I posted this topic in a physics forum on another web site, but I thought this forum might be a better place to get good answers.(adsbygoogle = window.adsbygoogle || []).push({});

So the other week, I tried writing an applet (using the new Javascript Canvas Firefox now supports) to simulate a thought experiment I use to explain the basics of special relativity to friends. The applet is at http://tac-tics.net/specrel.html [Broken]. However, there is an issue I'm having trouble resolving with it, and I'm hoping some helpful person can point out what I'm doing wrong. From my guess, though, I believe it has to do with my (mis)understanding of length contraction.

Before I explain my problem, let me explain the applet. I apologize if the applet doesn't work in your browser (I've only tested it on Firefox), but you still may be able to help me out.

There are two spaceships, A and B. A is on the left B is on the right. Earth is the circle in the middle, which, when you press "Go", explodes, releasing an electromagnetic wave. Spaceship A is at rest relative to the Earth. Spaceship B is moving at 70% the speed of light away from Earth. Each is 200 units away from Earth (and light moves at 1 unit per second in the model).

Each spaceship has a clock. There's a light, cyan clock hand which starts at 12:00 and moves around at a fixed rate (I think it's 1 rotation per 100 seconds or so). There's also a clock which is the horizontal yellow line which goes up and down. The clocks slow down as per the time dilation equation. At 70% the speed of light, the clock moves at just about 71.4% the normal rate.

The Restart A/B buttons restart the experiment from either Spaceship A's frame of reference or Spaceship B's frame of reference.

So my issue is this. Regardless of relativistic effects, the clock on a ship should always read the same time when the light strikes that ship. Suppose you are in Spaceship A. You see the flash of light from Earth exploding, and you look up at the clock and see the clock says 200 seconds. Then from Spaceship B's perspective, even though it happens in slow motion, an observer on Spaceship B would see you look up and see the clock says 200 seconds.

In my applet, that is not the case, unfortunately. In my applet, when Spaceship A is at rest, it takes 200 seconds for the light wave to hit, but from B's perspective, the clock on Spaceship A reads just over 478 seconds when it gets hit.

The way I usually state this problem when explaining it to my friends is that the electromagnetic shockwave *destroys* the spaceship (because it's funnier that way). The end result, is of course, that both spaceships observe the other "outliving" them.

My problem is more apparent when the light wave is destructive. Say that both ships send out another signal to a destruction-proof observer, one signal for every tick of their clock, encoding which ship sent it and the time displayed on the clock. This third observer only cares about what the *last* signal sent out by each ship was. If Spaceship A is at rest, according to my model, it's last pulse encodes "Ship A at 200 seconds". But from B's perspective, the last signal would be "Ship A at 478 seconds". This is a contradiction, so something in my model must be wrong.

Like I said at the start, my guess is that it has to do with length contraction. Currently, my model is free of length contraction effects, because I'm not sure how they apply, and I'm hoping someone can explain it to me clearly so I can incorporate into my applet. When an object moving at relativistic speed contracts in length, how are the individual points that make up the object transformed? I know how to calculate the amount of contraction (=sqrt(1 - v^2/c^2) ), but I'm not sure how to apply that scalar to the position of the moving spaceship. Watching my model, it seems like the distance between the spaceship and the Earth should contract as well, allowing the light wave to hit the ship sooner, correcting the time discrepancy. But if that were so, faster things would appear to be closer to you, which doesn't seem quite right, since anything moving at the speed of light would have to appear on top of you with zero length. So clearly, I'm missing something.

Anyone want to take a crack at setting me straight?

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# Special relativity simulation issue

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