# Twin paradox without acceleration - A different question

1. Jan 26, 2014

### rede96

Hi, I noticed this topic already being discussed but didn't want to hijack the thread with a different question. I don't know if this has been asked before but if it has I couldn't find it.

I was watching something recently about quantum physics and entanglement and it mentioned something about how teleportation (beaming from one place to another instantly) is something that could be possible, at least in theory. So it got me thinking...

Imagine two planets separated by some cosmically large distance. There are a set of twins who are both on Planet A when a space ship passes by at some relatively fast speed heading towards Planet B. One of the twins beams aboard the space ship and heads off towards planet B. At the point when the space ship passes Planet B (In the travelling twins frame) the twin beams onto a second space ship heading in the opposite direction back towards Planet A.

When the space ship passes Planet A the travelling twin beams back down to be with his twin brother.

As the travelling twin has not gone through acceleration (at least not as I understand it) will he still have aged less than his brother?

Or does the process of beaming instantly (as we are talking about entanglement) constitute acceleration?

Or is this just a stupid question :)

2. Jan 26, 2014

### JesseM

It's the geometry of his overall path through spacetime that creates a difference in aging, not the acceleration itself. In terms of a spacetime diagram based on an inertial frame, a straight-line path through spacetime between the event of the twins departing and the event of them reuniting will involve more aging then a bent path (one consisting of straight segments at different angles, like a V-shape). It's analogous to the fact that on a 2D plane, a straight-line path through space always has a shorter distance than a bent path. If you have two cars with odometers running between points A and B, and one drives on a straight line while the other heads off in a different direction away from A, then changes direction to drive towards B, the car that took the bent path will naturally have accumulated more miles on its odometer. This would be true regardless of whether it accelerated when it changed directions or if it could somehow instantaneously teleport from a state of moving in one direction to a state of moving in a different direction--what's important is the shape of the overall path as seen in a birds-eye-view, not precisely what happened at the turnaround point.

3. Jan 26, 2014

### WannabeNewton

That is not what quantum entanglement entails.

4. Jan 27, 2014

### rede96

To be honest I cant remember the exact process but it did involve seperated entangeled particles. The process invloved using the seperated entangeled particles to 'replicate' a person in a different place rather than transport matter.

In any case it doesn't matter for my example, just that in theory it was possible to transport a person from one place to another.

Last edited: Jan 27, 2014
5. Jan 27, 2014

### rede96

Im not sure I follow, sorry. To make it simple we could simply have the twins starting in the same frame, then one teleporting on board the spaceship going in any direction, then at some point the twin teleports back to be with his brother. Or we could even have the twin on the Planet teleport to join his brother on the spaceship.

What I am trying to understand is simply the paradox this seems to create as there is no change of direction that is special to either twin. The twin who teleports to the spaceship can say that it was his brother on the planet that speed off in a certain direction and vice vera.

In the normal twin paradox I can understand that one twin will accelerate (Change direction) but in my example, technically there is no change of direction. Just one twin moving instantly from one inertial frame to another.

I guess the only thing I could think of that made sense to me was if one of the twins changes reference frames, even if instantaneously, then it would be that twin that would age less. So the paradox is resolved because one twin changes reference frames and one doesn't.

6. Jan 27, 2014

### WannabeNewton

There's a difference between propagating information and states of systems from one place to another in a way that doesn't violate causality (by means of Lorentz covariant field equations) and instantaneously "beaming" information and states of systems from one place to another. The latter is not allowed by special relativity so you're talking about something that isn't even present in the theory. And certainly quantum entanglement does not imply instantaneous transfer of information. This is another artifact of inaccurate pop-sci storytelling.

7. Jan 27, 2014

### JesseM

Hi rede96, the experiment you are thinking of is "quantum teleportation" which could in principle be used to transport any arbitrarily-sized object although in practice this would be extremely difficult for objects larger than a few particles...see the article on the subject here. Quantum teleportation is not really "instantaneous" since it requires a classical message about the result of the measurement on one half the entangled system in order to for the other experimenter to measure the other half of the entangled system in a way that will cause it to replicate the original state of the first half immediately before measurement, and this classical message can't travel faster than light. But I don't think it really matters for your thought-experiment since you aren't talking about teleportation over large distances, just teleporting from a ship moving in one direction to a second ship moving in the other, with the two ships being potentially arbitrarily close together when they pass, so the time for a light signal to pass from one to the other could be made arbitrarily short--is that correct?
But there is a change of direction--you said yourself, he teleports from a ship moving in one direction to a ship moving in the other. This change in directions will be measured in any inertial frame, and the usual equations of special relativity, like the relation of time dilation to velocity, only apply in inertial frames. An inertial frame can be thought of as a grid of clocks and rulers at rest with respect to another, and filling of all of space, which can be used to locally assign position and time coordinates to every event--if you aren't familiar with this way of thinking of inertial reference frames, see the article here, or the little illustration of such a grid with accompanying discussion on this page. So the change of direction will be apparent if you plot the position and time coordinates of the observer at different points in his journey, measured relative to this grid. This is analogous to my thought-experiment where you have a car driving in one direction, then it teleports to moving in a different direction--if you have a coordinate grid on the plane where the car is driving and you record all the grid points it passes over and plot them on a graph, the change in direction will be apparent on this plot even if the driver didn't notice it.

