5 ms·

People keep asking this, and similar things like "if you were travelling in a vehicle at the speed of light and you turned on the headlights, what would happen?

People keep asking this, and similar things like "if you were travelling in a vehicle at the speed of light and you turned on the headlights, what would happen?" For me the easiest answer is to understand that from the point of view of the person travelling near the speed of light the beam of light moves away from them at the speed of light. So after ~1 second they are 300,000Km apart. On the other hand, from the point of view of a 'stationary' observer, the light and the spaceship emitting it are moving at almost exactly the same speed. So after ~1 second they are maybe 1 meter apart. How can this be? Our minds naturally want to reject this as nonsense. But the thing the gripping hand is holding that makes this true is that to the stationary observer and the person travelling near the speed of light time is moving at different rates. The person who is moving ~1m slower than the speed of light is experiencing time enormously much slower than the person 'standing still'. The time difference is 300,000,000 times (sic). Our brains reject this, because we think of time as an absolute rock solid constant, when in fact even with our primitive understanding and slow speeds we can demonstrate experimentally that time is in fact flexible, and it does slow down the faster you get.

Kilimanjaro 16y ago
Say you just flick the lights on and off quickly just to let one photon escape. Where will that photon be in reality in one second? 300kkm apart from the rocket? one meter apart?
- tel 16y ago
  The part that makes this so hard to grasp is that this question is ill-posed. The "in reality" part is nonsensical. A primary insight to general relativity is that it makes no sense to define location (or motion) except relative to an observer. This means there's no "true" position or motion, simply an infinite set of equivalently meaningful but disagreeing ways to observe them. (For interest's sake, acceleration is the lowest order local phenomenon. An object does not need an external observer to measure it's own acceleration due to the appearance of locally measurable "forces".) So the answer is to excise "in reality" and then state that both answers are equally meaningful and correct.
  - Kilimanjaro 16y ago
    When I say 'in reality' I mean physically. Say the rocket earthbound and is 2x300kkm from the earth, the question again, will the photon collide with the earth or still be 300kkm from it? The problem I have with light as a unit of reference is that 'perception' is not the same as 'reality' in the physical world.
    - T-hawk 16y ago
      Relativity demands and demonstrates that there is no such thing as "'reality' in the physical world". Events only occur and exist in the context of an observer. From the perspective of an Earthbound observer, the photon emitted by the ship will travel from 600kkm away to 300kkm away in one second. (Actually the observer cannot see the photon until another second elapses and it collides with him on Earth.) This observer will see the ship and the photon moving almost together, the ship slower by whatever infinitesimal fraction of c. From the perspective of a shipborne observer, the photon emitted by the ship will travel from 0 kkm (away from the ship) to 300kkm away also in one second. How do we reconcile this with the knowledge that the Earthborne observer sees the ship and the photon staying together? Length contracts in the direction of travel. So the shipborne observer's meters are very short. The small distance perceived by the Earthbound observer is perceived as a 300kkm distance by the shipborne observer. http://en.wikipedia.org/wiki/Length_contraction http://en.wikipedia.org/wiki/Length_contraction In general, this is how you resolve paradoxes in relativity: work it out from the perspective of each observer and understand that there is no central objective reality. You will find that you made an assumption that does not hold true across both observers. http://en.wikipedia.org/wiki/Ladder_paradox http://en.wikipedia.org/wiki/Ladder_paradox If you can wrap your mind around the Ladder Paradox, you're well on your way to understanding space-time transformations in relativity. The key to the ladder paradox is that there is no such thing as an objective standard of "simultaneous". Simultaneity is specific to each observer; two observers perceive the simultaneity of two events differently.
    - Stormbringer 16y ago
      From the earth observer's point of view in one second the photon will have moved 300 megameters, and the spaceship with astronaut will be 1 meter behind it. From the astronauts points of view only 1/300,000,000th of a second will have passed. They are going to smack into the planet and won't even know what hit them. The resulting explosion will make Tunguska look like amateur hour with a whoopee cushion.
- crux_ 16y ago
  The ill-formed part of your question is the "in one second" part. From the point of view of the observer on the spaceship, the photon will be ~300k km away after one second. From the point of view of an 'stationary' observer, the photon will be (one second * (c - spaceship_speed)) away from the spaceship. How can this be? Answer, as the grandparent said: time is passing differently for the person on the spaceship than it is for the person outside. It is passing in such a way that, for each of them, the speed of light is exactly c. (edit: corrected 300km to 300k km)

