studiot

Here is a most interesting applied maths (fear not you only need the four arithmetic functions to +,-, * ,/ to follow it) discussion which in cludes the answer to your question and may help with many of you other ones. https://risingentropy.com/matter-and-interaction-in-quantum-mechanics/

Whilst I can see this is not the best place to put an introductory post, I really can't see how it merits a negative rep point so I have balanced that out. William, welcome and start with a clean sheet. Well done for starting engineering college , I look forward to productive post from you, but please think about whare you place them.

Aren't these all provided for in 'the standard model' ? But how is this classical physics ?

There is no such thing as pure energy and the hot death of the universe is a self contradictory myth. I respectfully suggest you need to properly understand what these terms mean before you can understand entropy, which then really becomes very simple.

Nobody is mad at you, we are just trying to guide your thinking so you can see for yourself. 1) Black body radiation. I stick a poker in the fire and it glows red, then yellow, then white. I don't see any quantum interactions here and you have specifically limited this discussion to quantum matters. 1) Photoelectric effect Here there is an interaction because an electric current is produced when a light shines on certain materials. But there is nothing that suggests light needs to be a Field. Swansont mentioned one of the characteristics of this effect that lead to the conclusion that this must be a quantum effect since classical EM wave thoery will not produce this effect, but a different one that is not observed in practice. Read the attachment I previously posted before you reply. I don't think I have posted this analogy since you have joined but maybe it will help a bit. Think of a stream bed with an smooth clay or sandy bottom. The stream flows in steady parallel lines with no disturbances. This is an example of a Field, called a flow field. Now change the bed to a rocky bottom. The flow changes and eddies appear around some of the rocks. A few of these eddies are transient but many are persistent. These all constitutes a disturbance in the field and involve greater energy due to the rotation of the fluid field at the eddy location. Noone pretends that the eddies are points, they occupy real volume. So within the field there can bee seen persistent disturbances, of higher energy than the surrounding general field. These disturbances can be regarded as self contained entities, and if they relocate they move as self contained entities ie they have particle like characteristics This is a very simple picture of the proposition 'a particle is a disturbance in a field'. Does this help ?

Car batteries weigh somethng like 800 to 1500 lbs depending. Here is a list of some specs. https://motorandwheels.com/electric-car-batteries-weight/ However yous is a hiogher end battery so I would expect it to weigh in at the higher weigher, something north of 1000lbs. Particular manufacturer's wesites will tell you more specific information for their particular models.

Since I didn't see it before and I don't see it now, please enlighten me. Interaction of (what) with (what) ?

Thank you, but you also said a deal of other stuff, which is confusing as to your intentions. 1) I see neither a field nor a particle nor an interaction involved in black body radiation. 2) Not all fields are 'quantized. 3) Einstein's contribution was most definitely about the interaction, although as it takes two to tango, you can't simply concentrate on one or the other.

The short answer is "They don't" Actually that is not what Planck postulated, nor did he introduce the term quantum or quanta, that was Einstein a few years later. Rather than arguing back and for about it, here is the official Cambridge University history.

Please clarify the scope of this discussion. What do you mean by particles ? And is the discussion to be limited to particles as related to quantum mechanics ? The idea and knowledge of both waves and particles goes back several thousand years. Obviously these ideas have been extended and refined greatly over that period. In that time we have discovered phenomena that are best explained in terms of particles and also phenomena that are best explained in terms of waves and some phenomena that could be explained in terms of either. At first some aspect of each particular phenomenon allowed a distinction to be made. For instance the direction of deflection in refraction. But late in the 19th century phonema were discovered that fitted neither model (you haven't forgotten that both waves and particles are just models have you ?) completely and contradicted each model in some (different) way. QM was originally introduced as a way of reconciling phenomena that fitted this category. As many more such phenomena were discovered in the burgeoning scientific world qm grew in importance and value and developed to what it is today. A better model that describes more phenomena. But it is still only a model.

Sorry if the post was a bit rambling. What part was not clear?

Short version answer. No. Please also rember that there is more than one type of 'entropy'. Sadly, because the same distribution laws are followed by the the type of thermodynamic entropy you are referring to, which has a physical reality as a property, as the some of the purely abstract laws of information entropy the same term is used. Whilst there is much truth in this, see also my note above about other types of 'entropy'. A good reference for this is What is Random ? - Chance and Order in Mathematics and Life. Beltrami

Thanks, but it's more than just 'at distance' v small scale. There is also 'close up and personal'. Clasically we don't bat an eyelid with the concept that a system passes from one state to another, but we can only know the difference between before and after, not the values of the 'state variables' during transition. QM is also state bound or state based and has the same restrictions. Transitions beween states are defined by 'before and after' and are not instaneous. The closer we know the energy difference, the less certain we are about exactly when such a transition will happen. When two particles collide, where exactly is that collision ? At the point of 'first contact' ? Partway between their centres ? When they coalesce ? Again there is some position uncertainty. Matched by the small but finite distribution of the particles' masses which makes ther momntum slightly uncertain.

