Suppose that the rod the length l0 is fixed in the frame s. Use a spacetime diagram to show that both sets of observers are. Sartori covers general relativity and cosmology, but focuses on einsteins theory. We will draw our diagrams such the relative velocity of carol and bob is 0. What is the expression for the time interval of the door closings in the pole vaulters frame. The pole in the barn spacetime diagram stanford university. Clear up the paradox by making two carefully labeled space time diagrams, one an xt diagram, the other an x t. This means that we plot time on the vertical axis as a function of the. Style of the video was blatantly stolen from vi hart minus an. The worldlines for the doors at a and b are solid when the doors are closed and dashed when the doors are shut. The pole and the barn a 20 foot pole is moving towards a 10 foot barn fast enough that the pole appears to be only 10 feet long. This puzzle, like most apparent paradoxes in special relativity, is most easily. In the pole frame, the pole is 20 meters long and the barn is only 5 meters long.
Pole in a barn paradox in special relativity this is a classic. From the runners point of view, however, the pole is 20 m long and the barn is only 5 m. Lets try to analyse how we might work out the twin paradox using spacetime diagrams, in order to get a feel of how to work with the diagrams. Spacetime diagrams iii a229023 5 a229023 spacetime diagrams iii 9 twin paradox. Summary of lecture 3 spacetime diagrams lorentz contraction. First, however, we will need to introduce a few quantitative details to aid our treatment of the problem. Explain this paradox quantitatively and using spacetime diagrams. Spacetime diagrams for the pole in the barn paradox. Be able to interpret the behavior of worldlines on a spacetime diagram. Remember that both barn and pole frames use \q is at a as the zero of their spacetime coordinates.
Shown above is a spacetime diagram in the frame where the barn is at rest and the pole is moving. The pole and the barn california state polytechnic. As soon as both ends of the pole are in the barn, slam the doors. The two diagrams below show the farmers rest frame s and the runners rest frame s 0. The resolution to this paradox is that there is no sym.
Also shown above the barn is the spacetime diagram depicting the pole and the barn from two frames of reference. The pole and barn paradox or the ladder and garage paradox pose the question. Lorentz transformations and spacetime diagrams may be used to obtain andor illustrate the solution. In the frame of the runner, the pole is at rest of course. A runner carrying the pole frame s moving with respect to the barn and a farmer frame s runs into the barn. Pole %in% barn % paradox % a%sta1onary% barn %sits%in%a%. Lets finish off the pole in the barn paradox by doing a spacetime diagram, as weve done several times before now. The pole and the barn 6 aapt summer meeting 1991, vancouver, british columbia barn frame pole frame the barn is 40 lighttics long.
A good way to do it is to draw a spacetime diagram. Hit start to watch the pole move through the barn, or adjust the time slider to control its motion manually. Show that the farmer does see the pole in the barn, the athlete does not see the pole fit into the barn, and most importantly that both of these views are consistent with each other. With what speed must the triangle travel to be isosceles. In the next instant he will burst through the back door, which is made of paper. Spacetime diagrams one of the most illuminating ways of understanding the resolution of the socalled twin paradox is by analyzing carefully drawn, detailed spacetime diagrams for specific choices of trip distance and velocity. So, the pole and barn paradox taught us that events that are simultaneous in one frame are not. And heres a spacetime diagram, where the black axes, 90 degree axes, horizontal and vertical, are bobs barn frame of reference. Therefore at some instant the pole will be observed entirely contained within the barn. Since the order of events depends on the frame of reference, the apparent paradox.
He explores illuminating paradoxes, including the famous twin paradox, the pole inthe barn paradox, and the loedel diagram, which is an accessible, graphic approach to relativity. Lecture4 summary of lecture 3 spacetime diagrams lorentz. How do lorentz transformations deform the minkowski diagram. An explanation using spacetime diagrams of how the socalled twin paradox of special relativity is resolved. When an object is stationary in a reference frame it.
Minkowski spacetime diagram in the special relativity. After the collision, the pole and runner come to rest relative to the barn. A pole vaulter carries her pole towards a red barn. The ladder paradox or barn pole paradox is a thought experiment in special relativity. Which of the following is true for all relative velocities. Consider a pole 10 m long and a barn 5 m long with a front and rear door. Fast runner with 20meter pole enclosed in meter barn. Spacetime diagrams from six ideas that shaped physics, unit r. Draw a spacetime diagram from the friends point of view and use it to illustrate. Topics such as the lorentz contraction, time dilation, and related paradoxes such as the pole and barn paradox, can be discussed using the loedel diagram form. We stick with the idea of two inertial frames, s and s, moving with relative speed v.
But in the pole s frame of reference, the barn is only 5 m long, so the pole cannot possibly fit in the barn. Lecture 29 lorentz contractions unm physics and astronomy. Minkowski spacetime diagram for the lorentz contraction. The pole is seen to be 10m long when it is moving as seen from the frame of the barn. A spacetime diagram of the pole and the barn, showing events in th. Pole vaulter paradox x ct x ct ct0 x0 x0 back front ct0 doors are closed above, is a spacetime diagram that helps explain the pole vaulter paradox. An event has spacetime coordinates x, y, z, t in frame f and spacetime the two diagrams show the same two points, but each shows a different choice of in the pole in the barn paradox, call front door closes event number 1 and rear. Pole vaulter runs very fast length contraction his pole is shorter it can fit into the barn the pole vaulter then bursts through the second door. Physics 5i lecture 6 november 4, 2011 successive lorentz. This demonstration is similar to the previous one and illustrates the resolution of the pole in the barn paradox using spacetime diagrams. Pole and barn paradox wolfram demonstrations project.
