Twin paradox

  • Thread starter granpa
  • Start date
  • #26
645
0
Hello again.

One last thought.

If the travelling twin passes the stay at home twin on his outward journey and is the same age he cannot have been born at the same time. If they were born at the same their travel histeory i.e spacetime intervals covered, are differenttime they cannot be the same age. Time dilation between moving frames or something along those lines.

Either way they are not twins in the normal sense of twins.

Matheinste.
They could be cousins twice removed. But "The Cousins' Paradox" doesn't quite have the same ring.

Twins are used as a sort of shorthand (perhaps not intentionally) meaning "two of the same". So the twins could just be two copies of the same person, the traveller takes out some sort of special insurance, by jumping in the Duplomatic 2000 and making a back-up copy of herself. Then she gets fired off into space reaching cruising speed after a very short period of time and sails off to some destination, then turns around, reaches the same cruising speed in the opposite direction (again very quickly) and returns to see how the copy is going. The copy is older, and pissed. They get in a row and the older, stay-at-home copy loses it and goes on a rampage, leading to a confusing car chase with people shooting at each other for no readily apparent reason. In the end, you find out that in fact both were copies and the real original had gone off in another space ship which went much faster than the first and hence the original is still young and beautiful when she gets back and marries the policeman who solves the case by accurately shooting the bad copy (twice, because you thought she was dead, but she wasn't really the first time). Just before the credits begin to roll, you learn that the policeman is actually a grandson of the copy he just "retired" (he was raised by an Angolan sheep herder, so he never knew).

Oh, hang on, that has nothing at all to do with the original twins' scenario.

Feel free to pick holes in my alternative scenario.

cheers,

neopolitan

(Sorry about that granpa, it was just that the small-mindedness got to me for a moment there :smile: )
 
  • #27
1,060
0
Hello neopolitan.

Point taken

Matheinste.
 
  • #28
Garth
Science Advisor
Gold Member
3,574
105
Garth said:
Stella and Alf have different hyper-surfaces of simultaneity, this is where the paradox arises.

Alf cannot simply adopt Stella's clock reading as his own.
he doesnt. he just notes how much time elapsed for stella.

time elapsed for Stella on outward journey + time elapsed for alf on inward journey=total time elapsed for moving twin=acceleration is not necessary to explain the paradox.
There is no paradox in non-inertial observers experiencing less lapsed time than an inertial one, the paradox would be if two observers, Terra and Stella, each believe that they are in the inertial frame and therefore both conclude that they ought to experience the greater time lapse.

Stella + Alf cannot conceivably consider their combined experience to be inertial, there was a violent acceleration as your clock frame of reference went from Stella to Alf.

Garth
 
Last edited:
  • #29
3,962
20
..... btw, the total elapsed time is exactly the same.

..... For who(?)

stella + alf
ElapsedTime(Stella+Alf) < ElapsedTime(Terra)

For example let Stella's velocity (Vs) = 0.8c and Alf's velocity (Va) = -0.8c

Stella and Terra set their clocks to zero as they pass each other. Stella continues to a station that is one light year away in Terra's frame which takes 1/0.8=1.25 years according to Terra and 1.25*0.6 = 0.75 years by Stella's clock, Alf who is passing the station as Stella arrrives sets his clock to 0.75 years and when when he passes Earth, Alf's clock reads 1.5 years while Terra's clock reads 2.5years.

Of course this does not conclusively prove any observer is ageing slower than the others and to do that a fourth observer (Fred) would have to transfer from Stella's ship to Alf's ship as they passed the station and that would involve violent acceleration for Fred as Garth has pointed out.
 
Last edited:
  • #30
2,257
7
as i said before:
time elapsed for Stella on outward journey + time elapsed for alf on inward journey=total time elapsed for moving twin=acceleration is not necessary to explain the paradox.
 
Last edited:
  • #31
3,962
20
as i said before:
time elapsed for Stella on outward journey + time elapsed for alf on inward journey=total time elapsed for moving twin=acceleration is not necessary to explain the paradox.
All that is necessary is the path through spacetime. The twin that has taken the shortest path through spacetime when they meet again will age the most.
 
  • #32
2,257
7
All that is necessary is the path through spacetime. The twin that has taken the shortest path through spacetime when they meet again will age the most.
shortest path through spacetime=shortest path through time?

if all objects always move through spacetime at c then all paths of all objects through spacetime are the same length.
 
  • #33
3,962
20
shortest path through spacetime=shortest path through time?

if all objects always move through spacetime at c then all paths of all objects through spacetime are the same length.
shortest path through spacetime = longest proper time

this is sort of opposite to the normal intuition of the shortest distance between two points in 3-space being a straight line.

the 4-velocity may be interpreted as c for all objects but they can take different paths between events and the proper time recorded by the object taking the longest path will be the shortest time interval.
 