Kilimanjaro 16y ago

Say you just flick the lights on and off quickly just to let one photon escape. Where will that photon be in reality in one second? 300kkm apart from the rocket? one meter apart?

tel 16y ago
The part that makes this so hard to grasp is that this question is ill-posed. The "in reality" part is nonsensical. A primary insight to general relativity is that it makes no sense to define location (or motion) except relative to an observer. This means there's no "true" position or motion, simply an infinite set of equivalently meaningful but disagreeing ways to observe them. (For interest's sake, acceleration is the lowest order local phenomenon. An object does not need an external observer to measure it's own acceleration due to the appearance of locally measurable "forces".) So the answer is to excise "in reality" and then state that both answers are equally meaningful and correct.
- Kilimanjaro 16y ago
  When I say 'in reality' I mean physically. Say the rocket earthbound and is 2x300kkm from the earth, the question again, will the photon collide with the earth or still be 300kkm from it? The problem I have with light as a unit of reference is that 'perception' is not the same as 'reality' in the physical world.
  - T-hawk 16y ago
    Relativity demands and demonstrates that there is no such thing as "'reality' in the physical world". Events only occur and exist in the context of an observer. From the perspective of an Earthbound observer, the photon emitted by the ship will travel from 600kkm away to 300kkm away in one second. (Actually the observer cannot see the photon until another second elapses and it collides with him on Earth.) This observer will see the ship and the photon moving almost together, the ship slower by whatever infinitesimal fraction of c. From the perspective of a shipborne observer, the photon emitted by the ship will travel from 0 kkm (away from the ship) to 300kkm away also in one second. How do we reconcile this with the knowledge that the Earthborne observer sees the ship and the photon staying together? Length contracts in the direction of travel. So the shipborne observer's meters are very short. The small distance perceived by the Earthbound observer is perceived as a 300kkm distance by the shipborne observer. http://en.wikipedia.org/wiki/Length_contraction http://en.wikipedia.org/wiki/Length_contraction In general, this is how you resolve paradoxes in relativity: work it out from the perspective of each observer and understand that there is no central objective reality. You will find that you made an assumption that does not hold true across both observers. http://en.wikipedia.org/wiki/Ladder_paradox http://en.wikipedia.org/wiki/Ladder_paradox If you can wrap your mind around the Ladder Paradox, you're well on your way to understanding space-time transformations in relativity. The key to the ladder paradox is that there is no such thing as an objective standard of "simultaneous". Simultaneity is specific to each observer; two observers perceive the simultaneity of two events differently.
  - Stormbringer 16y ago
    From the earth observer's point of view in one second the photon will have moved 300 megameters, and the spaceship with astronaut will be 1 meter behind it. From the astronauts points of view only 1/300,000,000th of a second will have passed. They are going to smack into the planet and won't even know what hit them. The resulting explosion will make Tunguska look like amateur hour with a whoopee cushion.
crux_ 16y ago
The ill-formed part of your question is the "in one second" part. From the point of view of the observer on the spaceship, the photon will be ~300k km away after one second. From the point of view of an 'stationary' observer, the photon will be (one second * (c - spaceship_speed)) away from the spaceship. How can this be? Answer, as the grandparent said: time is passing differently for the person on the spaceship than it is for the person outside. It is passing in such a way that, for each of them, the speed of light is exactly c. (edit: corrected 300km to 300k km)