# A Relativity problem

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If you and I were travelling at high speeds in opposite directions. I would see that time on your clock was passing slower than time on my clock.

So far, so good, I understand the reasoning (assuming the speed of light is constant, no matter what your speed.)

However, at the same time you would see time travelling slower for me. So what happens when we slow down and meet at the same 'rest' speed, all the time continuing to observe each others clocks? Whose clock would be slower?

Can someone explain that to me please? Am I missing something obvious? The mind boggles.

Steve

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Oh poo. My head just caught fire!

Kaptain Klevtsov

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Couldn't you just wind one of the clocks on a bit so that they matched?

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It's all taken care of by the flux capacitor

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Assuming you're both travelling the same speed, why would one of the clocks be slower?

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Well, as observed by me, your clock would have slowed down whilst we were travelling in opposite directions (according to Einstein.)

Steve

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Actually, the phrase 'whose clock would be slower' is a bad one. What I meant was: whose clock would be behind?

Steve

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I think if you were traveling at the same speed in different directions then both the clocks would show the same time when compared at the end. You would see the other clock being slower than yours when traveling due to the time it took for the information of the state of the clock to reach you at the speed of light.

Thats my take on it at first look, it could well turn out to be a load of rubbish though!!

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I think if you were traveling at the same speed in different directions then both the clocks would show the same time when compared at the end.

That's what I thought, too.

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I think if you were traveling at the same speed in different directions then both the clocks would show the same time when compared at the end.

Compared to what? Where is the zero speed marker? I thought everything was relative?

Kaptain Klevtsov

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This is the "twin paradox" - it posed a problem for Einstein when he came up with special relativity in 1905. The key point is that in order for the two clocks to be brought together again there has to be an acceleration - both clocks slow down to a stop, then turn around and fly back together. And special relativity doesn't cover cases of acceleration, only constant speed. So to sort this one out you need a theory that includes acceleration, ie general relativity - which took Einstein another 12 years.

Sorry but I can't remember the general relativity answer.

I'm sure Themos can!

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Try this:

I only read the start of it which describes the case where one clock is on earth and the other is in a spaceship - this is clearly not symmetric because the person on earth doesn't feel acceleration while the spaceship does. Your case is harder and is the "true" paradox. Maybe the rest of the Wiki article explains that....

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The accelerated clock would have recorded the least time.

Remember, a photon experiences no time, the closer your trajectory is to a photon (zip over there and bounce back off a mirror or go round a black hole or two, say), the less time you will experience.

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the closer your trajectory is to a photon (zip over there and bounce back off a mirror or go round a black hole or two, say), the less time you will experience.

And what happens if you go in the opposite direction?

And if a lamp sends photons off in all directions, at (well doh!) light speed, doesn't the north direction one travel at twice light speed when viewed from the south direction one?

Kaptain Klevtsov

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It doesn't matter which direction you go, what matters is how close to the speed of light you've been travelling, relative to a person that stays floating in space. A photon that goes to Sirius, hits a mirror and comes right back will register zero time. The person that stays floating (until the photon comes back) will register the maximum time elapsed. Any other trajectory (that comes back simultaneously with that photon) will register something in between.

doesn't the north direction one travel at twice light speed when viewed from the south direction one?

No! That's why moving clocks appear to go slower and moving rulers appear shorter, to make sure that light is always seen to travel at a fixed rate, no matter what the observer is doing. In this case, the observer is a photon.

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I think if you were traveling at the same speed in different directions then both the clocks would show the same time when compared at the end.

Compared to what? Where is the zero speed marker? I thought everything was relative?

Kaptain Klevtsov

Relative to the speed of light, as pointed out its purely the speed that causes the time dilation, not the direction of travel.

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Suppose you are travelling in a spaceship. You have a clock which registers your time, call this proper time. Now suppose I'm watching you. As you approach the speed of light your proper time decreases as you are moving closer to the speed of light, this is time dilation. Now to answer your question, the person's whose clock runs slower is whoever is travelling the least fastest.

The reason direction doesn't matter is because there is no specified direction in the equations which govern this part of special relativity- the Lorentz transformations. These transformations tell us how to measure time and length between moving and stationary observers. Moreover, due to the symmetry in these transformations we can interchange accordingly. doers this help?

-Paul.

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Now to answer your question, the person's whose clock runs slower is whoever is travelling the least fastest.

Fastest relative to who? Both have the same speed relative to each other.

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the person's whose clock runs slower is whoever is travelling the least fastest.

But they are both travelling at the same speed, relative to each other.

Lets start again. If two people are in motion relative to each other, then each of them will observe the others clock travelling at a slower rate. Is this agreed? If not the we are not on the same page (and neither is Einstein.)

The question is; if they synchronise clocks at the start, and both observe the others clock as travelling slower whilst they are in motion, then whose clock will be behind the other when they meet again?

Steve

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They can't meet again unless one of them goes in an non-inertial frame, or "accelerates", in common parlance. The one who accelerates the hardest will end up with the slower clock.

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What if they both accelerate the same? Remember they are watching each others clocks at all times.

Steve

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In a symmetrical situation, one would expect a symmetrical outcome.

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Same acceleration= same time on the clocks, but if they were looking at each others clocks you'd have to allow for the time the information on the clocks took to travel to the other person.

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