- #1
DiracPool
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I feel I understand relativistic velocity addition fairly well. However, the way I usually see it modeled is with two travelers moving in the same direction. Bob is in a spaceship traveling at 0.6c and shines his flashlight in the direction of travel. An inertial observer, Alice, relative to the spaceship will not see the leading edge of the flashlight beam travel at 1.6c relative to herself, she will see a speed somewhat less than c once the two velocities are plugged into the relativistic velocity addition formula.
I've got that, but let's take another scenario. Let's say Charlie is now the internal observer, and we place Alice 10 light minutes to Charlies left, and Bob 10 light minutes to Charlies right. Each are stationary relative to one another and in the same proper time frame. Now we have both Bob and Alice shine a flashlight at each other, with Charlie hanging out in the center equidistant from the two. What I am visualizing is Charlie seeing Alice's light beam traveling to the right toward Bob at c, and Bob's light beam traveling to left toward Alice at c.
Sounds ok so far, but what about when the leading edge of the beams approach each other? Won't Charlie see these as traveling at 2c relative to each other? Or, to put it another way, won't the distance or displacement between the two leading edges of the beams be shrinking at a rate of 2c? Is this type of thing allowed? Or does the relativistic velocity addition formula have a way to handle this situation too?
I've got that, but let's take another scenario. Let's say Charlie is now the internal observer, and we place Alice 10 light minutes to Charlies left, and Bob 10 light minutes to Charlies right. Each are stationary relative to one another and in the same proper time frame. Now we have both Bob and Alice shine a flashlight at each other, with Charlie hanging out in the center equidistant from the two. What I am visualizing is Charlie seeing Alice's light beam traveling to the right toward Bob at c, and Bob's light beam traveling to left toward Alice at c.
Sounds ok so far, but what about when the leading edge of the beams approach each other? Won't Charlie see these as traveling at 2c relative to each other? Or, to put it another way, won't the distance or displacement between the two leading edges of the beams be shrinking at a rate of 2c? Is this type of thing allowed? Or does the relativistic velocity addition formula have a way to handle this situation too?