It is true that the formulas in special relativity for both time-dilation and length-contraction require to be solved in an inertial frame. However, that does not mean that accelerated paths cannot be solved in there - after all, we were able to calculate the proper time that passed for Twin B -- we only had to do it in an ienrtial frame (Twin A's system).

In that level, the paradox is solved simply by saying that it is not valid to simply assume the same formulas are valid for both for the WHOLE duration, since there is no inertial frame comoving with Twin B.


It may be derived without using Twin A's system [obviously], though of course it has to be an inertial frame, so "Twin B's system" is out of the question [no inertial frame].


~ ~ ~ ~ ~ ~ ~ ~ ~

I always wonder why in those science-threads, the tone often gets aggressive?
I do agree with Joey, your last comment can easily come across as arrogant. The fact that we're all speaking in different languages than our native one makes it all the more difficult to judge the intention behind comments.
Not sure how to resolve that, I'm just trying to explain why Joey might have reacted the way he did.

You might be correct about the tone of Joey's replies - for me, it feels different and less hostile (though maybe at times, there is a hint of arrogance), but again, I do believe that language (and maybe customs in those) plays a big part of it [Joey and I both are native germans].


I, for one, stick with my tone of careful idiocy

I'm sorry if my tone comes across in an arrogant way. In general I think I'm quite good at writing and understanding English, but I have no clue how my tone sounds like. I apologize.
Still I find it quite bothering that people (Alberto) keep telling me that I have no clue, that I should "study more" or "take my old physics books from the shelf - too long time has elapsed". Speaking of arrogant, stuff like "at 14 years old my main interest was soccer" is very helpful to keep arguments on an objective level.
I always try to give explanations, but what might sound clear to me might not be clear at all to others. Then ask. But I often have a feeling that posts are not read carefully and stuff is said only that something is said. I mean, we've already resolved the twin paradox like twenty posts ago and suddenly the discussion starts all over. In threads like these that's annoying. I spend quite a bit of time writing my posts, looking up stuff etc., but I don't see any sense in it if you're not interested. I could as well do other things.

So much for that. To repeat my arguments referring to the twin paradox let's look at it in a different way.

• Horizontal lines mean "at the same time" for A
• Red and blue lines mean "at the same time" for B
• Points mean proper time
• During flight, A thinks that B is aging slower while B thinks that A is aging slower (check that in the diagram, when B reaches point B he has passed 4 years proper time during which A has aged about 3.2 years - and vice versa)
• When B turns around - however that is acheived - A ages rapidly when seen from frame B
• This is what distinguishes both frames: while B ages slower all the time when viewed from A, A ages slower in frame B only while B is flying
• Both frames are clearly distinguishable
• There is no question whom of both will be older at the end
• No gravity involved whatsoever
• This effect is only due to the change of inertial systems of B

To calculate it with a cheap trick which completely obscures the physics behind it imagine that B travels for, say, ten years as seen from frame A and then beams back to earth. Of course his proper time is shorter than the time on earth (t/\gamma). As seen from frame B this picture is complete nonsense, though.

"While it might sound impressive for people who do not know much about it, I don't like to discuss with someone who can't express a clear idea."

Did you recognize who wrote above sentence ?
It doesnt sound quite nice , does it?
Anyway let's put aside such childish ( from both parties ) disputes

Now you provided an explanation
However unless I completely misunderstood your words,in my opinion it is a wrong explanation

You said

"During flight, A thinks that B is aging slower while B thinks that A is aging slower "

and then

•When B turns around - however that is acheived - A ages rapidly when seen from frame B"

for " turns around " do you mean that B has reached the farthest waypoint and he is returning to earth ?

If so
First of all I dont get what you mean for " When B is flying "
B is alwayes flying
except of course at the departure and at the arrival
Consequently the former sentence is alwaye true , the latter alwayes false

However to get rid of the complication due to the "inertial frame " and similar stuff, put it this way
Suppose that the duration of the journey ,at costant speed, is very long , so long to make negligible the departure / arrival / change of direction times

If so , the simple formula of the theory of the special relativity is applicable with a great degree of accuracy, you get:

A proper time higher than B proper time

It seems unbielivable but it is like that

This thread might now hold a record for the most solutions to the Twin-paradox.


Anybody wants to ask another question? As you can see, they're answered by EXPERTS (who will then proceed to argue about both content and semantics for four more pages).

It is not a question of sematics

The relativity of of space / time is a fact that it is explained by the theory of special reativity

Let's see the following examples

Bilions muons pass through our body every seconds

Muons are generated by the collision of cosmic rays with the atmosphere
You can generate muons also in lab and you can measure their decay time

If you multiply the decay time x the speed of light you get some hundreds meters

How can the muons reach us , the atmosphere being some km depth ?

