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I recently asked a question in Space Travel SE where we were exploring ideas on how to get a space craft that weighs 1 kg to travel at 0.1c (one tenth the speed of light). At this rate, it would be possible to reach Proxima Centauri, the nearest star after our sun, in 43 years. We concluded that repeated gravity assists with the solar system would become impossible once the spacecraft significantly exceeds solar system escape velocity, which is much much less than 0.1c.

While composing the question and much reflection afterwards, I couldn't help asking myself if there are objects in our Milky Way galaxy that are 1 kg or greater in mass that are traveling at speeds of 0.1c or greater. Without taking relativistic effects into consideration since they are still insignificant at 0.1c, the kinetic energy using E=0.5mv2 that one kilogram of mass traveling at 0.1c would be 449.4 trillion joules. This is the amount of energy equivalent to an earthquake of 7 on the Richter scale or a large hydrogen bomb.

Although such an object would not strictly be categorized as a relativistic bomb, it would still cause a very significant explosive release of energy upon collision with a massive object. The only events that come to mind that would be capable of accelerating a 1 kg or greater mass object to 0.1c or greater speed would be supernova. There may be others like gamma ray bursts, quasars, etc.

I am having trouble understanding if generation of such relativistic bombs can be generated by supernova explosions. What physical laws would prevent this or make it unlikely? If it is indeed possible, why don't we observe them? How can we observe them if possible?

How large would a mass have to be, traveling at 0.1c, that if it struck the earth, would cleave the earth in 2?

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    $\begingroup$ Re, "...cleave the earth in 2" The Earth is not a solid object. It's soft and squishy with a thin, solid crust. If the Earth were squarely struck by an object with more KE than the Earth's gravitational binding energy, it would not "cleave in 2", it would splash into many fragments. $\endgroup$ – Solomon Slow Nov 17 '17 at 17:42
  • $\begingroup$ Supernovas release on the order of ~$10^{53}$ ergs (or ~$10^{46}$ J), or something along those lines. Roughly 1% of that energy goes into the shock wave, which sounds small but ~$10^{51}$ ergs is not small! Most of the energy goes to neutrinos but that is beside the point. If you assume that ~1 solar mass is ejected as the blast wave material, then you can determine the kinetic energy (and speed) of that material assuming its total kinetic energy is ~$10^{51}$ ergs. $\endgroup$ – honeste_vivere Nov 22 '17 at 18:31
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    $\begingroup$ @jameslarge somehow your comment reminded me of this old cartoon pbs.twimg.com/media/COYoNDZUwAA1Ke9.jpg $\endgroup$ – Selene Routley Nov 22 '17 at 22:59
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While composing the question and much reflection afterwards, I couldn't help asking myself if there are objects in our Milky Way galaxy that are 1 kg or greater in mass that are traveling at speeds of 0.1c or greater.

The typical energy released in a supernova is ~1-100 foe (1 foe = $10^{44}$ J = $10^{51}$ ergs). Roughly 1% of this energy goes into generating the shock wave which can reach speeds in excess of ~20,000 km/s relative the core barycenter, i.e., roughly 6.7% of the speed of light, c. Note that the initial shock velocity can be higher at upwards of ~50,000 km/s, or ~0.167 c, and the initial total energy imparted to the shock can be as high as $10^{44}$ J.

One solar mass is roughly $M_{s} \sim 1.988 \times 10^{30}$ kg and we know that the relativistic kinetic energy is given by: $$ KE = m \ c^{2} \left( \gamma - 1 \right) \tag{0} $$ where $m$ is the rest mass, $c$ is the speed of light in vacuum, and $\gamma$ is the Lorentz factor given by: $$ \gamma = \left[ 1 - \left( \frac{ v }{ c } \right)^{2} \right]^{-1/2} \tag{1} $$ where $v$ is the speed of the object in question.

If we numerically solve Equation 0 assuming $v$ = 50,000 km/s (~0.167 c) and $KE$ = $10^{44}$ J, then the total mass ejected in the shock wave is $\sim 7.8 \times 10^{28}$ kg or ~0.04$M_{s}$. If the initial speed is lower, say, 20,000 km/s (~0.067 c) then the ejected mass increases to ~0.25$M_{s}$.

Thus, the answer to your question is absolute yes if you include plasma under the definition of objects.

Now suppose we assume that all $10^{44}$ J are dumped into ejecting the remnant core, which has a mass of roughly 1$M_{s}$. The speed of the core would then be ~10,000 km/s or ~0.033 c.

