From Ask Me Anything Expert: David Kaiser, Theoretical Physicist & Historian of Science, MIT

You asked; Theoretical Physicist David Kaiser answered.

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Without further ado…

Q: From Benjamin Winterhalter, HIPPO Reads Editor

I understand the idea that forwards time travel is theoretically possible, but what about backwards time travel? How could such a thing occur? Doesn’t it lead to all sorts of paradoxes—multiple “yous,” for example?

A: 

Dear Ben,

Although physicists (and science-fiction authors) have thought about time travel for a long time, the subject really got a boost in the mid-1980s. Around that time, Carl Sagan was working on his novel (later made into a movie), Contact, and he asked his friend Kip Thorne to help design a realistic-sounding mechanism by which the main character could travel across enormous cosmic distances in nearly no time at all.

Thorne is a renowned theoretical physicist at Caltech and an expert on Einstein’s general theory of relativity, physicists’ elegant theory of gravity. Inspired by Sagan’s question, Thorne and some of his graduate students continued to pursue the topic even after Contact was published, and their series of research articles launched a whole new phase in physicists’ study of time travel. (Thorne describes this work in his wonderful and accessible book, Black Holes & Time Warps: Einstein’s Outrageous Legacy, first published in 1994 and still well worth reading.)

So how might time travel be possible? The root of all modern efforts to think about backwards-in-time travel stem from some fascinating properties of general relativity. According to relativity, space and time respond — they warp and bend and distend — in the presence of matter and energy. Spacetime, in other words, can be as wobbly as a trampoline. Plop a large object like a bowling ball in the middle of a trampoline, and the trampoline’s surface will bend; likewise for the spacetime near a large object like our Sun. When smaller objects, such as the Earth, move in the vicinity of the Sun, they move along as “straight” a path as they can — but the region of space and time through which they travel is no longer flat, and hence their paths bend. Physicists can calculate how objects like the planets should move through the warped spacetime around the Sun using general relativity, and the calculations match the observed motions down to the finest detail.

Note that I described “spacetime” as bending. Near a massive object like the Sun, both space and time become affected. If an astronaut were in a ship near the Sun, her colleagues in Mission Control back on Earth would observe the astronaut’s clocks to tick more slowly than their own. (This effect is known as “gravitational time dilation,” and it has been measured to high precision in real-world laboratory tests. For a very good discussion, see chapter 3 of Clifford Will’s lovely book, Was Einstein Right? Putting General Relativity to the Test.) Hence gravity — warped spacetime — affects the flow of time.

Thorne and his students realized that spacetime could be warped into arrangements far more strange than the trampoline-like dent caused by the Sun. For example, there could exist “wormholes:” shortcuts or tunnels that connect locations in space that otherwise seem far apart. (Thorne’s own mentor, John Wheeler, had begun the serious study of wormholes a few decades earlier.) Now suppose that an astronaut somehow corralled one mouth of a wormhole into her spaceship, while the other mouth remained at rest near the Earth. The astronaut could then fly her ship close to a massive object like a star. Near the spacetime-bending star, all clocks on her ship would tick more slowly than clocks on the Earth.

If the astronaut waited long enough, the clocks on her ship would fall considerably behind the clocks of her colleagues at Mission Control. After hanging out near the massive star for a while — perhaps kicking back and reading Thorne’s book —she could then fire up her ship’s rockets and gently cruise back toward her starting location, with one mouth of the wormhole in tow. As her ship neared the Earth, her clocks would tick at a similar same rate as those in Mission Control, but they would show an earlier time: they would be offset by the “time-shift” she had induced by sitting for so long in a region of strong spacetime curvature. By waiting sufficiently long near the massive star, the time-shift between the astronaut’s clocks and those at Mission Control could become arbitrarily long.

And now for the kicker: the mouths of the wormhole connect distant locations in space at the same moment in time. So while her colleagues in Mission Control looked on, the astronaut could step through the mouth of the wormhole that was in her ship, and land at her colleagues’ location at an earlier moment in time — the time that her clocks showed on her ship at the moment she stepped into the wormhole, rather than the (later) time that her colleagues’ clocks registered at the moment she took her fateful step. She would have completed a short-circuit through spacetime, traveling along what is known as a “closed time-like curve.”

