PDA

View Full Version : Nukes, Magnetism, and Length Contraction

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.)

robross
2009-Aug-29, 01:05 AM
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.

Length contraction only occurs in the direction of motion, not in perpendicular directions.

jonderry
2009-Aug-29, 02:17 AM
Length contraction only occurs in the direction of motion, not in perpendicular directions.

Yes, the direction to the nuke is the same as the direction of travel, except in part 2, which deals with magnetism.

robross
2009-Aug-29, 02:47 AM
Yes, the direction to the nuke is the same as the direction of travel, except in part 2, which deals with magnetism.

Where is the explosion then? In front of B's direction of motion, or behind it?

Rob

jonderry
2009-Aug-29, 04:16 AM
Where is the explosion then? In front of B's direction of motion, or behind it?

Rob

In front, like this:

>[stat. rocket]>
>[mov. rocket]>-----------------------{h. bomb}

The stationary rocket is 100 km from the bomb, and the moving rocket is 1 km from the bomb in it's frame of reference when the flash hits it just as it flies by the stationary rocket.

Empyre
2009-Aug-29, 04:41 AM
As a complete non-expert, it seems to me that it is the frame of the bomb that matters most in this situation, because that determines how much radiation is where.

Jeff Root
2009-Aug-29, 06:27 AM
The rocket speeding toward the explosion is hit much harder by the bomb's
It takes some time for the speeding rocket to be heated to the point of being
completely vaporized. Maybe tenths of a second or longer. In that time it
moves a large distance. Because it is moving toward the explosion, the
speeding rocket encounters a larger number of photons, and in a shorter
period of time, than the other rocket. Observers will see the speeding rocket
vaporize like a meteor, making a long streak of plasma that extends from their
location to the place of the explosion and perhaps beyond. The vaporization
only begins at the instant the two rockets are abreast. At the speed the
rocket is going, you could just replace the gamma rays from the H-bomb
with air. The rocket would still vaporize.

-- Jeff, in Minneapolis

jonderry
2009-Aug-29, 06:49 AM
The rocket speeding toward the explosion is hit much harder by the bomb's
It takes some time for the speeding rocket to be heated to the point of being
completely vaporized. Maybe tenths of a second or longer. In that time it
moves a large distance. Because it is moving toward the explosion, the
speeding rocket encounters a larger number of photons, and in a shorter
period of time, than the other rocket. Observers will see the speeding rocket
vaporize like a meteor, making a long streak of plasma that extends from their
location to the place of the explosion and perhaps beyond. The vaporization
only begins at the instant the two rockets are abreast. At the speed the
rocket is going, you could just replace the gamma rays from the H-bomb
with air. The rocket would still vaporize.

-- Jeff, in Minneapolis

Let's not consider issues like the time it takes for the rocket to be heated up or residual photons. This has nothing to do with relativity and will only confuse the key issue. So, we could just consider a single EM pulse that both rockets simply measure. The speeding rocket should measure 10,000x as much EM radiation because of the length contraction of the distance to the pulse.

The question, I guess, is, how does the stationary rocket observer make sense of this. You point out that the stationary observer will be hit by higher energy photons, but is that really it?

Think about this: because the speeding rocket thinks it is closer to the bomb, it should believe that it is subtending a larger solid angle of the sphere of the flash, while from it's perspective, the stationary rocket subtends the same solid angle, but is flying away from the flash.

So the suggestion is that there is some kind of duality between solid angle subtended and perceived photon wavelength....is that correct?

robross
2009-Aug-29, 09:36 PM
The question, I guess, is, how does the stationary rocket observer make sense of this. You point out that the stationary observer will be hit by higher energy photons, but is that really it?

Think about this: because the speeding rocket thinks it is closer to the bomb, it should believe that it is subtending a larger solid angle of the sphere of the flash, while from it's perspective, the stationary rocket subtends the same solid angle, but is flying away from the flash.

So the suggestion is that there is some kind of duality between solid angle subtended and perceived photon wavelength....is that correct?

I was a little confused by this. I didn't understand the geometry you were trying to convey. Perhaps you can draw a little image to make it more clear?

Also, you say "the stationary rocket subtends the same solid angle, but is flying away from the flash". Again, I am confused because if the rocket is stationary, how is it flying "away" from the flash? Speaking relatively, you could say the flash is stationary and the "stationary" rocket is moving *towards* it, or the "stationary" rocket is stationary, and the flash is moving "towards* it.

Also, I think you are focusing exclusively on length contraction when really it goes hand in hand with time dilation. You can't really think about these separately. Length and time are relative, and are experienced by an observer to maintain the constant speed of light.

Also, you say "You point out that the stationary observer will be hit by higher energy photons, but is that really it?", but this is actually the *opposite* of what Jeff Root wrote.

Rob