I will now discuss some reasons why such a possibility is extremely unlikely.
Reason 1: The technical feasibility of such a simulation is very low.
Bostrom's paper glosses over the many huge technical hurdles of creating a computer simulation in which the end result is many conscious minds who think they are living on a planet when they really are just living in a computer.
Bostrom's first gloss is to ask us to suppose that in his alien-generated simulation of human experience “these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained
and if a certain quite widely accepted position in the philosophy of mind is correct)." We have no idea whether it is actually possible to produce human-like consciousness in a computer, so this is a very questionable assumption.
Bostrom estimates that all of human consciousness could be simulated in a computer that performs between 1033 and 1036 operations per second. He estimates that an alien civilization could handle this, because it could build a planet-sized computer capable of 1042 operations per second. Of course, the idea of a planet-sized computer is very farfetched. We have no experience with any computer a trillionth that size, and there may be all kinds of technical reasons why you can't build a computer even as large as twenty miles in width (such as the fact that the combined heat from all the circuits would cause everything to get messed up, the fact that the speed of light may slow down the communication between internal parts, and the fact that it may be impossible to properly cool a computer of that size).
There is also reason to think that Bostrom has vastly underestimated the required number of operations to simulate our existence in a computer simulation. Bostrom gets his number of between between 1033 and 1036 operations (for a simulation of all of human consciousness) by naively taking an estimate of the number of operations in the human brain per second, and multiplying that number by the number of humans and the lifespan of a human. But a simulation that allows for free-will and branching possibilities would seem to require vastly more computing power – probably far more than the operations of Bostrom's hypothetical planet-sized computer (or even a star-sized computer).
It requires a relatively small number of bits to display the famous film The Godfather. But imagine a computer generated virtual experience in which you are Michael Corleone, and you can make any choice at any point in the film – you can kill the guy in the restaurant, or kill any other person you see; you can marry the woman in Sicily, or marry any other woman in Sicily, and so forth. Every possible choice involves a combinatorial explosion which vastly and exponentially increases the computer operations needed for a free-choice simulation in which any agent in the simulation can do whatever he wants.
Bostrom seems to have made the mistake of calculating the computing cost of a passive human experience (one in which we are like roller coaster riders without any branching options), rather than computing the infinitely higher cost of a free-will human experience (in which we are like car drivers who can drive anywhere and get out of the car anywhere and interact with people anywhere).
In fact, the likely computing cost of a simulation creating something like the consciousness of all human beings (with complete free will and a full range of choices) would in all probability greatly exceed the maximum capability of a computer that had all of the mass in a solar system (the sun, all the planets, and all the asteroids). And forget about interstellar computers – there is no reason to think that computers spanning multiple solar systems are practical (because of the years it takes for light to travel from one star to another).
It short, it would not be technically feasible to create a computer simulation of all of human consciousness using any technology we can imagine.
Reason 2: Aliens would have no motive to create a computer simulation that consisted of lives like ours, having experiences like we now experience.
The question of motive is one that Bostrom doesn't even address. If extraterrestrials had the ability to create a computer simulation that could include our current experience, why would they go to all the trouble of doing that?
Let's imagine some possible motives. We can imagine a malevolent motive. We can imagine very evil aliens who get pleasure from creating pain for others, like a sick boy who enjoys sticking a lit cigarette on a caged mouse. But our human experience (with usually more pleasure than pain) doesn't correspond to the type of computer simulation that such beings would create, which presumably would be something more like one of Dante's depictions of hell.
Consider the opposite motive. We can imagine benevolent, loving extraterrestrials who create our lives in a computer simulation just so that there can be some more happiness in the universe. But presumably beings with such a motive would create a computer simulation in which there was more pleasure and less pain than we see in human experience.
What about the possibility that we were created in a computer simulation by extraterrestrials who are doing some big experiment, to find something out? This motive also doesn't work. Psychological or sociological experiments would be done by relatively ignorant beings with a whole lot to learn, not by godlike beings powerful enough to create computers the size of planets or suns (such beings would have presumably already learned whatever knowledge might be received from such an experiment).
In short, we have no plausible motive for why extraterrestrials would create a computer simulation consisting of minds like our minds, and lives like our lives.
Reason 3: If we were part of an extraterrestrial computer simulation, we would probably see “realism imperfections” in the simulation that we do not see.
Because of the combinatorial explosion problem described above, the computing cost of a fairly realistic computer simulation of human experience (with less than perfect detail everywhere) would be many, many orders of magnitude less than the computing cost of making such a simulation perfectly realistic, with perfect detail everywhere. So according to the principle that slightly imperfect things (and vastly easier things) should be far more likely than perfect and incredibly difficult things, we should expect that if we were living in a computer simulation, we would occasionally see signs of imperfection in the simulation: what we can call “realism imperfections.”
One can easily imagine the type of things you would be likely to sometimes observe if your life was part of a not-quite-perfect simulation. For example, you might look at a distant point in the sky, but see no further detail when you looked at it again with a telescope much more powerful. Or you might dissect an organism, and find only a featureless mass when you looked inside it, instead of all the realistic details. Or you might go to a randomly selected distant library and start opening books, and find that they had only white pages in them. But we never see anything like such “realism imperfections” in our universe. There are various strange, paranormal things that people sometimes claim to see or experience (UFOs, ghosts, and the like), but nobody sees anything like these types of “realism imperfections.” That's not what would be likely if we lived in a computer simulation.
The reasons above are good intellectual reasons for not believing that our lives are part of a computer simulation. There is also a powerful moral reason. If you believe that your life is part of a computer generated simulation produced by extraterrestrials, then the logical next step is to suspect that none of your fellow humans exist. Because if the extraterrestrials are simulating in their computers the sky, the ground, the trees, and the rocks that you see, you might as well assume that they are simulating all of the humans (except you) also. This is because doing a computer simulation with just one observer is so much easier than doing a computer simulation with billions of observers. So if you believe in Bostrom's simulation hypothesis, the next stop on the train is the belief that you are the only human that exists. Such a belief (which would give you a license to murder and rape as you please, since you're not really hurting anyone else) is morally suicidal.
In short, the simulation hypothesis is both intellectually untenable and morally disastrous.