For concreteness, alices diagram could be thought of as a splicing of two timedilation problems. Spacetime diagrams iii a229023 5 a229023 spacetime diagrams iii 9 twin paradox. A speci c point on a spacetime diagram is called an \event. Correct resolution of the twin paradox michael huem er in the following, i explain the twin paradox, which is supposed to be a paradoxical. However twin b must draw two such frames, and imagine jumping from one frame to the other as they decelerate and then accelerate homewards at event 2.
The statement of the socalled twin paradox the confusion caused by the phenomenon of time dilation has long been encapsulated in the socalled twin paradox stated as follows. Time, topology and the twin paradox jeanpierre luminet. In the introductory film clip, we saw that time was dilated when observed from frames of reference with a constant relative velocity v. The spacetime diagrams also illustrate the connection to the twin paradox by displaying ticking rates the dashes of the two twins travelling along the two branches. More comprehensive textual content than the other twin paradox animation page. Introduction to spacetime diagrams and the light cone objective. Correct resolution of the twin paradox michael huemer. Oddly enough, in a spacetime diagram under lorentz geometry, a straight. Returning to earth she finds herself much younger than her brother. Pdf time, topology and the twin paradox researchgate. The twin paradox and the principle of relativity i will first consider the usual version of the twin paradox 2,3 in the minkowski spacetime. Twin paradox two the second paradox is a bit more technical, and really comes to the heart of what physicists mean when they talk about relativity. Let us now consider the minkowskian spacetime diagram in the figure.
The twin paradox has nothing to do wit h gravi tation, nor. Beyond just using the diagram to calculate the age of a twin after she returns. It is shown with the supporting calculations for the. To make a spacetime diagram, take many snapshots of the objects over time and set them on top of each other. Now distance ac equals distance ab since 4cba is a 45. Oct 10, 2016 in this video, i show how to use spacetime diagrams to understand the famous twin paradox in special relativity. Jan 27, 2017 so twin b can draw their own spacetime diagram, in which they stay stationary and twin a moves away from them to the left, if twin a sees twin b moving to the right, and then towards them.
Pdf the twin paradox is the best known thought experiment associated with. The journey starts at a, turns around at b, and ends at c. This video is about the famous twins paradox of special relativity, how time can appear to be faster for two different observers at the same time, and which twin really is older or younger. And were going to use our spacetime diagram, to see if we can understand it graphically. An extended model of minkowski spacetime in order to avoid introducing.
Earth twin would say that all the spacetime points that lie on s are simultaneous with each other, and all of them occur at say t 0. Lines in the diagram are like \contrails through time. Embedded youtube animation, with textual description and a little math. Diagrams and equations demonstrating the symmetry of measures and timekeeping differential regarding case 1 and case 2.
It allows a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations minkowski diagrams are twodimensional graphs. One of a pair of twins the traveling twin travels to and returns from a very distant destination at a speed approaching that of light the other the earth bound. Pdf geometric resolution of the twin paradox in special. Wheeler, in his book spacetime physics, made three attempts to resolve the twin paradox and failed three times. The term minkowski diagram refers to a specific form of spacetime diagram frequently used in special relativity. The twin paradox several articles that discuss this thought. Spacetime diagram twin paradox page 2 physics forums. It is shown with the supporting calculations for the doppler effect on the observed time. Mar 17, 2003 for those with a little more formal physics background, a spacetime diagram also explains the paradox nicely. Why the twin paradox arises the twin paradox arises in the special theory of relativity sr.
