Eyes shut, can a passenger tell if they’re facing the front or rear of the train? Suppose you’re a passenger sitting in one of the carriages of a train which is travelling at a high, fairly steady speed. Your eyes are shut and you have no recollection of getting on the train or the direction of the train’s acceleration from stationary. Can you tell whether you’re facing the front or the back of the train?
This isn’t a theoretically perfect environment - there are undulations, bends and bumps in the track. Not a trick question - you cannot ask a fellow passenger!
Edit: This is intentionally lacks rigorous constraints. Do make additional assumptions if it enables a novel answer.
 A: I don't think this question as posed is really well defined. But here's an attempt at an answer.
In the real world the answer is yes. Assuming the train is longer in the direction of motion (as is the case for any train I can think of), you could determine the direction perpendicular to the motion of the train. Then you could put two accelerometers in two places on the train separated along the line of motion in different cars, measuring acceleration perpendicular to the line of motion. Then just wait for a bend in the track, the accelerometer in the front of the train will measure the bend in the track first. You could have the readout mechanism of the accelerometer be an audio readout so you would not need to use your eyes.
I suspect that the response I will get to this answer is "but you should solve this without..." introducing some additional constraint or idealization.
A: Yes, because the train predictably hits bumps/gaps in the track.
As you travel on a train, you hear first one set of wheels then the other then the other going from the front of the train to the back hit these imperfections in the track. If you are facing the direction of travel you hear these coming from in front of you. If you are facing away, they come from behind.
A: The simple answer is no, you would not be able to know. In fact you would not even be able to know that you are traveling at a constant speed. To you, the train could be completely still (assuming that the environment is perfect. Otherwise you could tell by for example sound). Even when the train starts to accelerate or decelerate you would still not be able to know which direction you are traveling. You could only know if someone tell you "the train is now decelerating" and by then observing how your body would react that you could tell which direction you are facing. For example, someone tell you "The train is now accelerating" and you notice that your body pushes into the seat (resisting the movement of the train accelerating 'forward') then you would know that you are facing the direction that the train are traveling in.
A: I never seen a train overtaken by another train in a parallel adjunct track lane. Usually there are trains bypassing opposite direction to each other from parallel track lanes.
I think it would be easy to distinguish with confidence if the passing train sound comes initially from your back or from your front.
Additionally you would be aided by the Doppler-shift effect of sound of the bypassing train that initially will increase in pitch and then lower in pitch as the two trains separate.
A: Bumps and gaps are asymmetric.
They make the cart jump up AND BACK and then, at slower rate, return to its equilibrium speed and direction. So you will detect rapid accelerations back and slower accelerations forward.
Curve handling (both intentional turns and railroad imperfections) happens at front wheels first and next at rear wheels.
This can be used for detection, too.
Of course, a straight, high-quailty railway and wheels can make the detection less reliable.
A: I think you might be able to distinguish the direction of motion by turning sideways and listening for the apparent motion of the clickety-clack sounds and vibrations from the carriage wheels (assuming old fashioned train tracks, on a modern high-speed rail line the sounds may not be perceptible).
At, say 100km/h and 20m between wheels the sounds would be separated by a bit less than a second.
A: I once conducted such an experience, just out of curiosity, when I was traveling on a train. I went out into the corridor, closed my eyes, they twisted me several times and put me down. I couldn't tell where I was facing, no matter how hard I tried.
A: I actually played this when I was young. If you close your eyes on a moving train, with some practice you can make yourself believe you are moving in the opposite direction. It is a bit like the spinning ballerina illusion, when you can alternate between two equally possible interpretations.
You can "keep going" in the wrong direction until the train accelerates or brakes. At that moment the changing sound will mismatch the force you feel (as Steve Saban commented) and you pop out of the illusion :)
A: It's possible. If you've been on a plane before you have experienced the effect firsthand.
The idea is that since the road is not completely flat, at some points it will ascend and at some points it will descend. When the train ascends, if you are facing the front of the train, you will be pushed back into your seat; conversely if you are facing the back of the train you will tend to slide off your seat. Similarly if you descend. Hence, you can tell which direction you're facing even if you're blindfolded.
