…punched a mile-wide hole from the north pole through the south pole?
Just…two new volcanos?
How many lasers does it take to get to the center of a giant Earth Tootsie Roll Pop?
I would suspect that the giant liquid center of molten rock would leak out. The Earth’s balance and rotation rate would change. The Tropics and Arctics may change places. Magnetic North would no longer be north. Gravitation force would be reduced.
No, none of those things would happen.
Remember…gravity?
There might be transitory volcanoes created at the exit holes, but the tunnel itself would collapse very quickly. Remember, the core of the earth, and mantle (90+% of the Earth’s volume) is molten. So, it would be like trying to drill a hole in a basketball full of pudding.
But only at the South Pole because it’s on the bottom.
Seriously though, why would the magma leak?
If anything wouldn’t there by a slight decrease in the Earth’s internal pressure
I suspect these are true, but how much of the Earth’s mass would that ~25k mi^3 cylinder represent? The degree of change wouldn’t be out of line with that, would it–a small percentage yields small change?
Why?
I’ll get things set up tonight and we’ll test it in the morning.
The mass would still be there. Unless you think it would go somewhere else but if so, how?
I think the most significant change would be to the atmosphere – there’d be megatons of vaporized earth pouring into the air. Just guessing, but blocked sunlight fucks up several years of growing seasons, leading to famines all over the world.
Also, is dirt vapor a greenhouse gas? I’m also guessing global warming will be either multiplied by 10, or switched to global cooling.
The laser vaporizes tons of rock that comes shooting out of the hole at incredible velocity. As you reach the molten layers the earths goo keeps trying to fill it back in and keeps needing to be vaporized. So basically you’ve created a rocket to move the Earth wherever you want.
I’d expect nasty earthquakes as everything settles down to replace the missing volume at the center. Probably civilization-wrecking levels of earthquakes.
How big a laser would this be? 
I imagine that molten rock would continuously flow in to replace that boiled away by the laser. Assuming enough power, eventually the entire middle of the earth would be converted to vapour, much of which would depart via the entrance hole. If you’re lucky, the crust of the earth would remain as a hollow shell, and Symmes would finally be proved right. More likely, the crust would be melted by the general amount of heat involved, and we would finally have eliminated the common cold (along with every other disease, or, indeed, life form).
It’s a frickin giant laser that punched a mile-wide hole from the north pole through the south pole.
A lot of mass will be missing. Internal pressure would push a lot of the remaining “mag-ma” out of the mile-wide chimneys. The Earth may be altered enough to seek a new axis. Reduced mass means less gravitational force. Dogs and cats may begin living together.
Where do you come up with this stuff?
A laser does not just make the mass vanish. It has to go somewhere, as others have pointed out, into vapor, into the atmosphere.
If you really wanted your hypothetical to be “what if you waved a magic wand that vanished a cylinder of diameter 2 miles from the north to south pole of the earth?” Then basically it would be that the hole would fill in rather quickly and the Earth would have a bit less mass than it did before. There would likely be a lot of seismic activity and probably a lot of global cooling as a result of atmospheric ash and such released during re-settling events. I doubt civilization or humanity would survive. This is just a guess though. Maybe a 2-mile wide cylinder wouldn’t be that big of a deal.
Sadly, the Giant Soil-and-Rock Destroying Laser Project has been placed on indefinite hold. Darth Vader, Moff Tarkin, and that whole Death Star crowd gave the idea a bad name by indiscriminately using it to destroy planets, even when there were no rebel bases present!
More seriously, the energy needed to blow up a planet – or even excavate a planet-sized hole – is ludicrously huge*, and lasers aren’t 100% efficient. That’s without considering all the other engineering problems that have already been pointed out. I’m sure there a much better way to carry out your mischief, or to satisfy your bpred curiosity.
*Heck, look how long it took them to bore a hole into a planet in the 2009 Star Trek movie – and that didn’t even go all the way through.
Wouldn’t a laser that big dump huge amounts of waste heat into the atmosphere? I’d imagine that would be more catastrophic than anything else about this scenario.
Ayup
Not to mention whatever was holding the laser. It’d get REALLY hot.
Okay, so the amount of energy is ludicrously huge. Fine. We have an entire sun nearby to power things. All we need to do is get the replicators going and we can build as many laser modules as we need, assuming we don’t run out of planetary debris* to feed them.
How much energy will we need to vaporize the initial 1-mile-wide column? This can be considered the bare minimum to complete the task: no doubt flow will bring more rock into the hole path to be vaporized.
*Like, say, Ceres. Or Mars.
As others have pointed out, no, the mass will still be there.
Secondly, even if we magically disappeared that mass instead of it still being around as particulate or gaseous matter, it’s not a whole lot of mass as these things go. It’s a lot compared to the works of man, but it’s a small, small, tiny amount of the mass of the earth. Like 1% of 1% of 1% of 1% of the mass of the earth.
Gravitationally, eating that extra cookie last night makes more of a difference to your weight.
Also, I should note that a lot of volcanos are situated on bigger holes than this. A couple tiny new volcanos isn’t that big a deal. As mentioned above, the ridiculous amounts of energy such a laser introduces to the environment would be a much bigger concern.
Do we need a giant shark to put a giant laser eye on it?
Volume of Earth 108.321 10^10km^3 or 1,083,206,916,846 km3
The polar radius of the Earth is approximately 6356.8 km.
The volume of a cylinder is (pi)((radius)^2)(height) so in this case the volume removed is (3.14159 {pi})x((.804672km{half mile radius})^2)x(6356.8km x 2 {height})
Which totals (3.14159) x (.647497) x (12713.6) = 25861.626 km3
As a percentage of the Earth’s volume 25861.626 / 1,083,206,916,846 = 2.387505626655003e-8 or .00000002387505626655003 or
0.000002387505626655003% of the volume of Earth.
Or 1 in 41,884,718.0436 … a minute fraction of the volume of Earth.
Now with regards to the ‘volume of materiel blasted out into the atmosphere’ issue,this Wiki article notes the volcano Krakatoa blew approximately 21 km3volume of ash, pumice, etc into the atmosphere with significant climate results.
That is 1231.5 times less than the volume described in this scenario. It is safe to expect that alone would wipe out life (as we know it) {Insert Dr. Strangelove dialog here}.
If that volume were to ‘magically disappear’ then the discussion of the collapse of the magma & how that would affect earthquakes and/or sudden heat released at the poles is a discussion I am not willing to jump into myself.
That’s all I got for 3:30am. Apologies if my math is off anywhere - I tried to double check everything. Just trying to place the idea in perspective.
We have a name for the exact situation the Earth would be in if the situation in the OP were to happen realistically, pumping that much energy into the planet (as opposed to a magic planet-corer neatly cutting a mile-wide hole, where the end result would just bemildly catastrophic)