The laser and the laser pointer are both traveling away from each other at the speed of light, so from the pointer’s perspective the laser is traveling at twice the speed of light.
You are being downvoted as if your point was offensive or harmful. You are wrong, but it’s totally counter intuitive and I think this is a mistake that everyone makes when studying introductory physics. This would be correct for anything moving at relatively low speeds. But when you’re talking about light, or anything that goes so fast that “percentage of the speed of light” starts being a useful unit to describe their speed, this concept starts being a bit weirder.
This is actually the basic principle of Einstein’s theory of relativity: the speed of light (in a vacuum) is the same for all observers, regardless of their frame of reference. That means that if the laser pointer emits a laser, the light is moving away from the pointer at the speed of light. If the pointer itself is moving at a speed reeeeeally close to the speed of light… Then the laser will STILL be traveling away from the pointer at the speed of light. And if you, an observer in a frame, see the pointer moving at near the speed of light emit a laser… The laser that the laser emitted is also traveling at the speed of light from your point of view.
And there’s no wordplay here. I don’t mean that it’s light, so of course any speed it travels at is the speed of light. I mean that if you measure its speed from any reference frame, you will get around 300000000 m/s, or around 671 million miles per hour. No matter if you are also traveling at near light speed.
I think you’ve got to be a little careful how you say what you mean here:
In light’s own reference frame, this is true-ish from a pure special relativity perspective. Velocity is sort of undefined in that case because at c, Lorentz transformations bring all distances to zero, meaning that the photon is everywhere at the SAME time. Or said another way, it’s everywhere on its own simultaneity curve. Maybe this is splitting hairs on the definition of “undefined” because, mathematically yeah you’re right, but a rock also moves zero distance in zero time. Its more like it’s velocity doesnt make sense to compute.
From the outside though (as in a non photon frame) this is not true at all. Using laws of refraction you can compute, and even photograph and verify a real, defined speed for a photon in a medium.
The laser and the laser pointer are both traveling away from each other at the speed of light, so from the pointer’s perspective the laser is traveling at twice the speed of light.
You are being downvoted as if your point was offensive or harmful. You are wrong, but it’s totally counter intuitive and I think this is a mistake that everyone makes when studying introductory physics. This would be correct for anything moving at relatively low speeds. But when you’re talking about light, or anything that goes so fast that “percentage of the speed of light” starts being a useful unit to describe their speed, this concept starts being a bit weirder.
This is actually the basic principle of Einstein’s theory of relativity: the speed of light (in a vacuum) is the same for all observers, regardless of their frame of reference. That means that if the laser pointer emits a laser, the light is moving away from the pointer at the speed of light. If the pointer itself is moving at a speed reeeeeally close to the speed of light… Then the laser will STILL be traveling away from the pointer at the speed of light. And if you, an observer in a frame, see the pointer moving at near the speed of light emit a laser… The laser that the laser emitted is also traveling at the speed of light from your point of view.
And there’s no wordplay here. I don’t mean that it’s light, so of course any speed it travels at is the speed of light. I mean that if you measure its speed from any reference frame, you will get around 300000000 m/s, or around 671 million miles per hour. No matter if you are also traveling at near light speed.
Oh wow. TIL.
speed is distance over time, and for light both of those are undefined.
I think you’ve got to be a little careful how you say what you mean here:
In light’s own reference frame, this is true-ish from a pure special relativity perspective. Velocity is sort of undefined in that case because at c, Lorentz transformations bring all distances to zero, meaning that the photon is everywhere at the SAME time. Or said another way, it’s everywhere on its own simultaneity curve. Maybe this is splitting hairs on the definition of “undefined” because, mathematically yeah you’re right, but a rock also moves zero distance in zero time. Its more like it’s velocity doesnt make sense to compute.
From the outside though (as in a non photon frame) this is not true at all. Using laws of refraction you can compute, and even photograph and verify a real, defined speed for a photon in a medium.