physics thought experiment

this has been bugging me all day:

Say I have built a ping-pong ball bouncing machine. It is a very precise machine. It bounces a single ping-pong ball vertically at the highest speed that a ping-pong ball can travel (it is the theoretical upper limit for rate of travel by a ping pong ball). It constantly bounces the ball, and is so precise that it could be used as a clock.


now, I want to take my machine to a ping-pong ball bouncing competition, and to do so I need to take a train. I decide to take the newest train which moves at a constant velocity and is so well made that there is no jostling of any kind while the train is in motion.

As I am on the train I decide to show someone my wonderful machine. what happens when I turn it on?

does anything change if someone is stationary outside looking in through a window and watches my wonderful ball bouncing machine?


please explain your answer.

edit: i had diagrams but they didnt turn out too well
edit again: if there are any problems with the above experiment please let me know

The theoretical upper limit of a ping pong ball, would be only restricted by laws such as gravity,mass and aerodynamics. I have no idea how physics works in the real world, but I would assume that on a train car the laws would allow the ball to move faster than it's previous speed in relation to the earth, but in relation to the train car, it won't. Once a car is moving so is the air, ping pong ball and bouncing machine. Within that environment I would assume only gravity would be in effect from outside the car, and I don't think it changes within the car anyway, when moving along a level plane.

Hills may cause some different problems though

the problem is, that to an outside observer the ball must now travel in a V-shaped path, and must do so along this longer path in the same amount of time.

(i had diagrams to make this clear but everything ended up squished over to one side :( )

I don't think so. The ball would actually follow this path, but in order for the observer to see the ball travel, his eyes would need to follow the train and focus on the ball travel within the train car to and from the bouncing machine.

The ping pong ball will bounce off the ceiling of the train car unless it's a very, very tall train, so the surface of the maching that bounces the ping pong ball has to be perfectly in plane with the ceiling, the ceiling has to be perfectly flat, and the train needs to be perfectly level. The ball will hit the ceiling and bounce back at a much faster rate than if it were ascending into the air and slowing down to zero before starting to descend and speeding up due to gravity, so it'll basically be bouncing between the ceiling and your machine at a very high rate of speed, just like in a game of pong when the ball gets trapped between the paddle and a wall.

And, yeah, to a stationary observer the ball would appear to follow a zig-zag path relative to the observer.

sorry, again the pictures would have helped a lot....

the machine has a top and bottom panel within which the ball is contained. they are of course perfectly level/smooth.

so according to a stationary observer, the ball is traversing a greater distance for each period (a period being here defined as the amount of time for the ball to go from the top panel to the bottom panel and back to the top).

does the ball take a longer time to make this trip (according to the stationary observer) or does the ball go faster than its' theoretical limit and make the trip in the same amount of time?

I may be misinterpreting the question, (as others have done previously), but from what I gather.... this high speed ball bouncer is only causing the ball to travel in a vertical direction in the rest frame of the train. The train is moving perpendicular to that motion. The path that the ball in the moving train travels (the zig-zag-esque path) is greater than the path of the ball moving at rest (straight up and down). The velocity of the ball on the train is also faster than that of the ball on the ground... since the ball on the train has some x-component (ball speed equal to that of the train speed) and a y-component (vertical ball speed due to ball bouncing machine). v_y^2 + v_x^2 = v_net^2....

So the horizontal speed affects the path length, but since it's orthogonal it doesn't change the time it takes the ball to complete it's vertical path. v_y (the vertical velocity of the ball) and d_y (the vertical distance the ball travels) don't change no matter how fast it's moving horizontally.

I'm not really sure what the whole point of the elaborate bouncing machine is here though... so I may well be misreading or misinterpreting something.

The ping pong ball itself is not traveling a greater distance because it's distance would be measured relative to the train, I think. So the person outside the train perceives it as moving a greater distance only because they also see the distance that the train is moving as well.

The ball is travelling both a vertical distance and a horizontal distance, both of which would be perceived by the stationary observer but only the vertical distance would be perceived bythe person on the train who is moving in the horizontal at an identical rate. It's a relativity example, and technically you should consider how quickly time is moving for both obervers because time is moving slightly slower for the person on the train, no?

isnt that the same old story einstein already brought up?

to the stationary observer the ball will follow a zig zag path and travel a longer way than he appears to to the moved observer. Since the ball has the maximum allowed ping pong ball velocity and therefore cant move faster to travel the longer way for our stationary observer, the clocks in our train will move slower relative to the outside observers clock.

