studiot

Perhaps some California syrup of figs, Sir? Made in the good ol US of A.

Then how do you explain the rules for Snell's Law? This was the original classical distinction between wave and particle theory of light (and other EM rays) Which theory won ?

You guys' wish to bring manifolds and fields into it got me thinking. What does this mean for local and non local ? What in fact are these terms applied to ? The space or subspace itself, or some property or characteristic of the space? A good working definition of global might be to take the expression used to define the property at some point in the space and see if it can be used at other points. If it can be used at every point it could be considered global, otherwise local. So let us apply that to a field which occupies the space. First a scalar field. Say temperature. If we have a table of T at some points can this be used to determine T at the rest of the points ? Interestingly for the other thread, isn't the answer "not without time" ? In other words, not without additional information. So temperature in a space that does not include time is local. So how about a vector field ? Well a vector is an object with a magnitude and a direction (isn't it ??) I am going to start with field that has no magnitude anywhere. A direction field. And my definition for the direction is derived from a purely random function. So the direction at every point is purely random. So the direction of not even neighbouring points can be determined from the direction at any point, although all directions at every point ae derived from the same function. So is this field local or global ?

Here are some definitions and uses of 'regular' in Mathematics. numbers 3, 4 and 5 under 'regular' itself seem the closest for your purposes.

If your answers here showed some connection to reality that I can measure, I would do that. But so far it is all just assertion and no reasoning.

What book is that?

With respect, this is a prime example of not being specific enough, which you can't do in Physics. Whatever the cross section of the ring, they are a linear distribution of charge curved into a ring. Linear by itself would imply a straight line.

That too is a good simple question since (EM) radiation is made of photons. +1

Nice simple question. +1

Actually I did read you previous posts, and found them to lack detail. So help yourself and everyone else by providing the necessary detail. In particular, you show two circular tori of charge, one positive, one negative. You say these are rigidily connected and rotating about a common centre (I think, but I am not sure from the drawing since it is not shown there.) You also say that each individual torus is rotating about its own centre. This makes a compound rotation.

The rings are clearly shown rotating individually in the OP

Not quite for me. I am examining( the stability of) each individual 'ring of charge' in its own right. I am not talking about coupling to another ring. I'm sure I remember someone proposing this before, and me saying it reminds me of the Rowland Ring theory of magnetism. Edit however I see the swansont has nailed the coupling aspect pretty tightly.

You haven't answered my question about your proposed Physics. If you have a positive (or negative) charge distributed in the shape of a torus, what holds it together ? The charge distribution is as uneven as it is possible to be since you have a charge on on side of the ring separated by empty space from another like charge. This is a most unnatural situation by itself and contrary to all observation. You are basically proposing that Physics is different within the empty space inside the ring and within the torus of charge.

I say again, why not ? You have posited a circulating ring of charge (two in fact, of opposite charge polarity). What causes the charge in each ring remain in the ring, when electrostatic repulsion would cause them to break up and their charges to fly apart. Invoking De Broglie does not help you for his theory has an additional force due to the field of the nucleus to balance this.

As I recall it goes like this The First Law states that you can't win you can only break even. The Second Law states that you can't break even.

Why do they rotate and not separate ? A ring of current produces a magentic force at right angles to the plane of the ring, not an in plane force.

Glad you (briefly ?) enjoyed my thread. The first time I visited Turkey (1970) I cycled across and then caught ferries back through to the Greek islands.

A worth topic sir. +1 Input = Output + Accumulation

Thank you for your replies. I particularly like joigus' idea of simplifying to two hemispheres to start with. I had considered that. The reason for suggesting this is to return to the thread question what is time. I posed a static time free situation. The next logical step is to examine the question What extra properties would that adding a 'time' axis (dimension) would be conferred on the system, that adding an extra space axis would not ? The answer to this question would go a long way towards the thread question in Physics.

I just caught part of a TV program called Spy in the Wild. BBC1 1735 - 1835 today. I will have to complete it on iplayer /catch up. It shows the most amazingly realistic robotic artificial animals designd to fool real animal herds in the wild in order to video the. These robots look like the real thing, orangutangs, crocs, egrets, penguins, sea otters etc and have sound vision and realistic action. These are unprecedented scientific tools but watching them made me wonder the title question How soon before we can make a Terminator ? They are so nearly there. Watch the programme if you get a chance.

@joigus and @Markus Hanke So how would you gentlemen regard the following simple example Consider a sphere divided into many conducting lands, insulated from each other, and each charged to some different electrical potential. The Field within the sphere can be determined from a knowledge of the position and potentials of the surface lands alone.

The Open University (OU) lists over 900 free short courses in 8 categories. In the Science category you can look at Babylonian Mathematics, Chemical in drinking water, antibiotic resistance, Toys & engineering materials, working on your own in mathematics, telescopes and spectrographs to name but a few. Or you could learn/ brush up a new language in the language section Something to do in theses Covid times for all ?? https://www.open.edu/openlearn/free-courses/full-catalogue

Since you continue to talk at cross purposes with me I see no point in my continuing the discussion. Thank you for wasting my time.

There a problem with following the meteoroligical formula for the troposphere as this is based on measurements at many values of r. The procedure runs as follows. Using the general hydrostatic equation for a fluid under its own weight in a gravitational field [math]dp = - \rho gdr..............1[/math] and the equation of state with variable density for an ideal gas [math]\rho = \frac{P}{{RT}}.....................2[/math] We obtain the aerostatic equation [math]\frac{{dP}}{P} = - \frac{g}{{RT}}dr...............3[/math] Now direct measurement show that the temperature in the troposphere (where most of the mass of air resides) is a linear function of distance, with a slope coefficient, alpha, called the adiabatic lapse rate. [math]T = {T_R} - \alpha r....................4[/math] Measurements show that [math]{T_R} = {288^o}K[/math] and [math]\alpha = {6.5^o}K/km[/math] substituting equation 4 into equation 3 we find [math]\frac{{dP}}{P} = \frac{g}{{R\alpha }}\frac{{dT}}{T}...................5[/math] Integrating [math]\ln P = \frac{g}{{R\alpha }}\ln T + C............6[/math] and using the measured data to quantify the constants [math]\ln \frac{P}{{{P_R}}} = \frac{g}{{R\alpha }}\ln \frac{T}{{{T_R}}} = \frac{g}{{R\alpha }}\ln \left( {1 - \frac{{\alpha r}}{{{T_R}}}} \right).........7[/math] Now the points here are that this equation is experimentally observed over many data points. You only have the one single data point. Secondly this is an adiabatic calculation. So if you are going to follow it you must have adiabatic conditions in the tunnel. Thirdly the trposophere is about 11 km so this is the range of r. This allows this analysis to assume g is constant over that distance, which is reasonable. but the radius of the Earth is nearly 6 and a half thousand kilometers so such an assumption is unwarranted.

Thank you for posting that. +1 I think that an underlying reason you can do all these mappings (Grassman and Hodge algebras etc) successfuly from dimension m to dimension n and vice versa goes back to Cantor since they all have the dimension (cardinality) of the continuum. Once you have R, you have everything else.