NASA Mission to Alpha Centauri: SR & Relativistic Effects

[LAP3141]

NASA has proposed a mission to Alpha Centuri:

https://en.wikipedia.org/wiki/2069_Alpha_Centauri_mission
This mission would involve a spacecraft traveling at 10% of light speed and therefore relativistic effects could be somewhat significant.

Let's assume this spacecraft is carrying a human being from the Earth. Let's also assume that this human is kept in some sort of a "sleep" state until after the 10% light velocity is achieved. Would this human measure a Lorentz contracted interstellar distance? If so, then how would this mesh with his prior knowledge of the distance as observed from the Earth? That is, if he knew that his observed distance was shorter with respect to that observed from the Earth then could he conclude that he was in the moving frame?

 

[Ibix]

Yes, he could measure a length-contracted distance - approximately 0.5% less than the distance measured by Earth. This only allows him to conclude that he is in a frame where Earth and Alpha Centauri were moving. That isn't moving in any absolute sense.

 

[jbriggs444]

Yes, he could measure a length-contracted distance - approximately 0.5% less than the distance measured by Earth. This only allows him to conclude that he is in a frame where Earth and Alpha Centauri were moving. That isn't moving in any absolute sense.

Of course, he can conclude more directly that Sol and Alpha Centauri are moving in his rest frame by looking at the absorption lines in their spectra.

He knows without even opening his eyes that the proper distance between two objects is larger than the measured distance in a frame where they are both moving together.

 

[Ibix]

He knows without even opening his eyes that the proper distance between two objects is larger than the measured distance in a frame where they are both moving together.

Indeed. And one further point that I forgot to mention is that, while the astronaut measures the distance between stars to be 0.5% short, the Earth would measure the ship to be 0.5% short. It's symmetric, because both sets of measurements regard the thing they are measuring to be moving and, hence, length contracted.

That might sound paradoxical (not to @jbriggs444, who knows this perfectly well), but it isn't. The short explanation is that the Earth and the astronaut disagree subtly on what "length" actually means in operational terms.