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A graphical explanation of Special Relativity

  1. Aug 9, 2012 #1


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    PLEASE NOTE: When replaying these animations, click on the circular arrow in the bottom left corner of the video window. If you click inside the video, you may end up running a different video.

    We start during the era before Einstein when most of the great scientists believed in an absolute ether rest state in which light propagated at the same constant speed in all directions. Imagine a very brief bright flash of light being set off in this stationary ether. It will create an ever-expanding spherical shell of light, centered on its point of origin with respect to the stationary ether. Here we picture a stick-man setting off a flash of blue light creating a wave much like you would see dropping a pepple in a pool of water.


    They believed that if the man were moving with respect to this stationary ether frame, he would not remain in the center of this expanding spherical shell but would move off-center.


    But the question is: how can the man tell if he remains in the center of this expanding shell or moves off-center? By analogy, we could visualize what would happen if we were observing an expanding ring of waves on the surface of a pool after dropping a pebble in the water because we use light to observe the water, but how can we observe a lightwave once it has started moving away from us? Therein lies the problem: we cannot directly observe the propagation of light so we do the next best thing which is to set up an array of mirrors to reflect the light back to us.

    Now the best way for the man to "observe" an expanding spherical shell of light is to set up a whole bunch of mirrors, all an equal distance from him and in all possible directions. Then when he sets off the flash it will expand until it simultaneously hits all the mirrors which turn the expanding spherical shell of light into a contracting spherical shell of light which will eventually collapse on the man simultaneously from all directions.

    For purposes of illustration, we will consider a two-dimensional subset of mirrors and an expanding ring of light, much like the expanding ring of waves set off by a pepple dropped in the center of a circular pool of water as it simultaneously strikes the entire pool wall circumference, reverses direction and simultaneously collapses on the center of the pool.


    Now it's really not practical to build a solid ring of mirrors but all we really need is four mirrors that are placed 90 degrees apart and all equidistant from the observer. In this animation, I have used four circular mirrors so that when the light strikes them, they each create a new expanding circle of light. Notice how the four reflections arrive simultaneously on the observer.


    I represent the stationary observer in green and I call him Homer (think green, green grass of home). I represent the original expanding circle of light in blue as well as a blue dot to represent its source, the mirrors in yellow, the collapsing circles of light in green when they reflect off stationary mirrors.

    Please note that just as in the previous post when the collapsing circle of light arrived simultaneously from all directions on the observer, the four reflections from the four mirrors all arrive simultaneously on the observer. Although this is not actually how the Michelson-Morley Experiment (MMX) was configured, it still represents conceptually exactly what the experiment was doing.

    The MMX experimenters assumed that the previous animation would represent only what would happen if they were stationary with respect to the ether which they assumed they never were. They believed that they were constantly moving with respect to the ether and also constantly changing their velocity through the ether as the earth rotated on its axis and as it revolved around the sun. This constant acceleration was very small so for all practical purposes, they could assume that they were moving at a constant speed through the ether during the brief time interval of the experiment. This is how they thought the light would behave and note that now all four reflection do not reach the man at the same time:


    I represent the moving observer in red and I call him Rover (think Red Rover). The light that reflects off the moving mirrors is shown in red and a red dot is placed at the origin of each expanding reflection.

    Note that when the light from the four mirrors arrives at Rover, it is not simultaneous, it first arrives from the top and bottom mirrors and then later arrives from the left and right mirrors. This is what the MMX experimenters expected to measure but instead, they got the same result as if they were stationary in the ether, the same result that Homer would have gotten.

    So now the question is how can this happen? Well, Lorentz and others came up with an explanation and we will go through a process that will arrive at the same explanation.

