Understanding Time Dilation: Explaining the Twin Paradox in Special Relativity

[Continuum]

Hey guys. :)

I'm learning Special Relativity at the moment and I'm confused by time dilation.

Let the Earth be the frame of reference and have some spacecraft leave the planet at 0.5c for instance. If the spacecraft travels for 15 years (as seen from earth), time dilation means that it seems like only 13 years has passed on the spacecraft . So now 15 years on Earth will seem like 13 years to those in the spacecraft .

If you now take the spacecraft as the frame of reference and 13 years has passed, the above would mean that 15 years would have passed on Earth wouldn't it? However, this isn't so, since from that frame of reference, you see the Earth move away and thus that undergoes time dilation - so time would appear slower on Earth. I was just wondering if you could explain it to me, since it seems like a contradiction. Some people said that it involves the twin paradox but that involves an accelerating frame of reference, yet this does not.

 

[Janus]

It involves the Relativity of Simultaneity. In short, frames of reference with relative motion with respect to each other will not agree as to what events are simultaneous.
IOW, the Earth determines that at the moment it clock reads 15 years, the spaceship clock read 13 years, while according to the ship, when its clock reads 13 yrs the Earth clock will read 11.26 years

 

[Continuum]

It involves the Relativity of Simultaneity. In short, frames of reference with relative motion with respect to each other will not agree as to what events are simultaneous.
IOW, the Earth determines that at the moment it clock reads 15 years, the spaceship clock read 13 years, while according to the ship, when its clock reads 13 yrs the Earth clock will read 11.26 years

Oh ok, thanks. :)

I was reading up on the Relativity of Simultaneity and I've got the gist of what it is: that frames of references which are moving will disagree as to whether or not events are simultaneous (like in Einstein's thought experiment involving the two lightnings and two observers - one stationary and another one moving). However, I don't really get what 'proper time' is. Can anybody please it's definition of 'time between two events in a frame of reference in which the two events occur at the same point in space'?

Thanks. :)

 

[robphy]

...However, I don't really get what 'proper time' is. Can anybody please it's definition of 'time between two events in a frame of reference in which the two events occur at the same point in space'?

Thanks. :)

Proper time ("your own time") is the time read off your wristwatch. [Your wristwatch is effectively at the same point in space in your own frame of reference.]
As noted by Special Relativity, different people ("observers") will generally disagree on the elapsed-time [read off their wristwatches] between two meeting events.

On a spacetime diagram, it is arc-length of the worldline of an observer.
(Spacetime and proper-time were introduced by Minkowski.)

 

[Dale]

To expand on robphy's post. There are two kinds of time in SR. One is called "coordinate time" and the other is called "proper time". As robphy mentioned proper time is the time read by a clock carried by an observer, the observer is not necessarily inertial. Coordinate time is the time as determined by a system of inertial clocks at rest wrt each other which are synchronized according to the Einstein synchronization procedure. If an observer is inertial then in the observer's rest frame the proper time will be equal to the coordinate time.

 

[Continuum]

Proper time ("your own time") is the time read off your wristwatch. [Your wristwatch is effectively at the same point in space in your own frame of reference.]
As noted by Special Relativity, different people ("observers") will generally disagree on the elapsed-time [read off their wristwatches] between two meeting events.

On a spacetime diagram, it is arc-length of the worldline of an observer.
(Spacetime and proper-time were introduced by Minkowski.)

So it's basically the time as measured in the inertial frame of reference of the object being looked at?

 

[meteor9]

Fortunately the science advisers are here to answer your question , but i wanted to say something about 'time dilation ' from another point of view , we are all familiar with the 'traditional' formula and theories about the GR and SR, so i will not stress on that and will rather express my own opinion which is based on all the physics and astrophysics theories but extracted from my own experience . To develop my analysis i just invite you to consider the music and the 'time' included within . For example when you spend 4 hours(based on your wristwatch) in an opera theater to listen and watch an opera of Wagner , Tristan and Ysold for instance, after quitting the opera theater , are you able to tell the quantity of time spent there ? Did it really last 4 hours ? No ! Time was dilated there and you were not in some sort of spaceship, then what happened? Quite simply you didn't notice parts of events coming one after another , you are even unable to remember a single melody, because the opera is built on a continuum without any beginning and an end , you could say that the opera lasted some hundred years or just a second , and both are correct , because you experienced the confusion of time and space at an original point , you could even have the impression that it didn't exist at all . Music structure is as mysterious as the big bang . You listen to music and you can't touch it , you can't reach it , because it is just a play and a game with the 'texture' of Time, it can dilate, stretch or shrink .