studiot

Yes it looks like it. In mathematics there is nearly always more than one way to do something. No it is not advanced maths. I think somewhere in these many pages I have already mentioned signed numbers and sign conventions. There are plain 'ordinary' numbers we use for counting, measuring etc. They may be whole numbers or fractions. We use them for the four basic operations of arithmetic add - subtract - multiply - divide. But often we want our numbers to represent more than this. For instance up or down ; electrical positive or electrical negative ; clockwise or anticlockwise ; left or right and so on. To do this we establish a sign convention. The most common convention is that we attach a plus or minus to each and every number so the numbers we use are then called signed numbers. We do this because we can benefit from using the signed numbers in the same formulae we use for basic arithmetic. However in order to make this work we must learn some extra rules for these basic processes. The Kahn narrator is using signed numbers, not plain ordinary numbers in his column vectors. does this help ?

This brings me to an important point about published papers. The publisher controls the length of the article, not the author. The grand sounding Empire Survey Review was in those days the size of a penguin paperback and colour printing had yet to be available. I was constrained to one and a half pages so I chose to lay it out in a way that would mean more to surveyors than to others, even mathematicians. Any whole circle bearing lies between 0 and 360, but there are only 180 degrees in any triangle. Surveyors wish to use right angle triangle trigonometry for easy calculation. So the whole circle of 360 degrees is divided into 4 quadrants of 90 degrees each. A suitable right angles triangle can be chosen in each of the 4 quadrants. There is, however, a price to be paid for this convenience. That is the equations are different in each quadrant. This menas that the first thing a surveyor has to do is decide which quadrant his bearing lies in and then he can choose the correct equations.. This is why my flowchart is laid out as it is, for ease of programming. There is no need for a loop back as the outcome must lie in one of the four quadrants so asking is it in the first quadrant, second quadrant, third quadrant in formal sequence will identify 4 quadrants ; if the answer is 'no' 3 times the bearing must lie in the 4th quadrant. Any surveyor will already know this so I did not need to spare too much paper on it.

Remember the spin quantum number is responsible for the magnetic properties of the substance.

OK so I was able to see what the narrator was talking about. He did go through it very quickly, not only because he was distracted by a malfunctioning pen but also becasue the issue has nothing to do with vectors. It is more basic than that and stems from the problem many people have with signed numbers. you have two signed numbers viz minus 4 as well as minus 4 again. That is one use of the negative sign -4 ; -4 The signs belong with the numbers. they do not signify any operation at all, they are part of the (signed) number. Then you have an operation - in this case subtraction. So you have minus 4 take away (or subtract) minus 4 (-4) - (-4) So the negative sign inside the brackets is a different animal from the negative sign between the brackets. For the operation subtractio I recommend the rule To subtract - Change the sign od the second quantity and add to the first. minus 4 subtract minus 4 Change the sign and add So we have minus 4 add 4 (-4) - (-4) = (-4) + (4) = 0 does this help ?

Well I disagree. Firstly atoms in the plural were mentioned in the quote I responded to. Secondly it specified that this was the only way atoms (not electrons) could gain energy. The scenariao you describe refers to electrons gaining energy, not electrons per se. Secondly I also referred to a gas, in which the atoms or molecules may well be isolated for the purposes of this context. Yet those individual atoms are constantly bumping into one and other and in that process gaining or loosing energy. Therefore it is not the only way an atom can gain or loose energy. Thirdly even in a solid steel bar the influx of EM radiation affects atoms individually. The same photon does not excite two or more atoms. Finally the full quote I responded to follows a chain of reasoning commencing with the true statement "Light energy is lost and gained in discrete amounts limited by the energy differentials between electron orbits within the atoms." But this is followed by the definitely untrue statement that does not follow from the true premise. "This is why atoms can only gain or emit energy in discrete amounts." It is untrue because atoms isolated or otherwise can gain energy in other ways as I have noted some of them.

There are very many Khan videos. We need a link to the one you are referring to along with a time in the video to look at.

