You would not destroy yourself either.
The grandfather paradox, in which a time traveler goes back in time to before they were born and kills their grandfather, is an example of a time travel paradox of self-interference that creates an inconsistency in reality. How that paradox gets resolved has been the subject of science fiction for much of the 20th century. Real scientific inquiry into it began sometime in the late ‘80’s and early ‘90’s when investigation into the consequences of so-called Closed Timelike Curves (CTCs) by a consortium of researchers called the Moscow Consortium (based in the former Soviet Union) looked into all sorts of questions surrounding CTCs including if they were even possible, if a human could travel through them, if a person could send messages, and most importantly how paradoxes could be resolved.
Many science fiction TV shows, movies, and books have explored the idea and come up with various solutions:
Altered timeline: in this interpretation the “timeline”, treated as a single reality, can be altered thus changing the future one left. This can be classed into two sub-interpretations: (a) self-destructive as in Back to the Future where you can erase yourself from history and this results in one’s gradual disappearance (DC’s Legends of Tomorrow had a fanciful interpretation where the altered history chases you like a monster through time) or (b) non self-destructive where the timeline is changed but you are somehow “protected” by virtue of traveling back into the past — Star Trek: First Contact took this route. In this interpretation you have free will.
Enforced self-consistency: the timeline asserts consistency and any action that creates a paradox becomes impossible: The Connie Willis books based on a future Oxford University such as Doomsday Book employ the idea that the timeline protects itself and prevents you from altering the future, although she violates it in To Say Nothing of the Dog, so it is more of a de facto than strict rule of time travel. This can be classed into a free will and a deterministic version: (a) free will exists but the universe renders your actions harmless by either altering circumstance beyond your control to re-enforce consistency (you go back to kill Hitler but something prevents you from carrying it out) or preventing your time machine from even accessing events that might radically alter the future or (b) no free will exists and every action you take is completely pre-determined.
Alternate universe: in this interpretation anything goes, you are not altering your own past but the past of another world. Once altered you become a part of that world’s future but it is still consistent with the world you left.
While #1 has been part of science fiction for decades, science has tended to focus more on #2, how to enforce consistency. Some scientists such as David Deutsch have promoted #3 and this resolution has made its way into popular culture as “the explanation” probably because it is so simple to understand. This is a consequence of the Many World Interpretations of quantum mechanics.
It turns out, however, that you can make the argument that any interpretation of quantum mechanics can resolve the paradox because the nature of the quantum wavefunction resolves it, not the interpretation. After all, interpretations are ways of understanding measurements not predictive theories. Every quantum interpretation assumes the same predictions.
Time Traveling Quantum Billiards
In order to support the idea, I want to talk about something less complicated than altering history. Instead, I want to talk about playing a game that has real possibility for paradox. I call this game quantum billiards. It is analogous to real billiards except that the balls are quantum particles. It doesn’t really matter what kind of particle they are, they could be photons or electrons. For now, I will just call them qballs.
Our qballs are placed on a quantum billiard table. This table has two pockets A and B. These pockets contain wormholes that form together a CTC. Pocket A sends the qball into the past a fraction of a second or so and causes it to emerge from pocket B.
Unlike ordinary billiards where we can just watch the balls progress, here we need to use some kind of detector to measure the balls and we can only measure them when they have completed whatever experiment we want to conduct. My pool cue is an emitter that fires qballs into Pocket A. I also set up detectors around the route it takes so that I can measure my qball if it does not enter Pocket A, but not if it does enter it.
The experiment is set up so that if the particle emerges from Pocket B it may interfere with itself in the past, so that it may cause it not enter Pocket A. In that case, while I would not measure the qball before it enters Pocket A the first time, the second time I would measure it. We will call the first kind of event “timeline alpha” and the second “timeline beta”
Consider the implied paradox here: will we measure one thing in timeline alpha and something else in timeline beta?
It turns out, however, there is no paradox. The particle will both enter the wormhole and not enter it and both exit the wormhole and not exit it because of the principle of sum over histories, meaning the particle takes all possible paths. Thus, what we will measure is an interference pattern of the particle with itself. The two timelines exist in superposition with one another.
But how do we get a real paradox like the grandfather paradox instead of some interference pattern? We can like this: instead of having the qball interfere with itself, it just turns off the machine that emitted it so it was never emitted.
In this case, the paradox emerges, but that is something of an illusion because what is happening is that we are interacting with the superposition and becoming part of a particular timeline. And that is precisely where MWI suggests that we exist in superposition with alternate copies of ourselves.
But MWI isn’t the only game in town. How do the other quantum interpretations handle this?
Most support the idea that you can alter the timeline. Here’s how:
Superselection theory would maintain that the alternate timelines are still in superposition but we can only observe one. Thus, those alternate copies of ourselves are physically suppressed somehow.
Others like the modal interpretation suggest that the alternate timeline just exists as a potential timeline.
Both of these interpretations would essentially support the idea that we can alter timelines by changing the wavefunction’s meaning, effectively switching from one timeline to the other. Because they maintain the set of superimposed timelines in the wavefunction, there is no inconsistency. (I personally don’t like these two interpretations because they feel like meta-physics rather than physics.)
Bohmian mechanics would have an easy time with it because it maintains the full wavefunction but has another set of states representing actual reality. So even though the particle turns its own emitter off and no longer goes through the wormhole, the wavefunction still goes through the wormhole! Thus, the alternate timeline becomes like a ghost, enabling the timeline to switch.
The consistent or decoherent histories interpretation introduces a random selection mechanism so that particles only have one state at any time. Yet, it doesn’t alter the equations of quantum mechanics that maintain the superpositions. It simply interprets those that are consistent with a measurement to be “real” and those not consistent to be “unreal”. In this sense, it is similar to Bohmian mechanics but doesn’t add an explicit state for particles. When a measurement is made, you can infer it had that reality all along. What if that reality is inconsistent? As long as you can construct a history for the particle that is consistent, it doesn’t matter. Similar to Bohmian mechanics, the previous timeline is like a ghost, still there causing the present, but no longer measureable in the altered timeline.
The theme is that, without Many Worlds, we are fixed in a single world with a single timeline yet quantum mechanics still offers a mechanism to alter that timeline because of the ghostly nature of the wavefunction representing all possible alternative timelines. If you don’t believe that all those alternate timelines are “real”, then you still have to accept that they represent potentialities that have a genuine influence on what is real. In quantum experiments, we show that these alternate realities interact with one another all the time, and yet we only ever measure one. Is it the only one that exists? That may be metaphysics at this point. Perhaps one day we will have a real answer.
One conclusion from this, however, is that the Back to the Future scenario where you can destroy yourself by changing the past doesn’t occur in quantum mechanics. The wavefunction, containing your alternate selves (whether real or ghostly), will save you. As for whether we have free will or if there are alternate universes, those remain to be seen.
Ringbauer, Martin, et al. “Experimental simulation of closed timelike curves.” Nature Communications 5.1 (2014): 1–7.