Examples and Analogies for Special Relativity




Einstein’s Analogy of science research



“We are in a position of a little child entering a huge library, whose walls are covered to the ceiling with books in many languages. The child knows that someone must have written those books. It does not know who or how. It does not understand the languages in which it has been written. The child notes a definite plan in the arrangement of books. A mysterious order, which it does not comprehend but only dimly suspects.’


To the voice-over of an actor reading out the above a child stands between two towering bookshelves, looking up. He walks along the shelves and admires the titles: Magnetism; Electricity; Electromagnetism; Energy; Mass; Speed of Light and E=mc2. He stretches to take out the last book.



Analogy for relativity and the concept behind inertial frames of references.



An analogy of two people living in the same country (so communication and understanding between the two are a given).


One person has lived in the city all of her life, and likewise for the person who lives in a tiny village, out in the country. Let's refer to them as City Girl and Country Girl, respectively.


Daily life is normal and routine for each person, in their respective places. They've never experienced the other life, and effectively have no real knowledge of it.


This week Country Girl watches a video city life. It's wildly different to what she is used to, in fact, a lot of things cause her confusion - where is the greenery, how do people sleep in such a noisy place, how do people survive with such expensive prices, where is the sense in everyone living so tightly together etc.


Country Girl struggles to understand the city culture because they not only differ from her own, some are also quite alien. The country represents a frame of reference. From her perspective the city is weird. However, according to City Girl, as we stated earlier, everything is normal. It's the culture she has grown up with. Hence it is WRONG to say that city life is weird. It is only weird RELATIVE/ ACCORDING to Country Girl.


The city represents another frame of reference, in this example, because no matter what, if she remains in the City and Country Girl remains in the country, she will NEVER, EVER see things the same way as Country Girl. Hence, if Country Girl was to travel to the city for the day, having done no research into city life, it would be equivalent to a violation of physical laws. This is because Country Girl will still be looking at the world as if she was still in the country. Hence, paying £1 for a muffin would make no sense to her at all.


Because there is no such thing as a universal frame of reference, all ideas Country Girl has about the city, based on accurate footage and books made by people from her village, will hold true with respect to her and only her (and the village). This is because whatever happens, however she tries, she is looking at the situation through 'country eyes' and not 'city' eyes', or the eyes of a passing spaceship. However, relativity dictates that the laws that govern an area, make complete sense in that area, and if an outsider, watching from afar - Country Girl and her educated ideas of city life - will make perfect sense but ONLY in her area.


This analogy should help to explain that in the study of physics you have to choose/realize your frame of reference and base your world from there. It's impossible to hop from frame to frame without giving regard to what it means to fully be in that reference.


Einstein discovered that no matter what, there is no such thing as a universal - absolute answer. Everything is relative to the frames of references which are making the observations.


Example 2: Emenike from Nigeria arrives in London for the first time in his life. He knows NOTHING about England, the English language etc. He could not possibly make sense of everything instantly. By not preparing (learning the language, finding hotels etc.) he has attempted to hop frames of reference, and his experience will be poor because of it. In terms of human relations, understanding observations from Observer 1 is about empathy.




Energy into Mass conversions at the Speed Of Light



          A SuperHero with a cape and the ability to fly to the other side of the planet near the speed of light has an added advantage. By travelling so fast, he is actually more massive than when he’s walking along the street. This makes him less vulnerable as any enemy trying to knock him off course will discover that he is close to impossible to budge at all. His mass is so high, and as his velocity is extremely high, his momentum is gigantic. This is because the energy required to travel at the speed of light converts itself into mass. But you can’t see it.




Mass Increase at High Speed



Glass Ship A. Mrs Thomas is wiping down the glass in her ship. Her ship has 'Super-Duper' which can capture things moving at high speeds. Another glass ship zooms past it at half the speed of light.


Glass Ship B. Bob is angry. He's just been fired, his wife has left him and his mistress, over the phone, has just come clean and said he was the worst shag in the universe. Literally. As he chucks the phone at the glass wall his ship skims past Glass Ship A. The phone hits the glass wall with a great deal of speed --and smashes into smithereens.


Glass Ship A. Mrs Thomas is angry as something has just passed her and shaken he ship. She talks to her ship computer and asks who was that jerk. The computer tells her that the man inside was in such a foul mood that he had thrown his phone at the wall and, oddly, it smashed into many tiny pieces. The woman asks why is this an odd occurrence. The computer replies that he had thrown the phone at such a slow speed at the wall. (In relation to Glass Ship A's recording of the speed, it is much slower). Mrs. Thomas tells the computer to calculate in time dilation factors. The computer replies to her that, yes, even with that taken into consideration, the phone may very well smash in his frame of reference but Glass Ship A must be able to make sense of it for their own reference. Mrs. Thomas ponders the problem:


Well, she reasons, if the phone smashes to the same extent from the points of view of both frames of reference, then the 'punch' or the momentum of the phone hitting the wall must be the same for both. The factors that affect the 'punch' of the phone are its mass and its velocity at which it is moving.


