studiot

I think you need more black coffee. Was he not only following your lead? Since you don't want to discuss the basics with me I will leave you with this 1950s University Physics textbook extract, which directly addresses what seem to be you basic misunderstandings. In particular it provides a simple mathematical derivation of the 1/r relationship from the 1/r2 Law. Please be aware this applies in any number of dimensions for Newtonian gravity. Also note the explanation about infinity and the negativity of PE and the difference between PE and potential. As regards the reasons for our universe being a 3 + 1 universe: Vector statics is complete in a 3 spatial universe and vector dynamics complete in a 3 +1 universe, but not a 2 spatial universe or a 2 + 1 universe. As I have been trying to lead you towards. In the early days of Einstinian Relativity, there was much discussion about the possibility of other universes with A spatial and B time dimensions and the consequences if these were assumed. Eddington provides a good mathematical reasoning to discount these for our own in his book 'The Mathematical Theory of Relativity'.

Perhaps you have no takers, because, like myself, others are confused as to where you are coming from or going to with this question. Please clarify.

Somewhere between a quarter and three quarters of the world's population suffer this. Is that good/bad? Thank you for your reply. I made that comment not realising that you might have meant something totally different from what I understood your statement to mean. That is why I subsequently asked you to clarify it. I still don't know what you meant. Only a few agree is quite clear, but what they agree to is not. Do you mean that they are prevented in some manner from speaking whatever they want or do you mean that they should not speak whatever they want (common colloquial use of can't) ?

You have made some very valid points in this thread, but I believe Vashta is talking about our Universe. Further the rules of SF require our Universe as this was posted in classical Physics. I agree, but would go further and suggest that GR is inappropriate in this thread, except as a passing mention. +1 Incidentally Markus said solve Laplace, not deduce it. I have plenty of expositions of Newtonian gravity involving Laplace, I just want to help Vashta find the appropriate format. Of course solving Laplace will not get us the potential. It will get us the potential function, which is different. It is confusing to those just studying this subject that the word 'potential' is used in several different ways. I actually must now apologise and correct an incorrect statement I made earlier about the units. I said that potential energy and potential (difference) have the same units. This is not quite correct. PE has units of energy, potential by itself or PD has units energy per unit mass.

You have placed your thread in the Mathematics section, which is totally independent of Physical Science, as are the respective disciplines definition and use of the concept of zero. Please clarify what answers/discussion you are seeking. You are correct in stating (in the title) that in Mathematics Zero (by itself) is a number. I note that your 'absolute zero', 'virtual zero', polar opposite, etc hint at mathematical set theory which leads to a mathematical notion of zero, but using unusual terminology.

Why don't you just clarify your originally ambiguous statement ? Who are the few and what do they agree with ?

Actually none of this is a solution to Newton's Law of Gravity. Newton did not use potential theory - It had not been invented in his day. In modern notation Newton's Law of gravity is [math]F = G\frac{{Mm}}{{{r^2}}}[/math] This is a straighforward algebraic expression and a solution means that you have a value for all the variables, except one so you substitute them into the expression to obtain the unknown quantity. So instead of arguing at cross purposes, Vashta how about posting your maths working to obtain whatever you have obtained ? Then we can help you tighten up your maths. As regards the curl, do you understand the concept of a vector that represents a turning moment ? I am convinced that this is the key to your difficulty reconciling 2D and 3D. Actually

You mean I can't blow my own trumpet ? But Zap, I love Daleks.

No, I was keeping in mind this is a discussion about Classical Physics. Working in terms of densities - something per metre, something per square metre, something per cubic metre is a very common technique. Of course if you go to two or three dimensions your integrals become area or volume integrals, which is why I keep recommending using the one dimensional case for starters. How about answering my questions, they are designed to help ?

Yes indeed but surely it is pretty damn obvious that the only way we can establish/measure how long the protection from a vaccine or course of vaccines will remain effective is to keep monitoring until the vaccination becomes ineffective.

I'm not sure what your idea of field dilution is or entails. However I have some suggestions. If you want to work in terms of what I suspect 'dilution' to mean, I suggest you work in terms of energy density not energy. This will also work more easily in any number of dimensions. This would be energy per unit length, area or volume as appropriate. I attempted to address to your idea of 'leakage' by pointing to the vector curl, but you have not responded to this. Perhaps I have misunderstood your explanation of this issue ?

The universes in this case cannot tend to a state of lesser energy. The total mechanical energy of an isolated system is constant.

If that were the case then the gravitational field would contain an infinite amount of energy. The point that I already made is that whilst the length of the bounding curve is infinite, the area under it remains finite. https://en.wikipedia.org/wiki/Improper_integral

I very carefully didn't say gravity was acting in this case, because some of what was offered was correct. In fact gravity is (also) responsible for the ordinary surface waves in water that we see in the ocean. However two members seemed to be suggesting rather strongly, that fluids cannot be elastic or support elastic waves. How would you describe a sound wave in a fluid, if not as an elastic wave ?

