studiot

This pdf article may well address what you are asking. It doesn't get any simpler but there is no heavy maths in it. Here is the first page

I don't follow the logic being presented. If the heat flux to space decreases with increasing concentration how does that lead to less warming since that basic chem eng equation: input = output + accumulation surely applies ? If the input remains constant, but the output decreases (heat flux to space) surely the accumulation (warming) must increase ? Well done for reading the graph correctly in that most of it is redundant. +1 For the last few million years co2 levels have been in the low hundreds of ppm. It has been several thousand million years since levels were in the thousands of ppm.

Agreed, I'm glad you figured it. Basically you have what you need for this topic in all the back posts now. Have a happy Christmas digesting it. Agreed. I'm glad you figured it out. Just to emphasis a couple of points. The Schrodinger eqaution is about particles, which is why we need to work in terms of photons. The solution, psi has some wavelike features. In the case of the slits; Between the source and the barrier with the slits psi looks the same and exhibits these simple wavelike features but there is no interference or diffraction so we cannot really distinguish between waves and particles, if we don't interact with the beam. When the beam reaches the barrier there is an interaction. As a result of that interaction there is a change of solution to the Schrodinger equation. However in this short section we cannot offer a solution (wavefunction) It is indeterminate. But the slit barrier is classed as an 'observer' because it interacts with the beam. Beyond the barrier the new wavefunction settles down and now includes the effect of the interaction with the slit barrier. If the geometry of the setup is wrong eg the photgraphic film or screen is too close we will not see an inteference pattern, but at a suitable distance, about 10 times the interslit distance the inteference/diffraction develops. This is a bit like the classical situation of nice tidy laminar flow in a pipe that leads to a sudden large pipe expansion and turbulence, followed by a funnelling back into the normal pipe diameter and laminar flow again. But this second laminar flow will often contain pulses or waves. The laminar flow regions are predictable, but the turbulent flow region caqn only be dealt with on a statistical basis. You now have all you need in the back posts here so Have a Happy Christmas digesting it all.

This is a really good time to review. A linear combination (superposition) of both slit one and slit 2????? Genady's formula is a linear combination of two fators. The effect of slit A and the effect of slit B That is the combination of the wave function of slit A divided by root2 and the wavefunction of slit B divided by root2 That is the new wavefunction after the barrier with the slits. The root2 occurs because, if you look back several members have noted that the probability of that wavefunction is proportional to the square of the wavefunction, not the wavefunction itself. It is observed that exactly 50% of the light passes through each slit which means that the probability of each is 1/2 (swasont has noted that probabilities must add up to 1) so when we take the square root of psi squared/2 we get psi/√2 This was also shown on the slits experiment attachment I posted as the pattern built up particle by particle. Superposition - everywhere A affect-influence B Yes electronics - current superposition is linear Yes, but both the defining equation (ohms law) and the linear combination are linear. Beam - Total deflection (concentrated, center deflection) is non linear Not quite. The formula the deflection due to neither load is linear, but these formulae can be used in a linear combination. LCAO is linear yes Schrodinger Equation applicable to atom Yes and to other particles. Each electron has a wavefunction yes Wave functions describe orbitals with 0, 1, or 2 atoms not atoms, electrons in orbitals. two atoms with one atom orbital each bond, creating a molecule and new bonding orbital; new orbital different from either two Again electrons in orbitals not atoms. A linear combination is used to calculate new bonding orbital? Yes adding a constant coefficient when nucleis are of different elements Yes but two constants, one for each nuclues and therefore each wavefunction (look back at my attachment) Surely entropy only applies to material things not 'potential things' ?

Well I don't see that anything here deserves negative point but I can only reverse one of them. After all you did what was asked and provided wht I take to be an English translation. However I do disagree with some of you claims, though considering the size of your post that is hardly suprising. Perhaps it is your English translator ? But surely there are many types of earthquake and many types of causes. The idea of exploding or expanding gases is interesting but cannot account for all earthquakes. This is just plain wrong. The Atlantic did not even exist until 175 MYA, which means it did not exist for 96% of the Earth's history. Whilst a complete axis flip is possible, though extremely unlikely, a change of 20 degrees or so is way outside the mechanics of the precession that is observed or can be justified. You mention the bouyancy of the Earth's crust several times. What do you mean by this ? I think that is enough for now as you seem to have mixed up several different theories and added stuff of your own.

12√ψ1+12√ψ2. So can you explain how Genady came by this formula ?

