When billiard balls go back in time

Some solutions of Einstein’s general relativity equations describe shortcuts through spacetime called wormholes (see my book [*], Chapter 11).

A simple wormhole model is obtained “by removing two balls of equal radius from Euclidean space and identifying their surfaces,” explains physicist Igor Novikov. “The surfaces then become the wormhole’s mouths.”

A physical object (think of a billiard ball) could enter one of the two mouths of a wormhole and exit from the other mouth in another place and another time.

But this opens the door to self-inconsistent causal loops in time (grandfather paradoxes). Nobel laureate Kip Thorne explains (see “Black Holes and Time Warps” and references therein) that a billiard ball “launched toward the right mouth from an appropriate initial location and with an appropriate initial velocity” could enter the right mouth, exit from the left mouth at a previous time, and “hit its younger self, thereby preventing itself from ever entering the right mouth and hitting itself.”

Thorne and his collaborators analyzed the classical mechanics of billiard balls in a spacetime with a traversable wormhole. They found that, for any inconsistent loop, there are also self-consistent loops that start with the same initial conditions. In a self-consistent loop, the ball hits its younger self and pushes it into the right mouth.

It turns out that, for many initial conditions, there are infinitely many self-consistent causal loops where the ball goes many times through the wormhole and eventually hits its younger self. The possibility for a ball to go back in time and hit itself breaks the determinism of the classical mechanics of billiard balls.

How does the universe choose which loop to follow? Thorne and his collaborators work around the question showing that a quantum analysis would deliver probabilities instead of certainties anyway.

I suspect that self-consistent causal loops are ubiquitous and necessary for the machinery of reality to work. In his science fiction novel “Einstein’s Bridge” (1997), physicist John Cramer (the originator of the related transactional interpretation of quantum mechanics) suggests that:

“This universe… moves forward in time at the quantum level by a chain of handshakes between past and future… the future reaching back to make an accommodation with the past that allows a quantum event to happen, to become reality. Each quantum event emerges into reality as the result of a feedback loop between past and future. These are allowed timelike loops that bring the universe into being.”

In this view, the time-traveling billiard ball picture shows the future reaching back into the past to make both the past and the future happen self-consistently.

What about the inconsistent loop? I think the simplest way out of the paradox is that an inconsistent loop knocks the billiard ball into another world in Everett’s multiverse [*].

In his time travel science fiction novel “Timescape” (1980), Gregory Benford suggests that:

“When a loop was set up, the universe split into two new universes… No one in either universe thought the world was paradoxical.”

In the Afterword to his thematic sequel “Rewrite” (2019) Benford summarizes:

“Timescape concludes with a solution to the paradox, based on… Hugh Everett’s Many-Worlds Interpretation… I trimmed Everett’s idea: only a paradox-causing event generates a split-off universe.”

Physicists who are also science fiction writers, like Cramer and Benford, often use science fiction to propose far out, highly imaginative ideas that would be canceled by academic “Scientific Justice Warriors” (SJW) mobs. Another highly imaginative physicist and science fiction writer, Robert Forward, contributed to Thorne’s research.

Thorne himself — a Nobel laureate too big to cancel — was a science consultant for the film “Interstellar,” by Christopher Nolan, and explored far out time travel ideas a book on “The Science of Interstellar.”

According to Thorne, perhaps an “infinitely advanced civilization” (one that is limited only by the laws of physics) could engineer wormholes. Hearing a Nobel laureate speculate on infinitely advanced civilizations with technologies “indistinguishable from magic” is refreshing, but to me a civilization that is limited by the laws of physics is not infinitely advanced: An infinitely advanced civilization could overwrite the laws of physics.

I often think of an infinitely advanced Mind (leave it impersonal, or personalize it and call it God as you wish) that dwells in the bedrock of fundamental reality beyond space and time, and subtly engineers causal loops across places, times, and worlds.

Update: I’m studying “Lectures on Faster-than-Light Travel and Time Travel” (2019), by Barak Shoshany. See also “Time Travel Paradoxes and Multiple Histories” (2019), by Shoshany and Jacob Hauser.

[*] My book “Tales of the Turing Church: Hacking religion, enlightening science, awakening technology” is available for readers to buy on Amazon (Kindle | paperback).

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Cover picture from Wikimedia Commons.