Somewhere between a quarter and three quarters of the world's population suffer this.

It's called the area-moment method for the bending of cantilevers (which is what your type of torque wrench is) https://www.engineersedge.com/material_science/areamoment_method_13659.htm +1

Gravitational potential is not 'energy' The PE results from a potential difference A potential is not the same as a potential difference, although they will have the same units. Take an isolated single body, possessing mass. There exists a gravitational potential around it. But there is no energy, potential or otherwise involved. Now introduce a second massive body. Potential energy now arises from the configurational interaction of the two bodies and perhaps also kinetic energy. This is the same for electric and magnetic fields. It is also worth noting that the potential energy is conventionally set to negative infinity at the source, reducing to zero at infinite distance. I repeat it is easiest to try these questions out in one dimension first.

The concept of elasticity has meaning in fluids.

Hello Vashta, This question of yours is about upper highschool / first year college level. Your presentation shows you are thinking hard about the subject +1 for that. However you seem you be having some trouble matching the classical Physics (where you have placed the question) with the Maths. This is not suprising as you will likely not yet have gone far enough in integration theory. First let me state quite plainly that gravity works well in one, two, three or more dimensions. It is probably easier to explain in one dimension what you need. The definition of the gravitational potential is an integral yes. But it is a definite integral. Using the definite integral avoids two problems. The constant of integration 'cancels out', so enabling the fact that you can choose any position as your bas point (as others have mentioned). It allows the use of the limiting process in evaluating an integral if one of the limits of integration (don't get these two different uses of the maths term 'limits' mixed up) is infinity. I assume you are aware of the difference between a definite and an indefinite integral ? But you may not have come across what comes next. If we integrate the work done F.dx from -∞ to ∞ or 0 to ∞ we have a problem. The curve is infinite, but we want the area under it to be finite as it represents the energy in the gravitational field. This type of integral is known as an improper intergral. Techniques for dealing with these are usually left until first year maths in college. OK in order to integrat this we need an expression for F in terms of x This is where Newton's Law comes in. At this point it is worth comparing Newtons Law for gravity, Coulombs Law for Electric charge and Michells Law for Magnetic Monoploles, which all have the same format. However there are also some not so suble differences. Gravity is the simplest because no other information is required Gravity has one direction (attraction) or sign (positive) only, in addition to magnitude. Electric fields have both direction or sign ( positive or negative) and magnitude. Magnetic fields have direction, magnitude and rotation or vorticity or vector curl. This last is most important because the vector curl represents a pointer or way into an extra dimension to the ones in use. So for a 2D surface carrying the mag field the curl points into the 3rd dimension and so on. There are no corresponding pointer vectors in the cases of charge or mass. Other differences are that it is possible to 'shield' agains an electric or magnetic field or introduce a physical device to set that field to zero. This is not possible in the case of gravitational fields.

Hello Cookie, perhaps if you rephrased the text of your question, so that you explained exactly what you are asking, you might get some more help. Did the electric field (strength) not come it to it somewhere ? When you reply you should also indicate your thought as to what might happen. (better to be wrong here than in your actual homework answer)

There has been a move in the UK NHS to invoke the technique of 'social priming' to improve workplace communications during these stressful times. The work of Yale Professor John Bargh has been put forward to support this. https://www.nature.com/articles/d41586-019-03755-2 However there has been more recent work to suggest this is less effect than JB found https://digest.bps.org.uk/2019/01/02/now-john-barghs-famous-hot-coffee-study-has-failed-to-replicate/ So my question for discussion here is In the light of some recent rather bitchy threads, could we learn anything at SF to improve our own communication skills ? I will apologise in advance for discounting my usual typolexis.

Why would you want to do this ? Lennard-Jones is one of a large number of empirical energy potential functions, obtained by fitting power law equations to observations, where the independant variable is distance. But all these have at least two parts a repulsive part and an attractive part. So the result is an interplay between the repulsive and attractive forcesand their variations ove the distance. On the other hand Gravity has ony an attractive part and additionally operates over a very different distance range. https://en.wikipedia.org/wiki/Interatomic_potential

Is that you excuse for not answering the technical questions I have asked you ?

Did you have something to say ? I'm sorry, could you speak up a bit please, the adverts on your post seem to be drowning out whatever it is you want to say.

Hello and welcome. I expect your 'prof' was talking about the Cantor set or Cantor dust. This reference may be a bit advanced but has some good diagrams https://en.wikipedia.org/wiki/Cantor_set Ask if you want something simpler.