Expert: Tom Whiting - 1/24/2010

Question
Hi Tom,im hoping you can help me with my memory! Many years ago i wrote to Stephen Hawking,no less, and received a reply that wasnt too clear to me and i wonder if i remember the response correctly. I wrote asking,what would happen if there was a spaceship pulling the axle of a circular object,such as a space station. The outside of this circular object connected to the axle by way of spokes. This arrangement similar to a bicycle wheel driven by a chain). If the spaceship accelerated to the speed of light,so turning the axle,the outside of that wheel would have to rotate faster than the speed of light. I seem to remember that the reply i received said that the speed of sound contained in the 'spokes' would cause the spokes to break. The mentioning of 'speed of SOUND' confused me. Is my memory deceiving me? If not,could you perhaps explain this to me a bit further. Thankyou very much Tom     Regards Richard

Answer
Hi Richard,
He probably meant "speed of light" instead of speed of sound...BUT
your entire question is hypothetical, or even impossible to perform in reality.
Mass cannot travel light speed (proven over and over in the world's cyclotrons)
because mass becomes infinite at light speed so it requires an infinite amount of energy.
(Recall your Lorentz transformation equation of change (increase) in mass at velocity v...
= rest mass divided by square root of 1 - (v squared over c squared).
So when v = c, denominator becomes square root of zero, which is zero, and any whole positive
number, the rest mass in this case, becomes infinite.

Evidently Dr. Hawking picked the weakest mass structure in your question, the spokes, and realizing that their mass would be increasing too as their speed approached light speed, that would be the structure that would ultimately fail catastrophically as their mass rose exponentially toward infinity.... which is what would really happen as your "hypothetical spaceship" approached light speed.  At somewhere around 99.9% "spoke" lightspeed, the increasing force would over-ride the molecular bonds in the metal spokes and they'd fly apart or disintegrate.
Hope this helps,
Tom Whiting
Erie, PA USA