Length contraction while traveling inside a space ship

  • #1

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Suppose I'm travelling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by spaceship (I mean by a device that can measure the distance ) will it be same as what I perceived from inside the spaceship(shorter) or will it show the actual distance travelled?
 

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  • #2
Ibix
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If the rulers are moving with the spaceship then they will measure the distance between the planets the same as you do. If the rulers are moving with the planets then they will measure a larger distance.
 
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  • #3
jbriggs444
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Suppose I'm travelling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by spaceship (I mean by a device that can measure the distance ) will it be same as what I perceived from inside the spaceship(shorter) or will it show the actual distance travelled?
When you say "actual distance", what do you mean?

One possible notion is that the "actual distance" between the event of your leaving planet A and the event of your arriving at planet B is the space-time interval between them. Assuming a ballistic trajectory, this is given by the elapsed time on your watch. This is a good choice since it is independent of coordinate system.

Another possible notion is that "actual distance" is the distance between the some event on the surface of planet A and a corresponding event on planet B at the same time according to a coordinate system anchored to planet A.

Yet another possible notion is that the "actual distance" is the distance between an event on planet A right now and a corresponding event on planet B also right now according to a coordinate system anchored to the seat of your pants.

You may notice that the relativity of simultaneity is tied up intimately in what we mean by "distance". If you want to measure the distance to a moving object, you have to specify when. If you want to measure the distance from a moving object, you have to specify when. If you want to measure the distance between two co-moving objects, you do not need to know when, but you do need to know how much delta there is between the two whens.
 
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  • #4
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Suppose I'm travelling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by spaceship (I mean by a device that can measure the distance ) will it be same as what I perceived from inside the spaceship(shorter) or will it show the actual distance travelled?
I want to comment on the use of the term 'point', which means a location in space. Points A and B are separated in the frame where the ship is moving fast, but from the ship point of view, the ship is stationary and thus points A and B are the same point, else the stationary ship could not be travelling between them. So the events of the beginning and end of the exercise occur at the same point but different times, and the ship will say that it traveled zero distance.

So for example, a fast ship goes to Mars at .99c, which is 694 light seconds away that day, so that takes 700 seconds in the solar system frame. Time is dilated onboard the fast ship, so they clock 100 seconds to make the trip.
From the point of view of the ship, they're stationary, and Mars takes 100 seconds to come to them from the length-contracted 99 light-seconds distance. Mars is not at 'point B' at first since it is moving fast and not arriving at point B (the ship) until time t'=100.
 
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  • #5
anuttarasammyak
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Suppose I'm travelling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by spaceship (I mean by a device that can measure the distance ) will it be same as what I perceived from inside the spaceship(shorter) or will it show the actual distance travelled?
As explained in previous posts.

Perceived inside distance and actual distance for the pilot coincide.

Say C is any point between A and B, AC and CB are shortened as well as AB does.
 

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