studiot

Paradoxically, it's very difficult to define a field in Physics without some mathematics! +1 I would say that in Physics if, in a simply connected region of space(either abstract or physical), some quantity (again either abstract or physical) has a defined value at every point in that space then a Field is said to exist in that space. thjis means that a Physics field may be either abstract in the sense of a direction field or have some physical presence as in a stress field. Mathematiclly a field is a non empty set of elements equipped with two binary operations, usually called addition and multiplication.such that the set is a commutative group under addition and the set, with the exclusion of the zero element, is a commutative group under multiplication and that multiplication distributes over addition. This makes some sets of numbers to be fields and other sets of numbers such as the integers not fields. The smallest mathematical field has two members 0 and 1. But they don't have to be numbers, they could be other symbols such as T and F or H and C or 'square' and 'circle' or 'facing forwards' and 'facing backwards'. However it is conceivable that an (infinite) Physics field variable has values running through all the integers, but is still not a field in the Mathematics sense.

I like the connection between coarse/fine graining and fractals, I had not though of it that way. +1 But connections to number theory ?

So you can't support your claims, you are only dreaming. I am self consistent in my like of lasagne, so I am pleased to eat some. I don't see any mathematics in that unless it is in the 10 of 10cc in their words "Life is a lasagne." Go well.

Can I borrow your rotating microscope ? You will get more help if you 1) Post a large enough trace to read 2) Post it the right way up 3) Post any thought you already have as to identifying the peaks ? This is, after all, a university level question.

Yes the title refers to number theory and 'the field'. Both have very specific definitions and places in Mathematics (they are mathematical terms). Some of their properties are borrowed for (extensive) use in Physics and other sciences, but, and I have already pointed this out, The type of field you are referring to is not a field is the mathematical (algebraic) sense of the word. The Physics definition is not compatible with the formal algebraic definition.

Looks like a corian worktop. They suggest ammonia, (you mask will come in handy and wear gloves) https://www.corian.com/-use-care-

If what you say as gospel is actually true you will be able to support it with mathematics won't you ?

+1

Go easy on the poor soul, PHI, he's just been watching too many marvel movies during lockdown. +1

What on earth does this have to do with number theory ?

Contrast this statement With this one If you don't/can't read responses how are you going to be able to respond (anywhere) to them ?

Short and sweet again. +1 Lack of Gravitation was the reason Einstein moved on from SR to GR.

Thanks for the reply, yeah it is beginning to look like a dodgy connection where the lead enters the back of the plug.

A funny thing happened, leaving me perplexed. A week or so ago a pair of usb powered + 3.5mm jack speakers stopped working. On removing the backs I saw that one of the leads connecting to one speaker itself had come off so this morning I soldered it back on. After testing the speakers on an older laptop where they now worked I returned the speakers to their original laptop where they also worked again. This evening the speakers had stopped working again, on firing up that laptop. Yet they started came back to life immediately on plugging them into the older laptop again. Back to their normal laptop and -- No joy no workee. Back to the older test laptop -- no problemo. Back to their original no workee. I am very puzzled. Another set of the same types works perfectly in either laptop. Final test the dead? speakers do not display the blue on light when plugged into a usb wall socket supply. Any help welcome. Is any other info needed ?

Especially relevant. +1 I stopped bothering with this thread since it left the title subject of number theory far behind.

Very quickly There have been some very good animations of the 'distortion' caused by speed. 1) Ask Janus, he posted some. Also this earlier thread, I havent had time to review it though. The university of Oz seems legit.

The point of spacetime is that the timelike and spacelike dimensions have a quadratic relationship, not a linear one so you can't separate them. 1-D space has no curvature. Space has to be at least 2 -D to have curvature. Please go back a few posts and read (the translation of) what Minkowski actually said. At the top of page 88 in my attachment. Euclidian space is the name given to space with the usual or standard metric distance function [math]dis\tan ce = \sqrt {x_1^2 + x_2^2 + x_3^2 + ......x_n^2} [/math] for n dimensions. The space can be physical or abstract.

What are you talking about ? [math]1 + n/\left( {n/2} \right) = 1 + n \times \frac{2}{n} = 1 + 2 = 3[/math]

Yes indeed, +1. However, as ever, life is more complicated than that. To the best of my knowledge Minkowski didn't write any books, only papers and died prematurely. Here is an extract from one of his papers on the subject. The first 13 pages of this paper are as Markus implies but doesn't say explicitly. They are couched in terms of the real numbers. That is all variables are are measured in real numbers. Minkowsk then introduced imaginary numbers (note not complex numbers) to the mix, near the end of the paper. I am not sure if the reference at the bottom of the left hand page to Schutz acknowledges that Schutz did this first. Some later authors formalised this by starting with the inclusion of i. The use of the 'mystic' formula from natural units is also interesting. [math]3x{10^8}kilometres = \sqrt { - 1} \sec onds[/math]

Inaccurate ? Damn perhaps that's why I never win those lotteries.

Note I wrote this earlier but obviously never got round to posting it. Sorry. I seem to be having all sorts of trouble with postings here and elsewhere just lately. Just think. We can't calculate the weather on our own planet over 10 days. I tell you what. When I win all the lotteries in the world at once I will buy lots of supercomputers from @Sensei and help you. How does that sound ? 🙂

No it would not be wrong to create a global picture, but you would have to do it as you describe in your second paragraph because GR functions are pointwise functions. You could create a standard net and calculate deviations from it, as opposed to calculate absolute (ie direct coordinate) values but you would still have to do this point by point. There is an analagous pair of approaches in fluid mechanics, respectively called Eulerian and Lagrangian.

Two neon atoms in an otherwise empty bar ?? Surely the sound is the question who is paying for the drinks ? 🙂

Indeed so. +1 I would just add to that :- The volume occupied by any wave has a time value attached since all waves expand from thier point of origin over time. So you can't just say the sound occupies 20 litres but you have to say "it occupies 169 litres after 1 second" or similar depending on when you measure it.

Rather than indulging in a non productive slanging match about mostly off topic material I suggest you go away and study Alfven and Lerner. Alfven got the 1970 Nobel Prize for his work on such theories.