Therefore, if Glass Ship A is recording a slow velocity for the phone, the mass of the phone MUST be the variable that differs from the point of view of the two frames of references. Therefore, it makes sense that the phone smashes.


A small example of the concept is sitting at the end of a long row of books in a library. Holding a ruler in the air to measure the book at the end, you'll end up with a book that is 2cm by 5cm! But if you were standing closer to it you'd get much larger measurements.




Example/Analogy of Time Dilation



Best possible analogy and example of this is a light beam clock. But we can simplify that even further by considering the New Warp Speed Train, ‘Hey, get there yesterday!’.


Ron gets on the New Warp Speed Train and needs to travel half a galaxy away. The ship travels at half the speed of light. As he travels the he bounces his basket ball exactly 30 times every minute. This means 30 round trips, from hand to wall back to hand 30 times.


Rachel sits at a train station platform, bored out of her mind. As the New Warp Train zooms past her she notices that the gentleman in it is bouncing his ball. She takes it upon herself to count how many bounces he completes every minute, by her watch. She counts about 15 bounces.


The reason for this is as the New Warp Train passes her, the ball seems like it is moving in a diagonal direction to the wall, and diagonally back to the catcher. By the time he catches it, his position, and indeed the position of the entire train has moved. Thus, each round trip of each bounce clocks in a slower time by her watch. For Ron, on the other hand, the ball shoots straight at the wall and back – no diagonal motion as his body and the wall of the train are moving together at exactly the same speed. For this example we are ignoring the time it takes for light to travel from the New Warp Train to Rachel’s eye.




Analogy 2 of Time Dilation.



Boy stands on a flat trolley. There is enough space on the trolley for him to bounce a basketball. As he dribbles it’s noticeable that the ball goes up and down directly. He now signals for the lights to go off and for the strobe to be switched on. The trolley on which he stands is then pushed along to the other side of the stage as he continues to bounce the ball. To the audience it looks as though the basketball is travelling diagonally after each bounce. However, to the boy, the ball is always bouncing up and down directly.




Example of Length Contraction



          Using the example of Ron in the New Warp Train again. Now let’s say that Ron bounces the ball against the back exit door. This means he is bouncing it in the same line as the movement of the train – perpendicular to Rachel. Now, according to Rachel, it will seem as though the ball isn’t travelling very far, in fact it would seem to her that a particularly thin Ron is standing particularly close to the wall as he bounces it.


          This seems like this because, again, from Rachel’s point of view, by the time he has thrown the ball, the ship has moved forward by the time the ball touches it. Likewise, on its return journey the ball travels an extra distance. However, calculations prove that the length is visually contracted on the whole. [See http://web.nt/~cbenton/relativity/exp5.htm




Time delays in the speed of light according to different frames of reference



As New Warp Train travels back, completely empty, it passes by the now even more bored Rachel. As it zooms the conductor decides to turn off the lights which are controlled by one switch and turn off all the lights simultaneously. TO Rachel sitting still however, as the lights go out, it would seem to her that the back end of the train (nearest to her) has gone out first followed by the front of the train. This is because, the last bit of light travelling from the bulbs at the back have a shorter distance to travel to her eye than the last bit of light from the bulb at the front.




The Twin Paradox



Twins standing on earth, one gets on a space ship and travels at 0.6 the speed of light, many light years away to a distant planet. Now, if this twin were to remain there, all would be fine because effectively both twins were travelling at the speed of light with respect to the other (according to her frame of reference her twin brother on Earth was moving away from her at the speed of light). However if she was to return, at the same speed, she would be younger than her other twin.


          Although this is best explained with General Relativity and with simple calculations (as it describes the effect acceleration has on the twin as she approaches 0.6c and her deceleration down to 0), the reason for the difference in age is the break of symmetry of the situation. Essentially, the twin has changed her frame of reference by making a return journey.




Brief Analogy for General Relativity’s concept of time as a fourth dimension.



One way of getting to grips with the concept of four dimensions is to understand that we’re not programmed to understand it.


Imagine a stick man drawn on paper. He is in two dimensions. Therefore his world, is purely in two dimensions. Now if you were to make a hole in the page with a pencil this would utterly confuse him as all he can see is a small hole getting bigger and bigger. He can’t see the three-dimensional pencil, it’s not part of his world. However he can only see the two-dimensional effect that pencil is having on his world. The same applies, in some respect, to us. We can’t see the time dimension, but we see its effect on our 3-D world.





Round Up



“Much of our confusion results from the assumption that time and space are things that exist independently of objects. However, try to imagine a universe in which no objects exist. In such a universe there would be no points of reference from which to measure the passage of time or distances in space. In such an existence, time and space would only exist as mental constructs. Thus, if we accept that time is only a measurement that is made of the separation between parts of an observed sequence of events and that distance is only a measurement of the separation between events that are observed to occur at the same time, then it is not so surprising that observers in different frames of reference will measure these things differently.”



This quote also touches on Positivism. This is a segment of physicists who believe that everything in physics must be described in terms of measurements or quantitative language. Analogy of that is the old tree in the woods. If a tree in the forest collapses and there is no-one there to witness it or hear it… did it happen?




Tez Asfaw