## Relativity of Length Contraction – Part 3

In this final installment on relativistic length contraction we’ll show some practical implications of the effect. Let’s imagine a scenario where a Rebel Alliance cruiser attempts to breach an Empire Death Star. There’s an open hatch but it’s protected by a radar system that can sense the speed of an incoming ship. When the hatch sensor detects the cruiser entering, it slams down the hatch door trapping the ship. The time it takes to close the hatch is based on the known length of a Rebel Alliance cruiser, and the speed at which the cruiser is moving. The Empire wants to trap the ship in the gate, where it can then be boarded and destroyed. The first animation shows how the system works.

Now let’s imagine the cruiser is moving at 0.866c, or 86.6% lightspeed. At that speed γ = 0.5, and the cruiser will appear to be half its usual length as seen from the Death Star FOR. Since the timing mechanism for the gate is set for a longer ship, the cruiser gets through, breaching the Death Star:

Of course, the cruiser must apply forward thrust to slow down once it gets through the hatch. Otherwise it would crash into the hull of the Death Star and fail in its mission. That thrust begins shortly after entering the hatch, so the cruiser expands to normal length as it enters the Death Star FOR by matching its speed.

Now we’ll look at this scenario from the cruiser’s FOR. In this case it’s the Death Star that’s contracted, and it’s clock is running slow by a factor of 0.5. Again, the cruiser succeeds, but this time it’s because the Death Star’s hatch mechanism is controlled by a slow timer:

For this animation the thrust was shown for added effect. The animation ends with the cruiser in the Death Star FOR with everything at “normal” size. The two clocks are running at the same rate. Again, the Rebel Alliance mission succeeds in breaching the Death Star.

At this point we can unequivocally answer the question that started this 3-part series: Is length contraction physically real? The answer is: Yes, and so is time dilation. The theory of relativity asserts that what is “real” depends on your FOR.

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