The Science of Interstellar

Rule 1: Physical objects and fields with three space dimensions, such as people and light rays, cannot travel backward in time from one location in our brane to another, nor can information that they carry. The physical laws or the actual warping of spacetime prevent it. This is true whether the objects are forever lodged in our brane or journey through the bulk in a three-dimensional face of a tesseract, from one point in our brane to another. So, in particular, Cooper can never travel to his own past.

Rule 2: Gravitational forces can carry messages into our brane’s past.

In the movie, rule 1 generates mounting tension. Murph grows older and older as Cooper lingers near Gargantua. With no possibility to travel backward in time there’s a growing danger he’ll never return to her.

Rule 2 gives Cooper hope. Hope that he can use gravity to transmit the quantum data backward in time to young Murph, so she can solve the Professor’s equation and figure out how to lift humanity off Earth.

How do these rules play out in Interstellar?

Messaging Murph

When falling into and through the tesseract, Cooper truly does travel backward relative to our brane’s time, from the era when Murph is an old woman to the era when she is ten years old. He does this in the sense that, looking at Murph in the tesseract bedrooms, he sees her ten years old. And he can move forward and backward relative to our brane’s time (the bedroom’s time) in the sense that he can look at Murph at various bedroom times by choosing which bedroom to look into. This does not violate rule 1 because Cooper has not reentered our brane. He remains outside it, in the tesseract’s three-dimensional channel, and he looks into Murph’s bedroom via light that travels forward in time from Murph to him.

But just as Cooper can’t reenter our brane in Murph’s ten-year-old era, so he can’t send light to her. That would violate rule 1. The light could bring her information from Cooper’s personal past, which is her future; information from the era when she is an old woman—backward-in-time information from one location in our brane to another. So there must be some sort of one-way spacetime barrier between ten-year-old Murph in her bedroom and Cooper in the tesseract, rather like a one-way mirror or a black-hole horizon. Light can travel from Murph to Cooper but not from Cooper to Murph.

In my scientist’s interpretation of Interstellar, the one-way barrier has a simple origin: Cooper, in the tesseract, is always in ten-year-old Murph’s future. Light can travel toward the future from Murph to him. It can’t travel to the past from him to Murph.

However, gravity can surmount that one-way barrier, Cooper discovers. Gravitational signals can go backward in time from Cooper to Murph. We first see this when Cooper desperately pushes books out of Murph’s bookcase. Figure 30.1 shows a still from that scene of the movie.

^{Fig. 30.1. Cooper pushes on the world tube of a book with his right hand. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]}

To explain this still, I must tell you a bit more about the bedroom extrusions, as Chris and Paul Franklin explained them to me. Let’s focus on the front blue extrusion in Figures 29.10 and 29.12, which I reproduce as Figure 30.2 with extraneous stuff removed. Recall that this extrusion is a set of vertical cross sections through Murph’s bedroom, traveling forward in bedroom time along the blue direction (rightward).

^{Fig. 30.2. The world tube of a book, within an extrusion of Murph’s bedroom. The book and its world tube are drawn much larger than they actually are. [My own hand sketch.]}

Each object in the bedroom, for example each book, contributes to the bedroom’s extrusion. In fact, the book has its own extrusion, which travels forward in time along the blue-arrow direction as part of the bedroom’s larger extrusion. We physicists call a variant of this extrusion the book’s “world tube.” And we call the extrusion of each particle of matter in the book the particle’s “world line.” So the book’s world tube is a bundle of world lines of all the particles that make up the book. Chris and Paul also use this language. The thin lines that you see in the movie, running along the extrusions, are world lines of particles of matter in Murph’s bedroom.