Does light take longer to go a set distance on a train?

[shawn9521]

Edit: Sorry, the title should say LIGHT, not time! << Mentor Note -- Title updated >>

Let's say you're on a train, in the back of a car. The train is stationary. You shine a laser to the front of the car, and you can measure the time it takes for the laser to reach the wall. Now, if the train starts moving forward, since the speed of light is the same no matter the reference, if you perform the same experiment, will the light take longer to hit the wall because the wall has "moved" away from the source during the time it took for the light to get there? If yes, is the travel time of light a function of the speed of the train? Thanks in advance!

 

[jbriggs444]

Let's say you're on a train, in the back of a car. The train is stationary. You shine a laser to the front of the car, and you can measure the time it takes for the laser to reach the wall. Now, if the train starts moving forward,

Details, please. How is the train starting to move forward? Is the person shining the laser moving along with the back of the train and using his stopwatch to measure the elapsed time between shining the laser and seeing the reflected light?

Details matter because how you accelerate the train determines whether the rail car is forced to stretch or compress as you do it. If your procedure is to pull the train car with an engine (stretching it) and then allow the train to relax into its stress-free length at a steady speed then the answer is that the measured round trip time on the moving train will remain unchanged.

 

[Ibix]

@shawn9521 - It depends on whose clocks and rulers you are using to make the measurements.

According to clocks and rulers at rest with respect to the track the light pulse has to play catch up when the train is moving. Since the light ends up moving more than the length of the train it will take longer to reach the front of the train in this case than when the train is stationary.

According to clocks and rulers at rest with respect to the train, the train is stationary in both cases (the track moves in this analysis, not the train - hence Einstein's famous quote about when Oxford stops at this train). Therefore light takes the same time to reach the front of the train in both cases.

In the case when the train is stationary, all the clocks and rulers are at rest in the same frame so all measurements made with any of them will agree. In the case where the train is moving, clocks and rulers in the train are at rest in a different frame from those on the track. Due to time dilation, length contraction and the relativity of simultaneity, nobody should have a problem explaining why the other guy's measurements don't agree with theirs in this case.

The difference between my answer and that of @jbriggs444 is that I am assuming that you are doing one set of experiments with the train stationary and one set with the train in motion at constant speed. JBriggs is asking if that's actually what you meant instead of assuming.

 

[shawn9521]

Details, please. How is the train starting to move forward? Is the person shining the laser moving along with the back of the train and using his stopwatch to measure the elapsed time between shining the laser and seeing the reflected light?

Details matter because how you accelerate the train determines whether the rail car is forced to stretch or compress as you do it. If your procedure is to pull the train car with an engine (stretching it) and then allow the train to relax into its stress-free length at a steady speed then the answer is that the measured round trip time on the moving train will remain unchanged.

Thanks for the answers, and sorry that my question was confusing. @Ibix interpreted my question the way I wanted to ask it. I wasn't concerned about the acceleration of the train. We can assume that the laser is turned off when the train is accelerating, and turned back on once the train gets to the desired speed.

Here's a follow-up question. Let's say that there is a photo-receptor on the wall that I am shining the laser at. My laser and the photo-receptor is hooked up to a computer next to me which can measure exactly when the light is emitted and when the photo-receptor detects the light. Would the travel time of the light be different according to the computer when the train travels different speeds? What if the emitter and receptor signals are transmitted wirelessly? And what if the signals are transmitted wirelessly to something in the frame of reference of the tracks, or even the internet?

 

[Ibix]

Here's a follow-up question. Let's say that there is a photo-receptor on the wall that I am shining the laser at. My laser and the photo-receptor is hooked up to a computer next to me which can measure exactly when the light is emitted and when the photo-receptor detects the light. Would the travel time of the light be different according to the computer when the train travels different speeds? What if the emitter and receptor signals are transmitted wirelessly? And what if the signals are transmitted wirelessly to something in the frame of reference of the tracks, or even the internet?

In the case where everything is on the train, all you've got is a fancy clock and ruler setup on the train. You'll measure the same in all cases however you gather and transmit the data. If it were otherwise, you would be able to tell that you were moving in some absolute sense, and one of the postulates of relativity theory (the principle of relativity) is that you can't do that.

