jonderry

2009-Aug-28, 06:48 PM

I'm having a hard time getting the intuition for length contraction. I understand that if length is defined by the round trip time for a beam of light to an object, that it must follow from the invariance of the speed of light. However, I'm having difficulty thinking about situations intuitively. Consider the following two cases:

1. One rocket, "stationary rocket," lies adrift in space and another rocket, "speeding rocket," flies toward it at 99.995% of the speed of light. 100 km away, a hydrogen bomb is detonated in frame of the stationary rocket so that the flash of gamma radiation it emits hits both rockets simultaneously as

the speeding rocket flies by the stationary rocket, narrowly missing it, toward the site of the bomb detonation.

The stationary rocket sees a pretty big flash, but nothing too catastrophic because of the distance to the bomb. However, the speeding rocket, due to length contraction, measures a distance of just 1 km to the detonation and is annihilated. Is this what happens? Or is the flash of the h-bomb distorted in the frame of the speeding rocket so that they both see the same intensity of gamma rays?

It just seems to defy reason that a passenger in the stationary rocket should be able to look out the window of his rocket and see a speeding rocket become vaporized by a distant explosion at the very instant that the speeding rocket passes by the window of the stationary rocket.

2. As for magnetism, I understand that if you have a wire with current that looks uncharged in a rest frame, that it will appear to be charged in the frame of a test charge that is moving with respect to the current because, e.g., the positive, stationary, charges will have a different distance between them than the negative, moving, ones from the point of view of the moving test charge.

However, is there any intuition for why this actually leads to a different force being felt? Why doesn't the shape of the electric field of each charge also distort so that the force that is being felt does not vary with the velocity of the test charge.

What is strange to me, is that the fact that magnetism exists seems to suggest that the speeding rocket in the above example would actually be destroyed. (Think of a long chain of millions of h-bombs detonating along a line that is parallel to the direction of flight of the speeding rocket, but 100km away from the line of flight. The speeding rocket would see many bombs concentrated at around 100km away while a stationary rocket would see only a few.)

1. One rocket, "stationary rocket," lies adrift in space and another rocket, "speeding rocket," flies toward it at 99.995% of the speed of light. 100 km away, a hydrogen bomb is detonated in frame of the stationary rocket so that the flash of gamma radiation it emits hits both rockets simultaneously as

the speeding rocket flies by the stationary rocket, narrowly missing it, toward the site of the bomb detonation.

The stationary rocket sees a pretty big flash, but nothing too catastrophic because of the distance to the bomb. However, the speeding rocket, due to length contraction, measures a distance of just 1 km to the detonation and is annihilated. Is this what happens? Or is the flash of the h-bomb distorted in the frame of the speeding rocket so that they both see the same intensity of gamma rays?

It just seems to defy reason that a passenger in the stationary rocket should be able to look out the window of his rocket and see a speeding rocket become vaporized by a distant explosion at the very instant that the speeding rocket passes by the window of the stationary rocket.

2. As for magnetism, I understand that if you have a wire with current that looks uncharged in a rest frame, that it will appear to be charged in the frame of a test charge that is moving with respect to the current because, e.g., the positive, stationary, charges will have a different distance between them than the negative, moving, ones from the point of view of the moving test charge.

However, is there any intuition for why this actually leads to a different force being felt? Why doesn't the shape of the electric field of each charge also distort so that the force that is being felt does not vary with the velocity of the test charge.

What is strange to me, is that the fact that magnetism exists seems to suggest that the speeding rocket in the above example would actually be destroyed. (Think of a long chain of millions of h-bombs detonating along a line that is parallel to the direction of flight of the speeding rocket, but 100km away from the line of flight. The speeding rocket would see many bombs concentrated at around 100km away while a stationary rocket would see only a few.)