studiot

How about this one HCL + 10H2O = HCL(aq) + 16.61 kcal

I didn't say you could but not all Scientific equations are, in fact, dimensionally consistent.

Thanks for the response, koti.. Comparing means creating some sort of ratio For instance the statement this glass holds three times as much whisky as that one obviously compares two volumes. For that purpose I suppose dimensional consistency is required. Not sure I'm with you, Mig. Dimensional analysis is unit free insofar as you can measure in any quantity you like, for instance cords, so long as the measure is the same for both.

So you expect us to drop everything and obey your rules, huh? What about reading the rules of this community / forum and following them? Why wasn't this speculation posted in the correct place?

I am not sure where to post this so have used Philosophy (of Science) to allow latitude in exploring this subject. I hope it will make a welcome change from the current Philosophy subject we have surely now done to surely death. Dimensional analysis is a very powerful technique in Science and is one of the things that distinguishes Science from Pure Mathematics, but to repeat the title, Is it necessary for all equations in Science to be dimensionally consistent?

While you are thinking please re read very very carefully what swansont told you. The point to note is that he was including the environment in the quantum answer about the electron.

Hello Fred, this seems a reasonable question. The difference is in the molecules, not the fields. The guy in the first video said that "water molecules are polar". What he meant was electrically polarised, because water molecules are bent. I am not sure whether the flame deflection in the second video is due to oxygen or carbon dioxide molecules but both are straight and not electrically polarised. However both have a magnetic moment, though the oxygen one is much stronger.

No I did not say they interfere, which is a wave phenomenon. The slope of a river bed affects the running of the river, it does not interfere with it. Asking questions is good, but please take notice of the answers.

So we are back to classical are we? What happened to the second part of my last post. You quoted it, but did a pretty girl walking by distract you from actually reading it? Yes a moving electron is another word for electric current is it not? And electron beams are focussed by electrostatic means in CRTs and other devices. That means deflected by force from another electric charge. But there is something quite diffeent about the quantum view and the classical. In the classical view you can draw a free body diagram around the electron and only consider its properties in isolation. You do not have to woryy about its environment. By contrast, in the quantum view everything is a system and if that system contains 'particles' then you must also consider the environment of those particles, you cannot use free body diagrams that is you cannot consider the particle in isolation without its environment.

I'm sorry but no. In the vibrating string (the one dimensional classical equation) the connecting variable, y is a space variable. The string occupies (more) space or moves about in space when it vibrates. However in Schroedinger the connecting variable takes up no space. Indeed. Nor will you until you can abandon the miniature solar system view of this subject. In wave mechanics the electron is confined to a particular region or part of space and smeared out over all of that region. This smearing has variable density and the Schroedinger equation provides the value of this density at every point.

That bloody flyout thing is a typical example of overengineering. It is far too easy to get the wrong thing and it took me at least 6 months to find out I could undo that. Simple separated static red or green blobs were easy and so much more fail safe. And , as I said in my thread on the subject, you can't be sure what you have actually done at the end of it.

Yeah you have to read a lot of texts to find the stuff between the lines. So order a large drum of midnight oil.

I think we are talking at cross purposes here. I put it down to this poxy website software that insists on presenting everything to me so tiny I get it mixed up. Looking closely in the clear light of day I see that last night i mistook your small r for a small t. Sorry for that. Don't forget I am starting with the one dimensional case so 'radial' has no meaning. I also indicated that I took some trouble to post a derivation of the Schroedinger equation starting with the classical wave equation but can't find it again. This derivation does indeed use an 'inspired guess' solution by separation of the variables.

Indeed time does not have negative values.

Well really x represents only 1D space. It is easier to work in a single space dimension to start with. But you also need time to set up the equation. going back to an earlier post of mine in this thread, which I think you didn't properly catch, You start with a solution Let the solution be a function of space and time y(x,t) Do you understand this notation? Now to find a time independent solution you separate the variables by Do you understand this ? This allows you to reduce the solution to y = A f(x), where A is a constant. But you are not yet done because x can take on any value between plus and minus infinity it is encompasses all 1D space. What you want is for your x to refer not to a single point but the region (of 1D space) where the wave acts. If you like to picture it this way, the whole of the wave must be concentrated between two values of x, say between x = -0.5 x10-11 metres and x = +0.5 x10-11 metres which is the diameter of a hydrogen atom. So for the Schroedinger equation the value of the solution y (I am trying to avoid greek letters) between x and (x+dx) give the electron density between these values. So if we add up (sum) all the small dx from x = -0.5 x10-11 to x = +0.5 x10-11 this must add up to 1 stating the obvious fact that a bound electron must be within the atom. You can also regards it as the probability of finding an electron at a particular x. But then you loose the time independence because you must specify how long you are prepared to wait observing that particular point! dammed if you do and dammed if you don't.

