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Try burning a matchstick with a magnifying glass then go bigger.
I was thinking the cannon could be fired at the centre of the galaxy and the shockwave would destroy everything
However it is done, you would need to exceed the gravitational binding energy of the Milky Way. Given that you need about 2×10^32 joules of energy to exceed the GBE of the Earth (1 joule = 1 watt for 1 second), I'm thinking the GBE of the entire Milky Way would be many orders of magnitude greater than 100 trillion yottawatts (10^34 W).
EDIT: The GBE of the Milky Way is approximately 10^61 ergs or 10^54 joules according to this arXiv paper[arxiv.org]. This means your 100 trillion yottawatt destroy-o-tron would need to run constantly for about three trillion years.
Then again, I know next to nothing about physics, so I might be wronger than wrong. EDIT: Actually, I'll be surprised if I'm anywhere even approximately correct.
So what would this cannon of mine do ?
If my maths are correct (big "if" there), it would destroy the Milky Way, but it would take about three trillion years to do so. Might want to up the power level a few orders of magnitude.
https://www.youtube.com/watch?v=8VGDhGsYoSA
What's stupid about this? Just think of the practical applications such a technology would have!
http://www.everydaysciencestuff.com/destroy-universe-part-1/
True.
Ahh, reddit-science. Totally believable.