Curtailed length and the twin paradox

In summary, the length of an object is shortened when it travels near the speed of light because we can measure the length difference.
  • #1
Quan Chi
7
0
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..


____________________
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?


Thanks for your replies.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
Quan Chi said:
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.
Acceleration is absolute in SR, just like in Newtonian physics. If you accelerate, you feel G-forces; the traveling twin feels them, but the Earth twin does not (ignore gravity since it's not dealt with in SR). So only the Earth twin stayed in a single inertial frame throughout the journey, and every inertial frame will say that the Earth twin maintained a constant velocity while the traveling twin did not.
 
  • #5
This helped me a lot. Thanks, guys.
 

1. What is curtailed length in relation to the twin paradox?

Curtailed length, also known as contracted length, refers to the phenomenon in which an object's length appears to decrease when it is moving at high speeds, as predicted by Einstein's theory of relativity. This concept is central to understanding the twin paradox, as the difference in curtailed length between two objects in motion can lead to a difference in their perceived aging.

2. How does the twin paradox challenge our understanding of time and space?

The twin paradox presents a thought experiment in which one twin travels at high speeds for a period of time while the other twin remains on Earth. When they are reunited, the traveling twin is younger than the twin who stayed on Earth, despite both experiencing time at the same rate. This challenges our traditional understanding of time and space as absolute, and instead suggests that they are relative to the observer's frame of reference.

3. Can the twin paradox be observed in real life?

While the twin paradox is a thought experiment, its principles have been observed and confirmed through experiments with atomic clocks and space travel. For example, astronauts who have traveled at high speeds for extended periods of time have aged slightly less than their counterparts on Earth. This supports the idea that time is relative to an observer's frame of reference and can be affected by speed and gravity.

4. What role does curtailed length play in the twin paradox?

Curtailed length is a key factor in the twin paradox because it can lead to a difference in perceived aging between two objects in motion. As one object moves at high speeds, its length appears to contract, causing a difference in the distance it travels compared to a stationary object. This difference in distance, combined with the constant passage of time, results in a difference in the objects' perceived aging.

5. How does the twin paradox affect our understanding of the universe?

The twin paradox, along with other theories of relativity, has greatly expanded our understanding of the universe and the fundamental principles that govern it. It has led to new understandings of time, space, and gravity, and has been confirmed through various experiments and observations. The twin paradox demonstrates that our understanding of the universe is constantly evolving and being challenged by new discoveries.

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