Other schemes to travel backwards in time that do not involve wormholes have also been considered. They all have in common the fact that time as well as space can become warped, according to general relativity. For other models, see the popular book by Princeton physicist J. Richard Gott, Time Travel in Einstein’s Universe.

Does backwards-in-time travel stir up paradoxes? It certainly does. The standard, rather gruesome scenario involves traveling back in time to murder your own mother, thus destroying the chance that you would be born in the first place. Or, on a happier note, you could travel backward in time to adjust your investment portfolio just before the huge financial bust of 2008 that triggered the Great Recession — and then buy your mother a nice gift (rather than killing her off). Either way, backwards-in-time travel suggests all manner of concerns about self-consistency.

On the matter of causal paradoxes, the physics community has come up with a few ideas but no solid conclusions so far. Stephen Hawking, for one, has proposed — or, rather, expressed a hope — that closed time-like curves simply are not possible in nature, and that some as-yet unknown loophole should scuttle clever schemes like those described by Kip Thorne, Richard Gott, and others. Perhaps if one could understand gravitation at a quantum-mechanical level — which no one has succeeded in doing yet, despite nearly a century of hard effort — then scenarios based on Einstein’s classical picture of continuous spacetime would be amended in just such a way as to block time travel. Research on this front continues. In fact, while I was working on my response to this question, Scientific American ran an article about some of the latest work on this very topic.

In the meantime, perhaps the best response to the open paradoxes is to accept the challenge from physicist Matt Visser: “Read a few science fiction books.” That would bring us full circle, back to Kip Thorne’s reading of Carl Sagan’s Contact — a fitting end (or beginning) to the exercise.

Q: From Ryan M., Tampa, FL:

Dear Dr. Kaiser, On behalf of my 8th grade Honors Geometry students, I would like to ask: What shape is the universe?

A:

Dear Ryan and students,

Physicists describe the shape and evolution of the universe using Einstein’s elegant theory of gravity, the general theory of relativity. General relativity describes how space and time warp in the presence of matter and energy. When we think about the shape of the universe, therefore, we have to think hard about the distribution of matter and energy — where the stuff is — and how that stuff should affect the overall shape or geometry of spacetime.

When we consider parts of our universe across relatively short distances — such as across our solar system — we find that it is very lumpy, with dense clumps of matter in some locations, separated by large voids that are nearly empty. But when we zoom out to consider our universe across the largest distances, all those lumps and voids average out. That is, when we average across the largest cosmic distances, the universe is remarkably smooth, filled with an average density of stuff per unit volume. In fact, across these large distances, the actual density in any given location tends to deviate from the average density only by about one part in one hundred thousand. (The best evidence for this large-scale smoothness comes from observations of the cosmic microwave background radiation, a remnant glow emitted soon after the big bang.)

Almost a century ago, mathematical physicists such as Alexander Friedmann and Georges Lemaître found exact solutions to Einstein’s equations that describe universes in which matter and energy are distributed nearly evenly throughout space. Those solutions correspond to three basic shapes, depending on the density of stuff filling the universe. If a universe contains more stuff per unit volume than some critical value (“overdense”), then the universe would become positively curved: space would warp and curve back onto itself in a closed shape, like the surface of a sphere. The size of the sphere would change over time — it could begin very small, expand up to some maximum size, and then collapse back to a small size again — but at any given instant of time, the shape of the universe would be a closed space, with some finite maximum distance between any two points.

Here I should be a little careful with my wording. Ordinarily when someone says “surface of a sphere,” I tend to picture the surface of a ball. The surface, however, is two-dimensional: an ant living on the ball could uniquely identify any point on the spherical surface by specifying just two numbers, or coordinates, such as longitude and latitude — and kudos to that ant for being so good with numbers. But the universe in which we live has three dimensions of space, not just two: length, height, and depth. Hence the “surface of a sphere” to which I referred in the previous paragraph means a three-dimensional surface of a four-dimensional “hypersphere” in spacetime: an analog, with one extra dimension, of the usual surface of a basketball with which most of us are familiar.