+1 Why does software have to work the other way every other industry? For example motor vehicles originally had solid tyres then went pneumatic. Some had no heater and no roof so drivers had to dress up like an artic explorers. They had starter handles bfore starter buttons. etc etc etc BTW this is what I mean. This screenshot was taken several minutes after upvoting.

Some modern physicists identify an aether with modern presnetations of spacetime. For example the book by nobel physicist Wilczek is accessible. https://www.amazon.co.uk/Lightness-Being-Ether-Unification-Forces/dp/0465018955

Before when I clicked on the upvote, the number incread by 1 so a post that had no votes yet would change from displaying nothing at all to 1. Today I noticed that the click produces a number 0. If I leave the thread and return 1 is then showing? Also what is the point of/difference between 'likes' and 'upvoting', it's all to easy to get the wrong one if there is a difference.

Just remember that although SJ referred to electrons in atoms, not many substances apppear in atomic form. Most appear in molecular form where the atoms are joined together, often many different atoms. It is some of the atomic electrons that allow this joining and the joins or bonds which are responsible for interacting with the light or not as the case may be. The arrangement of the particles may be regular as in crystals or jumbled as in grains (referred to in the excellent Wikipedia article SJ offered). These arrangements are the result of the bonds or joining mechanisms. +1 to SJ for a good answer.

About the same age as my icon. But well past the retirement age for my generation ( a Who record I remember).

Indeed. Nor will you until you can abandon the miniature solar system view of this subject. FYI there were three different approaches to the subject. There were subsequently shown to end in the the same model although they came from different premises. 1) Quantisation. The proposition that energy is quantised, and that the smooth classical laws should be represented by a series of permissible energy levels and forbidden zones. There was little or no justification for this except that it fits the observed (empircal) evidence. This results in the ladder type diagrams but it is only a small part of the story and nowadays considered a result that pops out of the equations offered in the second and third approaches. 2) Schroedinger. This is a complicated differential equation of motion (with many many solutions) from which the necessary quantisation emerges directly from solutions and the boundary conditions. That is why I started towards that, but you wished to plough on in your own furrow. 3) Heisenberg Matrix Mechanics The uncertainly principle emerges directly from this approach. Further (advanced) work can convert between this method and Schroedinger. It also leads directly to the tensor statement linking the energy tensor to the hamiltonian and to the linear algebra required for special topics such as entanglement. Method (1) does not need or introduce the non locality required in QM. Method (2) does this by means of assigning a meaning of probability density to the wave function. Method (3) does this directly.

Thank you for the acknowledgement. +1 "Should be" is a matter of opinion and you are entitled to yours.

Look at this bit of maths (arithmetic) first. to make a number, say 4, negative multiply by -1. So 4 * (-1) = -4 To return it to its original multiply again by -1. So (-4)*(-1) = 4. Now for the clever bit. Now let's look at this again from thenpoint of view of geometry. Arrange the numbers along a line (axis) positive to the right, negative to the left as shown in the first sketch.. The first sketch shows how to get from A at +4 to B at-4 geometrically as in the the calculation. It also shows the second multiplication to get back to the roiginal number or position at A. This sketch does not have a second axis. It only has one axis. The second sketch shows that if we make four multiplications by a quantity we call i we also get back to where we started. But in this case the first and third multiplications take us off the original axis. So we say that multiplication by i = √(-1) has the effect of rotation by 90o A second multiplication has the effect of rotation by 180o A third multiplication by 270o And the fourth multiplication returns us to where we started with a rotation of 360o. This construction is known as an Argand diagram. That generates the second dimension and axis which is at right angles to the first. But of course we can have another (third) dimension also at right angles to the first, but different from the second axis. This way of thinking is where the i,j,k notation came from. And that is all it is. A notation to represent the fact that we have 2 or 3 or even more dimensions, all at right angles to each other. We use different letters because we need to distinguish between each of the axes we use, but they are all have the same numerical value as there is only one √(-1). There is no information in the number √(-1) about which of the infinite number of possible directions we choose. That is up to us to specify in some other way. Normally, i j and k are enough as we only have three space dimensions. Does this help?

Perhaps if you spelled it correctly? Naphthalene Does this help?

Have you heard of Argand Diagrams?