The earth bound twin looks up and sees his travelling twin moving slower inside his spaceship because he is whizzing by at some percent speed of light. But what does the motion of the ship itself looks like to the Earth bound twin? As the ship flies by the events taking place inside appear to be happening more slowly to Earth twin, but does the ship appear to move slower as it travels a greater percent speed of light?
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$\begingroup$ The ship is in the same frame as the moving twin, so what do you think happens? $\endgroup$– Kyle KanosCommented Nov 22, 2014 at 14:19
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1$\begingroup$ @Kyle Kanos - I think the question is about whether the ship "moves slower" in the sense of its velocity appearing to slow, not whether physical processes in the material making up the ship appear slower for the Earth twin. If so, the answer is no, velocity isn't slowed in the same way that physical processes which can be measured in the ship's rest frame are slowed. $\endgroup$– HypnosiflCommented Nov 22, 2014 at 14:28
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$\begingroup$ You are using the word "move" to mean two different things. When you talk about the ship "moving", you are talking about its velocity in your frame of reference, but when you talk about the passenger "moving slowly", you are talking about his/her heartbeat or, how long it takes her/him to spear a piece of food with a fork. (i.e., how you perceive his/her motion relative to her/his frame of reference.) $\endgroup$– Solomon SlowCommented Sep 17, 2015 at 15:17
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2 Answers
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does the ship appear to move slower as it travels a greater percent speed of light?
When the ship moves faster, it appears to move faster.
When the ship travels faster and appears to travel faster, also the twin inside the ship travels faster and appears to travel faster.
If we carefully adjust the speed of the ship to be 4 km/s faster, that will surely cause the speed of the ship to 4 km/s faster, but it's not so sure that the speed of a passenger inside the ship is increased by 4 km/s.
The speed of the passenger might increase by 3.9999 km/s, or by 4.00001 km/s. Speed of the passenger does increase though.
The things that are called closing speeds are such speed-like things that decrease inside a ship whose speed increases.
Let's say a twin wants to push a button on the ship's front wall. He must chase down the button by moving forwards faster than the button moves forwards. He closes on the button at some closing speed, I guess that's where the name closing speed comes from.
closing speed = twin's speed - button's speed
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I am referring both to this question and to a previous one ""How will the twin paradox become ... if no acceleration was ever involved?" because they are related. For clarity let's call the twin remaining on the Earth, "Terrestrial" and the one in the ship "Traveler".
In the previous question an acceleration is involved twice because 1) after Traveler leaved the Earth, his ship stops, turns backwards, and returns toward the Earth. 2) When Traveler passes by the Earth he cannot see his twin because he moves too fast. But he can drop on the Earth a box with a picture of himself. Well, but inside the ship, the box moves with the ship velocity. To let it fall on the Earth one has to DECELLERATE it, otherwise the force of gravity won't change sufficiently the box velocity, and the movement of the box will miss the Earth. But, how to do this deceleration? Lowering the box velocity so much means to involve a tremendous energy given the almost luminal speed of the ship.
In short, how can we compare the age of the twins without involving accelerations, i.e. without reducing the velocity of one of the twins, or of some apparatus, to the other twin's velocity?
Good luck !
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1$\begingroup$ The standard answer is that each spaceship has a window, and when they fly by each other they directly look at each other's clocks through the windows. Whilst this involves a short delay (due to the speed of light), if they fly close enough together this can be reduced to as close to zero as you want. In the case of flying by the earth, you would pull out a big telescope and look at what some clock tower says. Or turn on your TV to breakfast TV and look at the clock at the bottom of the screen. $\endgroup$ Commented Mar 1, 2015 at 16:55