# Death by Lorentz Contraction

1. Jan 17, 2010

### Nabeshin

I have recently been reminded of a problem a friend posed to me many months ago in special relativity that I was never able to address:

Suppose we have a person inside a moving spaceship of proper length L. According to an observer outside the ship, the person inside the ship is at rest (corresponding to a relative frame velocity equal and opposite to the velocity of the ship). The ship, therefore, appears lorentz contracted to this observer. At high enough velocity, the proper length of the ship would be contracted to the point at which the man inside would appear to be crushed.

Initially when I examined the problem, I did so in three cases:
I) The person moves at constant velocity.
II) The person accelerates from v=0 while inside the ship.
III) The person accelerates from v!=0 while inside the ship.

Case I) has a solution I was able to obtain, in that the situation reduces to the "barn-door" paradox. For II and III I was unable to get very far, however. My intuition says the person must impact the opposite wall of the spaceship before ever being able to accelerate up to the required velocity for the "contraction death" to occur. I made some attempt to demonstrate this, but ultimately failed.

Any thoughts?

2. Jan 17, 2010

Staff Emeritus
Um...if someone is inside a ship, and they are at rest and the ship is moving close to the speed of light, they will get crushed into jelly as soon as the back wall of the ship hits them, no?

3. Jan 17, 2010

### Phrak

Assume that events that happen in one inertial frame happen in the other. In the inertial frame of the ship, the guy inside gets smashed by one bulkhead--the rear bulkhead. It's a bit more complicated to work-out in the inertial frame of the passenger.

4. Jan 17, 2010

### Nabeshin

Right. Obviously the guy will soon smash into one of the ends of the ship. My point is that in the outside guy's point of reference, if the relative velocity were great enough, the ship would appear Lorentz contracted to a size smaller than that of the man.

The thing to show, I guess, is that the man will always smash into a bulkhead before this requisite velocity is obtained.

Do we agree that it is possible for the ship to appear Lorentz contracted to the size smaller than that of a man, and that this would appear to pose a problem for the man inside? After all, if his velocity is so high as to cause the necessary contraction, he will simultaneously impact both the front and back ends of the ship, no?

Judging from your guys' cursory responses, it seems I am making a bigger deal out of this than you see it to be. Mind explaining the simplicity?

5. Jan 18, 2010

### Pythagorean

Won't the man himself appear to be Lorentz contracted with the same proportions as the ship? Notice also, that we're using the word "appear".

IIRC, the only reason it appears this way is because of how the light is hitting the observer at rest, not because anything is actually physically contracting.

6. Jan 18, 2010

### Algr

I think it might help if you work backwards and try to figure out what events could lead up to your scenario. Specifically, what was happening when the man entered the ship?

If the ship was already moving at the time, then he could never enter it, because a) he wouldn't fit, and b) he'd have to be moving near c perpendicular to the ship, which contradicts the original scenario that he is at rest.

If the ship suddenly accelerates while the man is floating inside it, then lorentz contraction occurs, but the contraction occurs only in the direction of motion. Lorentz contraction could not cause the front of the ship to appear to contract in the opposite direction to the motion of the ship, so the rear of the ship would impact the man first, in agreement with the inertial frame of the ship.

This is all a guess BTW.

7. Jan 18, 2010

### meopemuk

Hi Nabeshin,

a car at a distance looks "smaller" than a car next to you. However you do not worry that a person in the distant car will be smashed.

The length contraction in special relativity is like the "shrinking" of the distant car. It is closer to an optical illusion than to real compression.

Eugene.

8. Jan 18, 2010

### Nabeshin

Pythagorean: Hrm. This is why the man is stationary with respect to the outside observer, so that the ship appears lorentz contracted, but not the man inside. The bit about physical contraction is precisely at the heart of this situation, because if one person sees someone get squished, surely everyone should agree that he got squished!

Algr: "If the ship was already moving ...." Yes, this is what I meant by my scenario (I) in the first post.

For clarification, I drew a silly little picture to illustrate the situation: From the outside observer's point of view: http://i50.tinypic.com/14xmp3d.jpg From the ship's frame: http://i47.tinypic.com/2q3zl2d.jpg

Update because someone posted while I was writing this:
meopemuk: Yes, but that is precisely why this is a problem! I know it's more an illusion, but if one "saw" a distant car crush someone by shrinking, surely this is no illusion! My point is, the outside observer will "see" the ship crush the man inside!

Last edited by a moderator: Apr 24, 2017
9. Jan 18, 2010

### meopemuk

Both the moving ship and the man inside will shrink by the same factor. So, he will not be crushed.

Eugene.

10. Jan 18, 2010

### Fredrik

Staff Emeritus
I'm not going to ask how a stationary guy ended up inside a ship that's moving close to the speed of light, but by definition of "inside", the ship has to be longer than the guy when you put him inside. At this point, we have already made it obvious that the guy won't ever come near the front of the ship, since it's moving away from him. What happens when you accelerate the ship to make it shorter than the guy is that the rear is accelerating faster than the front*. The front will move away from the guy even faster than before, and the rear will move closer to him even faster than that, so he will get crushed by the rear slightly sooner than if you had chosen not to accelerate the ship.

*) Otherwise it wouldn't get shorter. Note that you don't have to forcefully compress the material to accomplish this. This is what happens when you accelerate a solid object by pushing or pulling it, and do it gently enough to give the internal forces a chance to restore the distances between adjacent atoms, as seen from an inertial frame that's co-moving with the atoms. (Yes, that would be a different frame for each pair of adjacent atoms). The only way to prevent this from happening would be to apply additional external forces that would tear the ship to pieces.

Last edited: Jan 18, 2010
11. Jan 18, 2010

### meopemuk

Nabeshin,

sorry I haven't paid attention when reading your question. So, the guy in the moving ship is not moving (wrt to the outside observer). From the point of view of the outside observer the man will be hit by a ship's wall. From the point of view of the moving ship the man is flying fast and hits the wall as well. In any case, there is a bloody mess, which I don't even want to think about.

12. Jan 18, 2010

### Bob S

Nothing inside the spaceship has shrunk. Ask the man in the ship. He will tell you that the laws of physics, his dimensions, and the dimensions inside his space ship, have not changed. Only his apparent dimensions have changed, when viewed from the observer's rest frame. As long as the acceleration is less than about 10 g's, he will not be injured.
Bob S.

13. Jan 18, 2010

### Nabeshin

Thank you for the response, this is more of what I was looking for. I think I understand why everyone should be in agreement that our poor test subject (who can run very fast) will simply splat up against the back wall in a perfectly fine demonstration of collision physics.

14. Jan 20, 2010

### sweet springs

Hi. As reflection at a wall change the motion of the person thus the case becomes complex, instead of a space-ship let us think of a space-train of infinite number of cars with all the junction doors open and the rest length of which is L0.

Outside view, the passenger is at rest and he belongs to multiple cars the unit length of which is L where L< The passenger's front-back width <L0

--- ** ** ** ** ** ** ** ** ---
|Front- Passenger's -Back|
--- ** ** ** ** ** ** ** ** ---

Inside view, the passenger is moving

--- ****** ****** ****** ****** ****** ****** ******* ---
←　○　Passenger contracted
--- ****** ****** ****** ****** ****** ****** ******* ---

Difference of simultaneity at the positions of the passenger's head and his back, between the two systems can explain it.

Regards.

Last edited: Jan 20, 2010