Sure. As to the non discreteness what happens to the atoms if I take a bar of steel or a bottle of gas and heat it up ? Alternatively what happens to them if I take them on the Edinburgh Express at 125 mph ? Or if I simply lift them 2 metres into the air. ? And what happens if one atom simply bumps into another ? One will gain energy, the other will loose energy. I think our mutual friend has forgotten about heat, kinetic and potential energy. Now for the poetic bit. The photoelectric effect was one of the two experiments that demonstrated that in some cases atoms can only take in some forms of energy in discrete amounts. But if you consider the whole experiment not just the sexy bit, energy input of too low a frequency will also be absorbed as above, but the expulsion of an electron will not occur. For example shining infra red light on ssomething will simply heat it up, shining UV or X rays will cause photon emission. Hope this helps

Actually no it is not a book for experts. Anyone can gain from it. I often find it fascinating learning the story behind many discoveries. It is not written in research paper style, but is 'popsci'. You might be suprised to find what can be learned when competent scientists put out their thoughts this way, as opposed to journalists and others. Of course that is not to say that all scientists are 'good' and all journalists are 'bad'. The great scientific discoveries are often made when someone (not necessarily a scientist) spots something that others have missed. My point about Roengten was not what he discovered (X Rays) but what he did with the information and how he published his paper, which is a very interesting and human story. Here is the short fifth quadrant paper. It was published in the Empire Survey Review in 1986 so has yet to reach Big G and M$. This puplication then had a circulation of perhaps ten thousand surveyors around the world. You should have no trouble with the maths.

But that was a pretty damn good summary of relevant aspects of quantum theory in refutation. +1 I think it is poetic that the very experiment that led Einstein to propose quantum theory and the word quanta also completely refutes this claim.

This thread is about reading papers. However I am happy to see it extended to writng them as that is the other side of the coin and the discussion is quite good. I am reading a new book by a particle physicist at CERN called 12 experiments that changed the world. It starts off with Roengten Many work like this today for fear of being gazumped. So how exactly is an artificial dumbness going to produce a paper on any such work ? AI only knows what has been fed into it. I am responsible for a handful of papers, all of which contained original (though of much lower import) work. Ask AI "How to use the fifth quadrant when converting eastings and northing to bearingas and distance or vice versa ?"

Hear Hear. I don't know what they do nowadays but when I first went to grammar school back in the early 1960s we were issued with exercise books to write in. I was suprised to receive two exercise books in at least one subject (definitely History was one). We were supposed to write 'rough notes and working' in class in one book and put a 'fair copy' of any exercise essay in the other for marking. I suppose this was in part preparing us for that method CharonY mentions.

Are you thinking of Fermat's Last Theorem ? Wiles proved it in 2003. https://en.wikipedia.org/wiki/Wiles's_proof_of_Fermat's_Last_Theorem But I don't see why that was a joke.

Ahem, pardo n me. Just to avoid any misunderstanding; strong not string ?

Let us change my diagram from the axes of a graph to this little story. My girlfriend and I live on either side of a crossroads. Fig A shows that I live 4 miles down East road at the end of the arrow. Fig B shows she lives 1 mile along West Street at the end of the arrow. How far must I walk to visit her ?

Here is the link, plus some discussion elsewhere https://www.wolframphysics.org/index.php.en https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/

Thank you, that was very clear. +1

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I don't know what you mean by 'discretized' but density has no meaning at the atomic and molecular scale. You need a sufficiently large sample to use a density model of composition, which is why I asked earlier about sample size. I am not aware of a satisfactory answer to this issue.

Back in the day in common with many students of technical subjects, I couldn't afford HiFi so I set about building my own. This led me to have a long term hobby interest in electronics. I used to buy technical magazines and had long loosing battle with them over the placement of advertisements. My view was (and still is) that I love and want advertisements. But in the right place. I used the articles and the advertisements in entirely dissimilar ways. The advertisements I went carefully through in case they offered something I wanted to buy, which I frequently did. But, unlike the articles, the advertisements went quickly out of date and I tore them out and threw them away to reduce paper storage. The articles I kept (and still have) as useful in the long term. So I tried to persuade publishers to separate articles and advertisements on separate pages as far as possible.

