Here’s a thought. Assume all the standard Catholic stuff about the sacrament of marriage, such as its indissolubility until the death of at least one of the two spouses.
Suppose you get married, and then at some later point, while both you and your beloved (love and marriage aren’t coextensive, but I’m assuming the best) are both still alive, you get into a time machine and travel back, alone, to a time before you were married to your beloved, and after their conception/birth. Are you married to them? I assume they are the same person as the person you married (i.e., they are identical to the person you married). It seems tempting to say that you would be married to them, but not them to you. However, we should, I submit, have strong reservations about asserting this, which I hope to illustrate below. But first, let’s have some fun with thought experiments!
Suppose you traveled, instead, to a time in the relatively distant future, at which point your spouse is dead. Clearly they are not married to you, but are you free to remarry (i.e., are you still married to them)? It seems like you are not, at least assuming that you can travel back in time to your point of departure. This raises the question of what Church teaching would look like if time machines allowed you to go back in time and visit your (now dead) spouse, and whether you could remarry given that invention. If you could, then you could have multiple married spouses without practicing polygamy since none of them would be married to you at the same time – presumably none would be married to you while any other is still living.
Suppose that you were temporally-stranded, so that you traveled into the future to a time when your spouse is no longer living, and you have no reasonable hope of going ‘back’ in time. That position seems no different from the (married) person who loses all contact with their spouse, as sometimes happens in times of war, and after years of waiting for confirmation of their death/life one is left in a kind of limbo. In such cases the best one can do is follow one’s conscience to the best of their ability, and so re-marriage is a possibility.
Suppose that you traveled into the future, after your spouse had died, and found yourself in a time at which an older version of you was married to somebody other than your spouse; would you be married to that new spouse? If you could be, then that would be a (very strange) argument for a possible form of Catholic polygamy, and (therefore) I think you could not be. However, if you are not married to the person who married you, even though they married a person identical with you, then clearly, returning to the very first example, you would not be married to the person identical with your spouse. Perhaps this is why you would not be married to the person identical with your spouse.
Suppose you traveled back in time to a point between the time you get in the time machine, and the time you were originally married (i.e., to a time during your marriage); would your spouse be married to two extensional instances of yourself? Just imagine all the fun consequences that would imply for the theology of the body and philosophy of sex! The answer, I think, is no.
Suppose, finally, that time machines were a commodity, so that it were possible to, post your beloved’s death, return to a time at which you would have been married to them, are you, therefore, still effectually married to them? Would you be free to remarry? It seems like you would still be effectually married to your spouse if you could travel back in time, as I said previously, but maybe that’s incorrect.
Perhaps, instead, marriage is so bound up with time and space that you would not be married to any ostensible instantiation of your spouse from some time other than the time at which you and your spouse are together living out your marriage. If you are 90 years old, and you travel back in time 80 years, and spend a year ‘in the past,’ you will clearly still be 91 years old by the end of that trip, not 11 years old (though there would presumably be an 11 year old version of you walking about). Maybe, in some similar way, a marriage has a certain age of its own as well. Marriage is thus shared by spouses who, with respect to their internal-time (if we can call it that) both reside the same temporal distance away from the time at which they were married. So, if you and your spouse got into a time machine and, for your honeymoon traveled back in time a few hundred years to some exotic local, you would both be married to each other, even though you are both located at a time prior to the time of your marriage. Indeed, if you spent a year there, you would have been married for (at least) a year, and so your marriage would be (at least) a year old. Similarly, if you travel back without your spouse to a time after your marriage to that spouse, they would not be married to you, nor you to them, precisely because you two don’t occupy the same place in the life of your marriage.
This handy notion of a marriage having its own age is not without its difficulties though. Suppose, for example, that I marry somebody, and then take a vacation in the future or the past for a year, and come back. From my spouse’s perspective, I have left and returned in an instant, but I have now lived ‘the married life’ for one year longer than she has! However, perhaps this kind of puzzle admits of a solution or two. Perhaps the age of the marriage is simply the amount of time ‘since’ the marriage that the spouses have lived the married life together. The odd consequence of this solution would be that my trip to the future would have been a vacation from my marriage, even though I would myself have been bound to marital faithfulness. Another solution could be to simply bite the bullet and argue that my spouse would indeed have experienced our marriage as an affair one year shorter (assuming she doesn’t take her own trip(s) to the future/past) than I experienced it (literally, not figuratively). Intuitively I want to say that marriage is about two people living together and growing together, and hence I am averse to saying that I and my (very hypothetical) spouse could have been married for literally different amounts of time, as though I have lived the married life (with her) for longer than she has (with me)! I can’t see how to do any better though.
Another way out of this whole mess is just to argue that time travel is not possible. Perhaps there are a few ways in which this could be argued. For instance, one could argue that time travel is physically impossible, and that God made it thus precisely so as to secure the rational institution of marriage against the kind of inordinate paradox I have been considering. However, this would hardly save face in the eyes of an analytic thinker, since regardless of whether something is physically possible, it remains conceptually possible for these circumstances to occur, and thus the questions can be posed as the hypotheticals they were in the first place. Perhaps time travel is metaphysically impossible, but that sounds to my ears like a trap, since by entailment it will mean that the A-theory of time is true, which by entailment means that God is not metaphysically simple, which by entailment means that the Catholic Church has made fallible pronouncements which were de fide infallible, which by entailment means that the Catholic faith is simply wrong. That consequence will be much worse for the Catholic who arrived at it simply by trying to secure themselves against challenges to the Church’s teaching about the sacramental nature of marriage. Perhaps one could argue that time travel is metaphysically impossible on the B-theory, but I can’t make heads or tails of that. To say that time travel is logically impossible is to say that what the A-theory proposes is a necessary truth, and the same series of unfortunate consequences would follow as outlined above.