I'd like to examine the apparent length of a space craft at speeds near, at, and exceeding the speed of light.

Let's say I am on a space craft that is capable of incredibly fast speeds. The craft is 300,000 kilometers long from nose to tail, and I am at the halfway point, 150,000 kilometers from the nose and the tail of the craft. At my location I am in possession of a radio receiver. This craft moves at a constant speed and direction through space. On its axis of motion are two radio transmitters positioned 300,000 kilometers apart. The nearer transmitter detects the tail of my space craft and upon detection transmits a radio signal which travels at the speed of light to my receiver. The far transmitter is the same as the other transmitter except that it detects the nose of my space craft.

At slower speeds, my space craft will trip both radio-transmitter detectors almost simultaneously. I will receive both signals on my receiver at the same time or so close to the same time that I can conclude that the signals are simultaneous. The reception of the two signals this way tells me that my space craft's length is the distance between the transmitters, 300,000 kilometers.

At 90 percent of the speed of light (270,000 km / s) things change noticeably. Let's call the time at which I reach the halfway point between the radio transmitters, t = 0. The time at which I receive the signal from the nose transmitter is the solution to the equation:

270,000 t = -300,000 t + 150,000; t = 5 /19 seconds

Similarly, the solution to the following equation provides the time for the tail-transmitter signal to arrive:

270,000 t = 300,000 t - 150,000; t = 5 seconds

The difference in the arrival times, about 4.74 seconds, indicates to me that the nose of the space craft has gone beyond its transmitter-detector before the tail has gone past its detector which can only happen if the craft is longer than 300,000 kilometers. In fact, to me, the space craft's length has increased to 1,578,947 kilometers!

What happens if my space craft travels at the speed of light? Simply put, the signal from the tail transmitter can never catch up with me. I will wait forever to receive it, and the space craft might seem to be infinitely long which is impossible.

If I set the speed of the space craft at 400,000 kilometers per hour, the signal from the nose transmitter would take time equal to the solution of the following equation:

400,000 t = -300,000 t + 150,000; t = 3 / 14 seconds.

I'm not sure what significance this time may have beyond what calculations I've already performed.

Conclusion 1: Lengths of objects near the speed of light seem to elongate from the perspective of a person moving with them.

Conclusion 2: It is impossible for any object to move at the speed of light because its length would be infinite from the perspective of a person moving with it.

Jagella