I see the original course (in pdf) I referenced is still available https://www.umsl.edu/~chickosj/c365/lectureNMR2.pdf 6 pages NMR2 through NMR7 https://www.umsl.edu/~chickosj/c365/lectureNMR7.pdf Are these any good ? You presumably know enough Chemistry to understand functional groups in substances that are being analysed ?

@bangstrom What you are doing is a good example of what swansont was gently warning you about. I have already indicated that I am having trouble correctly understanding what you mean and here you are crowing about using physics terminology quite differently from everybody else. And then you have the gall look down on me when I try to clarify what you are saying, I am reporting yours replies as discussing or arguing in bad faith.

Since you are studying Physics, may I introduce you to this little book, whcih will answer all your questions and more. When working with a subject, even one I know well, I like to keep two (sorts of) books on the subject. A very basic book that explains things, including the maths, but is not too big and encyclopaedic. A treatise type book that works out all the special cases, wrinkles and details for when I need to delve deeply at a particular part of the subject. Susskind has written 3 titles covering much of Physics using of the first type of book and this is the one you need. It contains the whys and wherefores of quantum calculations, including useful tables of results, for entanglement, density matrices and compares with classical analogues, discussing the difference between quantum and classical versions.

A someone who suffers more than most from what you describe because I tend to write longer posts than most one liners, I fully sympathise. +1 Yes I have yet to find a proper answers and have posted pictures of what I see here. Nor can I tell how any of this is benefitting anyone, since the last thing I would ever do would be to buy something that pops up and interferes with something I am currently engaged in. And, of course, those with suitable ad blockers who thing everything in the garden is rosy so they will never see and therefore buy as a result of these adverts either. I would certainly hate loosing someone of your calibre over this.

This is what I mean by a derisory dismissive reply. What you understand by a dimensional constant is clearly not what I understand from the way you have already tried to use it. Here is my understanding of the meaning. I hope you will agree that miles (or any other distance) are not hours (or any other time). As every schoolboy used to be taught the distance walked is proportional to the time taken, at constant pace. He is then taught that this can be converted to an equation by introducing what is known as a constant of proportionality. Some proportional relationships are only used occasionally so the constant is just called the constant of proportionality. In the example case we use it so often that it is given a special name - the speed. In some cases the constant of proportionality is just a number because the two variables involved either have not dimensions at all or the same dimensions. But we have already agreed that variable distance is not the same as the variable time, So the constant of proportionality also performs a second duty. It 'converts' dimensions of time into dimensions of distance. In that case it can legitimately called a 'dimensional constant' and will be necessary even if the conversion is 1 hour walked converts to 1 mile covered. Note that I have used units rather than the more general dimensions, which brings us to our second point, which you clearly did not understand from you answer to my question which was to find out if we can usefully employ the standard dimensional notation. Nor did I mention " the inverse of LT". I mentioned L T-1 to the minus one which read the product of L and the inverse of T. And yes you did indeed mention the ratio of distance to time, or if you prefer the fraction distance over time. Anyway it is a remarkable and very useful fact that all the variables or quantities in Physics can be put in terms of a handful of basic ones. These are for Mechanics Mass M, Length L and Time T. We add to this Temperature (usually greek theta) , and a brightness or illumination measure for optics and a single electrical variable , formerly charge but now current density. So the dimensional constant has a suitable value to convert hours to miles or milliseconds to micrometre or whatever these are the units. It also has the dimensions to convert different types of physical variable. So speed has the dimensions of distance over time or L T-1 This makes the schoolboy equation distance = speed times time dimensionally correct since L = (L T-1) x (T)

You might like to compare with the Joule Thomson effect where cooling does take place this is a good pdf https://byjusexamprep.com/liveData/f/2021/12/joule_thomson_effect_76.pdf