# Length contraction

1. Nov 11, 2006

### daniel_i_l

if you have a row of blocks, all touching eachother in your frame, then when observed from a frame moving relative to you in the direction of the blocks will the contraction make the blocks look as if they're not touching - each one will be shorter but the total length of the row will be almost the same? if this is true then why doesn't a normal rod look as if it got pulled apart in another frame?
Thanks.

2. Nov 11, 2006

### nrqed

They will still be touching one another. It's not just the blocks that are length contracted, it's space itself.

Patrick

3. Nov 12, 2006

### daniel_i_l

Thanks, but i don't understand how they can still be touching. because in the usuall case of a single rod, the back end gets closer to the front end. so if you have a row of rods and the back end of each one gets closer to the front then how can they stay together? do the rods themselves also get closer to eachother? if so then why does the rod behave differantly (move forwards in addition to being contracted) when there's another one infront of it?
Thanks.

4. Nov 12, 2006

### JesseM

Where did you get the idea that "the back end gets closer to the front end", as opposed to, say, "the front end gets closer to the back end" or "both ends get closer to the midpoint"? I don't think it's useful to imagine the rods going through a continuous process of "shrinking" from one length to another, since this would involve the rod accelerating and there would be a variety of ways the different parts of the rod could be moving depending on the method you chose to accelerate it (most forms of acceleration would actually physically distort the ruler, not just in the sense of length contraction but in the sense of a rubber band being stretched or compressed in its own rest frame). It's better to think of length contraction in terms of each inertial reference frame having a physical grid moving at constant velocity which that frame uses to assign coordinates to different events, and each observer will measure the other's grid to be shrunk relative to their own. Suppose at a particular moment a ruler moving at 0.866c parallel to the x-axis of my grid has its back end at x=2 meters on my grid, and its front end at x=3 meters, and another ruler has its back end at x=3 meters and its front at x=4 meters, so each ruler is measured to be 1 meter long and the two are touching. If we have a second grid that is at rest relative to the ruler, I will see its markings shrunk along the x-axis, so that it marks 2 meters for every 1 meter marked on my grid along that axis. In this case, at the moment I made the measurements above, the back end of the first ruler might also be at x=2 meters on the second grid, but then the front end would be at x=4 meters on that grid's x-axis, while the back end of the second ruler would be at x=4 meters and its front end would be at x=6 meters. So this second grid measures each ruler to be two meters long, but of course it still measures the front end of one ruler to coincide with the back of the other, since it's just a different grid placed next to the same two rulers that I'm looking at.

5. Nov 12, 2006

### bernhard.rothenstein

try please radar detection of the points where the rods contact each other

6. Nov 13, 2006

### Demystifier

7. Nov 14, 2006

### ChemGuy

What do the blocks look like in the plane orthongonal to the direction of motion? I would think it is unaffected because it is not moving in relation to the direction of motion.