studiot

Always remember that for any wave the motion of the particles is not the same as the motion of the wave. You should have covered waves at sea where the water aprticles go round and round in litle circles, whilst the wave travels along the surface. In electricity, the motion of electrons similarly not connected to the motion of the alternating current wave. I really think it is a counterproductive idea to introduce at all as so many have trouble with it.

So was that a yes or a no?

Commander, perhaps this will help clear up your difficulty. It is imporant to understand what a geodesic is. There are many types of geodesic. From your (are you retired?) former profession you will have studied navigation and probably met geodesics as a geometrical line in cartography which minimises the distance between two points. The geodesics here are not of this type. They do not live in normal physical 3 dimensional space, they 'exist' in an abstract mathematical space with abstract mathematical axes. They are defined as the line referred to these axes which minimises a particular mathematical expression. Have you studied the calculus of variations? You would need this for this type of geodesic. You are a clever fellow and I'm sure you will be able to follow what I'm trying to say (sorry I didn't put it very well to start with) so ask again if you want me to expand on this.

I am suggesting you reconsider this statement and supplied an example of when it is untrue. As a matter of interest, you need the force to exist continuously between at least two distinct points for there to be a potential. Potential theory is about fields.

Michael, your mirror image is almost there but the image is still real. I have already pointed out that virtual images in optics lead to negative lengths.

Yes I agree with enthalpy, the soundbox acts as an acoustic transformer to better match the acoustic impedence of the input to the air. The energy ultimately comes from the performer's elbow grease and cannot be greater than she inputs.

The difference is that in your examples the aircraft is not the only mechanical object in your test universe so you would have a mechanical reference, if you choose to use it. I specifically said that there is only one charge in the universe (as you noted that could mean sufficiently remote from other charges). So you say that there is definitely energy, but that it can't be calculated, and can't offer a physical law to describe it. Sounds like witchcraft.

So explain how you would calculate this energy and what form it takes, please?

No one said they were, in fact that is the whole point. Yes I did look at your link, but I couldn't see anything relevent. That is why I asked No one is suggesting superluminal transfer, that is the issue. Since other (Einstinian) Physics forbids superluminosity my original question explores was happens beyond that transfer horizon? I honestly don't know the answer to my original question, that is why I posted the OP in the first place. A universe with a single charge does not have any energy in its field. The energy arises when a second charge is introduced. So if there is now energy in the field of two charges what happens if one is destroyed or removed to the energy in the field that is further away from the destroyed charge than light can reach in the time to destroy the charge?

I see no problem with this part of MigL's post. We know from experiment that annihilation is both possible and takes finite time. However long that time is the charges can be separated by a greater distance than light can cover in that time.

This discussion brings a chuckle. Negative length is a perfectly valid mathematical concept, much used by those concerned with geometrical optics. I think ajb meant his topologies to be Hausdorff. I think that means they are also metric spaces, which means they have a metric. (I'm sure ajb will correct me if I am wrong here) The first metric space axiom is that it possesses a non negative distance function. Using the square root as a distance function therefore precludes the negative root by the first metric space axiom. However this colloquial definition of a Hausdorff space exemplifies the idea that a (finite) line require two points: "A space is Hausdorff if any two points can be housed off by separation in disjoint sets."

Again I didn't say that the man on the roof has no potential energy. What I said was that applying your statement means he does not. So let us re-examine your statement.

Yes the OP starts from a misconception and several have tried to explain this in different ways. A point has no length, of any value.

Thank you. But the question is about what happens after annihilation. Perhaps I made the scenario too dramatic. If I just said that the charges are moved further apart, no one would bat an eyelid about the signal that ensues. But the question of what happens to the energy in the field, before the signal arrives, still remains unanswered.

What bearing does this have on the question posed in the OP?

The ancient Greeks thought long and hard about this question and they came up with a notion that, when put in modern terms boils down to the idea of dimension. Euclid definition 1 A point is that which has no part Euclid definition 2 A line is a breadthless length Euclid definition 3 The extremities of a line are points (John made this point) Euclid definition 15 A circle is a plane figure contained by one line such that all the lines falling upon it from one point are equal. A modern translation of the above is that you require zero dimensions for a point, one dimension for a line and two dimensions for a circle. Extending that you require three dimensions for a sphere. The corresponding figure for dimensions greater than three is called a ball or an n-ball, and sometimes a ball is used in three dimensions.

Thank you MigL, you have encapsulated the question I posed exactly. +1 Indeed if you only annihilate one of the charges, this still must change the field and the question of what happens to the energy in the field (if there is any) before the 'change' signal has arrived from the destroyed charge.

I don't think it's as simple as that. When you are standing on the roof you are subject to a reaction force from the roof, of opposite direction to gravity. Applying your logic above, you would be subject to a negative potential equal and opposite to the gravitational potential., making your net potential zero. Potential and potential energy are not necessarily the same thing. Just as the reaction force and the gravitational field are not the same.

OK let us examine what you said in post19 more closely. I have underlined the bit which does not make sense. Any body which is stationary under the opposing action of two (or more) forces neither gains nor looses energy. Now you said that both airfoils (the free one and the constrained one) gain energy. Again I have underlined the part which is at variance with basic mechanics, for the same reason. It is quite simple. If the body does not move its energy does not alter, apart from any heating or cooling which is not determinate. This exemplifies the difficulty that you can get into with an energy analysis, rather than a force analysis, or mixing the two. It can be done but you have to be careful.

Because if it is truly STATIONARY it moves neither up nor down, nor at all.

I have no idea what you are studying or at what level. Geophysics is a college or university subject, not a school subject. Here is an extract from Kearney & Brooks An Introduction to Geophysical Exploration. We can discuss this list if you like, but only if you are prepared to answer questions, but as you can see, they have a different list of possibilities for your application. You have not answered my question about cost.

Well I've wasted enough time on this one sided conversation. If you have difficulty with English tell the next person who tries to help you before she starts.

If the airfoil is truly STATIONARY what form of energy do you think it gains? It obviously can't be kinetic or potential energy. True it may gain some heat due to friction, but it may loose heat by convective cooling.

I don't see you putting much in. Here is another hint, and the last one without some posted effort from you. How does the resolution of a seismic survey vary with detector spacing?

How would you conduct a resistivity survey to show the ditch?