Speed Kills?

Father & Son team, William and Arthur Edelstein discuss one of the dangers of near lightspeed travel in their paper published just last month: Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments [citation: Edelstein, W. and Edelstein, A. (2012) Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments. Natural Science, 4, 749-754.doi: 10.4236/ns.2012.410099.] They highlight the lethality of the high-energy proton head-wind that the Interstellar Medium (ISM) becomes when moving at near light-speed, which they define as above about ~0.9c.

I hadn’t realised the Edelsteins finally published their work until a Facebook friend, Jay Real, sent me a link. Of course these issues have been discussed in the literature for years so their discussion is nothing new – but welcome nonetheless as an explicit statement of the problem. High relativistic speeds are difficult to achieve, so most vehicles would probably stay below ~0.9c unless something exotic appeared, like an easy way of making one of Sonny’s warp-drive fields for rapid sub-light travel. In our part of the Galaxy the proton flux is much lower than the 1.8 protons/cc assumed by the Edelsteins. Some hot bubbles in the Local ISM go down to ~0.01-0.05 protons/cc and the local clouds are ~0.1-0.2/cc. This doesn’t change the results very much, but does lessen the local applicability.

Their analysis focuses chiefly on mass-shielding – big enough chunks of material to absorb the incoming flux. Magnetic shielding is mentioned dismissively, but I think that’s premature. Workable designs using known materials exist which can deflect 10 GeV cosmic rays, the equivalent of flying at 0.995c. Advanced superconductors, which will be needed for antimatter containment, plasma nozzles, magnetic-sails, will allow even higher protection levels. Thus I submit the Edelsteins’ negativity is premature.

The energy flux of interstellar matter hitting the ship can cause a lot of heating. If the ISM is just 100,000 atoms per cubic meter the flux is equivalent to 536 K temperature at 0.866 c. Peak temperature during re-entry is 2700 K for a moonflight – that level is reached at about 0.997c. Of course a starship wouldn’t just absorb that heat on its forward surfaces. A magnetic deflector would channel most of it away- but deflecting particles makes them lose momentum as high energy photons (x-rays) which would need to be shielded against. And the shield would get HOT! Fast starships would need to be long and narrow to minimise the energy absorbed. An x-ray reflective diamond coating could be used, but will need to be keep highly reflective while operating. Maintenance will be tricky!

As an example of the kinds of particle energies we can handle the Large Hadron Collider regularly bends a high energy stream of particles into a circle – the protons in the beam have a speed of 0.99999999c when it’s at full power. Cosmic-rays can reach much higher energies and need protection against. However the very highest energy cosmic rays are very rare, so only lower energy particles need deflecting in a crew habitat. The ones of biological concern, due to their numbers, are in the 1-10 GeV range. If we can deflect 10 GeV protons coming at us from our motion through space, then cosmic rays aren’t an issue.

Aberration comes into play at such high-speeds – the direction of origin of incoming particles and photons starts piling up directly in front of the starship. I would suggest the best protection at very high speed might be a “diffuser” – a high intensity magnet held far forward of the starship’s main hull which deflects the charged particles and creates a “shadow cone” behind it. The faster we go, for the same magnetic intensity, the further forward we put the diffuser. We fly, in safety, in its shadow thanks to aberration concentrating all the radiation to directly in front of us.

If we can deflect particles up to LHC energies, then how far can we accelerate at 1 gee? The acceleration distance required to increment the time-distortion/gamma factor (call it the TDF) by 1 is about 1 light year at 1 gee. At 0.99 c the TDF is about 7. So it takes about 6 light-years (because we start with TDF = 1) to get to 0.99c. To reach 0.9999c (TDF = 70) takes about 69 light years. Thanks to the time distortion, on ship the trip-time is much less. Remember a light-year is a distance, but as we’re flying so close to light-speed the ship is seen to take about 70 years to travel 69 light-years. A speed of 0.999999c (TDF = 700) takes 700 years Earth-time and 699 light-years of distance, but on the ship only just over 7 years have passed. If we decide to stop, then another 7 years ship time, 700 Earth-time, and 699 light years is needed – meaning we’ve flown 1398 light years in 14 years ship-time. But let’s push on. We’re pushing to TDF = 7,000 (0.99999999c) so the distance is 6,999 light-years, 7,000 years Earth-time, about 9.5 years onboard ship. Thus we could travel 13,998 light years and stop, in 19 years of our time, if can protect against proton energies equal to the LHC.

2 thoughts on “Speed Kills?

  1. I believe the TDF goes as powers of 7 for each “double 9”, so at 0.9999c it would be 49, and at 0.999999c it would be 343, and at 0.99999999c it would be 2401.

  2. Hi tmazanec1. Actually, no, it goes up by 10 fold with every extra pair of “9s”. Thus 0.99c is 7, 0.9999 is 70, 0.999999 is 700 etc. To see why consider the following…

    Gamma is (1-(V/c)2)-1/2

    for speeds close to c, make V = c(1-e) where is e < < 1. Therefore the square of (V/c) becomes 1-2e-e2.

    Gamma is approximately ~(2e)-1/2, since e2 is very small the closer we get to c. For V = 0.99c, e = 0.01, so gamma = 10/sqrt(2). For V = 0.9999, e = 0.0001, so gamma = 100/sqrt(2) and so on.

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