No. According to the observer for which the train is moving, the Ball travels form where A is when it leaves A( right next to a) to where B is when it arrives at B, and since both A and B move during that time, It travels along a long diagonal path. But according to the train, the ball just goes from A to B straight up, While a ( which starts next to A) moves off to the left. Please Register or Log in to view the hidden image! An observer at rest with respect to the train and one at rest with respect to a will measure different times. There is no absolute frame against we can measure motion and which can establish which of these two views is the "correct" one. It is, in fact, meaningless to talk about a "correct" viewpoint. This is no longer a matter of debate. Experiment after experiment has shown that the phenomenon known as "time dilation" really does occur.
Question: If the ball appears to move slower vertically when in motion horizontally, is this delay due to the movement or due to the greater distance between the ball and the external observer relative to the person in the train?
But it does not travel a greater distance, nor take any longer to complete the action. Is this not confirmed by Einstein's "man in a box" which is the same experiment but instead of moving horizontally the box (train) moves vertically and the light beam moves horizontally. In that thought experiment it is the man inside the moving box who observes the light to shift diagonally but does not take any longer to reach the other side of the box than if the box was stationary. Is there a difference and why? SOL?
The position of the "external observer is of no relevance. The the slower vertical component is due to the fact that from the external observer's frame, the ball travel along the diagonal not at sqrt (u^2+v'^2), where u is the relative speed of the train and v' is the vertical velocity as measured from the train as it would according to Newtonian physics, but instead it travels at sqrt( u^2+v'^2 -(uv'/c)2) which is a slower velocity. If the diagonal velocity is lower, but u is the same, then v ( the vertical velocity as measured by the external observer) will be less than v'( the vertical velocity measured from the train.) The person in the train measures the time for the ball to go from A to B as being L/v' The external observer will see it travel a distance of sqrt((ut)2+L^2) at a speed of sqrt( u^2+v'^2 -(uv'/c)2), which takes more time. With the "man in the box", it makes no difference between box moving horizontally and light vertically and box moving vertically and light moving horizontally. All you need is for the light to travel relative to the box at a right to the relative velocity of the two frames involved. As long as the source of the light shares the same motion as the box, the observer in the box will not measure the light as moving at an angle, but at a right angle to the relative motion ( at c relative to the box). The external observer will measure the light following the longer diagonal path at c relative to himself. Thus if we have two observer's each with his own light source/mirror set up and moving relative to each other: Each observer will see the light from his source as going straight up and down at c, and the light from the other observer's source as following a longer diagonal path at c. Each observer will say that the other light clock ticks slower than their own. If each observer also had a "ball clock" That ticks once for every n ticks of his light clock, Both observers would agree that each ball clock ticks once for every n ticks of its respective light clock (the respective light and ball clocks remain in sync), and each observer would say that the other ball clock ticks slower than his own( and by the same rate as he says the other light clock ticks slow)
Thank you. I'll need some time to digest this. I always understood that in the case of a light beam it makes no difference in the time for the straight and the diagonal paths. The light will hit the opposite target at the same time because the light itself has not traveled farther in distance. It is the train (or the box) that has moved, not the ball or the photon. Their paths are straight and cross the distance to the target at the same time, regardless if the train (or the box) moves or not. It's not the distance of travel that has changed, it's the target (train or box) that has moved, giving the appearance of a longer path, relative to the observer. Wow, this is disconcerting.....Please Register or Log in to view the hidden image! Does Einstein's "man in the box" predict a time dilation?
At Train position A, the ball leaves the hand of the person who drops it, at Train position B, the ball comes back to his hand. Time elapsed is Δt. The person in the train, and outside the train, both will measure the time elapsed of train to travel from A to B exactly the same. This is also the time for the Ball's event. Please Register or Log in to view the hidden image!
I mean , if the person in the train, and outside the train, both measure the same Δt for the train to travel from A to B, in this case, the ball's event has been completed at Δt also.
Again, that's how things would be if we lived in a Newtonian universe. But we don't, we live in a relativistic one, and the two observers will measure a different time for the ball to make the trip.
No.... https://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform https://web.stanford.edu/~oas/SI/SRGR/notes/srHarris.pdf
Speed of light is c according to all inertial frames (measured relative to the frame. Which "man in the box" thought experiment are you referring to? Are you thinking of the elevator thought experiment? This requires the elevator to be accelerating and not moving at a constant velocity. Acceleration opens a whole new can of worms.
Yep. I believe Einstein used in reference to GR? The difference between a steady speed and acceleration only affects the apparent trajectory of the ball or the photon, no? Steady speed produces an apparent straight diagonal path, acceleration produces an apparent curved path, which is even longer that the straight diagonal, yet the photon always reaches the opposite wall at exactly the same time, regardless if the elevator is stationary, @ constant motion, or accelerating. The beam is always in a straight line, it's the elevator (box) that moves and creates the appearance of different trajectory to the man inside the elevator; Please Register or Log in to view the hidden image! But to the man outside the elevator; Please Register or Log in to view the hidden image!