8. Jan 27, 2014

### ChrisVer

What for if the twin did not stop at point B to go back to point A, but the point B coincide with point A...
Like for example on a sphere, starting from point A, going around the sphere and then reaching again point A...

9. Jan 27, 2014

### WannabeNewton

The "resolution" (not really a "resolution" since there is no paradox to begin with) is still the same. The two twins have world lines in space-time with different arc-lengths between the two events.

10. Jan 27, 2014

### JesseM

If one twin's path through spacetime is a straight-line path on a graph of position vs. time in an inertial frame, while the other is not, the twin on the non-straight path always ages less. If neither path is a straight line on such a graph, then you can't really make any blanket statements, it depends on the specifics of each path.

11. Jan 27, 2014

### ChrisVer

well now I get it I think, but I still feel stupid enough to continue with the questions:
Again though on a sphere-like example as I recommended, would it be possible to define an inertial frame? How could we distinguish who is moving and who is not?

12. Jan 27, 2014

### JesseM

You could define an inertial frame in the 3D space (plus 1 time dimension) that contains the sphere, so every point on the sphere would be assigned a spatial coordinate at every time. But this coordinate system would also include points in space that aren't on the surface of the sphere. And any object that moves along the surface of the sphere would not be moving inertially, if you plot its path with respect to the inertial coordinate grid the path wouldn't be a straight line of constant slope.

13. Jan 27, 2014

### WannabeNewton

You can't. Motion isn't absolute. In the rest frame of the non-inertial observer said observer will always remain at the origin of the frame whilst the inertial observer travels on some curved trajectory whereas in the rest frame of the inertial observer the non-inertial observer travels on some curved trajectory (I'm using the term "frame" in a very sloppy manner here-what I really have in mind is a lattice of synchronized ideal clocks and rigid rods connecting the clocks so the term "coordinate system" is more appropriate). What is absolute is the non-inertial character of one observer and the inertial character of the other. If the non-inertial observer is in a rotating frame then this can be detected unambiguously by using comoving torque-free gyroscopes and if said observer is in an accelerating frame then this can also be detected unambiguously by using a comoving accelerometer. In other words the absolute quantities are the world lines of the observers and the transport (parallel transport, Fermi-transport, Lie transport etc.) of orthonormal frames along their world lines (don't confuse the trajectory an observer travels on as represented in a coordinate system with the world line of the observer).

Last edited: Jan 27, 2014
14. Feb 1, 2014

### rede96

Sorry for the late reply, been away on business for a few days. Yes that was the theory I was thinking of, thanks. I remember now about the classical message that needs to be communicated but thought the process itself was instantaneous. But as you mentioned, hopefully it doesn't matter for my thought experiment.

I think I get that now thanks. So if I understand that right it isn't so much the forced that one goes through during acceleration that effect the outcome of the twin paradox, just that fact that there has been a change of direction that breaks the symmetry. Is that right? (ish)

If we imagine a different scenario, one where the twin beams aboard the first ship but stays on that ship. Then at some point in the future the second twin beams to meet the first twin on his ship. Does that any effect on the outcome of who ages most?

I guess that part of the twin paradox that I could never get my head around is what point does the twin who ages the slowest, start ageing slower. As everything is relative, once the first twin has beamed upon the ship, then they are both moving relative to each other. I know this depends on who's frame you are observing from but at some point in time they are going to meet up again and by adjusting my thought experiment as mentioned above, there is no change of direction once the twin as beamed upon the ship or when the second twin beams to join his brother.

That's the part that really does confuse me.

15. Feb 1, 2014

### rede96

So as JesseM stated, I guess that means that we would still need classical messages to exchange information prior to the subject being beamed, but the change of state would happen instantaneously?