In the case where the sensors are transmitting to a computer outside the train the answer depends on the details. If you have "dumb" sensors that simply report that they have seen a light pulse, then you're going to need some kit outside the train to detect where the sensor was when it reported so that you can work out how long the wireless signal took to get to you and work out the original time of detection. This is just an overcomplicated set of clocks and rulers at rest with respect to the track (or the computer, at least). On the other hand if you have "smart" sensors that report that they received a pulse at a certain time then they are using their onboard clocks, at rest with respect to the train, to determine the time stamp. That's just a fancy set of clocks and rulers at rest with respect to the train.

You can complicate your experimental setup as much as you want, but you can always boil it down to "whose measurements am I using - ones in the train or ones on the track?" When you have the answer to that you have the answer to what you'll measure in my previous post.

 

[shawn9521]

In the case where everything is on the train, all you've got is a fancy clock and ruler setup on the train. You'll measure the same in all cases however you transmit the data. If it were otherwise, you would be able to tell that you were moving in some absolute sense, and one of the postulates of relativity theory (the principle of relativity) is that you can't do that.

In the case where the sensors are transmitting to a computer outside the train the answer depends on the details. If you have "dumb" sensors that simply report that they have seen a light pulse, then you're going to need some kit outside the train to detect where the sensor was when it reported so that you can work out how long the wireless signal took to get to you and work out the original time of detection. This is just an overcomplicated set of clocks and rulers at rest with respect to the track (or the computer, at least). On the other hand if you have "smart" sensors that report that they received a pulse at a certain time then they are using their onboard clocks, at rest with respect to the train, to determine the time stamp. That's just a fancy set of clocks and rulers at rest with respect to the train.

You can complicate your experimental setup as much as you want, but you can always boil it down to "whose measurements am I using - ones in the train or ones on the track?" When you have the answer to that you have the answer to what you'll measure in my previous post.

Alright, thank you very much @Ibix! You have given me the exact answer I was looking for, even though it wasn't the one I wanted to hear haha. You actually hit the nail on head of what I'm trying to do, and that is trying to come up with some way for a vehicle to tell how fast it is moving using only sensors available on-board. I have another idea, but I will start another thread for it. Perhaps you could help me there too? Thanks again!

 

[Ibix]

You can't tell if something is moving without reference to something outside. There's no such thing as absolute movement, only movement relative to something else, so it's impossible to measure such a thing.

Your other thread, at a quick glance, appears to be an accelerometer. That's fine - you can measure acceleration in an absolute sense, just not velocity. I'll take a look.

 

[tomfishertom]

What if it was sound and you were monitoring on said train instead of light? Would you see a difference in time to sense the same sound traveling forward along the train vs backwards along the train? Say the train was close to the speed of sound, would the sensor to the rear hear the sound sooner than the sensor to the front? Would it being an open deck of a train as opposed to an enclosed carriage make a difference?

 

[phinds]

What if it was sound and you were monitoring on said train instead of light? Would you see a difference in time to sense the same sound traveling forward along the train vs backwards along the train? Say the train was close to the speed of sound, would the sensor to the rear hear the sound sooner than the sensor to the front? Would it being an open deck of a train as opposed to an enclosed carriage make a difference?

Sound does not work the way light does. You are hijacking a thread on light so you really should open a new thread asking about how sound travels.

 

[Ibix]

What if it was sound and you were monitoring on said train instead of light? Would you see a difference in time to sense the same sound traveling forward along the train vs backwards along the train? Say the train was close to the speed of sound, would the sensor to the rear hear the sound sooner than the sensor to the front? Would it being an open deck of a train as opposed to an enclosed carriage make a difference?

Sound is very different to light. It has a constant speed with respect to the air, which may be carried along with the train or not depending on the design of the carriage, and which will be disrupted by the carriage moving through it. So what happens depends a lot on details of the carriage design.

That said, if we have a closed carriage then the air is carried along with it. If it is moving with respect to me then the relativity of simultaneity still comes into play and I will conclude that a rearward traveling pulse from the center reaches the rear before a forward going one does.

 

[vanhees71]

If you are interested for the Doppler effect of sound (as well as light) within relativistic physics, here are my 2cts:

https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf