I've been learning about special relativity and the Lorenz transformations lately (and I recommend this playlist), and I had an epiphany. The epiphany is that length contraction isn't really length contraction. Rather, it comes from the fact that different parts of a moving thing are in different times because of the relativity of simultaneity. Lemme explain.
Let's say we consider our own inertial frame of reference. For those not familiar with special relativity, an inertial reference frame is a reference frame that isn't experiecing any acceleration (i.e. change in speed or direction). If you were in a box that was moving at some fixed speed in one direction relative to, say, the earth, you wouldn't be able to tell that you were moving. If you had a small window to look out of, it might look like everything else was moving.
Special relativity says that the laws of nature and the speed of light are the same in all inertial reference frames. That means if you were standing on the earth, and you turned on a laser, the speed of light would be about 300k m/s. And if you were in a box moving at 30k miles per hour, and you turned on a laser, the speed of light would still be 300k m/s relative to you.
This is a little trippy because it's not like most other things. If you were on a bus, and you threw a ball 50 mph in the same direction the bus was moving, then the ball would move 50 mph relative to you. But if you were standing on the side of the road watching somebody on the bus throw the same ball at the same speed, the total speed of the ball relative to you would be the speed of the bus plus the speed at which the person on the bus threw the ball.
Not so with light. With light, whether you are on the bus shining a light forward, or you're on the ground watching somebody on a bus shine a light forward, you will measure the speed of the light as being about 300k m/s. It's this fact that gives rise to all the weirdness of special relativity, including time dilation, length contraction, and the relativity of simultaneity.
To illustrate this, imagine a light source sitting in the exact center of a box. When the light comes on, it hits both ends of the box at the same time.
But now imagine the box is moving relative to you. You're just standing there watching it go by, and the same thing happens. A light in the exact center of the box comes on. Since the light bulb is in the box, it's moving with the box, but that doesn't matter. Light will still move at the speed of light regardless of the movement of the source. So it will move just as fast to the left as it moves to the right. But since the box is moving, the light will hit each end of the box at a different time. Since the left side of the box is moving toward the source of the light, and the right side of the box is moving away from the source of the light, the light will hit the left side before it hits the right side.
This would be easier to show with an animation than with still pictures. Use your imagination.
Now, think about that for a minute. If you were in the box moving with the box, the light would hit both ends of the box at the same time. But if you're not moving with the box, and the box is moving to the right from your frame of reference, the light will hit the left side before it hits the right side. How is that possible?
Well, that's the relativity of simultaneity. Two events, like a light hitting a wall, can be simultaneous from one person's frame of reference, but they can happen at different times from another person's frame of reference.
Now, here's my epiphany with length contraction. Don't take this as gospel because I've watched a lot of YouTubers explain length contraction, and none of them have explained it like this. So maybe I've got it all wrong.
Anywho, let's say you are in the box, and the light hits each end of the box at 10 am. Let's say you actually place a clock at each end of the box, and they both read 10 am when the light hits each end.
But now imagine you're standing on the ground watching the box go by. From that point of view, the clock on the box in the back should read 10 am when the light hits the wall on the left.
We know from what we talked about earlier that the light hits the wall on the left before it hits the wall on the right from your point of view on the ground watching the box fly by. If the moment the light hits the wall on the left is 10 am, and it hasn't hit the wall on the right yet, that must mean the clock on the wall that's on the right is reading a time earlier than 10 am. Since the light hasn't hit the right end of the box yet, that means the right end of the box exists at an earlier time than the left end of the box.
Think about that for a minute. If the box is moving to the right, then as time goes by, it will have moved farther and farther to the right. So at an earlier time, it has moved less to the right than at a later time. If it's not 10 am on the right side of the box yet, then the right side of the box hasn't moved as far as it will have moved once it is 10 am on the right side of the box. If the left side of the box has moved to where it's supposed to be at 10 am, but the right side hasn't, then we should expect the right side of the box not to have moved as far as the left side of the box has moved. The result is that the box should appear to be shorter. The reason is because the person on the box measures the size of the box at 10 am on both ends, but the person on the ground measures the box at 10 am on the left side, but at some time earlier than 10 am on the right side.
The relativity of simultaneity is what explains length contraction. The length isn't actually different. It's the time that's different. Length contraction comes from the fact that the back end of the box has moved more than the front end of the box from the point of view of the person on the ground because the person on the ground is looking at both ends of the box at different times.
Does that make sense?
Notice that this weirdness is amplified the faster the box is moving. The faster the box moves, the bigger difference there is between when the light hits the back end and the front end of the box. The bigger that difference is, the earlier the front end of the box will be when the light hits the back end of the box, which means it will have moved less, and the box will seem shorter from the point of view of the person on the ground.
They should call it the relativity of length rather than length contraction. The person in the box measures each end at 10 am, but the person on the ground measures the left end at 10 am and the right end at some time earlier than 10 am. Of course 10 am and less than 10 am are actually happening at the same time for the person on the ground. I'm just talking about the person on the ground looking at the moving frame of reference. 10 am on the left side of the box happens before 10 am on the right side of the box. Let me know if I'm not explaining that clearly. I don't want anybody to get the wrong idea.
If you prefer, you can run the same thought experiment for when the light hits the right end of the box. The clock at the right end will read 10 am. But at the same time (from the ground point of view), the light has already hit the back end. From the grounded person's point of view, the time at which the light hit the left end of the box is in the past, and the clock at the back reads something later than 10 am. So the left end has moved farther than the right end, resulting in the box being shorter.
I don't know if this is right or not, but it makes sense to me. What do you think?
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