Ya, I was thinking it sounded just like the example used to explain all the theory of relativity things to me back in high school.

it is the same old 'light clock' thing (at least it is supposed to be), but I am trying to understand it in terms of a more mundane example. photons are claimed to have peculiar properties that tend to confuse things.

when the stationary observer sees the ball, if he is able to measure the speed of the ball, will it come out to the same speed as the person inside the train would measure...
does the fact that all actions inside the train appear to be moving slower cancel out the fact that the ball is traveling along a longer path? or would the measurement be achievable through some sort of vector addition (would vector addition result be the same as the straight measurement?)

eg. I clock the train at 50MPH. I know the maximum velocity for the ball is 200MPH and know this is it's current speed. I add the two vectors and come up with 206MPH [SQRT(200E2 + 50E2)]

what would I measure as the speed if I took a stopwatch and measured the time it takes to travel one cycle (assuming I know the distance between the plates and adjust the distance for the forward motion)?

Quote:

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Originally Posted by pgil

when the stationary observer sees the ball, if he is able to measure the speed of the ball, will it come out to the same speed as the person inside the train would measure...

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no, because the person inside the train isn't measuring the horizontal movement

Quote:

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Originally Posted by pgil

eg. I clock the train at 50MPH. I know the maximum velocity for the ball is 200MPH and know this is it's current speed. I add the two vectors and come up with 206MPH [SQRT(200E2 + 50E2)]

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wrong, if it was like this noone would know einstein. the point is, that the ball cant go faster than 200MPH and just adding the two velocity vectors is not allowed for that reason. instead of adding the vectors we have to acclerate/[english word for negative acceleration] the relative movement of time.

Quote:

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Originally Posted by XTR1000

Quote:

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Originally Posted by pgil

eg. I clock the train at 50MPH. I know the maximum velocity for the ball is 200MPH and know this is it's current speed. I add the two vectors and come up with 206MPH [SQRT(200E2 + 50E2)]

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wrong, if it was like this noone would know einstein. the point is, that the ball cant go faster than 200MPH and just adding the two velocity vectors is not allowed for that reason. instead of adding the vectors we have to acclerate/[english word for negative acceleration] the relative movement of time.

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I disagree that the maximum linear velocity for the ping-pong ball in the original problem will be the maximum velocity of that same ping-pong ball on the train. For light, this may be the case, but not for a ping pong. As light travels at only one speed. But the velocity of the ping-pong ball is wholly dependent on its environment.

Quote:

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Originally Posted by shazbox

The ping pong ball itself is not traveling a greater distance because it's distance would be measured relative to the train, I think. So the person outside the train perceives it as moving a greater distance only because they also see the distance that the train is moving as well.

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this I think

Quote:

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Originally Posted by XTR1000

Quote:

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Originally Posted by pgil

eg. I clock the train at 50MPH. I know the maximum velocity for the ball is 200MPH and know this is it's current speed. I add the two vectors and come up with 206MPH [SQRT(200E2 + 50E2)]

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wrong, if it was like this noone would know einstein. the point is, that the ball cant go faster than 200MPH and just adding the two velocity vectors is not allowed for that reason. instead of adding the vectors we have to acclerate/[english word for negative acceleration] the relative movement of time.

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If we were dealing with a ping pong ball moving at the speed of light that would be correct, because it can't move faster than the speed of light no matter what, but if we were to adjust time to compensate for the difference in observed speeds of the ping pong ball as presented, our math and the amount of time dilation would be way off.

Quote:

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Originally Posted by ProZachNation

Quote:

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Originally Posted by shazbox

The ping pong ball itself is not traveling a greater distance because it's distance would be measured relative to the train, I think. So the person outside the train perceives it as moving a greater distance only because they also see the distance that the train is moving as well.

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this I think

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When you talk about velocities it is always with respect to some frame. The frame can either be rotating, translating or inertial. The frame relative to the train is translating. Consider the problem from an inertial frame in space and we'll all be on the same page.

holy shit what is happening in this thread