# Basic question about the special theory of relativity

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Can anyone give me the outcome of the following situation ?

Let's say that I'm standing in front of a railroad, and a train travels at the speed of light, in a direction from my left to my right (but at this point the train is still several kilometers to my left).

Now, on the railroad, 100 meters from where I'm standing (to the *right* from where I'm standing), I put a sensor, that can detect light.

Now, 1 second before I can see the front end of the train exactly in front of me, the train switches its flash lights on (the lights are on the front end of the train).

My question is, after this second passes, and the front end of train is exactly in front of me, will the sensor (located 100 meter to my right on the railroad) at this moment will show that it already registered the light from the train's flash lights ?

I can see two answers for this question:

1. from my point of view, because the speed of light is constant, the sensor will not register the lights at that moment. It will register the lights exactly when the train itself will hit it, becuse the train's lights and the train are moving at the same speed.

2. From the people on the train point of view, when the train is in front of me, the lights from the train already passed 300,000 km from where the train was a second before, so the sensor will of course registered the lights from the train.

So, how could the sensor both register and not register the light ?, the registration of light can't be relative, either it registered or not, no ?, I mean, exactly when the front end of the train is in front of me, let's say I push a switch and the sensor is moved away from the railroad (so can't register the light anymore), then I go and take the sensor, and look if it registered the light or not, so the answer must be one, either it did, or it didn't.

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First off, in Relativity material objects like trains can not travel at the speed of light, 99.999...9% percent of the speed of light, yes, but not the speed of light itself.

The other thing is that, due to length contraction, the people in the train will not measure the distance between you and the sensor as being 100m. Nor will they measure the distance between the point at which the train turns on its lights and you as being 1 lightsecond in distance. The distance will contract by an amount dependant on how close to the speed of light the relative velocity is. At very nearly the speed of light, these distances drop to nearly zero in length.

So while form your perspective you would see the light strike the sensor just split seconds before the train reaches it, the people on the train see the light strike the sensor just split seconds before the train reaches its also, becuase by their measurement the train was almost on top of the sensor already when the lights were turned on.

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At very nearly the speed of light, these distances drop to nearly zero in length.

And what if the train switched on its lights 1 hour before it was in front of me (assuming a very large planet ), and the light sensor was 1 light hours to my right ?, then these distances will not drop to nearly zero in length, right ? (and if they will, then just pick large enough distances). My question then will be, when will the light from the train hit the sensor ?, for me it will be together with the train, but for the people on the train it should happen before, no ?

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from the observer beside the railway lines the train has come along, shone its lights, the lights have been projected at 1*c faster than the train is going as the train is projecting them forward, the train in traveling at 0.9*c, however the lights will only appear to be moving at c relative to the observer and the train at 0.9*c, from the observer on the train the light project normally but space seems distorted out of the front window due to length contraction.

Tell me if im wrong please.

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from the observer beside the railway-lines, the train has come along, shone its lights, the lights have been projected at 1*c faster than the train is going as the train is projecting them forward

" 1*c faster than the train " ?, are you implying that for the observer beside the railway, the lights from the train travels at 2x the speed of light ?

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from the observer beside the railway lines the train has come along, shone its lights, the lights have been projected at 1*c faster than the train is going as the train is projecting them forward,

...

Tell me if im wrong please.

If I read this correctly it's wrong. Light is projected forward at c, for any inertial observer, on the train or not.

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See my link, speeds of relativistic things don't add up linearly. I'm not implying anything moves faster than light speed.

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from the observer beside the railway lines the train has come along, shone its lights, the lights have been projected at 1*c faster than the train is going as the train is projecting them forward, the train in traveling at 0.9*c, however the lights will only appear to be moving at c relative to the observer and the train at 0.9*c, from the observer on the train the light project normally but space seems distorted out of the front window due to length contraction.

I think you're confusing the issue by saying '1*c faster'...surely you mean the light is travelling at c, which is faster than the train. The length contraction will increase, the closer to c the train gets for the occupants, regardless of distance. So yes, you'll see a distortion, as you put it.

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Ok, I should have said should be 1*c faster. However with speeds of stuff that fast not adding up linearally (again see the link) Its not going to exceed the speed of light, revelistic effects like length contraction and time dilation make it all work out and with the speed of light actually being c no tricky maths is needed as the the observed speed from the side would be c.