In a positively curved space, geometry behaves differently than what we typically learn in middle school. For example, consider meridian lines, the lines that run north-south along the surface of a globe. All meridian lines cross the equator at right angles, and hence (along the equator) meridian lines are all parallel to each other. But meridians don’t remain parallel everywhere on the space: they converge and meet at both the North and South Poles. Likewise, you could construct a triangle on such a positively-curved space, connecting two meridian lines with the portion of the equator between them. Both meridians make right angles (90 degrees) with the equator, and there must be some non-zero angle between the meridian lines as they converge near the North Pole. Thus, the sum of the angles within the triangle would be more than 180 degrees. These are strange results: in ordinary (or Euclidean) geometry, lines that are parallel at one location remain parallel off to infinity, and the angles within a triangle always add up to exactly 180 degrees.

On the other hand, if the universe had less stuff per unit volume than the critical value — if it were “underdense” — then spacetime would become hyperbolic, like the surface of a saddle. The overall size of the saddle could change over time, but at each moment, the universe would have negative curvature: lines that were parallel to each other at one location would diverge, getting further and further apart from each other. The sum of angles within any given triangle would be less than 180 degrees. (Here again, the two-dimensional surface of the saddle is a helpful analogue, in one lower dimension, of a three-dimensional space of negative curvature.)

Only if the amount of stuff per volume were exactly balanced at the critical value would space have vanishing curvature — zero curvature is a kind of “Goldilocks” solution, in which the density of matter and energy in the universe is just right. In that case, parallel lines remain parallel; the interior angles within a triangle add to exactly 180 degrees; and all the other rules of ordinary geometry hold.

Physicists and astronomers have worked hard to measure the amount of stuff per volume, or cosmic density, in our own universe. The latest data from both the Planck and WMAP satellites, combined with other sensitive observations, reveal that our universe has precisely the critical density, to an accuracy of about one-tenth of one percent. That’s good news: all of your hard work in Honors Geometry class will pay off, and you will be able to use those results from ordinary (or Euclidean) geometry to describe the shape of our universe to extraordinary precision!

Q: From Alex L., San Mateo, CA:

If you get sucked into a wormhole, is it theoretically possible to get back out? If so, what would you use to escape?

A:

Dear Alex,

Luckily for would-be time travelers, wormholes are different than black holes. Both are regions of intense spacetime curvature. But in the case of a black hole, spacetime warps so much that even light cannot escape: the path of a light beam that began near the center of a black hole would be deflected all the way back into the black hole itself. As Kip Thorne describes beautifully in his book, Black Holes & Time Warps: Einstein’s Outrageous Legacy, black holes are surrounded by something called an “event horizon.” An event horizon acts a bit like a trapdoor: matter can fall in (toward the black hole), but can never pass back out.

Although wormholes are also structures that should induce intense warping and curvature of spacetime, the mouths of wormholes are not surrounded by event horizons. At least in principle, therefore, matter as well as light can exit a wormhole.

There is at least one challenge to crawling out of a wormhole, though: unless the surface of the wormhole is threaded by a strange, special sort of matter, then the mouths of a wormhole are predicted to close up and remain shut within a fraction of a second (crushing any would-be time travelers in the process). A wormhole filled with ordinary matter — of the sort that makes up atoms and molecules, and ultimately people, planets, and all that good stuff — would likely pinch off into two black hole-type formations almost immediately.

For a wormhole to remain traversable, it must be filled with what Thorne and his students simply called “exotic material.” Such hypothetical stuff is “exotic” because it needs to carry negative energy density. Ordinary matter, with which we are familiar, contains positive energy per unit volume. Toss some pebbles, and they will acquire positive kinetic energy (from their motion); bring the pebbles to rest, and they will still retain positive energy from their mass, as expressed in Einstein’s famous relation, E = mc2. Even massless forms of energy, such as light beams, carry strictly positive energy per unit volume. So finding some sort of material that carries negative energy density is no mean feat.

