General / Off-Topic Firing a gun at the speed of light.
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w = (u + v)/(1 + uv/c²)
where c² is the speed of light squared. At so-called Newtonian (i.e., slow) speeds, the term uv/c² is pretty close to 0, and the equation reduces down to the familiar w = u + v. However, if we are traveling at, say, 0.9c (nine-tenths the speed of light), and we shoot a bullet forward also at 0.9c, we discover via the above formula that the slug doesn't attain an overall speed of 1.8c (i.e., more than the speed of light), but rather a modest
(0.9c + 0.9c)/(1 + [0.9]²) = 0.994c
(roughly).
Does this mean the bullet just dribbles out of the gun like a gumdrop, Not at all — to you, the space traveller, everything looks normal. However, a stationary observer would note that you were suffering from the unique effects of the Fitzgerald contraction — which is to say, (1) time would slow down for you (although you wouldn't realize it), and (2) you and your spaceship would get compressed like an accordion along your axis of travel.
where c² is the speed of light squared. At so-called Newtonian (i.e., slow) speeds, the term uv/c² is pretty close to 0, and the equation reduces down to the familiar w = u + v. However, if we are traveling at, say, 0.9c (nine-tenths the speed of light), and we shoot a bullet forward also at 0.9c, we discover via the above formula that the slug doesn't attain an overall speed of 1.8c (i.e., more than the speed of light), but rather a modest
(0.9c + 0.9c)/(1 + [0.9]²) = 0.994c
(roughly).
Does this mean the bullet just dribbles out of the gun like a gumdrop, Not at all — to you, the space traveller, everything looks normal. However, a stationary observer would note that you were suffering from the unique effects of the Fitzgerald contraction — which is to say, (1) time would slow down for you (although you wouldn't realize it), and (2) you and your spaceship would get compressed like an accordion along your axis of travel.
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As Einstein pointed out, when things start travelling at or near lightspeed, what you see and experience depends on your point of view. It's all got to do with relativity.
Relative to you and your frame of reference (in this case, your spaceship is your frame of reference), the bullet is travelling at about the speed of sound. In relativistic terms, it's barely moving. So your perception of it would be identical to your perception of a bullet being fired on Earth, or onboard a spaceship that isn't moving at all with respect to nearby stellar objects.
From the point of view of us sitting in a nearby stationary spaceship, however, the view is different. If you were travelling at just a smidgen under the speed of light (so that a bullet fired in the direction of travel might logically be expected to exceed the speed of light), "your time" slows down compared to everyone else. so it would take ages for us to see the gun to fire, and the bullet would seem to move in slow motion relative to you. The net effect of this is that neither you nor the bullet would be seen by us to be travelling above the speed of light.
If you had somehow managed to acquire infinite energy and/or infinite time and thus were actually capable of travelling at exactly lightspeed, then from our perspective, your time would appear to have stopped completely. We wouldn't ever see the bullet leave the gun, because the universe would end long before you finished pressing the trigger.
Relative to you and your frame of reference (in this case, your spaceship is your frame of reference), the bullet is travelling at about the speed of sound. In relativistic terms, it's barely moving. So your perception of it would be identical to your perception of a bullet being fired on Earth, or onboard a spaceship that isn't moving at all with respect to nearby stellar objects.
From the point of view of us sitting in a nearby stationary spaceship, however, the view is different. If you were travelling at just a smidgen under the speed of light (so that a bullet fired in the direction of travel might logically be expected to exceed the speed of light), "your time" slows down compared to everyone else. so it would take ages for us to see the gun to fire, and the bullet would seem to move in slow motion relative to you. The net effect of this is that neither you nor the bullet would be seen by us to be travelling above the speed of light.
If you had somehow managed to acquire infinite energy and/or infinite time and thus were actually capable of travelling at exactly lightspeed, then from our perspective, your time would appear to have stopped completely. We wouldn't ever see the bullet leave the gun, because the universe would end long before you finished pressing the trigger.
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