Is there a way to intuitively understand proper time in special relativity?

[minijumbuk]

i have a question...
according to time dilation...as an object travels close to the speed of light, relative to antoher observer, the time goes slower in the moving object and it will appear to be "younger' if it was a person on the space travel...
however, relative to the person on the spacecraft travelling, the EARTH is moving at the speed of light and they will see Earth traveling at the speed of light and we will be the ones slowing down, relative to the person on spacecraft

we see the person in slow motion and
they see us in slow motion...
which one is correct?
i need someone to explain this to me T_T

 

[rbj]

i think this is called the "twin paradox".

 

[G01]

Yes, this is an example of the Twin Paradox.

As long as the spaceship keeps moving at the same speed with no acceleration what-so-ever, both observers can be considered correct!

Now, if the space traveler decided to come home, that's a different story. In order to return, he would have to turn around. This unavoidably involves acceleration. Once the space traveler accelerates, he is no longer in an inertial frame and his point of view is not equivalent according to Special Relativity. When the space twin gets home, he will definitely be younger than the other one.

Does this help. I'm no expert, but I think I am at least somewhat correct here. If someone notices an error I made, please correct me, for my sake and the OP's.

G01

 

[HallsofIvy]

It's not exactly the "twin paradox". The twin paradox usually involves two people who are exactly the same age in the same frame of reference. One, A, moves away at high speed so that the one that remains still, B, sees him as aging more slowly. A sees B moving very fast relative to him and so aging slower. When A manages to get back to B, who is older? Of course, the difficulty is that A cannot move away at high speed and then come back without accelerating so we no longer have "inertial frames of reference".

The idea of two observers, each moving at high speed relative to one another, both see the other as aging more slowly is not a "paradox"- it is a fact of nature that has been experimentally verified.

 

[minijumbuk]

oh ok i understand now! XD thx

 

[MeJennifer]

Actually in space-time nothing slows down or speeds up!

The total accumulated time of a particle in space-time is the path length between two events (longer paths accumulate less time).

So when we have two particles, or two twins, that travel between two events (the departure and the joining) on paths with different lengths their accumulated times will be different.

 

[masudr]

longer paths accumulate less time

Indeed this is correct if we consider the paths in space only (and looking at it from certain frames of reference only).

I personally prefer to think of it as a longer path in spacetime accumulating more time, but I think this requires one to be somewhat accustomed to 4 dimensions, and this may not be at the level of the OP.

 

[MeJennifer]

I personally prefer to think of it as a longer path in spacetime accumulating more time, but I think this requires one to be somewhat accustomed to 4 dimensions, and this may not be at the level of the OP.

You are absolutely correct masudr, in space-time the length of a path is the accumulated time and thus the longer path accumulates more time.

I think the main problem in understanding is not that we have to deal with 4 instead of 3 dimensions. One can reduce many problems to only 2 dimensions by having only one spatial direction. The main problem is the way those 4, or 2 reduced, dimensions are constructed.
You find you can't really draw it on a piece of paper and then expect to get intuitive lengths.

 

[robphy]

You find you can't really draw it on a piece of paper and then expect to get intuitive lengths.

You can, if you change your intuition about lengths seen on a spacetime diagram.

(My paper, "Visualizing proper-time in Special Relativity", http://arxiv.org/abs/physics/0505134 , shows where to draw the tick-marks on an observer's worldline. The associated animations are here: http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/ )