studiot

Zet, please note that you have to restrain the object both against the drag and the lift in the restrained case. JC has the right of it +1 However please also note we are talking about the lift and drag of aircraft in the atmosphere. The aircraft has kinetic energy, which is replaced by the engine when under power. When gliding the aircraft looses both gravitational and kinetic energy, eventually coming to rest on the ground. No glider flies forever. You are describing the action in a wind tunnel, where the energy comes from the fan that drives the airflow. In the free atmosphere the energy comes from the natural forces that created the wind, which (I think) are usually temperature differentials. As regards you question comparing the energy in lifting a heavy object v a lighter one. The lift force is determined by geometry so will not be able to lift a heavy object so far or so fast ( as you have shown in your diagrams) so energy conservation is preserved.

I didn't say otherwise, but since that was not a permissible setup I did not consider it. Perhaps didn't make a very full statement, which led to misunderstanding. All three train clocks are specified to be in physical and temporal alignment at rest and side by side with the three platform clocks at the start of the experiment. However this leads directly to the issue Strange and I have been discussing. Two light signals travelling at (obviously) the same speed for different times (measured in the same frame) must perforce have travelled different distances to arrive together at the same point. It would be perverse to measure the times in one frame and the distances in another. Equally clearly if they travelled for different times and arrived at some point together, they cannot have started at the same time in that frame.

The end clocks on the moving train can't be opposite the platform clocks in either frame since the train appears shortened in the platform frame.

If you think that an equation will is deterministic what is the output of this equation? x + (-x) = 0 So what is x?

No. What about do we know of any successful mathematical modelling of the universe? Again No. You need to understand what is meant by an equals sign in mathematics. It often indicates the result of a process (Chemists for instance used to use it for this but now more often use an arrow). That process may or may not produce a predeterministic result. Sometimes an equation may have an infinite number of valid solutions, so any one chosen at radom will hold true. Sometimes we say 'an equation cannot be solved in closed form'. Does that make it deterministic?

I respectfully suggest you go and measure some Hall voltages before you make such sweeping pronouncements. You do not need to be near a black hole or other exotic body to do this, nor do you need exotic substances, copper, gold, magnesium and aluminium will suffice. I await your results and explanation with interest.

Well poisson's equation in cylindrical coordinates is [math]{\nabla ^2}V = \frac{1}{r}\frac{\partial }{{\partial r}}\left( {r\frac{{\partial V}}{{\partial r}}} \right) + \frac{1}{{{r^2}}}\frac{{{\partial ^2}V}}{{\partial {\theta ^2}}} + \frac{{{\partial ^2}V}}{{\partial {z^2}}} = - \frac{\rho }{\varepsilon }[/math] The reference to a long cylinder provides a value for [math]\frac{{{\partial ^2}V}}{{\partial {z^2}}}[/math] and radial symmetry provides a value for [math]\frac{1}{{{r^2}}}\frac{{{\partial ^2}V}}{{\partial {\theta ^2}}}[/math] Leaving only the first term and therefore reducing the equation to a solvable ordinary one. Now the physics is that the potential at the boundary with any conductor is a constant. So if we reckon zero potential at the inner surface of the outer conductor as zero and the potential at the outer of the inner one as v (a constant), we can obtain an expression for V®. This leads to the logarithmic ratio solution. You are then asked to rework with v = 0 in part c. I hope this is enough of a nudge as I'm off out on the town tonight.

How far do you wish to take the concept of a machine? So how about a greenhouse as a machine-building that concentrates solar energy? If you accept this what about modern energy recovery installations or older north light roofs? And what do you mean by a building? Does a wave-wall count in flood defence work? Scientific instruments also come to mind, The camera obscura of old and the modern telescope like Palomar.

"Which is Professor Challenger's room?" Down the corridor. Down the corridor, on the left. Down the corridor, third door on the left. Down the corridor, room 15. Each may be adequate or inadequate, depending upon circumstances.

Trying reading again whatever you misread before, I made no such claim.

Since you were again so hasty in replying perhaps you would like to show how the following system of two particles (mass m1 & m2) and one force (F) is inertially invariant when transformed to a new system whose origin is at (x0 , x0) compared to (in) the original. The Newtonian equations of motion in the original are [math]{m_1}\frac{{{d^2}{x_1}}}{{d{t^2}}} = F({x_1},{x_2})[/math] [math]{m_2}\frac{{{d^2}{x_2}}}{{d{t^2}}} = - F({x_1},{x_2})[/math]

Newton's First, Second and Third Laws. A good background book on this stuff is the University of Sussex student booklet Relativity Physics by R E Turner

You have to be careful with this one. There are many 'laws of physics'. Some are the same some are not and some need to be (can be) adjusted to be the same in all inertial frames.

I have already mentioned the muons. http://web.mit.edu/lululiu/Public/pixx/not-pixx/muons.pdf

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