Let's put some flesh on the bones Microstates v Macrostates. Here is an extract from a lovely article

Genady has answered youquestion about the slits, with - yes you guessed it - a linear combination. OK so let's get a handle on superposition so we can see move on to see how is can be employed in QM. Like before I will start with a couple of classical examples which are easier to countenance. (I hope you have fun translating the English) Superposition basically means 'in the same place' By 'place' we mean that the effect of process B anywhere that process A exerts an influence. Linear superposition requires that "The resultant effect of B superposed on A is the sum of A acting alone and B acting alone" In other words it is a linear combination of A and B. I am being deliberately a bit vague about place to leave it open ended. Place can be a real region of space or it can be an abstract region of a theoretical mathematical space. Right so real world example 1 from electronics. So translated into electronic terms the superposition principle becomes When there is more than one voltage source in a circuit the effect due each (current flows) may be considered as if each were the only source and the resultant current flows obtained by adding the individual flows obtained. Here is a simple worked example. I have not given details of the individual current calculations, but only note they themselves are part of linear mathematics via Ohm's Law. Right so those are individual spot values, about as simple as you can get. I hope you realise that some currents are negative because they are going in the opposite direction from the assumed. The next example is from mechanics. A simple beam carries two loads, its own self weight and a point load in the middle. This time I have given a formula rather than specific numbers to show that linear combinations can be for more complicated things than simple point values. Superposition says that the deflection at any point (I am just showing the centre) is the sum of the deflections due to each load acting alone. As you can see neither individual deflection is anywhere near linear. Yet we can place them in a linear combination (( i like your word) package. So we come to quantum mechanics. Our model, the Schrodinger Equation, can be solved explicitly only in a very few cases and these are for atoms. Most of the material world is made of molecules, which are packages of atoms bonded together by chemical bonds. Each electron in an atom has its own wavefunction. These wave functions describe atomic orbitals, where the electrons reside. When two atoms bond they approach each other untill an orbital of one overlaps the space of an orbital form the other atom. Part of QM tells us that a single orbital can contain zero, one or two electrons. If both of these overlapping atomic orbitals contain exactly one electron they atoms may bond. That is a new 'molecular orbital' is formed, called the bonding orbital. This new orbital has a different wavefunction from either of its constituents. We are only just beginning to be able to solve one of these molecular orbitals directly with our best computers. In the meantime we do what every scinetist and engineere does. They ask themselves will a linear combination do the trick? Yeha enter KJW's formula (with a small adjustment) see 1 on my attachment. Try the orbital of the combination as the sum of the individual orbitals. This works directly for a few molecules for example the hydrogen or oxygen molecules, where both atoms are of the same element. But most molecules are made of a variety of elements. The nuclei of different elements have different 'pulling power' on electrons so to reflect this I have taken hydrogen and oxygen and added constan coefficients p and q to the linear combination to compensate for this, just as we did with ax + by + cz before. So this is the final form of the LCAO method of describing what may be the most important natural process to all of us. LCAO means Linear Combination of Atomic Orbitals and it works pretty well in most cases.

Any chance you could rewrite this in English for us plebs please ?

Suggest an old fashioned mechanical metronome. They can be had second hand very cheaply since electronic ones took over.

There have been lots of discussions about the the self, soul, mind, body, brain, consciousness and other notions disposition of in humans and other beings. Your impressively long list of references bear evidence to it being a very popular subject of discussion that has not been resolved. I like the writings of this Man.

Clearly I am not following you meaning. What about zero point energy ? please note I am working towards developing the LCAO bonding method as an final answer to Luc's question about QM and Superposition.

My apologies to @Genady for being so short just now. I was yet again loosing the tussle with the world's worst input editor, whils overcooking the dinner. Anyway thanks for quite rightly raising the question as it does point to our destination and prmpted me to elaborate more fully. Exactly so. You have got it in one. So back to the program. Please remember that if you can add two things this way you can add three or four or....... Can you give an example ? Do you for instance mean an unoccupied state such as an anti bonding orbital ?

Well Luc did better than you then because I assume that the small mistake was the missing z in As for you question, this is very fundamental and basic so I will labour the point. Let someexpression≡5 then we have 5 + 5 = 2 * 5 Yes ? Which is trivially linear. But the kicker is Let someexpression≡x4 Then [x4] + [x4] = 2 * [x4] even though x4 itself is decidedly non linear.

OK but it's still bottom of the list. If you are genuinely interested in verified information about what we know about the magnetosphere and geostorms, try reading the book by plasma physicist Melanie Windridge. It is readable by a lay person. Melanie has studied this in Antarctical, Canada, Scandinavia and elsewhere.

Many thanks +1. What an Idiot I be. The messages are white on black and have been going on for some months now. I just was quick enough to catch it before it disappeared this time.

Can anyone tell me the meaning this this strange message when often but not always pops up briefly when I log in ? I have arrowed the message on the screeshot. It shows the notifications bell plus the words " you have 5 personal messages " - the actual number varies. But as can be seen from the top there is only one message listed and it is not a personal one. I have never been able to find the alleged sender either . Who or what is C-19 ? Thanks.

