Paradox free time travel is possible.
Quantum mechanics resolves the problem no matter what interpretation you use.
Quantum mechanics resolves the problem no matter what interpretation you use.
I noticed a headline in my science news feed the other day:
A Student Just Proved Paradox-Free Time Travel Is Possible
Time travel is deterministic and locally free, a new paper says-resolving an age-old paradox. This follows recent…www.popularmechanics.com
Naturally, I was intrigued since this is right in my wheelhouse, so I went over and read the paper.
It turns out that the headline is misleading since the paper does not prove time travel is possible. It actually assumes it is possible. Rather, it proves that you can avoid paradoxes. Basically, the paper shows that if a “process” such as a person exists in both their past and future (as you would expect in a paradox) that you can carry out “arbitrary local operations”, i.e., do whatever you want at a particular time and place, without contradictions arising. The work builds on the work of others (which is true of all good science). It is hardly a Back to the Future scenario though.
A story by best selling author of Arrival Ted Chiang, who is one of the smartest and best science fiction short story writers I’ve encountered since Asimov, called “The Merchant and the Alchemist’s Gate” (found in his recent collection Exhalation) explores the idea of time travel when you can’t make free choices although you aren’t aware that you can’t. In that story, an alchemist in Baghdad owns a portal that can take one into the future or past of that same portal. Thus, stepping through it from one side can take you 20 years into the past while entering from the other takes you 20 years into the past.
He explores how people can travel into their own past or future and appear to make decisions freely while everything that happens is inevitable. Thus, freedom of choice is an illusion. He does this using a classic mechanism time travel writers have used for decades: the universe prevents paradoxes by influencing circumstances beyond your control.
So, if you go back in time to try to save somebody who died (or kill somebody who lived), the universe will prevent you from carrying it out.
Thus, free will is possible, but you are part of a complex dynamical system and whenever you make a decision it has consequences both in the past and future. If you travel back in time, you can do what you want, but the universe will snatch away anything you want to change that would create a paradox. Is that really true?
It would be interesting to look at the issue with something simpler than people. How about balls? Billiard balls in particular.
In 1991, Echeverria, Klinkhammer, and subsequent Nobel laureate Kip Thorne of LIGO-fame, published a paper on exactly this case. What would happen if you had a special kind of billiard table where the pockets were wormholes and caused the balls to travel back in time, possibly striking their past selves?
The goal of this work was to explore whether the dynamical equations for a billiard ball traveling through a wormhole into its own past has a solution. If there is no solution, of course, then the path isn’t physically possible. The other goal was to explore if there was a unique solution, i.e., that ball could only follow one path given its initial velocity and position. If the solution is not unique, then it is ill-defined and there are many possible solutions. In that case, you need to add some condition to further constrain it or discover a logical contradiction in your setup.
A wormhole that allows an object to travel from the future and influence its own past is called a Closed Timelike Curve (CTC). These are the types of solutions to trajectories in Einstein’s general relativity that allow for paradoxes. Other kinds of wormholes can exist of course. There are some that take so long to traverse that you don’t end up back in time even if the mouth is in the past. Others might take you so far away that there’s no way you could return to interact with yourself.
If you don’t have a CTC, there is only one solution to any given initial value problem. This is just basic high school physics.
If you do, something interesting happens.
Consider the problem when you have a ball that hits itself in the past: essentially, in your assumptions for your initial conditions, you assumed there was no collision. Then, of course, there is one. So doesn’t that create a logical contradiction that should prevent a solution at all?
It turns out not.
The authors call these self-interacting trajectories dangerous.
The authors expected these trajectories to have no solutions (be impossible) but it turned out that when they did the calculations, they found they had an infinite number of solutions. That means that there are an infinite number of trajectories for every set of initial conditions if a self-collision occurs.
Obviously one of the problems of most interest is called the self-inconsistent solution. In this case, the ball enters the wormhole and then emerges and knocks itself away so it doesn’t enter the wormhole after all. What happens then?
The infinite number of solutions indicates that the problem is not well-posed, meaning that there is something wrong with the way it is set up.
The authors show that the problem is classical mechanics itself. Newtonian mechanics is only an approximation for quantum mechanics which suggests that every object follows not one path through space and time but a multiplicity of paths that all contribute probabilistically to any measurement. Thus, the ball isn’t following one path but many paths simultaneously, each with an associated probability contribution.
In this case, the problem is resolved because you can simply assign different probabilities to the different quantum trajectories depending on self-interaction or not. A self-collision that creates a paradox simply increases the probability of paths that do not enter the wormhole, but doesn’t eliminate those that do enter it. Likewise, the collision itself is only a probability. There is no certainty in quantum mechanics.
A misconception is that the Many Worlds Interpretation of quantum mechanics resolves the paradox. I.e. when you create a paradox you are simply influencing another world different from the one you left. But it turns out that quantum mechanics itself resolves it. The interpretation of quantum mechanics just tells you how to interpret the resolution.
The point is that quantum mechanics allows classically contradictory things to happen no matter how you interpret it. Paradoxes influence the shape of the quantum wavefunction (the quantum state of the ball) but do not violate any laws.
Thus the problem is no different than the famous double slit experiment where individual particles interact with themselves. The resulting interference pattern is the resolution of a similar paradox in space rather than time.
In quantum theory, when you make a measurement like observe a billiard ball’s position, you will get an answer, but you can’t attribute a clear classical trajectory to its cause. Rather, you have to sum over all possible trajectories that could have contributed to it. In that case the inconsistency evaporates since there are trajectories that go into the wormhole and those that don’t existing simultaneously.
Thus, the problem with how we understand the grandfather paradox is rooted in our mistaken assumption that reality has a single, consistent state. That is a classical assumption that makes no sense in the context of quantum mechanics, Many Worlds or not. There is no contradiction.
So does this mean we can go back in time?
Not with known physics. Although CTCs are possible in Einstein’s relativity, we do not know of any matter or energy that would allow a person or any macroscopic object to travel into the past (or go faster than light for that matter). We couldn’t hold such a wormhole open without some kind of matter or energy that hasn’t been discovered yet that violates certain tenets of quantum physics (the achronal average null energy conditions) that have never been observed to be violated.
So, don’t hold your breath for a time machine any time soon, but rest assured that the grandfather paradox is a paradox only in how we think of reality in classical instead of quantum terms.
Tobar, Germain, and Fabio Costa. “Reversible dynamics with closed time-like curves and freedom of choice.” arXiv preprint arXiv:2001.02511 (2020).
Echeverria, Fernando, Gunnar Klinkhammer, and Kip S. Thorne. “Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory.” Physical Review D 44.4 (1991): 1077.