Nonetheless, physicists are familiar with some examples of such exotic stuff. For example, our universe appears to be filled with something we have dubbed “dark energy” — the name, which sounds mysterious, is simply a stand-in for the fact that we can observe the effects of this strange substance but don’t yet have any convincing ideas of what it is. Dark energy dominates the overall balance of matter and energy in our universe as a whole — indeed, dark energy is making our universe speed up in its rate of expansion — and it carries negative energy density. But unlike the “exotic material” required to keep a wormhole open, dark energy does not seem to clump. It remains (so far as we can tell) distributed perfectly smoothly throughout the entire universe. So it is unlikely that anyone could gather up a bunch of dark energy and stick a blob of it in a particular location, such as the mouth of a wormhole.

Before venturing into the mouth of a wormhole, therefore, it is advisable to study Matt Visser’s textbook, Lorentzian Wormholes: From Einstein to Hawking. Pay particular attention to Chapter 13, entitled “Engineering considerations!”

Q: From Bella S., Savannah, GA:

They say the universe is always expanding. But what lies beyond the end of the universe, the space it has not yet expanded into?

A:

Dear Bella,

Physicists and astronomers have indeed been able to determine that our universe is expanding, using a variety of types of measurements and observations. That means that if we were to consider any pairs of distant, astronomical objects — galaxies, or supernovae, or even strange, bright, ancient stellar objects called “quasars” — the distance between them grows over time. In fact, astronomers discovered compelling evidence about fifteen years ago that our universe is not just expanding, but accelerating in its expansion: it is getting bigger, at a faster and faster rate. We attribute this accelerated expansion to the effects of “dark energy.”

As seen from within our universe (where we happen to live, after all), such expansion would looks exactly as we observe. This would be true even if the universe were infinitely large, with no boundary or edge. Even in an infinite universe that was filled with the types of matter and energy that we know are filling our own universe, in other words, we would expect to see objects moving apart from each other over time, at a quickening rate. The space between (astronomical) objects stretches over time.

I inserted the word “astronomical” in that last sentence because the cosmic expansion applies over very long distances, such that gravity is the dominant or most relevant force. Atoms in our body are held together by electromagnetic forces, and on the typical sizes of atoms, those forces absolutely dwarf the strength of gravity — hence neither the atoms in our body, nor even planets like the Earth, are expanding apart from each other over time. But as we zoom out and consider the spaces between entire galaxies, we can measure the universal expansion.

So much for the view from inside our universe. Even though we are stuck here, we can imagine what things might look like from outside our universe — and we can use Einstein’s general relativity, combined with quantum theory, to try to reason about such a view. Given our present understanding of quantum theory and the behavior of matter like the Higgs particle, combined with what we know about general relativity, it is possible that our own universe is actually just one bubble or “island universe” within a much larger sea or “multiverse.”

I like to think about the multiverse as a huge bathtub, within which tiny soap bubbles (individual universes) occasionally form and grow. Inside one of those bubbles, an observer would see a huge — in fact, infinite — space that is stretching larger and larger over time. (The interiors of bubbles that form this way are spaces of negative curvature, like the horseback-riding saddle I mentioned above.) Yet from outside the bubble, looking from some other point within the “bathtub,” we would see a bubble of perfectly finite size. From outside, we would see the bubble get larger over time — we would see the walls of the bubble move outward at the speed of light — but at any finite time the volume would remain less than infinity.

This is a delicious example of how general relativity and warped spacetimes can play tricks with our intuitions. The coordinates that an observer would use inside the bubble-universe, which would best respect the symmetrical distribution of matter and energy within the bubble, would make the bubble appear to be infinite in extent, whereas an observer outside the bubble would see the walls of the finite-sized bubble expand into the neighboring, pre-existing, space of the bathtub-multiverse.

And what about the bathtub? There would also likely be a universal, accelerating expansion of the space within the bathtub as well: the distances between bubble-universes would stretch over time, faster and faster. (Do you see a pattern here?)

 

Many thanks to Prof. Kaiser and all who participated in the Hippo Reads Inaugural Ask Me Anything challenge.

Image credit: Sebastian Bergmann via flickr