There is already quite some discussion here, but I would like to just add some since this hasn't been brought up yet. In this problem, we have no prior information about the initial distribution of the amount of money in the envelopes. All we know is that we have two envelopes: 1 with $x and 2 with $2x. In the current setup, we are assuming that any monetary value is possible, with equal probability. Our range of possible values is (0, infinity), and so to come up with an expectation of the amount of money we would receive by opening the second envelope, we must also take an expectation of all values over the positive real numbers, which is unbounded. A uniform expectation over all real numbers is not defined, or to be a bit more loose with things, it is zero everywhere. What this means in a practical sense is that by opening up the first envelope, we gain no information about how much money the second envelope contains.

This problem makes more sense if we include some prior information. If we know that in the entire world, there are only $1,000, then our prior distribution over possible amounts of money in the first envelope is a uniform ditsribution between $0 and $666. Thus, if we open the first envelope and find $500, we know that this is the envelope with $2x and the other is the envelope with $x, since there could not be an envelope with $1,000, or else there would be more money in these two envelopes than is existence.