From alices point of view, the pole is 20 m long and the barn is 5 m long. Pole in a barn paradox in special relativity this is a classic braintwister, up there with the twins. Spacetime diagrams revisited regions of spacetime faster than light. Apr 29, 2020 jan 24 lorentz transformation spacetime wheel 3. Just as the tip of the pole reaches the closed back door, it opens allowing the runner to pass through. The ladder is imagined passing through the open front and rear doors of a garage or barn which is shorter than its rest length, so if. The pole and barn paradox ladder and garage paradox. The polebarn paradox the polebarn paradox is a famous variation on the twin paradox which must be addressed with the ideas of simultaneity in relativity. Explain, quantitatively and by means of spacetime diagrams, the apparent paradox. The leading end of the pole, q, follow a worldline that lies on the time axis, x0 0. D is the point where the end of the pole enters the barn ab is simultaneous in barn frame so this will be what the barn sees as the pole length at the time of event a and thus, the pole. Now, lets specialize my spacetime diagram to the twin paradox.
The farmer gathers 100 witnesses and this is what they see. Physlet quantum mechanics by belloni, christian, and cox. Spacetime diagram explanation of the twin paradox the answer to this question is that for the astronaut to return to the earth, heshe must change direction and thereby switch from one inertial frame to another, and that breaks the symmetry between the two observers. Jan 18, 2017 spacetime diagrams make it easy to tell which is which. Consider a flight to a star 3 lyr away at a speed of vrel 0. Suppose the front door opening of the barn is located at x 0 at t 0. Flashes are set to go off as soon as the right edge of the pole is inside the rightmost edge of the barn. There is a pole vaulter with an the 11ft long pole running toward a 10ft barn.
The pole has a rest length of 60 light tics and moves to the right at 0. We put position on the horizontal axis and time times c on the vertical axis. Fullscreen this demonstration shows spacetime diagrams and illustrations for the pole and barn paradox. Choose the relative speed of the pole the yellow line segment and the barn the blue line segment. The fact that two events are simultaneous in one frame of reference does not imply that they are simultaneous as seen by an observer moving at a relativistic speed with respect to that frame. A graphical introduction to special relativity based on a modern. When an object is stationary in a reference frame it is red and when it is moving it is green. In this version, you can still choose one perspective barn or pole, but now you can also see the other perspectives spatial slices or the others now slices. Spacetime diagrams spacetime diagrams spacetime diagrams spacetime diagrams spacetime diagrams barn and pole paradox barn frame spacetime diagrams barn and pole paradox pole frame spacetime diagrams spacetime diagrams 18 july 2006 k. The pole is entirely inside the barn in its rest frame, but in the rest frame of the pole the barn is much shorter and both doors are simultaneously open.
The pole vaulter then bursts through the second door. Explain how the pole and the barn are treated by relativity without internal inconsistency. The twin paradox in special and general relativity. Cen pole in barn paradox jan 29 video on special relativity. The pole and the barn 2 aapt summer meeting 1991, vancouver, british columbia recap of the paradox 36 lighttics good.
Johns doppler effect the doppler effect is the shift in frequency and wavelength of waves that results. We do so with a spacetime diagram in which spatial axes. It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed near the speed of light and therefore undergoing a lorentz length contraction. Be able to calculate relativistic momentum, rest energy, relativistic kinetic energy, and total relativistic energy. The worldline of the trailing end of the pole, p, is the line x0 20m. The pole carrier, however, say no way, the barn is much too small. A pole is 20m long, a barn is 10m long, but the pole is moving at u0. I noticed a severe lack of youtube videos about it.
If two events are timelike or lightlike separated, the earlier one. Spacetime diagram explanation of the twin paradox the answer to this question is that for the astronaut to return to the earth, heshe must change direction and thereby switch from one inertial frame to another, and that breaks the. Im having trouble reconciling two different versions of the pole and barn paradox. An introduction to special relativity focused on the geometric.
The invariant interval c2t2 x2 and the light cone or zero lightlike. Since the order of events depends on the frame of reference, the apparent parado. Special relativity department of applied mathematics and. Spacetime diagram what the rocket ship really sees is not odd. This demonstration shows how the pole in the barn paradox plays out in a spacetime diagram. The basis for the socalled twin paradox early in the study of special relativity students learn about the phenomenon. In order to find the time interval, i tried using the spacetime interval. Einsteins theory of special relativity makes several predictions, some of which seem counter intuitive. The tilted dark solid lines are snapshots of the pole in its rest.
The farmer will see that the pole fits into the barn if the. Aug 10, 2007 the pole and barn paradox is a classic demonstration of the breakdown of universal simultaneity in special relativity. An athlete carrying a pole 16m long runs toward the front door of a barn so rapidly that an observer in the barn measures the pole s length as only 8m, which is exactly the length of the barn. You can even view both perspectives spatial slices at the same time. Imagine a pole carried by a pole vaulter who is running along the ground at a speed b 35.
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