sure Strange is bursting to tell you.

For those that like reading, Roger Penrose devotes a whole chapter (chapter 29) of his book The Road to Reality to this question. He examines 6 different interpretations, including Copenhagen, in some (mathematical) detail.

The following might help. A space is the set of all possible values, whether we want them or not, of a given condition. So the usual cartesian 3 dimensional space is the set {x,y,z} where x, y and z take on every possible numerical value. x,y and z are then said to form a basis for the whole space since we can generate the entire catalog of triples from them. We can restrict this in two ways. We can select a subspace of the whole space. For instance the plane z=0 is a 2 dimensional subspace of {x,y,z} since it ranges through every possible value of x and y and does not need or use any values of z. This subspace is also a subset of {x,y,z}, but not all subsets are subspaces. The cube bounded by the six planes x=0, x=1, y=0,y=1, z=0, z=1 is a set of triples, {x,y,z}, where 0<x<1 , 0<y<1 and 0<z<1 Naturally there is a difference in some rules for subspaces and subsets or there would be no point in making the distinction The difference between a subset and a subspace is important in the definition of real world fields, which can occupy a subset or subspace.

Also make offline backup copies of all your datafiles now in case the virus also introduced one of those ransomwares that become active after a month.

How is your understanding of matrices? I think they are a good place to start for those who want the Physics, but not the detailed maths. Most tensors in the physical world are second order so can be written as matrices.

If you haven't already done so, delete all non Microsoft browsers, especially Chrome, restart and then reinstall after the full cleanup. Some further tips. Revo Uninstaller is better than Microsoft uninstaller If possible run CCleaner as soon as you have enough control of an infected machine. This substantially reduces the amount of crap malware scanners have to wade through, speeding them up. Run it again last thing after everything else. Run HitmanPro as well as adw cleaner. You will have to manually delete anything it finds or pay for the autodelete. The french program JRT.exe is also a good rogue finde in the early stages to help regain control of an infected machine.

No, just as examples the stress tensor, the strain tensor, the dielectric tensor, and the inertia tensor all have 9 elements and the same form but very different units. Tensors properly don't have units, but their elements may have units. Some may refer to the units of the elements as the units of the tensor. Some tensor elements are simply coefficients or just plain old numbers, some have units. I think all the elements in a particular tensor must have the same units as each other. Perhaps someone else will confirm that. Having the same units as each other does not necessarily make the elements of the same type, for instance the stress tensor contains shear and direct stresses which are different, although they enjoy the same units. Well sort of. Tensors are essentially point functions so some tensors do not involve a cell at all. Those that do involve a differential cell in the calculus sense that shrinks to a point in some limiting process. Some 'cells' are composed of differential elements, dx, dy and dz in the engineering 'control volume' sense and actually exist in the same space as the x,y and z axis. That is they have measurable length along these axes of dx, dy and dz. For some quantities resort has to be made to the phase space referred to in the post#88 in the Fields thread.

To move this thread forward let note that it is a spin-off from a history thread. So to look back at the history of gravitational measurements I note that from Kepler and Newton to the 1930s the main thrust was to determine big G, the universal constant. Here is a table from Newman and Searle (1957 edition) : The General Properties of Matter : showing the state of knowledge at the end of that lengthy period. Between about 1880 and 1930 another g, little g, was coming to prominence as the science of Geodesy matured. It can be seen from the table that D, the average density of the Earth was also becoming considered when the last (Heyl) measurement was listed and that now new information was added on G in the next nearly 30 years. Newman and Searle also give an account of the detailed study of the factors that might be able to affect the value of G, in the latter part of that period. Good quality gravity measurements are not cheap undertakings so I surmise funding considerations played a part Geophysical exploration by gravimetric surveying was becoming possible so the impetus moved from big G to little g. For instance Clark at the NPL obtained an accuracy of 2 parts in 10-8 in 1940. The measurement of little g does not suffer the same objections to I am not an astronomer so I will leave it to a real one to tell us what is accurate enough for astro/cosmological purposes.

Although you will win no prizes for fine prose, I see no reason for anyone to mark this down twice. Particularly as it contains the good manners to thank someone (me). So +1 from me.

Not intending any condescension. I am trying to pitch my replies at an appropriate level and I seem to have hit that mark with the extract from Baden-Fuller. Exchange or mediating particles form no part of classical theory, so I don't think your question was stupid at all, just off topic. Since I have not managed to explain my contention that the field variable may require a space of additional dimensions I will try the extract method again since I have found someone else who may explain it better. Here is a short extract from Beiser : Concepts of Modern Physics. The author has the knack of introducing just enough Mathematics at just the right level to promote understanding without obscuring the Physics. Not only that but the excerpt provides a bridge from classical to quantum theory that you seem to want. Note he describes the situation for a system of particles, using position and momentum. You should replace that by a system of values of the field variable, using appropriate phase variables for the particular field. Note that this can incorporate the derivatives Xerxes referred to - I never denied this only meant that it is not the whole story. Hopefully readers will get on better with this.

All Physics theories are models and suitable for some purposes but not for others. This subforum is about Classical Physics and the models are not suitable for QFT. If you want to study Quantum Field Theory there is a sub forum provided. You should be aware that models may differ in the answers/solutions they offer to particular questions and we chose the most appropriate by experimental comparison with reality. Sometimes the models offer the same answer but one is much more computationally difficult than the other. Would this one not then be the one of choice? Here is an example: An electromagnet lifts a car to the crusher. If we model the electromagnet as a slug of ferrous metal encased in a solenoid and the car as a free slug of ferrous metal, provide a formula for the necessary current to lift the car and the resulting magnetic field between the electromagnet and the car. Now this takes a few lines using Classical Theory and I once had a debate (elsewhere) with a Doctorate in this subject who visits here occasionally. He said no magnetism does not work like that and produced at least three pages of fancy more advanced mathematics to come up with the same formula! So if you want to learn more about the subject, all well and good. There are several lifetimes worth of material out there. But please don't try to pick off odd isolated statements to try to prove your (mis)conceptions about something.

Yes indeed. But, with respect, that is because you are only looking at what you have said, not what I have said. Did you try my practical demonstration? No, nor have I said I disagree. I fully understand what you are saying but it is not relevant. You need to go beyond that to the logical consequences of the definitions and compact notation you are using. Things often look a bit different when worked out in full for particular cases. Mathematicians like to use compact generalizations, but Engineers have to make particular cases work. Yes this is the same idea. +0.1 for remembering it There are no virtual photons in Classical Physics and no the force exerted by a magnetic field is not mediated by photons. Paradoxically the force can be calculated by virtual work in the Classical Physics interpretation of a magnetic field, much more simply than a more advanced treatment, which yields the same end result.

You are just dodging the issue. Where is the scale axis the the scalar constants ak lie on, for it is not parallel to any of the existing axes xk. Try this practical demonstration. Take a piece of gridded paper, draw a pair of ordinary axes and mark the point 5,5. Now at the point 5,5 draw a vector of magnitude [math]\sqrt 2 [/math] at 45oso that it takes up zero room on the paper, because one thing is for certain That vector does not extend from x =5 to x = 6 and y = 5 to y = 6 You require a new coordinate system in a new space, joining the old coordinate system at one point only, to be able to accomplish this plot.