# Length Contraction: Row of Blocks & Rods

• daniel_i_l
In summary, Length Contraction is a concept in physics that explains the decrease in length of an object when it is moving at high speeds. This phenomenon is demonstrated through the Row of Blocks and Rods experiment, where a row of blocks appears shorter when viewed from a moving frame of reference. This is due to the compression of space and time at high velocities, as described by Einstein's theory of relativity. This concept has been proven through various experiments and has significant implications in our understanding of the universe and the laws of physics.
daniel_i_l
Gold Member
if you have a row of blocks, all touching each other 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.

daniel_i_l said:
if you have a row of blocks, all touching each other 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.
They will still be touching one another. It's not just the blocks that are length contracted, it's space itself.

Patrick

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 each other? 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.

daniel_i_l said:
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.
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.

daniel_i_l said:
if you have a row of blocks, all touching each other 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.
try please radar detection of the points where the rods contact each other

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.

## 1. How does length contraction occur in a row of blocks and rods?

Length contraction occurs when an object is moving at a high velocity relative to an observer. In the case of a row of blocks and rods, the objects are moving at a high velocity relative to the observer, causing the objects to appear shorter in length along the direction of motion.

## 2. What is the formula for calculating length contraction?

The formula for calculating length contraction is L = L0 * √(1 - (v2/c2)), where L is the contracted length, L0 is the original length, v is the velocity of the object, and c is the speed of light.

## 3. How does length contraction affect the measurement of an object's length?

Length contraction causes the measurement of an object's length to appear shorter when it is moving at a high velocity. This is due to the fact that the distance between two points on the object is compressed along the direction of motion.

## 4. Does length contraction only occur in objects moving at the speed of light?

No, length contraction can occur in any object moving at a high velocity relative to an observer. However, the effects of length contraction become more significant as the velocity approaches the speed of light.

## 5. What are some real-life examples of length contraction?

Some real-life examples of length contraction include subatomic particles moving at high speeds in particle accelerators, the wings of an airplane during flight, and objects traveling at high speeds in outer space. However, the effects of length contraction are usually too small to be noticeable in everyday life.

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