  • #34
3,962
20
THe attached image shows the paths taken through spacetime according to Terra, Stella and Alf. The red path taken by Terra is always the shortest according to any inertial observer so all observers agree that Terra ages the most.
 

Attachments

  • #35
2,257
7
ok. but what about the usual version of the twin paradox. dont both twins consider the other to be the one that is moving? what do their paths through spacetime look like?

just to be clear, path through spacetime is not the same as 'interval', right?
 
  • #36
1,060
0
Hello granpa.

Quote!

----ok. but what about the usual version of the twin paradox. dont both twins consider the other to be the one that is moving?-----

Yes but one is undergoes acceleration, the travelling one

Matheinste.
 
  • #37
2,257
7
ok. i didnt understand the image the first time but i get it now. so all you are saying is that the one that travels in a straight line without accelerating always travels the shortest route and is always least time dilated. i agree.

but it is a fact that no individual undergoes acceleration during this thought experiment. every individual is already time dilated at the start and remains at that time dilation throughout. the full solution can be calculated without ever referring to acceleration at all. all you need to know is the velocities of the rockets and the distances involved.

when people refer to path through spacetime i always think of Minkowski space. thats quite different.
 
  • #38
3,962
20
ok. but what about the usual version of the twin paradox. dont both twins consider the other to be the one that is moving? what do their paths through spacetime look like?

just to be clear, path through spacetime is not the same as 'interval', right?
In the usual version of the twin's paradox, where one twin goes on a long fast journey and returns to the the static twin, their paths will look like the red and green paths in the left most diagram of the picture I posted showing Terra's point of view. It is not possible to depict the point of view according to the traveling twin in a single space time drawing because of the change of direction and it that change of direction that breaks the symmetry and the paradox. The traveling might consider himself to stationary for part of the journey but after he changed direction he would have felt acceleration and would have to conclude that he can not be stationary for all of the "journey".

The symmetry is also broken if each sends signals at yearly intervals on their respective birthdays. When the traveling twin changes direction he sees an immediate increase in the frequency of birthday signals coming from his stationary sibling ,while the stationary twin only sees an increase in birthday frequency of his traveling sibling later on in the experiment. When they count up the number of birthday siganls they each recieved during the entire experiment it will agree with their difference in ages. As soon as one twin changes direction the symmetry is broken. Before the change in direction, no one can say with certainty which twin is ageing faster. I hope that sort of makes sense :P
 
  • #39
3,962
20
ok. i didnt understand the image the first time but i get it now. so all you are saying is that the one that travels in a straight line without accelerating always travels the shortest route and is always least time dilated. i agree.

but it is a fact that no individual undergoes acceleration during this thought experiment. every individual is already time dilated at the start and remains at that time dilation throughout. the full solution can be calculated without ever referring to acceleration at all. all you need to know is the velocities of the rockets and the distances involved.

when people refer to path through spacetime i always think of Minkowski space. thats quite different.

Although I did not put labels on the axes, the paths I drew were plotted on a graph with distance on the hororizontal aaxis and time on the vertical axis which is exactly how Minkowski spacetime diagrams are plotted. There is no difference.
 
  • #40
2,257
7
i meant that the interval is calculated differently. as i am sure you know.
 
  • #41
3,962
20
... but it is a fact that no individual undergoes acceleration during this thought experiment. every individual is already time dilated at the start and remains at that time dilation throughout. the full solution can be calculated without ever referring to acceleration at all. all you need to know is the velocities of the rockets and the distances involved.
In your slightly modified version with 3 observers and no acceleration it is impossible to prove whether Terra, Stella or Alf aged the least.
 
  • #42
2,257
7
In your slightly modified version with 3 observers and no acceleration it is impossible to prove whether Terra, Stella or Alf aged the least.
you may be right, but it is a fact that it produces exactly the same result as the usual version. the total transit time of stella + alf = the total transit time of the moving twin.
 
  • #43
Garth
Science Advisor
Gold Member
3,574
105
you may be right, but it is a fact that it produces exactly the same result as the usual version. the total transit time of stella + alf = the total transit time of the moving twin.
So there is no paradox.

Two observers meet at one event and meet again at a later event.

The non-inertial observer experiences the smaller time elapse.

As I pointed out, Stella+Alf is a non-inertial frame of reference.

Garth
 
  • #44
2,257
7
i know there is no paradox and the supposed paradox can be explained quite easily without reference to acceleration. all you need to know is the velocity of the rockets and the distances involved.
 

Related Threads for: Twin paradox

  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
5
Views
930
  • Last Post
2
Replies
25
Views
8K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
16
Views
5K
  • Last Post
Replies
5
Views
2K
Top