This thread has offically turned stupid.
I think it's gotten pretty interesting, actually, and evolved from a simple fun question into a rather complex philosophical issue.
As for myself... given the power granted by this scenario... my cellphone rings, as originally suggested, and I beam up to my own personal starship. What do I do with it? What would you do with it?
The power to obliterate all life on Earth.
The power to
threaten to obliterate all life on Earth.
The power to transport materials from any point on Earth to any other point on Earth.
The power to replicate material goods for needy peoples.
And so on.
What to do? You might go with the most humanitarian of pursuits and try to fulfill the needs of the needy. Problem is, as with virtually any other decision made, there are unintended consequences. Charity has depressed third-world economies in many ways; people in the most remote parts of Africa wear old Hilfiger shirts because countless well-meaning charitable drives have taken our first-world cast-offs and donated them to the worse-off. The result? Local clothiers that eked out a living fabricating the native pre-charitable garb are now out of business.
To lend a hand to American farmers growing crops in an increasingly post-agrarian society, our government has decided to subsidize the farming industry with tax dollars in order to keep prices low and competitive on the global market. The result? Kenya, whose major export was cotton, has found it impossible to sell their cotton on the global market at a price competitive with our own, even given their extremely favorable exchange rate - they can't beat the price we sell it at, because much of the cost of our cotton is hidden in tax dollars.
So, you donate an industrial replicator to poor African countries. They may be able to replicate food and clothing, but what unintended harmful effects could this have on their economy/society/etc? Will they ever improve their standing now that they can simply materialize the fruits of their labor, minus the labor? You may say, 'nobody need labor any more! we can replicate whatever we want!' Okay, then who, for example, will keep the peace? Who could possibly want to work in the dangerous world of police work or firefighting when they can just sit around and have all their needs replicated for them? Etc, etc.
To quote Alan Moore's 'Watchmen' - 'We have labored long to build a Heaven, only to find it populated with horrors.'
Okay, you say, so charity is not as easy a pursuit as I might have imagined. What about enforcing peace on Earth by show of force?
The answer to this one is shorter and simpler: no power, real or imagined, will EVER hold dominion over a people indefinitely. You will find that there are those so deep in their convictions who will, even if those convictions only differ slighty from yours, fight until their dying breath to resist you, which means you'd better be willing to back up your show of force and be willing to kill. Kill millions. To serve as an example. This will ensure their obedience - for a generation or two. Then, they will find a way to swat your starship out of the sky. We humans are very clever, and very good at killing things.
I read a wonderful short story once by Robert Sheckley called 'Diplomatic Immunity', written in the 1960s. In the story, an alien ambassador appears on Earth in human form, at the White Hourse of course, to deliver a message of peace and prosperity, and to invite Earth to join a galactic union of peaceful planets.
As you would expect, the government will have nothing to do with this. Then they start trying to kill him, as he represents a threat to their power. Seems he's rather Q-like - he can change form at will. When they try tricking him into entering a room and then shooting flame-throwers into the room, he'll briefly turn into flame. When they try sending a man-eating tiger into the room, he turns into a tiger, and they play, as tigers do. Et cetera. No matter what threat they throw at him, he patiently puts up with it, and transforms himself INTO that threat to avoid harm.
Well, humanity won't accept this, of course. They bring the best and brightest minds together in order to find a way to stop the menace of galactic peace. Eventually, a scientist reasons that
some sort of pattern must remain consistent in the alien's makeup no matter what he transforms himself into.
So here's what they do: They rig a chair to charged electrodes. When he sits down in it, he is electrocuted. Wires run from the chair to a specially designed box that is designed to add noise to, and scramble, the electrical signal that contains the Ambassador's 'form'.
It works. The Ambassador considers himself immune to harm, having a special sort of 'diplomatic immunity' (hence the story name), but is destroyed in the end by human ingenuity - because if anything is true about we humans, it is that we know how to kill and destroy and are very good at it. Their 'success' in the end promises that Earth will remain in isolation from the Galactic paradise that was offered them.
I imagine holding the world random by phaser bank would yield a similar result.