    First, we want to learn how we know where to put the mirrors so that the expanding circle of light can create a reflection that results in a collapsing circle of light in just the right place at just the right time. For Homer, it's easy:


    Just note the intersection of the blue expanding circle and the green collapsing circle and in this animation, we draw a black dashed line to show where that intersection occurs:


    Now for Rover, it's a little more complicated because his collapsing circle of light is not centered on the expanding circle of light but rather the location of where he will be later on, shown as a red dot. Try to visualize in this animation where the blue and red circles intersect:


    And here we have the black dashed line to show the points of reflection:


    Now this black dashed line shows the points of relection relative to the ether but we really want them relative to Rover, so here we show both for comparison:


    Also, note that Lorentz realizes that everything contracts in the direction of motion so we now show Rover as being length contracted as well as his arrangement of mirrors. In addition, the time it takes for the light to traverse from Rover to the mirrors and back to Rover is longer than it was for Homer which illustrates time dilation. We can also see the issue of Relativity of Simultaneity because the reflections for Rover do not all occur at the same time whereas they do for Homer.


    This illustrates how Lorentz believed MMX produced the null result. He believed that the experiment was moving through the ether and experienced length contraction, time dilation and relativity of simultaneity.

    He also believed that Rover would measure the speed of light to be the same as Homer because even though time was going slower and stretching out (time dilation), it is the actual length that the light has to travel relative to the ether that is used to calculate the speed (length divided by time), so we need to use the lengths defined by the black dashed line, not the moving brown line representing the length contracted mirror. This length is dilated to the same extent that time is dilated and so the two dilations cancel each other out and give the same calculation for the speed of light.

    However, Einstein put a new spin on the interpretation. He said that we could assume that MMX was actually stationary in the ether and everything else that was moving with respect to MMX was experiencing length contraction, time dilation and relativity of simultaneity.

    Now I want to show what would happen if instead of a solid ring of mirrors, we used individual mirrors with gaps between them. This will allow some of the light to be reflected and some to pass through. First we go back to Homer:


    Now we do the same thing for Rover:


    And finally, we show combine the two of them:


    This shows how two observers moving with respect to each other can both conclude that they are each in the center of the same expanding sphere of light that was emitted when they were colocated.

    An important concept to learn through this series of animations is that even though we see that Homer is stationary in the ether and Rover is moving, they themselves cannot tell the difference. Whatever Rover does to measure the positions of his mirrors, he will conclude that they are in a perfect circle since his ruler will contract when he measures the shortened distances. And whatever clock he carries will be time dilated to the same extent as the time it takes for the reflection to return to him. And of course, he has no way of knowing that the light is not reflecting off his mirrors simultaneously.

    When Einstein came along, he re-interpreted the ideas of Lorentz by saying that Rover could consider himself to be "stationary in the ether" so that his ruler was not length contracted, and his clock was not time dilated, and the light reflects off his mirrors simultaneously, and all those things happen to Homer instead. Thus he showed that the concept of an absolute ether rest state was useless as any inertial state is indistinguishable from it.

    For those that are familiar with Special Relativity, view these animations from the stand point of a Frame of Reference.
  2. jcsd
  3. Aug 12, 2012 #2
    That's awesome. The next step would be to put all the animations together into a single video with naration to explain what you typed in between.
  4. Aug 12, 2012 #3
    Great video. But what program did you use? How did you plot the intersections?

    Also, I find the concept of circular mirrors quite hard to grasp. Can you do one but featuring a beam of light moving linearly?
    Last edited: Aug 12, 2012
  5. Apr 3, 2013 #4
    Very good Explanation and video!! I really liked it!! I think i now understand SR!! Thank you!!
  6. Dec 17, 2013 #5
    A very good animation.
    But I have a more general question. If for Rover, we show the expanding circle of light also moving/shifting along with Rover, (rover as always the center of light circles, outward or inward) we don't even need explanation of length contraction or time dilation. Isn't that an equal possibility, that light speed is dependent on source, through which also we can interprete the negative result of MMX. Why don't we do that?
  7. Dec 17, 2013 #6
    That's called "emission theory" or "ballistic theory of light", and was refuted countless times by different experiments.

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