Special relativity simulation issue

[Tac-Tics]

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.

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 . 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?

 

[granpa]

my advice is to think in terms of 2 long lines of clocks which are stationary and perfectly synchronized with respect to each rocket (within the frame of the corresponding rocket) extending, of course, form rocket A to rocket B. imagine that the clocks are 1 light sec apart and each sends out a radio pulse at 1 sec intervals.

first, have rocket B pass rocket A and synchronize their clocks when they pass.

the Earth could explode at precisely the time and place where 2 clocks line up and send out radio pulses.

I strongly advise using gamma=2 or 3. I use gamma=10 for calculations in my head.

 

[Tac-Tics]

my advice is to think in terms of 2 long lines of clocks which are stationary and perfectly synchronized with respect to each rocket (within the frame of the corresponding rocket) extending, of course, form rocket A to rocket B. imagine that the clocks are 1 light sec apart and each sends out a radio pulse at 1 sec intervals.

first, have rocket B pass rocket A and synchronize their clocks when they pass.

the Earth could explode at precisely the time and place where 2 clocks line up and send out radio pulses.

I strongly advise using gamma=2 or 3. I use gamma=10 for calculations in my head.

I'm not sure what you're trying to lead me to see. Trying to visualize a multi-clock scenario is quite difficult in my head (and it'd take a while to write a simulation). But it seems like it should be similar to another way to set up the problem.

What if each spaceship had a "tail" following it. The tail would be rigid and would extend the same length. As the ships pass, first the "cockpits" of the ships pass each other, allowing them to synchronize. Then, the light waves will be produced when the tails pass each other at the position that the tails meet.

Would such a scenario lead to the same result you're trying to get me to see?

 

[granpa]

everyone is familiar with length contaction ond time dilation but most seem to underestimate the importance of loss of simultaneity. it completely overwhelms the other two. that's why both are able to see the other one as contracted and dilated. determining time becomes trivial with such an arrangement of clocks because each clock ticks as it receives a radio pulse. this is true for all observers regardless of velocity and regardless of loss of simultaneity.

remember that the length of an object is the distance from the position of the front to the position of the back AT ONE SIMULTANEOUS MOMENT.

 

[Tac-Tics]

It sounds like you're saying the Earth isn't exploding at the same time for both spaceships?

I had actually wondered about that at one point. I will have to go back and investigate. It seems like the synchronization of the clocks is a big part of it, which is hard with my set up, because the spaceships never cross paths.

 

[granpa]

exactly why I always suggest using them (lines of clocks). they make complicated problems much simpler to solve.

 

[granpa]

you might consider doing the twin paradox this way. you would need a third line of clocks synchronized with the returning ship.

 

[ZikZak]

If all three clocks are synchronized at t=0 in Earth's reference frame, they will be out of synchronization in B's reference frame. As observed by B, when the Earth explodes (when it's clock reads t=0), B's clock will already be reading positive values, and A's clock will be reading negative values. Yes, it takes more than 200 ticks of A's clock for the blast to reach it, but its clock started out very negative. Granpa is correct: everyone ignores loss of simultaneity, but it really is the most important of the three kinematic effects in problems like this.

You have also ignored length contraction. Both initial distances should be contracted, because in Earth's frame those distances are measured with meter sticks that are contracted in B's frame.

 

[RandallB]

Special relativity simultaneity issue

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.

Anyone want to take a crack at setting me straight?

No, this is not the problem you are having.
What you have done wrong is assume you could mark a time on Spaceship A clock and also on Spaceship B clock to indicate “When” the Earth explodes. You cannot establish such simultaneous events when they are 200 units apart. Those clocks can only read when the flash comes by and not when the flash started.
If an extra clock synchronized and stationary with respect to A and another extra clock synchronized and stationary with respect to B both happened to be at Earth at the moment of explosion those two clocks could record that as a simultaneously because they are all at the same place. But they will not be able to agree as to what time their synchronized clocks are simultaneously reading at Spaceship A or B at that moment.
The SR rules of simultaneity make it clear that neither spaceship can know when Earth actually blew up using the ship clock as a reference. Thus you cannot and must not show a time in either ship that represents “when Earth blew up”, no matter how well you might think you can synchronize it with a clock that happens to be near Earth at the time it blows. If you do you are assuming to have a “preferred frame” and NOT describing SR.
You need to be sure you understand “simultaneity” as defined by SR.

 

[Tac-Tics]

After mulling it over a while, I've come to the conclusion I don't quite understand granpa's line of clocks setup.

Correct me if I make a mistake.

So take one rocket. At intervals of 1 light second in either direction, we have a clock moving in the rocket's frame. The rocket sends out an initial signal at that rocket's t_0. It reaches a clock n light seconds away exactly n seconds later, and once a clock receives this, it begins to tick at 1 second intervals.

Now an observer on the rocket could look out at a clock n light seconds away and see the number of times it has ticked. He knows his own rocket's clock has ticked n more times than the number he sees on that clock, because the latency of the light traveling n light seconds.

Another important phenomenon for that observer on the rocket would be that the reading on *any* clock n light seconds away will be the same at any given moment. So if clocks were lined up to both the left and right, the clocks on either side, but at equal distance from the rocket will always read the same.

Now when a second rocket (rocket B) is added, all this gets messed up. Because the rocket we were talking about (rocket A) is now moving through space, light waves do not propagate at the same rate on different sides of the ship. The opposite the direction of the ship will start firing off first. The ones in the direction of the motion will try (in vain) to outrun the light, and they will appear to tick later.

I think typing it out helped me think more clearly than trying to draw diagrams. Let me know if any of this is incorrect and I'll keep thinking it over.

The SR rules of simultaneity make it clear that neither spaceship can know when Earth actually blew up using the ship clock as a reference. Thus you cannot and must not show a time in either ship that represents “when Earth blew up”.

From what you're saying, Randall, it appears the answer to my question is Mu. I need to think up another scenario to use. One that is more consistent.

 

[granpa]

Now when a second rocket (rocket B) is added, all this gets messed up. Because the rocket we were talking about (rocket A) is now moving through space, light waves do not propagate at the same rate on different sides of the ship..

no. but the round trip time is the same.

the rocket sends out a radio wave, it reaches a clock, the clock ticks, the light from the clock reaches the rocket. its the same on both sides.

 

[Tac-Tics]

no. but the round trip time is the same.

the rocket sends out a radio wave, it reaches a clock, the clock ticks, the light from the clock reaches the rocket. its the same on both sides.

Yes, so the events look like they happen at the same time for A, but for B, it looks like the clocks on one side are lagging behind the others (by a constant phase shift). Correct?

I was thinking about the problem while driving earlier (the time for thinking), and it occurred to me why my scenario doesn't make sense. I think I had been underestimating the importance of distance between objects. When two objects are on top of each other, that event marks a unique point in time for both objects, because the time it takes light to travel zero distance is zero time no matter what frame or what object you're measuring against. If distance is nonzero, the amount of time it takes for light to travel between two objects is a subjective value.

I think I have a good enough idea now of what I did wrong that I can try making another applet. I will try tackling the length contraction issue and the twin paradox over the next few days. Thanks for all your help guys!