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You are here: Experts > Science > Physics > Physics > Time Dilation with acceleration
Physics - Time Dilation with acceleration
Expert: Expert - 11/6/2009
Question
Hi Expert!
I'm not an expert, but am hoping for a bit of a reality check as to where I have gone wrong in understanding Time Dilation.
Allow me to ask the question by giving a scenario.
There are two identical trains with an observer and a clock both ticking away and travelling away from each other at a constant velocity which is close to the speed of light. To make things easier, I will be one of the observers.
I begin with my train right next to the other, and set my clock to the same time as his, as we move off and get close to the speed of light, I will see the other clock slow down. When I reach a constant velocity, the other clock will appear to be at a constant speed which is slower than my own.
At any given point, I will observe the time on the other clock as being behind my own, and that gap will be increasing.
Both trains then stop and begin moving towards each other again, besides the dip in speed difference when we were accelerating, once we reach the same speed but in the opposite direction, I will be able to observe exactly the same difference in speed as I did earlier, and the other clock will still appear to be behind my own.
When we reach our initial point, we stop, and the other clock now appears to be moving at the same speed as my own, but appears to have a different time to my own. The person on the other train will see my clock as behind his, and I will see my clock as faster than his.
That’s a bit too trippy to be true, so where did I go wrong? Or should I just quit while I’m not too far behind and study arts instead?
Thanks heaps for taking the time to consider my silliness!
- Alex
(oh, and may I ask, why can't we mention the gooey things with shells?)
Answer
What you described above is essentially correct. HOWEVER, you left something out: namely, acceleration. Instead of two clocks on two trains, each train moving away from each other, let's have three clocks, all of which start at rest on the surface of our Earth. Two of the clocks are put on the rockets, which ACCELERATE away from the third clock, but in opposite directions. The two clocks quickly reach an identical speed near that of light, and travel for an identical time (on their clocks). They both ACCELERATE (ie, change velocity) and travel back towards our Earth at this same near-light speed. When they each get there, they both DECELERATE to zero motion relative to the surface of the Earth. What will we see?
The two clocks will have the same time, and both of these times will be less than that of the clock that never accelerated. I emphasize that it is NOT the case that they "seem" to have less time or "appear" to have less time. There really HAS been less time transpired on these clocks that traveled than the one that did not -- and none of the three clocks can claim to have the "correct" time!
When you do the calculations rigorously, taking acceleration into account, you will get the above results. And we know this is correct every instance when we use a GPS system. How? Because GPS satellites have their precise timing signals adjusted to take this dilation into account -- if they didn't, after a few years GPS would be off by tens (if not hundreds) of meters.
Oh, and the reason I specifically exclude questions regarding eggs is because I (long ago) got tired of getting questions about how to do an egg-drop experiment. I still get them every few months, but that is down from the one or two a month I used to get.
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