studiot

Your lad needs also to start learning to 'read around' a subject as well as just lapping up the formal course material. I would avoid additional outside classes in the same curriculum as the school's. This will only demotivate him in class. Two fun books to help here could be Things to make and do in the Fourth Dimension By Matt Parker Mathematical Models Cundy and Rollett

The formula was originally due to Michell in 1750. The actual units have varied over time and there should be constants added depending upon the system of units you are working in. In modern MKS units the formula is [math]F = \frac{{{{\bar Q}_1}{{\bar Q}_2}}}{{4\pi {\mu _0}{r^2}}}[/math] where the pole strengths Qbar are measured in ampere-metres (amps times metres) Does this help?

I don't, it is one of the questions no one knows the answer to, although many have considered it over the millennia. But then, exactly the same can be said of a finite system. But I will wait for you to have time to respond properly to my last two posts instead of misreading them in haste.

I have already answered this more than once. The First Law does not apply to infinite systems, though relying on Wiki is dicy at best. Furthermore it is not known if the Universe is an isolated system. I find this too restrictive a condition on the definition of Science. For instance in many cases you have no way to test the actual happening of a historical event, but Science can investigate and provide probabilities of possible facts. A simple example would be the so called coffin ships.

Duplicate thread

I wonder if you are referring to where I offered a case in Mathematics of something which has a beginning, but no end? For instance the natural counting numbers. I was going to observe that there is another process in Mathematics whereby something is generated indefinitely, constantly expanding the something. For instance between every pair of real numbers there is another real number. The same is true of the rational numbers, but in that case there are also other non rational numbers between every pair. I thought you had given up responding to me, and as everyone else seems only to want to take the piss I had given up on the thread.

Forgive me but what's a micromole per minute per micromole? I've never heard of them.

Hello, KFs, and welcome to ScienceForums. You have done some good work and congratualtions on posting your attempt. So why not amaze yourself and finish the job? When x = 1 [math]\frac{{ - 4{x^3}}}{{\sqrt { - 4{x^4} + 13} }} = \frac{{ - 4}}{{\sqrt { - 4 + 13} }}[/math] Which you have already calculated.

You can't seriously be denying that surveyors on Earth have a different correction for spherical excess than hypothetical surveyors on Jupiter? So are you saying that if the Earth expanded to the size of Jupiter, surveyors would notice no difference?

But we are talking about dilation. Indeed so, but as noted, we are talking about dilation, which is a dynamic thing, not the static one both you and Strange are describing. Is it not true that the intrinsic indicators of curvature will change with expansion? For instance spherical excess on the balloon will increase as the balloon expands. Further you are both ignoring my earlier comments about the subject.

Ok smartypants, how would the analogy be possible if the surface of the balloon was not curved in the third dimension?

Why would it change? Would that not imply this additional space is different from the previous space. So what is your proposal for phenomena that cross the boundary between the old space and the new space? Well I think it good enough to give +1 to. SJ has effectively put forward the Physics definition of a Field. Far better than the sort of Field the OP seems to envisage as some sort of web spun out by spiderman. Please, please get hold of a copy of "The Lighness of Being" by Nobel physicist Frank Wilczek. He dedicates this book to developing this sort of Field and the idea that 'particles' are disturbances of it. Please tell me how the balloon could exist or expand without the third dimension? Perhaps not time itself, but Minkowski ct, which would be a length and therefore accaptable as a measure of radius. Do you have a reference, If so I would be very interested. The diagram of this is what I was considering for geordie. Still thinking about this, my trip up Crook Peak offered wonderful clarity.

But charge may 'bend' a field, but it can't bend space. Mass, by way of gravity 'bends' space. Do you consider space to be finite or infinite? The answer makes a very big difference since infinity plus 20% is still just infinity. As to which type of field, your answers elad me to believe that you are referring to what is known as the common background radiation along with the general distribution of light (EM radiation) we observe, which varies from direction to direction. Such 'fields' are indeed one use of the word but they are neither the formal definition of a Field as used in Physics or in Mathematics (The one in Mathematics is different). I am just going out onto the Mendips, so you will have to educate me another time as to how you find these past trheads so readily and quickly. I can never find them when I want them.

