The Twins Paradox and the speed of light

Cool Welcome aboard!

Really? What do you do? It's always great to find direct applications of complex equations in the workplace, rather than just in academia. I used to work in derivatives - actually, I do feeel a bit guilty at the moment, as one of my main areas of expertise is calculating a bank's exposure to complex credit backed securities... Perhaps if I hadn't left the sector all those years ago Ok, is this simple Euclidean space, with the basic Pythagorean metric? I'm unsure as to how f() represents a change in coordinates - is f a vector, a more general tensor, or is it just a scalar as you have written? Let's say we go from the triple (x,y,z) to (x+dx, y+dy, z+dz) - how do we encode this change in f? And I'm not sure what you mean by f(x,y,z) necessiating time - do you mean we should really write f(x,y,z,t)?

Perhaps the confusion is that there is no paradox. The effect is real but there is nothing paradoxial about it...

If you're asking if gravitation and cosmological expansion can create a 'twins paradox' effect, then the answer is yes. We see this here on Earth with just the GPS system, where the satellites are aging differently to us owing to Earth's differential gravitation.You get a much more pronounced effect around compact bodies such as neutron stars and black holes, and you can use these to fire yourself far into the future. This is a bit confused. 'somehow managed to arrive on Earth instantaneously' means very little unless you can specify details. I think I understand what you are getting at - one moment the alien has a time direction aligned with that of his own galaxy, and the next moment he is soemwhere where the time direction is very different - does this affect him in any way? The trouble is, the detail is all in the mechanism of your 'simultaneous travel'. You cannot postulate magic and then hypothesise how science behaves in the presence of this magic. To do this, you need to understand the science of the magic, and then it is science, not magic

Ok, a wormhole we can deal with - BUT the space-time curvature of the wormhole will have a far more massive effect upon our time reckoning than the cosmological effect. And more importantly, bringing the wormhole into a situation where it does connect two distant areas at the same 'time' is already involving quite serious time-travel (being able to break the causal structure of space-time is time-travel) and in that case, quite frankly, who gives a damn about piddling little effects such as the twins paradox

No, you cannot split the issue like this. The Twins Paradox and associated gravitational and cosmological time-dilation issues are all inextricably linked to the method of travel. Time-dilation itself is a factor of Lorentz Transformations (and the finite speed of light), but you are not performing a Lorentz Transformation with your 'instantaneous' travel, and you're completely circumventing the finite speed of light.You may be thinking that teleporting from galaxy A, with time direction T_A, to galaxy B, with time direction T_B has the traveller arriving somewhere where time moves differently to his own. But I have no idea how to explain what this situation means because the situation is an impossibility. It's very similar to the question - well, what would happen if we could go faster than light? The question itself is sufficiently ill-defined that there is no possible answer, without replacing the question with one that is actually reasonably well-defined. In your case, you have to specify the mechanism of travel to be able to make any sense of your question.I guess a similar question would be - if I teleported from here in the UK to Fremont, would I arrive leaning over at an angle? (because of the difference in normal vectors to the Earth's surface) Again, it depends upon the technical spec of the teleport device...ABE: just getting back to the other reason this is all immaterial, if you can teleport instantaneously, this can be used as a time-machine by time-dilating one end of the teleport device. This is how we turn a wormhole into a time-machine. So you can stargate to somewhere else, spend a year there, then stargate back and simply pick at what time you'd like to return: a moment after you left, the same time as now, or anything else you choose. You can't postulate FTL teleportation and ignore the time-machine implications. Breaking the speed of light by whatever method has consequences... Edited by cavediver, : No reason given.

Not quite - it's the twin on Earth that ages more slowly than the twin on the space-station. There will also be a relative-velocity time dilation which will work to reduce the difference.

Welcome to EvC Though it's not a good start because you're completely wrong Strange, because I have been performing SR calculations in accelerated frames for over twenty years. I think you need to get a proper book on Special Relativity (Rindler's Essential Relativity is a good old-school undergrad-accessible textbook), and stop depending on garbage you read on the internet - present company excluded of course

The problem that both you and Iblis are having is that you are not being specific enough, and therefore it is equally easy to agree or disagree with anything you both say. If one of your clocks is next to me, and the other is "half a universe" away then, definitely, there will be a difference. But if I observe them from a point equidistant between the two clocks, then they will appear to run at the same rate. Because they are at different points in space, you cannot make any direct comparisons. Absolute (non-observer dependent) comparisons can only be made at a point.Just because the two clocks' time directions are different, does not mean that the two clocks are running at different rates, any more than it means that they are running at the same rate. The terminology used is far too loose to be able to make sensible, well-defined statements about what is actually happening. Edited by cavediver, : No reason given.

Only by way of gravitational-well time-dilation, and that would take some g to generate the day/year ratio.

No, not at all I'm sorry I speak harshly but it is for a purpose: the internet is full of incorrect information regarding relativity, and I want to ensure that any readers will not be confused or persuaded that your view is correct. Hmmm, are you sure? Which textbook is it? It is an old mistake to think that accelerating frames require GR, and some old textbooks may have this error. If it is a new book, then I may write to the author If your GR professsor says this, then there is a problem. What is his name? Is he a professor of relativity, or some other area of physics such as particle physics, astrophysics, etc?So, you cannot possibly change the metric of space-time by simply observing it from an accelerating point of view!! The Universe likes you but it doesn't care about you that much Your coordinate system may look weird from your point of view, but the space-time of Special Relativity starts off flat, and stays flat. The Einstein Field Equations are trivially satisfied (g_uv=diag[1,-1,-1,-1], g_uv,w=[0], R^u_vwx=0, R_uv=0, R=0) and a change of coordinates to an accelerating frame is not going to change this.

There's nothing wrong with using GR to solve the problem - and this is by using a global homogeneous gravitational field as an equivalence to the acceleration - it's claiming that you can't use SR that I object to. We can simply calculate the proper length of two different length paths from Event A to Event B, and voila, we have the twins paradox.ABE: he may be objecting to using SR in a real world example, which I can appreciate. As ever, you have to be very specific in relativity. Edited by cavediver, : No reason given.

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The principle of relativity, however, tells that Eva can consider herself at rest and Elizabeth as the traveller.

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No, it doesn't. There is no one frame of reference in which Eva remains at rest.

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In order to arrive at a clear answer (...) we shall have to use a result from the general theory of relativity

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And this is where this goes wrong. There's nothing wrong with using GR, but SR is just as good, and there are even papers demonstrating the equivalence of the two. What do you mean, as "seen" by the twin? Do you mean his observations of the home bound twin as he travels? This can be done by basic hyperbolic geometry - just trace the null rays from the home path to the travelling path. In terms of the actual age experienced - this is just the proper time along the respective paths.

No, he will see the Earth turn more slowly - the Earth will appear red-shifted.

No - from the point of view of the astronaut, the Earth is turning less and less. Each day Big Ben sounds noon in London, we sends a signal to the astronaut. But each day, the astronaut is further away, so the time interval he measures between receiving each signal gets longer and longer.