I understand that if I am standing on earth and a space ship takes off and travels at .6c, then I perceive the space traveler receding at .6c relative to me, and the space traveler perceive me as receding at .6c relative to him. If another traveler takes off in the 180-degree opposite direction, then likewise I perceive the other space traveler receding at .6c relative to me, and the other space traveler perceive me as receding at .6c relative to him.
So why don’t they perceive each other as traveling faster than c, the speed of light?
In: 29
Because of time dilation and length contraction.
Remember velocity is distance over time.
In relatively those two things are not absolute they are relative to The Observer.
What you as a stationary Observer thinks is certain distance in a certain time someone on the spaceship does not
Because you’re resting this on an incorrect assumption; that velocities are simply additive. In reality, they’re actually not.
For an example; say you have two people, one on a moving train, and one outside the moving train, standing on the ground. At the moment the person on the train passes the person on the ground, the person on the train fires a gun (in the same direction the train is traveling) at a certain speed relative to themselves.
One would think that the speed of the bullet relative to the outside observer is just the speed of the train plus the speed of the bullet on the train…but it actually *isn’t*. It’s slightly less. The difference is imperceptibly (and honestly near-immeasurably) small at lower speeds, but as you get to higher and higher speeds the deviation from just adding the speeds together will get greater and greater.
In the most extreme example (the bullet being a photon traveling at the speed of light), the bullet is observed as traveling at ***precisely*** c to both observers, despite their different velocities relative to one another.
Because of time dilation and length contraction.
Remember velocity is distance over time.
In relatively those two things are not absolute they are relative to The Observer.
What you as a stationary Observer thinks is certain distance in a certain time someone on the spaceship does not
This question touches on some of the ways relativistic motion is so strange.
Normally you would expect speeds to add together like those we interact with on a daily basis. For example if there is a car going 40 mph one direction and another is approaching it at 40 mph then their closing speed is 80 mph. Easy, simple, intuitive. But that isn’t how things work at speeds approaching the speed of light.
Instead moving near the speed of light results in some changes in the frame of reference of the traveler. Two major factors are time dilation and length contraction. Time dilation gets a lot of press, where less time passes for the traveler than in an “at rest” reference frame. As a result the travelers won’t agree on how much time has passed and therefore can disagree about their relative speeds.
Another significant factor is length contraction, where the shape of the surrounding universe changes according to the traveler. Things in the direction of their travel are compressed and shortened which means they don’t agree with other observers about how quickly they are traveling.
To illustrate imagine you have a traveler who is going to a destination 1 light year away at a speed close enough to the speed of light that it will seem to take only 10% of a year. Now the traveler is only going to experience 10% of a year in time so they can’t perceive themselves as having covered 1 light year or they will view themselves as having exceeded the speed of light! So not only is their time frame slowed to 10% they also view the distance to that destination as being somewhat less than 10% of a light year away!
This works not just for their destination but the universe as a whole, so the traveler watching the other ship flying away would view it as covering less distance just like it does itself.
This question touches on some of the ways relativistic motion is so strange.
Normally you would expect speeds to add together like those we interact with on a daily basis. For example if there is a car going 40 mph one direction and another is approaching it at 40 mph then their closing speed is 80 mph. Easy, simple, intuitive. But that isn’t how things work at speeds approaching the speed of light.
Instead moving near the speed of light results in some changes in the frame of reference of the traveler. Two major factors are time dilation and length contraction. Time dilation gets a lot of press, where less time passes for the traveler than in an “at rest” reference frame. As a result the travelers won’t agree on how much time has passed and therefore can disagree about their relative speeds.
Another significant factor is length contraction, where the shape of the surrounding universe changes according to the traveler. Things in the direction of their travel are compressed and shortened which means they don’t agree with other observers about how quickly they are traveling.
To illustrate imagine you have a traveler who is going to a destination 1 light year away at a speed close enough to the speed of light that it will seem to take only 10% of a year. Now the traveler is only going to experience 10% of a year in time so they can’t perceive themselves as having covered 1 light year or they will view themselves as having exceeded the speed of light! So not only is their time frame slowed to 10% they also view the distance to that destination as being somewhat less than 10% of a light year away!
This works not just for their destination but the universe as a whole, so the traveler watching the other ship flying away would view it as covering less distance just like it does itself.
Because of time dilation and length contraction.
Remember velocity is distance over time.
In relatively those two things are not absolute they are relative to The Observer.
What you as a stationary Observer thinks is certain distance in a certain time someone on the spaceship does not
Because you’re resting this on an incorrect assumption; that velocities are simply additive. In reality, they’re actually not.
For an example; say you have two people, one on a moving train, and one outside the moving train, standing on the ground. At the moment the person on the train passes the person on the ground, the person on the train fires a gun (in the same direction the train is traveling) at a certain speed relative to themselves.
One would think that the speed of the bullet relative to the outside observer is just the speed of the train plus the speed of the bullet on the train…but it actually *isn’t*. It’s slightly less. The difference is imperceptibly (and honestly near-immeasurably) small at lower speeds, but as you get to higher and higher speeds the deviation from just adding the speeds together will get greater and greater.
In the most extreme example (the bullet being a photon traveling at the speed of light), the bullet is observed as traveling at ***precisely*** c to both observers, despite their different velocities relative to one another.
Because you’re resting this on an incorrect assumption; that velocities are simply additive. In reality, they’re actually not.
For an example; say you have two people, one on a moving train, and one outside the moving train, standing on the ground. At the moment the person on the train passes the person on the ground, the person on the train fires a gun (in the same direction the train is traveling) at a certain speed relative to themselves.
One would think that the speed of the bullet relative to the outside observer is just the speed of the train plus the speed of the bullet on the train…but it actually *isn’t*. It’s slightly less. The difference is imperceptibly (and honestly near-immeasurably) small at lower speeds, but as you get to higher and higher speeds the deviation from just adding the speeds together will get greater and greater.
In the most extreme example (the bullet being a photon traveling at the speed of light), the bullet is observed as traveling at ***precisely*** c to both observers, despite their different velocities relative to one another.
This question touches on some of the ways relativistic motion is so strange.
Normally you would expect speeds to add together like those we interact with on a daily basis. For example if there is a car going 40 mph one direction and another is approaching it at 40 mph then their closing speed is 80 mph. Easy, simple, intuitive. But that isn’t how things work at speeds approaching the speed of light.
Instead moving near the speed of light results in some changes in the frame of reference of the traveler. Two major factors are time dilation and length contraction. Time dilation gets a lot of press, where less time passes for the traveler than in an “at rest” reference frame. As a result the travelers won’t agree on how much time has passed and therefore can disagree about their relative speeds.
Another significant factor is length contraction, where the shape of the surrounding universe changes according to the traveler. Things in the direction of their travel are compressed and shortened which means they don’t agree with other observers about how quickly they are traveling.
To illustrate imagine you have a traveler who is going to a destination 1 light year away at a speed close enough to the speed of light that it will seem to take only 10% of a year. Now the traveler is only going to experience 10% of a year in time so they can’t perceive themselves as having covered 1 light year or they will view themselves as having exceeded the speed of light! So not only is their time frame slowed to 10% they also view the distance to that destination as being somewhat less than 10% of a light year away!
This works not just for their destination but the universe as a whole, so the traveler watching the other ship flying away would view it as covering less distance just like it does itself.
None of those things is an absolute; rather, they are dependent on who or what is doing the observing.
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