Also, a brief discussion of the classic twin paradox of special relativity is presented in order to illustrate the principal of maximal or extremal aging. The proper time from o to c to b is less than the proper time from o to a to b. A worldline is a continuous, onedimensional curve in spacetime. One of them gets in a spacesh ip and flies around really fast. A world line is a plot of the position of some object as a function of time more properly, the time of the object as a function of position on a spacetime diagram. Spacetime diagrams and einsteins theory for dummies. The twin paradox is the best known thought experiment associated with. Suppose that two identical twins start out on earth, the same age. First let me introduce the paradox for you to understand the diagram. Spacetime diagram what the rocket ship really sees is not odd. The minkowski diagram, also known as a spacetime diagram, was developed in 1908 by hermann minkowski and provides an illustration of the properties of space and time in the special theory of relativity. Representing events on a spacetime diagram as points representing the positions of a moving particle on a spacetime diagram by a curve the worldline representing more than one inertial reference frame on the same spacetime diagram. For those with a little more formal physics background, a spacetime diagram also explains the paradox nicely.
Time and space are two separate spaces and the movement in one space. In many cases, with a properly drawn spacetime diagram you can estimate an answer without working any. Pdf in the standard formulation of the twin paradox an accelerated twin considers. Feb 12, 20 i was studying the twin paradox of einstein special relativity and everything was working well until i get to the travelers spacetime diagram. The twin paradox several articles that discuss this. Stellas frame of reference is just a curvilinear coordinate system. In the spacetime diagram on the right, drawn for the reference frame of the earthbased twin, that twin s world line coincides with the vertical axis his position is constant in space, moving only in time. This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect and naive application of time dilation and. Representing events on a spacetime diagram as points representing the positions of a moving particle on a spacetime diagram by a curve the worldline representing more than one inertial reference frame on. In this video, i show how to use spacetime diagrams to understand the famous twin paradox in special relativity. The twin paradox part 2 paradoxes to ponder coursera. This theory predicts that if one of a pair of twins were to fly away from the earth all the way to alpha centauri for instance and then fly back again.
The twin paradox heres a statement of the twin paradox, designed to make it seem paradoxical. On the first leg of the trip, the second twin moves to the right black sloped line. Lecture 2, slide 8, using spacetime interval a229019 twin paradox 14 the twin paradox revisited one twin travels away from the earth at high speed for a long time. Time and space are two separate spaces and the movement in one space time is independent of movement through the other space. As john mentions and as you can see from the spacetime diagram, bob needs to accelerate at some point to return to the same spatial location as alice only straight lines on a minkowski spacetime diagram are unaccelerated and bobs path has a bend.
One of a pair of twins the traveling twin travels to and returns from a very distant destination at a speed approaching that of light the other the earthbound. I was studying the twin paradox of einstein special relativity and everything was working well until i get to the travelers spacetime diagram. Imagine that twin a remains at rest on the earth and twin b travels with velocity v 0,8c to the nearest star alpha proxima 4 light years from the earth and back. The twin paradox in compact spaces cern document server. There have been other threads showing that the simplest twin case, restricting all acceleration to one twin will appear to be explained by the non inertial asymmetry, but in general cases involving both twins accelerating, the aging question is decided by which twin loses the most time, which is path dependent. Optional problems in the use of the calculus of variations as applied to lagragian mechanics and other problems in the extremization of path integrals. Special relativityspacetime wikibooks, open books for an. In this diagram, which events out of a, b, c and d occur at the same time. In the following, i explain the twin paradox, which is supposed to be a paradoxical consequence. Before he does, the bottom green line represents the events that he regards as simultaneous. This entry borrows heavily from the original faq entry for the twin paradox, by kurt sonnenmoser. Aug 26, 2016 this video is about the famous twins paradox of special relativity, how time can appear to be faster for two different observers at the same time, and which twin really is older or younger. An explanation using spacetime diagrams of how the socalled twin paradox. Otop and ptoz, where opz is along alices inertial worldline.
