studiot

Can the properties of a wave be changed without interacting with its particles? Is that (relative velocity) because of the observer effect? Scattering imo means a change in direction due to a form of interaction. 'A form of interaction' can mean anything. Frequency would be one such property. I had in mind the Doppler effect. That is too wide a definition. Yes scattering is a deflection of path. But scattering is a random effect. From a particle point of view it means that every particle is scattered a different variable amount in a different variable direction. From a wave/geometric point of view the same applies to rays. For light of a given frequency The turning of all particles or rays by a fixed or set amount within a single transmission medium is called reflection. The turning of all particles or rays by a fixed or set amount when passing from one medium to another is called refraction. Light of different frequencies may be separated by refraction as the turning is frequency dependent. Concentrating waves into regions of high and low intensity within a single medium or widening a geometric beam past obstacles within a single medium is called diffraction.

Not at all unfair. I said "evaluate to" which is the most common use of the equals sign. I agree is also is used to represent "defined as" although there is a perfectly good and proper symbol available for that meaning. That is of course the identity symbol which is what some that is defined as is. Unfortunately, x was also 'defined' as a number, causing endless confusion. My question is simple, and if the definitions provided in this thread would enable the proverbial Man on the Clapham Omnibus to determine what x is for any conceivable situation, I would be glad to have it pointed out to me. (25,25), if I ask someone else does not cut it. And I still don't know what process goes on inside that bracket.

That is not an answer. The difficulty I face is that what appears on one side of an equation must evaluate to whatever appears on the other side. [ Remember you wrote x = (x,x) ] Your assertions do not explain, back up or develop how this can happen with what you wrote. In particular using your discussion with uncool, whatever appears in parenthesis must evaluate to x by some process. What is the process? You have not defined it, even for uncool. I have told you this several times and have been left to guess what sort of process you might have in mind. You introduced the mention of ''tables', so when I tried to discuss tables with you , you backed away and said that I should forget tales. If they are so forgettable that they have no bearing on your assertion why did you introduce them? So what the hell is going on in those parentheses that something can evaluate to "itself, itself" ? What does it mean to say A number, x = (a number, x ; a number , x) Which is what you have continued to assert. Introducing further symbols like z1 and z2 or anything else that has not been defined only serves to further confuse matters. Here is a way in which splitting the number makes some sort of sense (to me anyway) Consider the number 25 (let's avoid 1s and 0s for now) We cannot directly combine the 2 and the 5 to make 7, because neither 2 nor 5 nor 7 equals 25. Twentyfive means two tens and five units and could be written, (2,5) although that would be rather clumsy notation. Considered this way the two tens and the five ones obey all the usual rules of arithmetic you have been arguing with uncool about. I doubt this is what you mean, because I am still forced to guess.

Perhaps I should have said that omega 1, omega2 and omega 3 are the angular velocities about the 3 Euler axes. A, B and C are the positive constant moments of inertia about these axes. Without perturbation the system is stable. If we introduce even the slightest perturbation to omega 2 the instability you are modelling results. If we introduce that perturbation to omega 1 or 3 then something different happens. I was asking if your animation can show what happens then? What equations are you solving to generate the vectors?

I understand the first part: For every element, X, of the set of real numbers, R, and with the sole exception of zero, It is the next part of the statement that is unintelligable. What is x, what is (x,x) and what is the equals sign doing there? Above was my question and below was your non-answer. Question What is the equals sign doing there? (Correctly followed by a question mark to tell you that it was a question) Answer I am not using the equal sign exactly as intended. No further explanation of how you have redefined a basic and standard mathematics symbol. Assertion x = (x, x) Question what is x? No answer whatsoever and as far as I can see you have not mentioned 'x' again in this thread, except when quoting another.

Yes this can be true, but where is the guarantee that the photons will interact, they may not. What about the other circumstances that can change the properties of observable light, such as relative velocity? I am concerned about this assertion as it suggests you mean something different from the rest of us by the word 'scattering' Would you please explain what you mean.

If you look at page 1 of this thread, you can see that we had an adult converstation spread over several posts where I was trying out a new idea in the hope of understanding your proposal.. Unfortunately you eventually baulked at answering my direct question, offering me all sorts of other things instead, but no answer to my question. I reserve the right to call that half listening, not trolling and most certainly not a personal insult which I have not proffered to you throughout this thread. Rather, and having withdrawn as above, upon seeing you making some sort of progress with another, I thought to offer some encouragement in the way of a +1 point. I call that biting the hand that feeds.

I'll second that +1 to uncool and also +1 to conway for (half) listening.

Glycerine solution. Look here to find the % appropriate to your density requirement. http://www.aciscience.org/docs/physical_properties_of_glycerine_and_its_solutions.pdf

So the tighter inequaltity with the half is the correct one in the case shown. But in some circumstances the bigger uncertainty may be appropriate. However the question of what the undertainty refers to is worth discussing further if anyone less impatient than the OP wishes to do so. It is quite possible to generate examples of either with the 1/2 or without in classical situations, which may be easier to understand.

In a perfect world rotation about any of the three Euler axes is stable, an governed by three non linear coupled differential equations. [math]A\frac{{d{\omega _1}}}{{dt}} = \left( {B - C} \right){\omega _2}{\omega _3}[/math] [math]B\frac{{d{\omega _2}}}{{dt}} = \left( {C - A} \right){\omega _3}{\omega _1}[/math] [math]C\frac{{d{\omega _3}}}{{dt}} = \left( {A - B} \right){\omega _1}{\omega _2}[/math] Where constants A < B < C Because of the couping the slightest perturbation of [math]{\omega _2}[/math] will lead to regenerative instability of rotation about the intermediate axis as your vids show. The equation set can be linearised and the linearised equations set still exhibits this instability. Would you like to explain how your animations improve on this? Also the above calculations show what happens if you introduce the perturbation into either [math]{\omega _1}[/math] or [math]{\omega _3}[/math] Can you animations show this?

