studiot

Perhaps the assumption that the acceleration is always in a plane through the centre from which the position vector r is measured should have been stated explicity.? Perhaps more interesting, is the assumption Since c is a constant we have [math]\frac{{{\partial ^2}{X_{32}}}}{{\partial {t^2}}} = 0[/math] In other words the acceleration component in the third dimension is zero. But at the expense of a constant light speed in the third dimension. Perhaps some additional words of explanation would not go amiss? Perhaps also using g for the generalised acceleration rather than another symbol will lead to confusion with gravity?

The mineral concentration occurs due to chemical reactions between the water circulating in volcanic zones and the hot rocks. http://nzic.org.nz/ChemProcesses/water/13A.pdf

The mineral concentration occurs due to chemical reactions between the water circulating in volcanic zones and the hot rocks. http://nzic.org.nz/ChemProcesses/water/13A.pdf This should be in Earth Sciences.

Another way to analyse this is to consider a momentum balance. The rocket plus its fuel starts off with zero momentum. As the fuel is burnt the exhaust is expelled backwards and the rocket moves forwards. The momentum of the backward moving exhaust equals the momentum of the forward moving rocket. This balance allow you to calculate the maximum speed attainable for a given fuel load, or how far the rocket can go before it has to turn round if it is going to be able to return.

Well you are asking about a set of four simultaneous equations. The set are shown in the upper part of my attachment, could you not have done this? You cannot fully solve ODEs without boudnary conditions. It would seem that the next few equations specify these boundary conditions, as shown on the next page, at the bottom of my attachment. However there would be a great deal of reading for anyone to become familiar with these equations, you need to flesh out your post in order to hold, a sensible discussion. What do the symbols stand for?

As a matter of interest why is this thread in speculations? So far as I can see it is not a proposal, but a discussion about scientific progress and the scientific method and all the better for now being back on track. So I would think it part of the philosophy of science. As to the relationship between theory and practice, IMHO they go hand in hand. There are many examples in history of one getting too far ahead of the other with undesirable consequences. Plato's theory of shadow's in the cave had too much theory and tool ittle practice. The observations of the motions of heavenly bodies originally had too many observations and not enough theory.

Concise and fairly balanced. Thank you Mike for keeping the verbosity down to the technical. +1 In particular I endorse the question (underlined in the quote) as to the lead player in modern times.

Bill Angel Thank you, Bill for the thought. Negative mass is indeed an interesting subject. Certainly sticking a negative sign in front of something that Physics takes as non negative but is allowed in Maths is worth thinging about. Unfortunately I'm not sure it shows a difference for negative mass since negative (effective) mass is already in use in Physics and important in semiconductor Physics amongs other places. But there may well be some negatives that are OK in Maths but not Physics. Acme Thanks for the contribution Acme, Again unfortunately I don't see where Physics forbids irrational or trancendental numbers. Both the radius and circumference of a circle are real world objects. Incidentally this thread was stimulated by preparing a response to a question about the origin of energy bands in semiconductors.

I am collecting examples of where maths and the physical sciences differ over something. Examples offered would be gratefully received. For instance cos (z) = 3 has no solution in the real world and this fact is of vital importance in creating transistors. However in the mathematical world the equation has complex solutions.

Maybe you are focused on something, but the title of this thread is about two things. Mathematics v Observation and Hypothersis. Observation represents Physics which represents the real or concrete. Mathematics represents the abstract. I didn't see any reference to Art or English in that title, or the original post. I would suggest that rather than combine hypothesis with observation I would say hypothesis represents the link between the abstract and the real.

Since there are differences between Physics and Maths, why have you missed out Physics?

Are we done with the original topic?

I Know you wouldn't, but I was trying to get the OP (as well as sensei) to do some work (thinking)

Well I'm glad Ophiolite has chosen to return. That was a professional summary of current knowledge. +1

Would you consider testing the gas with lead acetate paper?

So long as y is not zero.

Jerico

So when are you going to change your handle to Joshua?

The best way to do this is to look at the COSH regulations (control of substances hazardous to health) eg http://www.jmloveridge.com/cosh/Copper%20Sulphate.pdf By the way have you completed your lab you haven't come back on your thread there? Edit A further comment. this is not Organic Chemistry, why is it posted here?

It would be helpful if you can tell us whether you are an studying electrical engineering, physics or chemistry and if you have heard of Fermi?

This is where lord Kelvin went wrong 100+ years ago http://apps.usd.edu/esci/creation/age/content/failed_scientific_clocks/kelvin_cooling.html

To understand this first you need the Pauli Exclusion Principle. This states (for this purpose) thjat no two electrons can have the same set of quantum numbers. Now the usual quantum solution that we use to describe an atom is for an 'isolated' atom. That is it specifies a set of quantum numbers for an single atom in isolation. But if we have two such atoms the set will be the same. So what happens if we join them together? Well each nucleus influences the other's bonding electons (that is what bonding means) and the electrons directly involved in the joining enter what are known as molecular orbitals with enough quantum numbers to hold them all. Move on to a full crystal which is also called a periodic structure and you find 'super molecular orbitals' which can hold all the input electrons. Obviously in order to obey the Pauli Principle the super molecular orbital must 'split' into many closely spaced (sub)orbitals to accomodate all its electrons. Does this help?

Several questions at once here. I will try to sort them for you. No metallic bonding is not simply a big communal cloud of electrons. Yes there is what might be so described but the bonds remain directional and only certain electrons are able to join the party in the commune. Because the bonds are directional the bonds direction (and their valences) have to match to allow alloys - bonding between dissimilar metals. The bond's directions are reflected in the crystal structures of the metals. Now to you example of the same metal. If you machine chemically clean (oxide free) surfaces and press them together you can indeed 'weld' this way. Welding is another name for joing crystals. This is an established technique of cold welding. What else do you want to know?

Well you have three 'chemicals' in your list and HypervalentIodine has already told you what one of them is for. So what do you think the reactants are? Do you think the green colour is a reactant or a product?

You want levitation try this https://www.youtube.com/watch?feature=player_embedded&v=OqpPi8wNed8