I suppose it depends upon your background. I have done so much surveying in my time that the idea comes naturally to me. Do you remember I once tried to explain the surveyor's concept 'through chainage' to (I think) you. This is an elementary example of it in everyday practice.

No, geordie, I know that. But then nobody else has either. Everybody glibly says words to the effect "There is no centre of dilation" for this expansion and the balloon analogy is offered with the statement There is no centre of expansion for the balloon. This statement is untrue and hides the fact that There is no centre of expansion in the manifold that forms the surface of the balloon. However the centre of the balloon is also the centre of dilation, but it is not in the surface manifold. In fact it is not in the same dimension as the manifold. The connection between this statement and curvature and dimension is fundamental and usually glossed over. I am trying to work out a way to draw this for you, but would welcome anybody else who has a good answer.

I'm not sure what you mean by this. Can you elaborate? I agree it's unfinished or something, I don't know what. I asked you before and you didn't answer You need to distinguish what sort of field you are talking about please? I would suggest that you also need to distinguish between energy and mass as they are somewhat different. Energy is not a sort of liquid form of mass that can be transferred from one body to another. But you can coalesce two masses to form one.

Well that's wrong. You can have space with no field at all. So how is this different from space where there is a field? You might say that a field is the influence or effect of a source (or sink) on a region of space.

Good stuff. You can write powers directly using superscript on this forum. Having superscript and subscript is a great boon. Look for the X2 and X2 symbols on the toolbar at the top of the text entry editor.

Hello and welcome to St. Please explain what you mean by the above statement. Strain is a dimensionless quantity, not measured in metres.

That is what I asked you. (except that the edges of the block are not outer walls) This apparantly innocuous question seems to be causing a deal of difficulty. Perhaps that is because expansion and contraction is more complicated than at first meets the eye. Let me ask again. Suppose you were to printout my sketch and then photocopy it on the 100% enlargement setting. Would the hole get bigger or smaller? Would every point in the solid part of the block be further from its neighbours than before? To save time: Yes, of course the hole would get bigger. Yes every point would be further from its neighbours. Now there is a point to all this because the expansion of the universe is not like my example (with or without the hole) The expansion of the Universe is an entirely different sort of expansion. And you need to understand this difference before trying to discuss the expansion of the Universe. Interestingly this difference has to do with curvature and another dimension, which everyone seems anxious to discuss.

Realistic of what? Your choice of scenario, so long as it is clearly stated.

Expansion (and contraction) are actually peculiar processes. Here is a simple block that expands (equally) in all directions, as shown by the arrows. But it has a hole in the middle. Can you tell which way the sides of the hole move? That is does the hole get larger or smaller?

No you are missing my (our) point. This is not Star Wars; Jedi knights and 'The Force' is a work of fiction. There is no such thing as 'an all-universal permeating field'. So decide what you want to discuss, picking only from that we can observe.

No there is no contradiction. Strange touched on the why of it but only briefly. It is space that expands, not matter. Matter is not space. Now consider our solar system. The disposition of the planets is governed by the balance of the gravitational forces within the solar system. In turn these are governed by the amount of the matter in the system. But matter does not change. So the balance of forces will not change. So the disposition of matter will not change. That is the solar system will remain the same size. However the distance between our solar system and the next will increase. In the 'empty' space between solar systems there field strength is low. The % of 'empty' space will increase in a given portion of the universe. So the average field strength will go down. You can make the same case for galaxy sized agglomerates and atomic scale assemblies (molecules), although at the atomic scale the fields and forces have a different origin. Note I emphasised the phrase 'in a given portion of the universe'. This is because of the peculair behaviour of infinity. We have to discuss a limited volume, because the introduction of additional volume in an already infinite volume presents mathematical and philosophical difficulties. We do not know if the universe is actually infinite or is finite.

With respect you have spent too much effort on clever drawing/animation and not enough on laying out the maths properly. A much simpler drawing would be adequate, accompanied by better presented maths.