I thought that the number of solutions to the general polynomial is always exactly equal to the degree of the polynomial, which in turn is given by MAX(n). There may, of course be repeated or complex solutions in this reckoning.

I see QM uncertainty as being a manifestation of the fact that ours maths tries to place properties as concentrate at a point (in the coordinate space concerned) when they are not so concentrated in fact. Alternatively what does it mean to say both "The electron wavefunction has a presence throughout all space" and to say "the electron is also at point x in space "?

I will have to look closely at your references, but sorry I thought you would have no probs finding the plato article. https://plato.stanford.edu/entries/intuitionism/ As for 'information'. The mathematical theory of information is seriously limited to its domain of definition, which most of mathematics is of course. And people so often forget this limitation. Maths inormation is about subjects which are carefully specified. So there is no mathematical definition or description of indirect forms of information. As an example, I don't know if you have seen the pigeon advert for the Vauxhall Mokka - (I don't know what it is called in the US) - I don't know of any way of translating the advertising information into maths or logic, but they certainly get their message across to any human. Look forward to it !

Thank you for posting this +1. I would warn that intuitionism is in area of (mathematical) philosophy the Stanford Encyclopedia (Plato) is highy questionable about.

I can't possibly imagine why this post would have offended anyone, so I am adding a counterbalancing+1. Willem has actually told us about one of his limitations and, i believe, asked for help. I am not exactly sure what is meant by a shift operation, but I can guess. That would certainly be one way of putting. Not my personal favourite however because I am used to the shift operator being something from numerical analysis, not something defined by a programmer. But if my guess is correct then W is right.

I expect he means orthoclase, which is the softer of the two main minerals in granite.

I don't know how long is a long time for you, but do you remember old fashioned steam railway engines or steam powered traction engines, steam rollers or other steam propelled equipment, or have you seen pictures of them ? They had one thing in common, they were big and very heavy. All that machinery to provide steam propulsion is very bulky and heavy. And yet their makers knew about thermondynamics and mechanics and made them about as efficient as it is possible to be. With various grades of liquid or liquified gas fuels it became possible to use different and far lighter mechanics for the propulsion drive. Now that is where the internal combustion propulsion is at today. A far ligher drive mechanics meaning a far lighter chassis meaning far more efficient use of the fuel. Furthermore it doesn't require to carry either a large and weighty tank of water or additional weighty mechanics to recover the water from the steam and recycle it. And don't forget that some heat is extracted in cold countries to heat the passenger cabin. So yes, it is possible but just not practicable, there are better ways to use the fuels. Note also the even more and smaller engines such as racing car engines wear out far more quickly than engines designed for road vehicles. It is somebodie's law that says the more efficient and highly tuned a car engine is the more servicing it needs and the shorter its service life.

Yes +1 I would just lik to add to this part "in fact you could turn a ball into anything at all in this manner, no matter how big or small. " the following in response to the OP's assertion. You are right the the proposition works the other way round as well, but adding to Markus comment that it anything at all does not have to have the same shape as a ball and could have 'holes' in it. So no you don't have to exclude turning a pincushion into a pumpkin. It is true however that doing this topologically (ie continuously) means you can't make a doughnut into an apple.

Hello rufus and welcome. Good, well founded discussion is always welcome here. I can assure you that whilst many scientists and mathematicians are too busy in their working lives to sppend much time on the history, this is not the case with all of them. Some even make a career out of it and I can recommend some top notch material as a result. For myself, as a retired applied mathematician I understand fully the pressures of 'getting an answer' in the working world. It is called "shut up and calculate" But since retirement I have been able to look around at the History and Philosophy of Science and Maths which has enabled me to fill in many gaps and achieve a more rounded view of it all. edit. Please note (did you read the rules here?) that for your first 24 hours you can only make 5 posts - so use them wisely - This is a very effective anti spammer measure.

OK I'll accept that it is not homework. I do not see any essential difference between looking up on Google and asking a real person so Granite has a Moh's hardness of 5.5 - 6.5 and decays by chenmical weathering to clay, which was (and still is) used to make bricks and tiles and of course Hammurabi's famous clay tablets for writing cuneiform on.

What was the question ?

I have repeatedly said they do not separate. But I have also repeatedly said they were not mixed in the first place. Convection requires a source of heat. I did not say anything about heatng the bucket or having the bucket at 0oC. You seem hung up on diffusion, yet you ar starting to admit that other mechanisms and processes are acting. That is good. Now let us take the experiment a little bit further, remembering that my bucket was freely suspended in the open air, clear of walls, rooves and so forth. How quickly would the bucket of hydrogen empty compared to a bucket of plain air, noting that other air would diffuse into the bucket in both cases ? In the experience of every engineer I know said bucket of hydrogen would empty immediately and pretty well all the hydrogen would go straight up, the plume widening with ascent as Seth says. Whereas the bucket of plain air would take a long time to homogenize with the plain surrounding air. This is always provided that both the hydrogen and the original plain air in the bucket were originally at the same temperature and pressure as the surrounding air.