Thus, a world line is really a line in spacetime, while an event is a point in spacetime. In between these events, twin b must be seen by twin a as traveling first away from, and. The socalled twin paradox in special relativity, first introduced by paul. The other twin, earth twin, stays on earth the whole time. The eulerlagrange equations and constants of the motion. First, however, we will need to introduce a few quantitative details to aid our treatment of the problem. So, just to reiterate this actually the outbound trip is similar to the things weve done before but just to make. Spacetime diagrams, spacetime, geometry introducing spacetime classically we have an absolute time, which can be viewed as a onedimensional euclidean space, r, plus an absolute threedimensional space, r3. The spacetime diagram explanation this entry borrows heavily from the original faq entry for the twin paradox, by kurt sonnenmoser. The twin paradox part 4 of the series proper physics. Spacetime diagrams worldlines the twin paradox applications and skills. In general, a minkowski diagram is a twodimensional graphical depiction of a portion of minkowski space, usually where space has been curtailed to a single dimension. The key point in the twin paradox is that for the return trip bob needs to introduce a new set of observers that are at rest with respect to him, the set b. The vertical axis represents the worldline of a stationary particle, called observer 1.
Spacetime diagrams lab exercise the spacetime diagram also known as a minkowski diagram is a tool that can used to graphically describe complex problems in special relativity. Drawing a spacetime diagram draw horizontal and vertical axes. May 28, 2014 twin paradox through spacetime diagram. The usual version of the twin paradox qualifies as a pure sr problem by modern standards. Suppose noninertial bob tries to draw a spacetime diagram as alice did earlier. But how do we understand that conclusion from the point of view of the traveling twin. Twin paradox explained the red x represents the moment in time when the traveling twin turns around. The twin paradox spacetime diagrams cal poly pomona. The term is used in both a generic and particular sense. In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a highspeed rocket and returns home to find that the twin who remained on earth has aged more. In the default scenario the light signals sent from the moving twin are depicted using a spacetime diagram and are shown as seen in the stationary twin s reference frame the home frame. A graphical introduction to special relativity based on a. The twin paradox in special and general relativity. 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.
Feb 12, 20 there have been other threads showing that the simplest twin case, restricting all acceleration to one twin will appear to be explained by the non inertial asymmetry, but in general cases involving both twins accelerating, the aging question is decided by which twin loses the most time, which is path dependent. The key explanation of the twin paradox is now some kind of asymmetry between the spacetime paths joining two events. The spacetime diagram analysis is closer to the spirit of gr vintage 1916 than the equivalence principle analysis. The entire scenario is based on the idea that biff was traveling very fast, so time slowed down for him. The twin paradox in special relativity has a simple for mulation and. In the default scenario the light signals sent from the moving twin are depicted using a spacetime diagram and are shown as seen in the stationary twins reference frame the home frame. But it has also been extensively modified, so he is not responsible for any sloppiness or infelicities. This is the famous twin paradox time goes by more slowly on the starship than earth.
How does relativity theory resolve the twin paradox. The story now proceeds just as before, each observer in a sees the. The twin paradox in the theory of relativity article pdf available in european journal of physics 274. The twin paradox program displays the effect of time dilation on a moving twin as seen from a stationary twin. However, it has also been extensively modified, so he is not responsible for any sloppiness or infelicities. When he turns around and heads back, his velocity is different and his line of simultaneity is also different. To make a spacetime diagram, take many snapshots of the objects over time and set. Notice the line of simultaneity now, it slopes upwards and the intersection with alice is much later than with set b.
Theory of relativityspecial relativityspacetime diagrams. Because of the relatively crude state of technology ca. Embedded youtube animation, with textual description. So we can understand that from our spacetime diagram here. Geometric resolution of the twin paradox in special relativity. We have two models of spacetime, neither of which is capable of describing all the phenomena we observe. What is the proper way to explain the twin paradox.
Consider a flight to a star 3 lyr away at a speed of vrel 0. The horizontal line is considered the space axis of observer 1. Absolute frame of reference in the physics community. Naturally the graph is symmetrical about this angular velocity. Observations versus measurements stanford university. 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. Now, lets specialize my spacetime diagram to the twin paradox. Previous lesson current lesson next lesson introduction to spacetime diagrams regions on spacetime diagrams and the light cone relativity of simultaneity. How to understand the twin paradox science publishing group. He never stood a chance, as he limited himself to einsteins narrow interpretation that of simply assuming symmetrical measures across inertial frames. 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.
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