Alberto, it seems that you still haven't noticed that we've mostly been talking about the other part of the twin paradox. We weren't wondering about the fact THAT the twins have different ages - I believe that this is true has been established early. The fact is merely that people say (**NOT ME**, by the way. I add this disclaimer since that went wrong last time :P) that since everything is relative, you should be able to do the same for Twin B, giving you the opposite age difference. That this is false (because of the fact that twin B is not moving in an inertial frame, see below) has been established on page three.


However, I'm getting really tired of discussing this here, since - again - there is absolutely nothing LEFT to discuss.
I really feel that I've answered this "paradox" about ten times already. I really don't feel like doing it yet again.


But fine, one last time: Here's my answer regarding everything of the twin paradox: Calculate it in Twin A's system, which is an inertial frame. You'll get the result that we've seen above several times.
Now, since that it a completely tensorial equation, it'll be true in all coordinate systems.

Yes, different paths trough spacetime will have a different "length" (referring to the Minkowski-metric here, which, as we know, is no real metric), so the age-difference will depend on parameters that define the path, including the relative percentage of constant movement, acceleration and "turning around".



[The term "inertial frame" has definately something to do with the twin paradox: the formulas are only valid in inertial frames. Twin B's system is *NOT* an inertial frame. It follows that the equations cannot be used in his system - and applying them in that system was the essence of the twin paradox (well, it's second part)].

How would stars look like when you travel at the speed of light and faster?

i also wonder about this.

is the effect on the enterprise windshield realistic? or those points/lines star systems?

The aging process occur during the whole flight




Your scenario is exactly what I meant but, in my opinion, you draw a false conclusion

Before explaining my point of view,let's make a simple consideration :

a) a mission to mars : departure - 1 year flight to go - turning back - 1 year flight back - landing
b) a mission to juppiter : departure - 4 year flight to go - turning back - 4 year flight back - landing

Following your reasoning the time shift ahould be the same but in case b) it is higher than in a)

Having said that, my point of view :

The two twins have been living for a period of time in different " time / space domains" which caused the de syncronization of their clocks
The logical but non intuitive explanation of this effect has been already discussed
Once the twin is back, his clock remains desyncronized
This effect is described in the special relativity whereas both twins are in a inertial system ( exactly the same system according to the Galileo's definition of inertial system)
Therefore there is no reason to emphasize the concept of "inertial " system

Someone claimed that the scenario of the special theory is not realistic due to the fact that in the reality the pilot must reverse his velocity

Ok but such kind of abstractions are normal in pyisics !
You can figure out a realistic scenario whereas the effect of turning acceleration / deceleration are negligible
The velocity is , in the equation, in term of : V^2 thus the sign does not play any role



You must apply the theory of general relativity
I agree with you and Error00014
But in my opinion you and Erro014 missed, so to speak, "The big target"
In other words
To explain the time shift in a real situation you dont need to evoke "inertial system" and all that stuff which are redundant or even deceiving
The " essence" of the twins paradox lies in the special relativity

Puh.


It doesn't, as my example proved. Anyway, if you don't believe me, believe Wikipedia or any text book on that issue.



no, I didn't say that. The inertial systems that B changes are not the same in scenario a) and b).


Ok, one last question on this, maybe then you'll see that you are wrong on that.
Following your reasoning, which is - again to make sure we're talking about the same thing - turning around has nothing to do with it but ONLY the free (no acceleration/turning/whatever) motion of B in space. How do you explain that B is the older one in the end if NOTHING distinguishes their relative motion?


It is, because without it the twin paradox is a paradox.


Tell us that scenario, I am quite sure that in this case you can't.


What does the sign of v have to do with that?


Maybe you can do such a calculation for us. The steps B moves away from earth, B turns around and B moves towards earth should be done separately. You may neglect the middle step if you think it is not important.

Mathematically this is whole simple. Just take the speed, multiplied by gamma and you get the speed of the ship it has when you take Einstein's formulae. Like that, the travel is for B much shorter than for A. This should be common knowledge for everyone seriously into game programming as it is mathematically trivial.

I suppose I made myself understood on this point
I said that both the free motion and the turning around cause a permanent time shift
The former can be calculated using the simple equation of the special relativity
The latter need the much more complicated general relativity theory

I said also that in case of a long journay the former definitely prevail over the latter which can be therefore ignored
The special relativiy only is therefore sufficent to explain the time shift which occur in spatial missions without the need of further complication




This question has been asked also by Error014

The twins are identical at the beginning but their Hystories are differnt

a spend the whole life on the earth
b part on the earth and part in the space

It is b who returns to earth ,iit is not a

We are talking about a " principle of equivalence "

Equivalence entails "symmetry" , it does not entail "identity"

There is thereforo no logical contraddiction in the claim " A is older than B"

It is not , of course, an intuitive claim

These are the only serious questions, and you got my answer
The others are only issues...sorry

If you say that the turning point can be neglected then there is no such thing as a different history for A and B, as both - according to your symmetry principle, or better special relativity - are moving relative to each other. With constant speed. Thus, A is older in B's frame, B is older in A's frame. Contradiction.

As relative motion does not distinguish A and B, what does? (I give you the answer: B turns around.)

@AdrenalinMob: Maybe you can make such a trivial calculation for us. I'd really like to see it.

@Joey: no time

Now this is an interesting question, deserving of a thorough discussion!


One of the effects predicted by Special Relativity is that moving things (imagine a one-meter long pole) appear shorter in the direction they're moving in for an observer at rest. I.e., if I throw a 1-m-pole past you:



Then it'll appear shorter than 1m to you. Instead, it'll seem to be 1m/\Gamma for you.


So if you're moving at a noticable fraction of c (let's ignore velocities bigger than c for now -- on the grounds that since the energy needed to get you there approaches infinity, but we can try and discuss that theoretical thing later if you want), in a system that has you at rest (your rest frame) will see the stars moving in a noticable fraction of c. In turn, they'd appear shorter.

But here's the thing: This is all regarding the pure length of the object. We're interested in what we see, right? If that is the case, then we'll find the complete opposite to be true.

This is known as Terrell Rotation (or, depending on who you ask, Penrose-Terrell rotation).
Here's a nice article on it: Link!

Now, if you do the math, you'll find:
objects passing you appear rotated (see above)
objects moving away from you appear contracted
objects moving closer to you appear elongated.


So yes, you might actually see those kind of lines.

Joey, Alberto -- does anyone of you know more about this Perrell-Tenrose-effect that you'd like to add?