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Ok, I should have said should be 1*c faster. However with speeds of stuff that fast not adding up linearally (again see the link) Its not going to exceed the speed of light, revelistic effects like length contraction and time dilation make it all work out and with the speed of light actually being c no tricky maths is needed as the the observed speed from the side would be c.

You're still sounding a bit confusing... why do you keep saying '1*c' ? What does that mean? 1*c = c so why not just say c. At any rate, saying that is wrong. A person on the track watching the train approach would NOT see the light approaching at 1*c faster than the train. The light from the train would approach the observer at exactly c. The train itself would have to approach the observer slightly slower than c (since the train cannot actually be moving at c relative to anything)

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On the train reference, not looking out the window, the train appears like it is the same, as it was, when it was sitting at zero velocity. If one looked out its window, it will look like the train station got skinny. If it flashed its front light, exactly at the censor, in its reference, it would expect we would know the front of the train was at that point at that time.

But from our stationary reference, we will see the train looking distance contracted. It will appear like the entire train has narrowed. To maintain a sense of proportion, it will narrow relative to its center point. The result is that although the train has actually triggered the censor, it will look like this skinny train, has not yet reached the censor. What happens is sort of analogous to the Heisenberg uncertainty principle. One can either know position or momentum but not both. Or we can know, by its calculated speed, it should have triggered the censor (momentum), but the distance contraction will make it uncertain where the front of the train is. If the light was in the dead center of the length of the train, then the distance contraction will shink into this center, allowing the momentum-position to coordinate.

A good analogy is a have a fat person stand behind a large lense that makes them look really skinny. Next, using dead aim, fire a bullet at the flag dangling on the side of his belt. Based on the lense, we would hit the fat guy in side, because his real position behind the lense is uncertain. If we are told to aim for hardened target on its his belly button, we would hit it, since the center is not dependant on the type of lense we use. If we told the fat guy to take a step sideways, to hit a bell with his hip, the skinny image would look like it still has to move a little further, but the bell already rang. The relativity lense will mess with our expections.

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On the train reference, not looking out the window, the train appears like it is the same, as it was, when it was sitting at zero velocity. If one looked out its window, it will look like the train station got skinny. If it flashed its front light, exactly at the censor, in its reference, it would expect we would know the front of the train was at that point at that time.

But from our stationary reference, we will see the train looking distance contracted. It will appear like the entire train has narrowed. To maintain a sense of proportion, it will narrow relative to its center point. The result is that although the train has actually triggered the censor, it will look like this skinny train, has not yet reached the censor. What happens is sort of analogous to the Heisenberg uncertainty principle. One can either know position or momentum but not both. Or we can know, by its calculated speed, it should have triggered the censor (momentum), but the distance contraction will make it uncertain where the front of the train is. If the light was in the dead center of the length of the train, then the distance contraction will shink into this center, allowing the momentum-position to coordinate.

A good analogy is a have a fat person stand behind a large lense that makes them look really skinny. Next, using dead aim, fire a bullet at the flag dangling on the side of his belt. Based on the lense, we would hit the fat guy in side, because his real position behind the lense is uncertain. If we are told to aim for hardened target on its his belly button, we would hit it, since the center is not dependant on the type of lense we use. If we told the fat guy to take a step sideways, to hit a bell with his hip, the skinny image would look like it still has to move a little further, but the bell already rang. The relativity lense will mess with our expections.

I don't think you've got that right. The train contracts in the direction of travel... if the train was moving toward you, you wouldn't have a skinny train, you would have a short one (The distance between the front of the train and the back of the train would become smaller) The way your describing it, the distance between the left and right sides of the train becomes smaller ie. a skinny train. I'm no expert, but that doesn't sound right.

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For an observer on the train, the light from the train is travelling at c away from the train, hitting the sensor within that next second. For you who are watching the train at 0.95c lets say, see the light travelling at c as well. That is, 2 objects with positive rest mass,having their velocities added with respect to an inertial reference frame would would be v1 + v2, but with light it is not linear...i.e. regardless of the v of the material object light will escape at c from it. For you who was seeing the person then, also will see light hit that sensor before the train is in front of you, simply because a second was a large time interval for the example of v very close to c.

Ant to last poster, yes, length contraction or the laplace factor works in the direction of the sum of forces no oops sorry in the direction of the velocity vector.

in this case , since the velocity is linear and from front to bacl , only in that direction does special relativity predict contraction.

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