# Do stray photons become interstellar daggers to a space traveler near the speed of light?

Suppose I am traveling through space, accelerating closer and closer to the speed of light. As I speed up, photons traveling towards me become blue-shifted to higher and higher frequencies. When I am traveling fast enough, even what used to be visible light would all be shifted into very high energy x-rays or gamma rays. This seems like a big problem for my ship. Would my ship get torn/radiated pieces? How slow would I have to go to avoid this issue?

• This is a very reasonable concern, pertinent to anybody building a near light-speed spaceship without a warp drive. Maybe the interstellar or intergalactic gas would inflict much greater damage than photons; and unlike photons, it could do so even without relativistic effects. Feb 3 '16 at 20:51
• Yes, one can shift visible light into the x-ray and gamma ray-region. That's what some gamma-gamma collider experiments are proposing. The interstellar space traveler, on the other hand, will long be atomized by hydrogen and small dust grains that are eating away on his ship. Nobody will ever build fast spaceships, anyway. A 0.1c ship is fast enough. Feb 3 '16 at 22:08
• Another concern is the aberration of light during acceleration, which results in your field of view (i.e. the angle of photons incident upon you) being concentrated to the front of you, so not only is the radiation more damaging due to blue-shifting, but also more concentrated on certain faces of your ship. Feb 3 '16 at 22:27

Yes, but you'll have to go really, really fast. And even then, don't worry about the photons.

The relation between velocity $v$ and the observed and "true" wavelength $\lambda_\mathrm{obs}$ and $\lambda$ of the light is $$\lambda_\mathrm{obs} = \sqrt{\frac{1-v/c}{1+v/c}} \lambda.$$ If you consider optical (i.e. visible to humans) light with a wavelength of, say, 5000 Å (green/bluish), then to be observed in your reference frame as a gamma-ray of, say 0.5 Å (roughly the wavelength of the softest gamma-rays) you'll have to go at $$v = \frac{(1-\lambda_\mathrm{obs}/\lambda)^2}{(1+\lambda_\mathrm{obs}/\lambda)^2} c = 0.99999998 c.$$ The bulk of photons in space aren't optical, though. Optical photons are outnumbered by photons of the cosmic microwave background by roughly four orders of magnitudes (see this question on the number density of photons). In order to blueshift these photons to gamma-rays, you'll have to go at $v=0.9999999999999988c$.

At this velocity, your biggest worry won't be radiation: Let's start by assuming that you are in intergalactic space. Galaxies are dispersed in space with typically a few Mpc$^\dagger$ between them, or very roughly $L = 10$ million lightyears as measured by an observer in one of the galaxies. However, your extreme speed means that, in your reference frame, relativistic length contraction ensures that the average distance is $L\sqrt{1-v^2/c^2}\sim0.5$ lightyears, i.e. you will hit a galaxy once every six month. Galaxies are typically 100 kly ("kilolightyears") in size, or, in your reference frame, roughly two lightdays. Your risk of hitting a star is small, but you'll go through a column density of roughly $10^{20}$ hydrogen atoms per cm$^2$, all hitting you with almost the speed of light. I assume the cross section of your space ship is 10 m, so you'll be hit by $\sim10^{26}$ hydrogen atoms. Although this has a mass of only 200 g, its total energy is $$E = \frac{10^{26}m_\mathrm{H}c^2}{\sqrt{1-v^2/c^2}} \sim 10^{23}\,\mathrm{J},$$ or $\sim10^{18}\,\mathrm{J}\,\mathrm{s}^{-1}$, roughly corresponding to being hit by a pyramid at 20 km/s. Every second.

On second thought, you're probably not even going to make it to the nearest galaxy…

$^\dagger$1 Mpc = 1 million parsec ~ 3.3 million lightyears.

• Pretty sure the interplanetary and interstellar dust would destroy the ship long before one got to another galaxy... Micron sized dust is capable of cutting kevlar cables on spacecraft moving at very slow speeds with respect to Earth (thus, the dust is moving at ~10-30 km/s), let alone light speed dust! Feb 4 '16 at 23:17
• @honeste_vivere: Yeah, that's why I ended by saying "You're probably not even going to make it to the nearest galaxy". But since it's a well-known fact that near-light speed space crafts need a couple of kpc to accelerate, it will be in the intergalactic medium before reaching fatal velocities :)
– pela
Feb 5 '16 at 8:41