What are the effects of slicing the Earth in half with a particle beam?
Scenario:
- An exact copy of our world is sliced in half by a particle beam.
- The beam has a diameter of 40 meters and moves at a speed of 0.999c.
- The beam slices the earth from top to bottom in 600 milliseconds or 0.6 of a second
What are the implications of this? I'm assuming that the Earth itself would still remain as a singular planet and not split into two separate bodies due to gravitational binding but I would like to know some specifics of the other effects.
How large would the earthquakes be? What would the Earth's atmosphere be like after the split? How large would the tidal waves be? Would the damage done last for months, years or decades? Would there even be human civilization left?
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1 answer
Practical issues with the whole cut-a-planet-with-a-beam idea.
Your fundamental problem is that if you dig the trench by sequential applications of a beam with shallow penetration the time scale is dominated by how long it takes the already heated material to clear out of the way and that scale is long enough that the hole keeps collapsing on you.1
Instead you have to vaporize the whole cut in one rapid go.
So you need a penetrating beam by which I mean one that will deposit energy all the way through a diameter of the Earth. And do it without excessive difference in the power deposited on the near and far side.
That leaves out all beams that interact by the strong or electromagnetic interaction because the distance scale for those beams too short (even extremely high energy muons are lucky to go a few kilometers in rock-like materials).
So, your beam is going to be neutrinos or something exotic and not yet discovered (but with interaction cross-sections comparable to or smaller than those of neutrinos).
The good news is that you actually want a fairly low energy neutrino beam (neutrino interaction cross-sections scale linearly in energy over a wide range), but that bad news is that a beam that will still be depositing useful amounts of energy after passing through a whole diameter of the planet will waste a large fraction (even most) of its energy by over-penetration.2
And then we get to that energy cost. The current way of making neutrino beams is vastly inefficient, and there are no better proposals on the horizon. So you have a vast energy cost for doing the damage, a significant loss to over-penetration (at least a factor of two), and a high multiplicative factor for losses in beam generation.
All together you are looking at an energy cost at least ten times the energy applied to the event which is already above the scale needed for moderately relativistic interstellar colonization.
And you have to do all that on a time-scale around a few hundredth of a second or so.3
1 The mantle is viscoelastic and rather thinck and slow to react, but that is its behavior under pressure. When mantle rock is brought quickly to the surface if forms a low viscosity lava that flows fast and smoothly. The mantle is going to keep pouring into the trench almost like water.
2 And because your beam is highly collimated you'll need to worry about what it does across distance at least the scale of the solar system. And remember that you sweeping the beam, so it is a fan-shaped danger region.
3 No point in going a lot faster because the beam propogation time is about $0.04\,\mathrm{s}$, but you don't want to go much slower because that gives the remaining structure time to react and the whole effect is ruined if the edge where you started has stuck itself back together before you get done at the other side.
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