John is quite correct to highlight threshold current (not maximum current) as the important parameter. +1 Threshold current is the minimum current at which lazing starts. Threshold current increases with increasing temperature. Laser diode characteristics are normally given at a case temperature of 25oC. Increasing temperature creates heat which increases case temperature so ther possibility of thermal runaway or at least degrading should be considered. Considering where you live and your requirements this could be more difficult as running the laser current too low on cold nights will increase the risk of laser dropout. Since absolute temperature is an absolute maximum you need to run the device between a current suitably above threshold for your minimum temperature but as far below you maximum current as you can, consistent with the requirement that the top level will be determined by your maximum ambient + 5oC (and you live in a hot area). Without further details of your requirement, but guessing from your other thread that you want the laser to sweep to and fro for a year I really can't be more specific on diodes. But I would like to note that lasers are inherenttly dangerous things so you need to consider safety in the illuminated area. Also note that laser diodes require a current controlled drive, not a voltage drive.

In English and in French we have letters, words, phrases, clauses, sentences and paragraphs, in order of complexity. That is we build up more and more complicated structures by combining simpler ones. In mathematics we really only have two basic building blocks; the symbol and the expression. Expressions possess several subtypes such as equations, statements of combination (like linear combination) and so forth. If an equation is roughly equivalent to a full sentence, then linked or simultaneous equations are equivalent to several sentences with a common link ie a paragraph. So ax + by + cz is not an equation but is a statement of combination of 3 different variables, combined to form one unit. each constant may be a different number, so the 'operation' (multiplication by a, b or c) carried out on each variable is different, but still linear in itself by our definition. But considered as a whole we have that if we multiply the whole by another number, say 2, we obtain 2[ ax + by + cz ] = 2ax + 2by + 2cz = (a+a)x + (b+b)y + (c+c) = (ax + by + cz) + (ax + by + cz) or twice our 'considered as a whole' combination. So if we condense this and say C = ax + by + cz then 2C = C + C So C is a linear combination. The point of my square brackets (did you nitice them ?) is that if we can show that [some expression] + [some expression] = 2 [some expression] Then the combination is linear. Next time we will explore the significance of this in relation to all those very important areas of applied maths I mentioned. L(ψ+ϕ)=L(ψ)+L(ϕ)

No it's the plus sign. So far we have only scratched the surface of 'linear'. We have only dealt with expressions that are linear in one single variable. The plus sign is how we combine variables or other mathematical objects (which may or may not be linear in themselves) To form expressions that are called linear combinations. Look back at KJW's expression - it contains a plus sign. Linear combinations have the form ax + by + cz + ...... where x, y, z are variables and a, b, c are constants. This is the underlying reason why linear mathematics is so wide, rich and varied. It covers maths from differential and integral calculus, differntial equations, matrices, fourier methods, linear simultaneous equations, and just so much more. We are off to the seaside for the rest of today so I will produce the next sheet tonight or tomorrow morning. Keep smiling.

Thank you. Yes indeed I misspelled 'to fast' it should have been too fast. As in many subjects, we distinguish between Pure Maths and Applied Maths. The pure subject is all about the theory of that subject, for its own sake. This is regardless of whether this theory is of any use or not. The applied subject takes that theory and uses it to study, analyse explain and predict phenomena in the real world to create things. For example the theory of structures is applied maths. For the next page we will need to know and understand a few technical terms The difference between an equation and an expression. The mathematical form of something. What functions , operators, mappings are. What a polynomial is. Please indicate if you are unsure of any of these so I can expand the explanation for this as I go along.

Paul died around 65 AD The first Christian Emperor converted 312 AD. This was the start of the Holy Roman Church. Prior to that I understand that Christians were persecuted on and off by the Roman Empire and survived as widely distributed small groups, I suppose you could call 'churches'. I also understand that those early Christians are described in sociological terms as 'primitive communists' , rather like some small isolated sects to this day. I also note, addressing the thread title, that even up to the end of the 19th century, most geologists were spurred on in an effort to scientifically prove God. An endeavour in which they discovered many things but spectacularly failed in their stated objective.

Great so we can carry on with the program in this fashion. Rather than worry about Chaos theory, which has little or nothing to do with Quantum theory, can I point out that there is something else basic in the post from KJW that I keep referring back to, that I have yet to mention. I will leave you for the moment to try to figure out what this or you can wait for the next sheet where I will introduce it. It's also good that you are beginning to tie together statements from others within this framework I am building for you. There is a huge area of Mathematics called Linear Mathematics; it is even more important in Applied Mathematics.

Clearly your recovery is pretty much complete. Welcome back. +1

Well I don't usually respond to this member as responses are never acknowledged, but I don't see this question as an ethical security issue. Windows has always done the logging noted in the OP, provided a text file and deletion facilities and the user has always had the ability to control the level of logging. No special 'spy software' is rrequired, nor would I recommend it.