Do headlights shine if the car moves at the speed of light?
1) Does the headlights illuminate other objects and is reflected back into the eyes?
Not. As you know, you can not exceed the speed of light. This means that in one of the directions the light can not shine at all, because it is not capable of exceeding the speed of the car, so it will never come out of the headlights. However, we live in a multidimensional world and not all the light shines in one direction.
Imagine a two-dimensional car without mass (that is, moving at the speed of light), which emitted two photons, one up and one down. Two beams are separated from the car and remain behind it. They move at the same speed of light, but cannot move forward as fast as one of the velocity vectors is directed up / down, so we are overtaking them. These photons then encounter some kind of obstacle in their path, such as a road sign or a tree, and are reflected back. The problem is that they can no longer catch up with you. Other people walking along the sidewalk are able to see reflected light, but you have already left and you will never see it.
')
Here you are, everything can be explained on the mere fact that all the light moves at the same speed, no matter where. This is hardly relevant to the theory of relativity.
However, there is a more hardcore version.
2) Can things moving at the speed of light have headlights? Can they even have a vision?
That's where the crazy truth of the theory of relativity really comes into play, so no need to be ashamed if you don’t understand something, but the answer is again negative.
Perhaps you are familiar with the concept of relativistic time dilation. Suppose I and a friend get on different trains and go to meet them. Passing by, if we look through the window at a wall clock in a compartment with each other, then both will notice that they go slower than usual. This is not because the clock slows down, but because the light between us comes into play: the faster we move, the slower we grow in relatively less mobile objects. This is because time is not absolute for all objects in the Universe, it is different for each object and depends on its speed. Our time depends only on our speed in the Universe. You can imagine this as a movement in different directions on the space-time scale. There is a certain problem here, because our brain is not adapted for understanding the geometry of space-time, but is inclined to represent time as a kind of absolute. However, after reading a bit of literature on this topic, you will normally be able to perceive it as a natural fact: those who move quickly in relation to you are aging more slowly.
In fact, you can calculate how much more slowly. If you have one second, your friend in a very fast train will have one second
of your seconds, where v is its speed and c is the speed of light.
Suppose your friend is sitting in a hypothetical car and is racing at the speed of light. So, we will substitute its speed in our formula and we will look what will be the answer.
Oops! Looks like he didn’t have any time at all! Probably something wrong with our calculations ?! It turns out that no. Time. Not. Exists. For. Objects On. Speeds Sveta.
He simply does not.
This means that things at the speed of light can not perceive "occurring" events in the same way as we perceive. Events can not occur for them. They can perform actions, but cannot gain experience. Einstein himself once said: “Time exists, so that everything does not happen at the same time” (“Time doesn’t happen at once”). This coordinate is designed to build events into a meaningful sequence, so that we can understand what is happening. But for an object that moves at the speed of light, this principle does not work, because everything happens at the same time. A traveler at the speed of light will never see, think and feel something that we consider meaningful.
Here is an unexpected conclusion.
Not. As you know, you can not exceed the speed of light. This means that in one of the directions the light can not shine at all, because it is not capable of exceeding the speed of the car, so it will never come out of the headlights. However, we live in a multidimensional world and not all the light shines in one direction.
Imagine a two-dimensional car without mass (that is, moving at the speed of light), which emitted two photons, one up and one down. Two beams are separated from the car and remain behind it. They move at the same speed of light, but cannot move forward as fast as one of the velocity vectors is directed up / down, so we are overtaking them. These photons then encounter some kind of obstacle in their path, such as a road sign or a tree, and are reflected back. The problem is that they can no longer catch up with you. Other people walking along the sidewalk are able to see reflected light, but you have already left and you will never see it.
')
Here you are, everything can be explained on the mere fact that all the light moves at the same speed, no matter where. This is hardly relevant to the theory of relativity.
However, there is a more hardcore version.
2) Can things moving at the speed of light have headlights? Can they even have a vision?
That's where the crazy truth of the theory of relativity really comes into play, so no need to be ashamed if you don’t understand something, but the answer is again negative.
Perhaps you are familiar with the concept of relativistic time dilation. Suppose I and a friend get on different trains and go to meet them. Passing by, if we look through the window at a wall clock in a compartment with each other, then both will notice that they go slower than usual. This is not because the clock slows down, but because the light between us comes into play: the faster we move, the slower we grow in relatively less mobile objects. This is because time is not absolute for all objects in the Universe, it is different for each object and depends on its speed. Our time depends only on our speed in the Universe. You can imagine this as a movement in different directions on the space-time scale. There is a certain problem here, because our brain is not adapted for understanding the geometry of space-time, but is inclined to represent time as a kind of absolute. However, after reading a bit of literature on this topic, you will normally be able to perceive it as a natural fact: those who move quickly in relation to you are aging more slowly.
In fact, you can calculate how much more slowly. If you have one second, your friend in a very fast train will have one second
of your seconds, where v is its speed and c is the speed of light.
Suppose your friend is sitting in a hypothetical car and is racing at the speed of light. So, we will substitute its speed in our formula and we will look what will be the answer.
Oops! Looks like he didn’t have any time at all! Probably something wrong with our calculations ?! It turns out that no. Time. Not. Exists. For. Objects On. Speeds Sveta.
He simply does not.
This means that things at the speed of light can not perceive "occurring" events in the same way as we perceive. Events can not occur for them. They can perform actions, but cannot gain experience. Einstein himself once said: “Time exists, so that everything does not happen at the same time” (“Time doesn’t happen at once”). This coordinate is designed to build events into a meaningful sequence, so that we can understand what is happening. But for an object that moves at the speed of light, this principle does not work, because everything happens at the same time. A traveler at the speed of light will never see, think and feel something that we consider meaningful.
Here is an unexpected conclusion.
Source: https://habr.com/ru/post/376041/
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