studiot

That kinda depends on what you mean by slow. The postulates in particle physics in natural and artificial accelerators has been tested at greater than 0.9C I expect swansont or sensie has better inofrmation here.

And I always thought it was QM that was probabilistic, not relativity.

Sure I'll do the experiment, where do I get the ideal equiment? This reminds me of a book I had as a kid called the "Book of Experiments" Each experiment started with a list of equiment and I remember one that started You will need 1 Thunderstorm ....... ....... Far better to discuss this rationally from the comfort of an armchair with whisky in hand.

My house was built with a timber ground floor suspended 2' 6" above formation by rat trap sleeper walls in 1938. The timber was fine until the early 1970's when central heating (radiators) was installed. This led the timbers to rot within 20 years in the resulting damp. An unfortunate example of an unintended consequence due to an engineering change.

I didn't say it wasn't, and indeed the OP took pains to specify this condition. robbitybob, the whole point is that yes the history of the forward and rear clocks is not quite the same subsequent to synchronisation, but the OP has taken pains to make this effect negligable. It could have been reduced even further by placing the train on a turntable and rotating 180 half way through the slow walk back with the clocks. Equally the issue of front v rear acceleration is a non starter. For instance the train could have beeb pushed from the rear or driven by two locos from each end. But hey, these are ideal though experiments so we can have ideal equipment, just as the centre clock can be a true ideal simultaneity detector.

The history is interesting. Especially as there is one known Handle House left in Somerset in very poor condition and this one in Wiltshire. So there are probably only two left in the World. A river Biss crossing was strategically important since early times and the Romans probably were the first to bridge it, hence the timber foundations. In later times that part of the country became a centre for the wool trade and a masonry pack horse bridge was built across the river (we now know on the old Roman foundations). A particular type of thistle (teazle) grows naturally along the river here, more were probably planted. The thistle head has curved hooks. 'Handles', like clothes brushes with thistles instead of bristles were employed to 'raise the knapp' on the woollen cloth. This process was carried out wet and the hooks straightened with the moisture so the 'handles' were hung up to dry in drying sheds to recurve the hooks. These drying sheds were called handle houses and were once common in the Cotswolds and Mendips. In the Victorian era business boomed even more and brick sheds were built using the perforated brickwork to allow free airflow to promote the drying. (In bricklaying terms this is called rat-trap bond and was also used in other places to allow airflow such as under timber ground floors.) The Trowbridge Handle House is such a building. It was quite fun to lift it up and rebuild the river channel underneath.

So you were too hasty in contradicting me. I see this problem as more akin to the extended lifetime of the muon than an Einstinian simultaneity issue. The key to question 2 is to realise that the crucial frame is that of Cm for simultaniety purposes. This happens to be that of the train in this case. @gib65 I don't know what you are unsure of and most here have given rather cryptic responses instead of detailed explanations. Your basic experiment description is understandable and I think you realise that most of the analyis is designed to confuse the issue to establish the paradox.

Let us examine this exchange carefully. Set aside the issue of simultaneity for just a moment. and measure in the trackside coordinate system. Call the clocks Cf, Cm and Cr for front, middle and rear. Let Cf emit a flash as it passes point f and Cr emit as it passes point r on the track. So Cf emits a flash at f which travels back towards Cm, as well as towards the trackside observer. But Cm in in motion towards f so in the time it takes for Cm to encounter the flash it has shortened the distance and so the trackside observer will see Cm receive the front flash slightly earlier. Similarly whenever Cr emits its flash, simultaneous or not, Cm is in motion away from it so the trackside observer will see Cm receive the rear flash slightly later. So the non-simultaneity does not follow from the Cm being equidistant from Cf and Cr and would be true whether or not equidistance holds. It is a direct consequence of the motion of the train, relative to the track.

Surely both ends of the train (and therefore sources) have the same relative velocity to the stationary observer?

So far as I can see your last word on this was to repeat the so called paradox. Which would be (if it were a paradox) why does the middle clock stop if it is observed to receive the flashes non-simultaneously?

1) Does the middle clock stop? 2) What is the correct line of reasoning leading to this conclusion? 3) What is the fault in the reasoning presented in post#1? Note this is the reasoning, not the statement of conditions. Of the three questions the first one is now answered, yes the clock stops. To answer the second and third it is good to point out that analysis and calculations are best done entirely in a single frame of reference and that this is possible in this case since the three clocks are in a common frame. Mixing information from different frames so easily leads to incorrect conclusions (I'm sure we've all done it). At this point it would be nice to hear from gib65

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.