Special relativity thought experiment

[tkmanutk]

The subject of relativity has been haunting me for while now. Everytime i feel i understand a concept, there comes questions withtin that contradict the undestanding. Have been trying to digest the time dilation & symmetry of how it is felt mutually by observers in two different frame of reference. Let me try and present a simple thought experiment below.

Let there be 2 frames of references Fa & Fb. Each of these reference frames be infinite in length. Now let us line up kids who are 5 years old in both the reference frames with clocks in their hand. Assume we have them lined up infinitely on each reference frame facing each other, with all their clocks synchronized.

Let Frame Fa & Fb be moving in oppposite directions each with velocity v/2 (for an external observer), which makes each reference frame feel that other one is traveling with velocity v towards the opposite direction. At the origin of the corindates we have KidA (on frame A) and KidB (on Frame B). While they pass each other, we set Ta=Tb=0 (clocks are synchronized).

Question is: Looks like everything is symmetric here. After time passes by, will KidA see all opposite frame kids to be growing younger than him? What about KidB then? Will he see the same symmetry when he looks at kids on the other frame. How can both be correct here when kids within the same frame of reference be all of the same age.

May be the very way i am thinking of the problem itself is wrong. Would like to see some explanation to understand the correct experience in such a scenario.

 

[jerromyjon]

May be the very way i am thinking of the problem itself is wrong.

It seems to me you have the basic understanding correct, perhaps searching this forum for "twin paradox" might lead to the answers you seek. I myself only have a basic understanding as well.

 

[tkmanutk]

thanks! twin paradox has other issues like accelaration/decelaration etc., however with this one, i wanted to keep the frames inertial..

 

[jerromyjon]

thanks! twin paradox has other issues like accelaration/decelaration

I remember there being a thread about the twin paradox without acceleration

 

[jerromyjon]

Oh yeah and acceleration has no effect on time dilation, only relative velocity...

 

[Dale]

Now let us line up kids who are 5 years old in both the reference frames with clocks in their hand. Assume we have them lined up infinitely on each reference frame facing each other, with all their clocks synchronized

Due to the relativity of simultaneity this is not possible. You could say the A kids are all 5 and synchronized in the A frame, and the B kids are all 5 and synchronized in the B frame. In that case in the A frame the B kids would be all different ages and have unsynchronized clocks. All of the B kids would be aging slower in the A frame.

Both A and B kids will agree on the age of any pair of kids when they meet. The relativity of simultaneity will correctly offset the time dilation in each case.

 

[Ibix]

Dale beat me to the answer here, but there is one additional point I wanted to bring up:

Let Frame Fa & Fb be moving in oppposite directions each with velocity v/2 (for an external observer), which makes each reference frame feel that other one is traveling with velocity v towards the opposite direction.

This is not correct. Velocities do not add this way in relativity - look up the relativistic velocity addition formula. This doesn't matter for your scenario, since you do no further maths with it, but is worth mentioning.

 

[tkmanutk]

Thanks Dale & lbix. I think i have a food for thought now to go back and spend more time. Thanks for the point on simultaneity. Probably i should practice more spacetime diagrams :).

So what i understand is KidA should see kids on other frame younger to him at any point in time. Same goes with KidB from his frame. Right? It is just that the amount of dilation with different kids in the opposite frame will look different.

 

[Dale]

So what i understand is KidA should see kids on other frame younger to him at any point in time.

KidA will see kids on the other frame aging slower. However, because of the relativity of simultaneity some will start out older and some will start out younger, and then they will all age slowly from there.