presenting paradox-free quantum time travel?
Time travel is a pretty tough topic to study since any trip backwards in time triggers seemingly endless ways a paradox could unravel the entire timeline. Think of the good, old fashioned grandfather paradox in which a very disgruntled time traveler goes back in time and kills his grandfather as a baby. According to causality as we’re familiar with it, this would mean that our time traveler would effectively cease to exist. No grandfather, no father or mother, therefore, no him. But then who went back in time? And why? Well, some physicists working on the theoretical problems with time travel think that there might be a perfectly plausible way to answer the paradox by using causality itself. Rather than just vanishing into existence, our time traveler out for his grandfather will never be able to carry out his homicidal plans. His gun won’t go off, he won’t find his intended victim, etc. He’s simply not going to be able to kill his grandfather due to the nature of space-time. And while that’s certainly an interesting and workable hypothesis, one wonders how you test it. It’s not like we can build a time machine.
Well, we can’t build a machine that can transport anything other than photons back in time, or rather, put a very small sample of photons in a quantum state we would expect after venturing back in time and seeing how the photons will react. As it seems to turn out, following the rules of general relativity, time and space can from an enclosed loop in which the outcomes for a photon’s position and state are limited. Try to create paradoxes as you change the photons’ quantum states, and these photons will just end back where they began, or refuse to travel back in time at all. Of course this experiment has only been done on paper so far and no one ever saw a photon behave as if it’s been traveling through time, so we really don’t have much in the way of proof for these concepts, but they do have a very appealing logic. If you can’t disrupt the past, you can certainly travel back to it and return with no problem. Try to change it and you’ll fail. It would be somewhat like visiting an interactive and very immersive museum without worrying that you’ll break an exhibit. But of course getting to the past if you’re unfortunate enough to actually have mass, any mass at all, is a major problem. It simply takes too much raw energy to physically traverse the fabric of space and time and hurl yourself back into the past.
Granted, traveling back in time should involve less energy that it takes to power a warp drive, but we would still be talking about energetic outputs on at least a planetary scale. Making a tear in space and time just wide enough for a pretty average 6 foot human to pass through would take roughly the mass of Jupiter crushed to the density of a black hole. No device that we’re even able to imagine could possibly handle this much energy at such incredible densities without a runaway collapse into a fully fledged black hole with tidal forces extreme enough to swallow and disintegrate anything that strays too close. In order to actually build a wormhole out of this gravitational collapse, you’d need to do it twice, making sure the resulting gravitational wells will spin at a certain speed to hurl travelers during a certain time range within the causal loop in which they’ll exist. Sounds complicated? Well, keep in mind that trying to join two black-hole like structures will result in an unstable and extremely energetic tunnel which can pop at any moment, instantly killing any time traveler in it or nearby. And while we might have the chance to send photons, or even electrons which have a very tiny mass, but a mass nonetheless, human time travel is going to be far out of our reach for the foreseeable future and we probably shouldn’t be all that concerned about time traveling paradoxes since they simply won’t apply to us…
See: Lloyd, S., Maccone, L., Garcia-Patron, R., Giovannetti, V., Shikano, Y., (2010). Quantum mechanics of time travel through post-selected teleportation arXiv: 1007.2615v2