The explanation is given by the theory of special relativity

muons travels at a speed close to the speed of light
If you multiply the muon decay time by the cofficient of time dilation than you find out that the muon can cross the atmosphere

We can therfore state that the speed by itself slow down the decay process
For the same reason it is reasonable to assume that the speed slow down also the aging process of the twin pilot

This is however valid only for us , living in the earth spatial/temporal dimension

From the muon viewpoint the decay time remains constant but the atmosphere is only some hundreds meter thick

It is the time / space symmetry

P.S.

Just to clear up
The key concept is the so called :

Time / space interval

Common sense assume that space and time are unrelated measures

The theory of special relativity on the contrary demostrate that all the observers share the same " space / time interval" which is a combinattion of local time and local space

The twin of the earth "consumes", so to speak, only "time"
The twin on the srarcraft "consumes" both time and space thus his time consuption is lower ,the "space/time interval " being a constant for both twins

Useless to say that a/m explanation is non intuitive but it is confirmed by the experience :

a) Spatial missions
b) decay time of particle in particle accelerators
c) Behviour of particles coming from the space
d) Spectrum of far stars

You know... I was only trying to end this discussion, since there's actually nothing elft to discuss (though we've reached that state at about page 3).

Error014

I definitely agree with you that a thread sooner or later must come to an end

However I don agree with you that a solution has been reached at page 3

If you go through the thread the term "inertial system" is recursive

Sorry , it has nothing to do with the twin paradox

The twin paradox is an immediate and exclusive consequence of the special relativity

The relative speed only generate the permanent shift of time
You dont need anything else

The poblem of acceleration and deceleration is a false problem

I ask you a question :
Suppose that the duration of the journey at constant speed is very long,so long to make negligible the departure the arrival phases

Do you mean that the twins on arrival are equally aged ?

PS

if joey is not yet upset with me I would appreciate also his comment

I'm not upset.
I don't get the question though. The duration of the journey for B is very long and acceleration at the beginning and deceleration at the end should be neglected. That's ok, we could assume (*) that B doesn't have to accelerate/decelerate at all, for example he has already some speed, flies by the earth and in that moment synchronizes clocks and compares them at the end of his journey. (Just to avoid that we're again talking about different things - is this what you mean?)

What I don't get though is what you mean with constant speed. Do you mean the modulus should be constant? Or how is turning around managed for B? Since, when the direction of his travel changes, he also changes his inertial system and his internal clock (or better: the relation internal clock - exterior clock) changes in a non-trivial way.
Having said that, if you would calculate it like that anyway - wrong, though - and just take the time to be the same for B before and after he has turned around (neglecting the time which passed in between) (assume for example that B flies away from earth and then, instantaneously, has turned around and now flies back to earth, neglecting all physical effects this action comes with) and plug in special relativity, you would get a paradox. Namely, for B, A has aged slower. At the same time, in the rest frame of A, B has aged slower. According to special relativity, both are correct. When they come to compare their clocks, clock A shows less than clock B in the B fame and vice versa. Since both clocks are at the same place (on earth) when they compare them this result is nonsense.
=> something has to happen during turning back.

Note the "=>", since this is actually a valid proof - we can describe physics during flight with special relativity and we haven't cheated at the beginning or at the end when we assume the experiment conditions to be as stated at the beginning (*). You can check it, or ask Error if you trust him more.

So I can't answer your question. Could you restate it?

So let me ask you a question: How - with which formulas, which theory - would you describe the change of flight direction from "away from earth" to "towards earth", so that the outcome of the experiment unambiguously gives the result "B is younger than A"?

Thanks for the answer
Actually my example was a little bit obscure

Consider the following cases :

#a departure - acceleration - turn - deceleration - arrival
#b departure - acceleration - cruise - turn - cruise - deceleration - arrival

I think that the permanent shift of time in case b) is higher than in case a) due to the two cruise time intervals at constant speed ( module) , assuming of course that the acceleration , deceleration and turn phases are the same both for a) and b)

b) is a pratical case of a shuttle which remains in the space for a long period
I mentioned in my previous post that a starcraft travel at about v = 40.000 km/hour
Suppose it remains in the space for 1 year
If you put these data in the simple equation of the special relativity for the time dilation, you get a time shift t = 3 - 4 secs

Well this is exactly what has been experienced in the spatial missions
The clock on board were found 3-4 sec late on the arrival

Summing up

I did not mean that all the discussion about the change of " inertial frame " etc are wrong , I mean they are redundant

The "essence" of the twin paradocx lies the time / space symmetry
whereas the twin at rest "moves" only in time , the pilot "moves" both in "time" and in "space"
The time shift is a immediate consequence of the fact that time and space are related items , even though it is hard for everybody to really grasp this claim
For common sense time and space are unrelated measures

According to you, at which point does the relative aging process (making A older than B) occur? During flight? The cruise time?