# Curtailed length and the twin paradox

## Main Question or Discussion Point

Hello,

I've got two quick questions.

Why is it so that they say "if a object moves extremely fast then we see it curtailed/shortened a little bit"? But if it moves that fast that the length even may be noticeable, how on Earth do we SEE it shortened when it moves THAT fast past us? If a spaceship flies by in the speed of light, we see nothing but a wave. I might be wrong here, I hope I am, that's why I want to know why people still say that we See it shortened.

And besides, if an airplane flew by us even as slow as 1000 km/h. How much exactly does the aeroplane shorten then? I have no time to calculate, but was it less than a millimetre..

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Second problem
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Why is it so that if one twin steps on a spacecraft and goes for a flight in the speed of light and after returning his twin brother is the one who became older? I mean isn't it the same if the spaceship stays put and the whole universe went for a flight in the speed of light?

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Janus
Staff Emeritus
Gold Member
The word "see" is a bit misleading here, as what we would "see" regarding an object traveling at near c speeds depends on more factors then just the object's length contraction.
"Measure" or "determine", would be better choices. For instance we could lay out a measuring stick right next to the objects path, and as it passes by note at what points of the measuring stick the endpoints of the object are opposite at a given instant.
Or we could time how long it takes between the front and back end of the object to pass a given point and determine its length from its known speed.

For a plane of 30m in length, you would get a shortening of about.02 millimeter.

As for the second question, this is the standard "twin Paradox" which has been discussed a lot on this board already try doing a search on the term. The upshot is that the twin in the Spaceship makes changes to his velocity and the Earth twin does not.

Oh yes, I checked all the topics in this Relativity forum, but still... the spaceship twin makes changes to his velocity in relative to what? To the Earth twin? But it would be the same if the Earth twin made the changes in His velocity in relative to the spaceship twin.

JesseM