Doppelgänger

One of the stock objections to Calvinism is the allegation that according to Calvinism, the spiritual experience of the reprobate may be indistinguishable from the spiritual experience of the elect. 

i) To begin with, evangelical Arminianism believes that some people are deluded about their salvation. For instance, there are nominal Christians and progressive Christians who imagine they are heavenbound, when in fact they lack saving faith. Not to mention members of cults who imagine they are heavenbound (e.g.  Muslims, Mormons, Jehovah's Witnesses). So Calvinism is hardly unique in taking the position that people can be deluded about their salvation. It doesn't require an inner experience by an outside agent (God, Satan) to produce that delusion. Mundane factors can have that effect. 

ii) It depends on what is meant by indistinguishable. Is the allegation that they have the same spiritual experience? If so, that's not the case. The elect experience regeneration and sanctification while the reprobate do not.

iii) Or does it mean that even though their psychological experience is different, they have no intersubjectival basis of comparison to determine whether their perception is what the elect experience or the reprobate experience? Even if that were the case, so what? Assuming that's a consequence of Calvinism, how does that disprove Calvinism?  

Let's take a comparison. Here's a philosopher invoking the science-fiction scenario of machines that can duplicate a human being. He's using this thought-experiment to undermine dualism, but we could tweak it to stipulate that the machine duplicate the soul as well as the body:

Those who believe this will concede, after a moment's reflection, that just as most of the duplicate's memories will not be real memories, so most of his beliefs about himself and his history will be false. The duplicate will, for example, believe that he is the [original] Alfred, and he is not. That is, he is not a man who has existed for such-and-such a number of years (he is only a few minutes old) and is married to Winifred (he has never met her), and so on. The duplicate has no sense of Alfred. He is someone else, for if you stick a pin into Alfred, the duplicate feels no pain. Nevertheless, it seems to the duplicate that he is Alfred. What it is like to be the duplicate is just exactly what it is like to be Alfred. If Alfred was unconscious when he was duplicated, and if he and the duplicate were then "scrambled"…no one, including Alfred and the duplicate, could ever know which was Alfred and which was the  duplicate. P. van Inwagen, Metaphysics (Westview Press, 4th ed., 2015), 264. 

In this scenario, the original and his duplicate are physically and psychologically interchangeable. Exact same mental furniture. Same memories and psychological makeup. Identical bodies. There's nothing they can point to differentiate the original from the duplicate.

Now that might have unsettling consequences. But you can't disprove it just because it generates an identity crisis. You can critique it on other grounds, as unrealistic or impossible. But the fact that it has unnerving or creepy consequences doesn't make it false. And that's much more extreme than comparing elect and reprobate.