This may seem slow, but think of it in terms of something tangible like the time it takes to reach the termination shock of the heliosphere. Suppose this is located at 100 AU (AU = astronomical unit ~ $1.495 \times 10^{8}$ km). A speed of ~10,000 km/s corresponds to ~1 AU per ~4.1 hours, so it would only take ~17.3 days to reach 100 AU. For comparison, it took Voyager 1 a little over 27 years (~9965 days) to get out to ~94 AU to cross the termination shock, or ~576 times longer than it would have at ~10,000 km/s.

I am having trouble understanding if generation of such relativistic bombs can be generated by supernova explosions. What physical laws would prevent this or make it unlikely? If it is indeed possible, why don't we observe them? How can we observe them if possible?

There are objects called hypervelocity stars that have speeds of upwards of ~1200 km/s (~0.004 c) relative to the other local starts/objects. While this is still a factor of ~25 smaller than what you seek, these are stars moving at these speeds, not a tiny 1 kg object. The fastest one observed is US 708, which is an O-type star, i.e., it's large, massive, and hot. Even if it only has $M \sim 10 M_{s}$, its speed amounts to ~$10^{43}$ J relative to the local stars/objects.

So I am not sure that the statement claiming we do not observe high energy objects is not accurate. The speed of our solar system about the galactic center is, on average, ~230 km/s. The Andromeda Galaxy is approaching the Milky Way at ~110 km/s. Supposing another solar system orbiting the Andromeda Galaxy has a similar rotation speed, we already have a maximum relative speed of nearly 600 km/s without including the orbital speed of the objects gravitationally bound to each stellar system. Most comets reach at most ~70 km/s in our solar system but the sun is not a huge star. Even so, Comet ISON was able to exceed ~370 km/s at perihelion.

If one looks at the speed of a hyperbolic trajectory for the same orbital parameters as Comet ISON (i.e., e ~ 1.0002 and $r_{p}$ ~ 0.0124526 AU, where $r_{p}$ is the perihelion radius) orbiting a star with $M \sim 10 M_{s}$ then the perihelion speed can reach ~1200 km/s. Suppose the stellar object had $M \sim 100 M_{s}$, then the perihelion speed now reaches nearly 3800 km/s (~0.013 c).

In short, I do not find it impossible for the relative speed between objects of at least 1 kg in mass to exceed 10,000 km/s in some special cases. The probability of occurrence in any given unit time is, however, a different matter that some of my astro colleagues would be better at addressing.

How large would a mass have to be, traveling at 0.1c, that if it struck the earth, would cleave the earth in 2?

This was already properly addressed in the comments.

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After reflecting on the question, 2 reasons came to mind as to why relativistic bombs are unlikely in our galaxy.

  1. While a supernova explosion would indeed have the energy needed to accelerate 1kg or greater solid masses to relativistic speeds or at least to 0.1c, the dying star pre-supernova and post-supernova is composed of plasma, where it would not be possible for anything to be in a solid state. Any cooled off plasma would still be thousands of degrees too hot to be anything other than gaseous plasma.

The plasma nuclei and alpha particles are indeed sent out with lots of energy at near the speed of light and we witness these as cosmic rays. It is simply not possible for stellar plasma to accrete together to form any kind of solid mass.

Ok, what about the small rock fragments and mini asteroids that were orbiting close to the dying star pre-supernova? While the supernova explosion would likely blow many apart and vaporize them, it is not impossible that some of these stay in tact and accelerated to 0.1c or greater from the explosion.

If such rocks were indeed accelerated to 0.1c or greater, would they survive the journey through many years of travel through space, which brings up the next reason.

  1. Space is not a complete vacuum.

The density of atoms per volume in interstellar space averages about 1 hydrogen atom per cc (cubic centimeter). This is a weighted average ranging from 1 atom per 10cc on the low side to 1000 atoms/cc in the galactic core region. 1 atom/cc is very very low and any friction encountered by spacecraft at usual speeds are nano-scale. This may not be the case at 0.1c or greater. Indeed at a certain relativistic speed or greater which can be calculated, any such rock would 'burn up' just like solid mass entering our atmosphere from space.

While 0.1c would not instantly vaporize a space rock, it may gradually get eroded away on its long journey. The interstellar gas friction does not increase linearly with speed of travel, but rather as the square of the speed since the kinetic energy is directly proportional to the square of the speed. The momentum of each atom strike becomes significant at such high speeds.

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