studiot

This is a really silly digression. The OP asked specifically, in so many words and in more posts than one if the clock stops or not. The only reasonable interpretation of that is he doesn't know and is not afraid to ask and doesn't claim it as a reasonable interpretation after the event. So can we agree that the middle clock is found to be stopped at the end of the experiment and proceed from there?

The only reference that I can find is post#14 where pzkpfw thinks the clock stops (apologies if your statememt was meant to be stonger than this). I think it is imperative to establish what would actually happen before arguing about why. Once that is done a properly forumated explanation can be provided to gib65.

It is interesting that I am the only one who has ventured an opinion on the question Does the clock stop or not? Yet one of those who did not dare answer this question has graced me with a red point.

Thank you pzkpfw and swansont for replying and thank you gib65 for not replying. But you all missed my point. As a matter on interest this problem is different from Einstein's train because there the flashes occurred in the track system, not on the train. I said that I don't see a paradox because of the given conditions set out in the OP and I highlighted the offending words. 'The train is moving'. It doesn't matter if the train is accelerating or keeping constant speed, it is specified as moving. So how does the observer on the train know he is moving? And what is his (the whole train system) velocity? It is a relative velocity, but relative to what? By specifying that the train moves the OP has provided additional information ie an additional condition. This condition is tantamount to specifying an absolute system of reference. As I understand the properly posed analysis the external trackside observer does not see the train clocks as keeping the same time or travelling the same distance. So to her the light from the end clocks travels different distances in different times. These alterations to times and distances are just appropriate for the light to arrive at the 'centre' (she does not see this as the centre) clock together and trigger the stop mechanism.

Thank you pzkpfw, But the original conditions state Which is not a simple rest frame for the train.

I'm sorry I can't see the paradox here. Why is there any suggestion given the original conditions, that the light flashes would reach the centre clock together? Whenever the flashes are emitted they will take a finite time to travel to the centre, but in that time the centre will have moved, closer to emission point of one flash and further from the emission point of the other.

Look up the term effective mass in solid state physics. This can be positve or negative as in the case of the Hall effect for certain substances. Also https://www.google.co.uk/search?q=negative+effective+mass&hl=en-GB&gbv=2&oq=&gs_l=

I agree with John, there is a difference between an assertion and an assumption. The use of the word 'Let' is the beginning of an assertion. Assertions are considered true for the entire proof. Proof by contradiction is carried out by assuming that which you wish to prove and demonstrating that the assumption leads to the contradication of an axiom or assertion and so cannot be true.

Water has fairly strong surface forces acting in addition to gravity and any atmospheric pressure and container reactions.

The manifold in cartographic geodisics is a surface in normal xyz space. The manifold in other forms of geodesic is not in xyz space, but in some lagrangian dimensional space. Further the cartographer's geodesic path minimises the distance function through the manifold, whereas other geodiscs may minimise some other function.

All geodesics have the same common idea. It's just that Mathematicians & Physicists have extended the idea from the original cartographic one. This is indeed a cartographic geodesic (for want of a better term) It is not a geodesic in the externsion of the term to Hamilton/Lagrange mechanics and General Relativity. A ballistic trajectory is one thing any geodesic most definitely is not. See what you make of my post 10

Help is available at ScienceForums if you want it. The name comes from cartography, and the cartographic explanation is the easiest to digest.

Not sure where your photo came from, imatfaal, it's 20 years and more since I've been there.

I remember working on the underpinning and strengthening of The Handle House, built across the river Biss between an ancient pack horse bridge and a later brick arch. We came across more ancient timber (possibly Roman) foundations beneath the pack horse bridge. They were more difficult to break out than the masonry.

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."