Special relativity?

>  Isn't time (whatever time is) constant?
Only within a particular reference frame.

The twin situation involves at least 3 different reference frames.

Although there can be a change in the aging process for the space twin during acceleration, that is not relevant to the paradox
More relevant is that since the space twin occupies different reference frames during the outward and inward legs of the journey, their notion of "now" that is attached to that frame changes, which changes their measurement of the "current" age of the earthbound twin.
That the notion of "future" and "past" can be different for people who take different paths through space-time is not unlike the way the notion of "ahead" or "behind" can be different for people who's paths face different directions in space.
When the space twin turns around, the earth twin changes from being far "behind" from one point of view, to being far "ahead" from a different point of view.  This does not mean that the earth twin suddenly moved a great distance, or that either point of view is incorrect.


there are both illusory and real aspects of special relativity


if the twins have a proper understanding of relativity, they will no be surprised.

Hi,
One of the key things that you need to understand is the concept of space-time and frames of reference. So the twins share the same frame of reference when they are together. But once one twin separates and goes her own way, the time they experience is going to be different. This was the fundamental revolution that Einstein introduced. Only when the come back together, and into the same frame of reference, do they see the difference in their relative experiences of time.

So to answer your first question. The differences they experience in time occurs when they move apart and continues to be different once they remain apart. Acceleration doesn't come into this as Special Relativity only deals with uniform motion; there is no acceleration. So there is no way to really answer the question using SR. What the acceleration does highlight is a separation in the twins' frame of reference and hence the differences in experiences in time.

So now you have the scenario where they are both moving away from each other.

Yes, they will see each other's clock tick slower.

Not sure what you're asking in part b, but yes. That is what Time Dilation means.

As far as c goes, yes, it is possible for a tock to arrive before a tick. That deals with simultaneity. If we assume that the tick and tock are two seperate events, it is possible to move a frame of reference to reverse the observed order of events. No. It does not violate causality.
(Please, do not ask me to write on this. A chapter just explaining it may be necessary. If you need further clarification I'll do my best"

As to d. no it's not illusary. It is reality. The key concept that you have to get is that time is not static or the same for different observers. So it is not an illusion. It's real and how the universe works.

and for the last question. No they will be of different ages. As they are moving away from each other at a uniform speed, they will experience a time dilation. How much depends on the relative speed of the frame of reference they return back to. The situation that you are describing involves more than two frames of reference; there are three and possibly more. So the math is going to be a little more involved.

Believe it or not, what you are describing HAS been performed in 1971. They flew two atomic clocks in opposite directions and they observed time shifts that was predicted by SR. The rotation of the earth had to be taken into account and not just the relative speeds to each other. Only when did the two clocks come back to earth, and in the same reference frame, were they able to compare the time differences.

I hope that helps and hasn't confused you more.

Hi Photon0137,
Thanks for your response. But I'd like to clarify something about Scenario 2. In it both twins start off talking to each other close by undergoing no acceleration. They agree on a shared itinerary to follow:
a) Then they both accelerate in opposite directions at constant same acceleration to a specified speed
b) They turn off engines for an agreed amount of local time
c) They turn around (in a shared plan - a loop at same speed)
d) They approach each other undergoing no acceleration for an agreed amount of local time
e) They decelerate at constant same acceleration meet at the starting point at zero speed

Firstly, I never meant to infer that a tock would arrive before a tick since the speeds are always < c.

In a, b, d, e, it would appear that both twins would see each their twin clock as slower than their own. Right?

And the shared itinerary requires same acceleration, speed, and deceleration all for agreed upon specified local clock time.

From symmetry, it would seem to me that when the twins reached their rendezvous, that their clocks and their age would be identical. So, all the slower clock that they saw would appear illusory.

Furthermore, when they were approaching each other, the tick tocks should appear to be faster than their local clock due to Doppler shifting. Whether the received tick tocks is faster or slower than SR time dilation is not clear yet. As they approach there is a blue shift so the tick tocks should appear faster than expected. And in the initial departure phase, the tick tocks should appear even slower than expected SR results, maybe?

I was thinking that some of the perceived tick tock increases or decreases may be due to SR and also may be due to Doppler shifting.

> In a, b, d, e, it would appear that both twins would see each their twin clock as slower than their own. Right?
correct

> From symmetry, it would seem to me that when the twins reached their rendezvous, that their clocks and their age would be identical.
correct
> So, all the slower clock that they saw would appear illusory.
If you want to call a different perspective "illusory"
You might call Doppler effects  "illusory"
But time dilation is real, regardless of any illusion.
Just as one person can measure a certain interval as 5 steps forward, and another person might measure the same interval as 4 steps forward, 3 steps left.
Neither measurement is illusory, they are just made from different perspectives.

We are used to this kind of perspective change, with rotations between "forward" and "left"
but rotations between "future" and "left" are less familiar because at ordinary speeds, everyones "future"
is so close to the same direction that we do not notice the differences.

But in d) They approach each other so the tick tock received would appear to be arriving at faster rate than when they were in b) where they were moving away from each other. Right?? (just like blue shift when a star is traveling towards the receiver and red-shift when traveling away)

I just saw post http:#31838721
My post http:#31838823 was in response to http:#31837874

> But in d) They approach each other so the tick tock received would appear to be arriving at faster rate than when they were in b) where they were moving away from each other. Right??
Yes, this is the Doppler effect.

OK, thanks!