I A problem with how the speed of light connects to special relativity

[The Baron]

TL;DR Summary

I have a problem with how a person traveling at the speed of light views his speed.

[Mentors' note: This question was orginally assumed a train traveling at the speed of light. Further discussion shows that this assumption is not required for the question; any relativistic velocity is enought to raise the question. The post has been edited, changes in boldface, to reflect this]

Okay so here is my question:
Let's say you are inside of a train that's moving at some speed that is close to the speed of light.
And you look outside and try to measure your speed.

to a viewer outside the train, it seems like you're moving at the speed of light, let's say 10 minutes for A km.
for you inside of the train you have moved Akm, in less than 10 minutes because of special relativity.
Now that means that you think that you are moving faster than the speed of light. because you moved the amount of distance a person in the speed of light will pass, but in less time.

Where am I mistaken? because this shouldn't be possible.

 

[PeroK]

Summary:: I have a problem with how a person traveling at the speed of light views his speed.

In the theory of SR it is impossible for a person (or anything with mass) to travel at $c$, the speed of light in vacuum. Moreover, you cannot (even theoretically) make measurements of time and space from a frame of reference moving at $c$ with respect to another.

 

[The Baron]

In the theory of SR, it is impossible for a person (or anything with mass) to travel at $c$, the speed of light in a vacuum. Moreover, you cannot (even theoretically) make measurements of time and space from a frame of reference moving at $c$ with respect to another.

But these are merely "technical" difficulties because if what I am saying is TRUE(which it isn't) then it can be applicable to the way two beings at the speed of light perceive each other and it could mean that the speed of light is NOT equal in all speeds. Can you contradict it without relying on assumptions that are meant only to illustrate the problem better
Can you please explain to me why is it theoretically incorrect?
(Sorry if I come off angry that is not my goal I just want to understand where is my logical mistake.)

 

[PeroK]

Can you please explain to me why is it theoretically incorrect?
(I just want to understand where is my logical mistake.)

This is the basic postulate of SR: that the speed of light is invariant across all inertial reference frames. It's simple to deduce from that that no two inertial reference frames can have a relative speed of $c$.

There is no speed limit in Newtonian physics, so it's not a question of logic. It's a question of experimental evidence.

The test is whether you can accelerate a particle (e.g. at CERN) to beyond $c$. Classical physics say you can, SR says you can't. You find you can't, so by experimental evidence our universe has SR spacetime and not Newtonian space and time.

 

[The Baron]

This is the basic postulate of SR: that the speed of light is invariant across all inertial reference frames. It's simple to deduce from that that no two inertial reference frames can have a relative speed of $c$.

There is no speed limit in Newtonian physics, so it's not a question of logic. It's a question of experimental evidence.

The test is whether you can accelerate a particle (e.g. at CERN) to beyond $c$. Classical physics say you can, SR says you can't. You find you can't, so by experimental evidence, our universe has SR spacetime and not Newtonian space and time.

But that is not the point. I am not talking about which one of them is correct I am saying that if my idea is theoretically correct then it means that the speed of light is not equivalent to all viewers.

 

[PeroK]

But that is not the point. I am not talking about which one of them is correct I am saying that if my idea is theoretically correct then it means that the speed of light is not equivalent to all viewers.

There's no problem with that except that your idea doesn't agree with the experimental evidence. The speed of light is not invariant in Newtonian physics. That's why it had to be upgraded to SR.

 

[The Baron]

There's no problem with that except that your idea doesn't agree with the experimental evidence. The speed of light is not invariant in Newtonian physics. That's why it had to be upgraded to SR.

But experimental evidence are not always true. and it might be that maybe at "lower" speeds the speed of light is the same with all viewers because the differences are very very small but as you get closer to the speed of light you will not see it the same as people in different speeds. if my idea is correct then that is the required conclusion, one that can not be tested (with our current technology) because we can't move at a speed that is close to the speed of light.

 

[Ibix]

Where am I mistaken? because this shouldn't be possible.

You are mistaken in thinking that it is possible for a train to travel at the speed of light in a relativistic universe. It isn't, not even in principle. Attempting to describe something doing it involves self-contradiction, and that's why you are getting nonsense - because your premises are not consistent.

 

[The Baron]

You are mistaken in thinking that it is possible for a train to travel at the speed of light in a relativistic universe. It isn't, not even in principle. Attempting to describe something doing it involves self-contradiction, and that's why you are getting nonsense - because your premises are not consistent.

As I have said before the train thing, was only in order to illustrate the problem better.

 

[PeroK]

But experimental evidence are not always true.

We cannot discuss your alternative theories on this forum. If you don't accept experimental evidence, then there can be no further discussion.

 

[Nugatory]

Where am I mistaken? because this shouldn't be possible.

As other have pointed out, assuming a train moving at the speed of light leads to logical inconsistencies and impossible results, but that's the because we started with the inconsistent assumption that the train can move at the speed of light.

However, we can avoid this problem by saying that the train is moving at 99.9999% of the speed of light - that is possible - and the same paradox you've described

to a viewer outside the train, it seems like you're moving at the speed of light, let's say 10 minutes for A km.
for you inside of the train you have moved Akm, in less than 10 minutes because of special relativity.
Now that means that you think that you are moving faster than the speed of light. because you moved the amount of distance a person in the speed of light will pass, but in less time.

will still appear.

What's going on here is that you have not accounted for length contraction (and possible relativity of simultaneity, although you may not need it to explain this particular thought experiment). Do the speed calculation properly and including these effects and the apparent paradox will go away.

And here's a hint to help you see what's going on: For you inside the train, you have not moved at all. You and the train are at rest while the ground, the rails, and your destination are moving towards you.

 

[FactChecker]

But experimental evidence are not always true.

It has always been true so far.

and it might be that maybe at "lower" speeds the speed of light is the same with all viewers because the differences are very very small

The accuracy of the experiments are astounding. They are far beyond the accuracy needed to disprove that the velocities are just added (or subtracted). The speed of light has been measured to be constant with astounding accuracy.

but as you get closer to the speed of light you will not see it the same as people in different speeds. if my idea is correct then that is the required conclusion, one that can not be tested (with our current technology) because we can't move at a speed that is close to the speed of light.

It is not necessary to get close to the speed of light. It is only necessary to get a velocity large enough so that the experiments should be able to detect the difference. The experiments have gone far beyond that. In addition, there are other consequences of SR that are clear to everyone, like the atomic bomb.

 

[Herman Trivilino]

Let's say you are inside of a train that's moving at some speed that is close to the speed of light.
And you look outside and try to measure your speed.

You can see things pass by and measure your speed relative to them. Let's say that someone has placed markers one kilometer apart along your line of motion, as measured by someone at rest relative to the markers. Since you are moving past the markers you will observe the distance between them contracted. But your clocks are still ticking at a rate of one second per second.

To an observer at rest relative to the markers, your clocks are running slow, but the markers are one kilometer apart.

You can measure the speed of the markers relative to your train. Someone at rest relative to the markers can measure your train's speed relative to the markers. Both measurements yield the same result.