So suppose a stream of quantum particles of mass m moves along the x axis with speed v as shown. Let us try to determine the y coordinate of the particle by placing a slit of height [math]\Delta y[/math] in its path. The De Broglie wavelength, lambda, is [math]\lambda = \frac{h}{{mv}}[/math] It is an observed fact that diffraction will occur as the particles passes through the slit (this is a single slit and not the double slit experiment) causing a new direction and momentum to the aprticles, within an angular spread[math] \pm \alpha [/math] where [math]\sin \alpha = \frac{{ \pm \lambda }}{{\Delta y}}[/math] The attempt to determine the y positionof the particle has led to an uncertainty [math]\Delta {p_y}[/math] in the y componeent of the momentum. [math]\Delta {p_y} = 2p\sin \alpha [/math] Thus [math]\Delta y\Delta {p_y} = 2p\lambda [/math] or of the order of 2h However the particle may be considered anywhere within that range so it only provides the outer limits. This boils down to the greater than or equals sign [math]\Delta y\Delta {p_y} \ge \frac{h}{{4\pi }}[/math] Some years alter it was found convenient to introduce a revided version of Plank's constant and add the bar to the h. So [math]\hbar = \frac{h}{{2\pi }}[/math] In this format the HUP becomes [math]\Delta y\Delta {p_y} \ge \frac{\hbar }{2}[/math]

When I've complete my sketch in about 5 minutes, I will post a nice easy derivation, without the difficult maths. Meanwhile look again and check if your sources use an inequality. The Uncertainty Principle is not an equation.

Since neither are correct what is the book? And what are X and P ?

I'm trying very hard to be heard here, without shouting. Your plots are titled "Buildup of gravity in a sphere" Perhaps this is where your difficulty lies? I (and I believe the rest of the members responding) have been talking about gravity outside a sphere. The distribution of gravity inside that same sphere can be quite complicated. The study of gravity inside the sphere (or other shape) is known as Geodesy (Greek for the shape of the Earth) and the world standard textbook for this, which I used as my postgrad text in that subject is Geodesy by Bomford. Oxford University Press. You need to be aware that the 'sphere' reaches to its highest point - Mount Everest in the case of the Earth. The existence of the Himalaya was originally deduced by the deflection of survey plumb bobs due to increased gravity on one side. Today satellites and aircraft routinely conduct gravimetric surveys which reveal all sorts of local variations in the strength and direction of gravity and thus tell us about the underlying rocks. But these effects are all 'within the sphere'. Gauss' Law still holds

Well it can in New Zealand. https://www.theguardian.com/world/2017/mar/16/new-zealand-river-granted-same-legal-rights-as-human-being

Distribution is not the same as composition. We have an old saying in English ( a trick question) Which weighs more a pound of lead or a pound of feathers?

You can't draw power that isn't there. That's called - yes you guessed it - conservation of energy. Now please tell us why you haven't commented on the Elihu Thomson stuff swansont introduced and I gave you more about. That really is the fun part of basic electromagnetics.

The composition of the matter have no effect on gravity , I only claim that the number (amount) of protons +neutrons is proportional to gravity . This (p+n ) is the same we put on the scale every day , and only reserve I have is that speed of light stays the same for Ti . NA because mol is the only quantity with weight(known by the grams /NA (that I know ) , in this case 1kmol =kg = 1000 NA (p+n). Since kg*kg =kg2 *N2 division by 1000NA give kgNA , I divided by kg and NA have no quality . Your question on conversion factors I do not find. Timo, look carefully where you are copy/pasting from or you will be attributing quotes to the wrong person as you have done here. I didn't say that and have not been discussing composition or Avogadro with you. I came back to this thread to add something to my last post but you got here before me, so please consider this as further explanation of the attachment in my last post. No doubt you will notice the derivation uses the Normal component. This is because the normal (and outward normal at that - are you aware there are two normals?) is the only part of the flux that can pass through the enclosing surface without being balanced out by a corresponding oppositely directed contribution from another part of the enclosed mass. In other words for every component at a point on the surface perpendicular to the normal there is an equal an opposite component somewhere else on that surface. Thank you for taking notice about my comment on chemistry, did you notice I had responded in that thread?

You missed my point. The total flux through a closed surface is independent of the angle of incidence on that surface or how smooth or wrinkly that surface is. It is rather like that old theorem from Euclid that all parallelograms on the same base have the same area, no matter how skewed they are. Notice that the derivation refers to the total mass enclosed, the distribution of that mass is unimportant ouside the surface.

Gauss's Law refers to the integral of flux through a closed surface. The only directional effect is (for 3D) in or out.

Thanks for participating in the community. +1

Nor am I sure, but if you don't thinks solitons are matter, try standing in the way of the Severn Bore. I have heard of people modelling sub atomic particles and photons as solitons. There is some stuff about this is the University of Cambridge Applied Maths series books. Solitons an Introduction Drazin and Johnson, but they understandably concentrate of calculation methods. I don't have Drazin's other book to check.

Doesn't the sun shine out of your President's _ _ _ ? So perhaps you could dispense with the satellites if you placed your solar panels in the right location.