Do you mean the man outside elevator will see the beam Straight line? If the time Δt of light is always constant, then the man who see the path curved, will measure the speed of light >c, correct?
But our common sense tells us, from A to B, the time is constant Δt for both insider and outsider. The ball was observed to complete the trip within this duration Δt.
Common sense also once told us that the Earth was the center of the solar system and it was flat. The evidence of time dilation and length contraction. The ball has a longer path to travel in one frame then the other. Therefor time dilation and length contraction.
Indeed the ball takes a longer path in the frame of the outside observer, but that just means the ball moves about 20 times faster in one frame than in the other. This is not the 'therefore' in time dilation. The ball takes a path 20 times longer in the one frame, but it doesn't take 20 times as long to bounce. There are very few bits of equipment sensitive enough to detect the time difference between the two observations. See my post 17. This is why such thought experiments are typically done with light, which has a constant frame-independent speed (but not frame independent velocity), as opposed to the ball, which very much has a frame dependent speed.
One thing to note is that in the scenario in these diagrams, the light source and elevator have a relative velocity with respect to each other. If the elevator had it own source (attached to the wall next to the hole the outside light enters), The light from this source will hit a spot an equal height from the floor as the light is when the velocity is constant. if the Elevator is accelerating, the path will curve as measured from the Elevator, but it will hit a spot a little higher than where the light coming from the outside source hits. As far as the speed of light is concerned. When the velocity is constant (inertial frame) The speed of light is c globally throughout the frame. Our observer would measure light at the top of the elevator as moving at c relative to himself, as well as light near the floor of the elevator. Under acceleration, this is not the case. An observer will always measure the Local(proper) speed of light as being c, but would measure the coordinate speed of light as being faster than c everywhere "above" him, and less than c everywhere below him. In the top diagram below if we assume an observer at the where the light path crosses the red line, he would measure the light as traveling at c as it passes him, but traveling faster than c along the part of the path above the red line, and moving slower than c along the part of the path below the line. Another difference between an inertial and accelerated frame is what happens to clocks spread out in the frame. In an inertial frame all clocks at rest with respect to the frame tick at the same rate regardless of where they are located. In an accelerated frame, this is not the case. As shown in the second image, for our observer in the elevator, a clock near the ceiling of the elevator runs fast compared to one on the floor.* This behavior is not confined to clocks that share the elevator's acceleration either. A clock "above" the elevator towards which the elevator is accelerating will run fast according to the elevator observer and one "below" him will run slow.** Please Register or Log in to view the hidden image! The additional factors that have to be taken into consideration when dealing with accelerating frames makes it important that you are very comfortable in dealing with inertial frames first, prior to tackling acceleration. * This makes sense even if we look at things from the frame that the elevator is accelerating with respect to. As the elevator increases speed relative to this frame, the elevator length contracts, Thus the distance between "top" and "bottom" of the elevator decreases. For the inertial observer this means that the bottom of the elevator is slowly creeping up on the top of the elevator, which can only happen if the bottom is moving at a higher speed. The inertial observer will also measure a time dilation for the elevator due to its relative speed. And since the bottom of the elevator at any moment is moving a bit faster than the top, a clock located there would exhibit more time dilation than one at the top. ** this measurement is not to be confused with the speeding up and slowing down one would see due to Doppler shift. This difference in tick rate is what is left over after you account for the Doppler effect.
One way to look at it is to take the equation I gave for the addition of orthogonal velocities. W = sqrt(u^2+v'^2 - (uv'/c)^2) which gives the velocity along the diagonal for the ball when the box is moving at u and v' is the upwards velocity of the ball as measured from the box. If we substitute c for v' (The observer in the box measures the light as traveling at c upwards relative to the box.) Then you get W= sqrt(u^2 +c^2 - (uc/c)^2) W= sqrt(u^2+c^2- u^2) W= sqrt(c^2) W=c For the speed of the pulse along the diagonal as measured by the "external" observer. Using a ball instead of light doesn't change the end result in terms of time dilation, but it is clearly easier to calculate things out using light vs. using the ball.
Your "common sense" is honed by everyday experience, which, in turn, is limited to relative velocities that are very small compared to c. So for example, as shown in Halc's earlier post, a velocity difference of 180 km/hr between train and external observer results in a difference of time measurement so small that it would go unnoticed unless you used extremely accurate clocks. It's not that the difference isn't there, it just not enough to make a difference for most practical cases. Because the effect is so small in our everyday lives, it becomes natural for us to assume its non-existence. If I ask a friend to drive over from another town to meet me in an hr, I don't need to account for the fact that his "hour" while driving isn't the same as my "hour" waiting for him. Mainly because this would account for a difference that is so many times smaller than other factors that can effect exactly when he arrives. So. in everyday life, we can get away with assuming that an hour is an hour for everyone, even when that is not strictly true. "Common sense" can get us through our normal daily activities, but it is a poor tool for locking the inner workings of the universe.
