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Special Relativity and the Twin Paradox


NanakiXIII
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But I still don't understand how the Twin Paradox works.

 

If the person on earth received a message ever 2 hours, shouldn't he have received 6 messages by the time the second person turns around, and receive the other 6 while the other person was on the way back?

 

Isn't that correct?

 

Also, why exactly is the time doubled at 60% lightspeed? The article also said it was tripled at 80% lightspeed. Why? Wouldn't 50% and 67% make more sense?

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NanakiXIII said in post #27 :

But I still don't understand how the Twin Paradox works.

 

Because time dilation is an upshot of the speed of light being constant for all observers. There's another thread on this in this very forum. ('Twin story but without the planet').

 

 

NanakiXIII said in post #27 :

Also, why exactly is the time doubled at 60% lightspeed? The article also said it was tripled at 80% lightspeed. Why? Wouldn't 50% and 67% make more sense?

 

time (at velocity v) = time (at rest) * SQRT ( 1 - v^2/c^2)

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NanakiXIII said in post #40 :

I just read the thread you referred to. I think I understand now. It said something about the clocks going faster when moving towards them, and slower if moving away. Is this caused by the Doppler Effect?

 

The Doppler effect is a completely different effect from time dilation. Usually iin Relativity, we assume for simplicites sake that the doppler effect has been factored out, and we are just dealing with time dialtion.

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NanakiXIII said in post #40 :

I just read the thread you referred to. I think I understand now. It said something about the clocks going faster when moving towards them, and slower if moving away. Is this caused by the Doppler Effect?

 

The Doppler Effect in astronomy has to do with electromagnetic waves and not the distance between two objects.

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NanakiXIII said in post #46 :

When you move towards it it moves faster, since the same amount of light bouncing off the click is heading your way, but in a shorter time since you're moving towards it.

 

So you're talking about when observing it, and not that the clock itself is speeding up. I miss understood you earlier... :P

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NanakiXIII said in post #27 :

But I still don't understand how the Twin Paradox works.

 

 

 

Isn't that correct?

 

Also, why exactly is the time doubled at 60% lightspeed? The article also said it was tripled at 80% lightspeed. Why? Wouldn't 50% and 67% make more sense?

 

Check out the following attachment.

It shows the light clock arrangement as seen by both the person next to the clock and by the person for which the clock is moving.

 

For the first person, the distance between emitter and mirror is ct0 (the speed of light times the time it takes to traverse the distance as measured by him.

 

For the second person (who sees the light clock as moving) the light follows the diagonal path shown, and this distance is ct1. The distance the clock travels is vt1, where v is the velocity the clock is seen as moving.

 

The distance between the emitter and mirror at any instant (x) can be found by x² = (ct1)²-(vt1)²

 

Now x is the same distance the first person got by ct0, so x=ct0 and therefore:

 

(ct1)²-(vt1)² = (ct0)²

 

c²t1²-v²t1² = c²t0²

 

c²t1²/c²-v²t1²/c² = t0²

 

t1²- v²t1²/c² = t0²

 

t1²(1-v²/c²) = t0²

 

t1 sqrt(1-v²/c²) = t0

 

( Usually this is written with t0 and t1 reversed, but I intially got them switched around when I drew the diagram, and was too lazy to go back and change it later. It doesn't effect the math any.)

lightclk.jpg

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