More on this book
Community
Kindle Notes & Highlights
General relativity is perfectly time-symmetric; for every specific spacetime that solves Einstein’s equation, there is another solution that is identical except that the direction of time is reversed. A black hole is a particular solution to Einstein’s equation, but there are equivalent solutions that run the other way: white holes.
Black holes turn out to provide the strongest connection we have between gravitation and entropy—the two crucial ingredients in an ultimate explanation of the arrow of time.
6
LOOPING THROUGH TIME
Traveling to the future is easy, and getting there more quickly is just a technology problem, not something that conflicts with the fundamental laws of physics.
CHEATING SPACETIME
In a Newtonian universe, traveling backward in time is simply out of the question. World lines extend through a spacetime that is uniquely divided into three-dimensional moments of equal time, and the one unbreakable rule is that they must never double back and return to the past. In special relativity, things aren’t much better. Defining “moments of equal time” across the universe is highly arbitrary, but at every event we are faced with the restrictions enforced by light cones. If we are made of ordinary stuff, confined to move from each event forward into the interior of its light cone,
...more
CIRCLES IN TIME
Such a world line—always moving forward in time from a local perspective, but managing to intersect itself in the past—is a closed timelike curve, or CTC. That’s what we really mean when we talk about a “time machine” in general relativity.
Spacetime is not stuck there once and for all, but can change (and even come into or pop out of existence) in response to the effects of matter and energy.
THE GATE INTO YESTERDAY
ONE SIMPLE RULE
Paradoxes do not happen.
At the moment, scientists don’t really know enough about the laws of physics to say whether they permit the existence of macroscopic closed timelike curves.
The more interesting question is, do closed timelike curves necessarily lead to paradoxes? If they do, then they can’t exist, simple as that.
Consistent stories happen; inconsistent ones do not.
ENTROPY AND TIME MACHINES
Our concept of free will is intimately related to the idea that the past may be set in stone, but the future is up for grabs.
So either closed timelike curves can’t exist, or big macroscopic things can’t travel on truly closed paths through spacetime—or everything we think we know about thermodynamics is wrong.
PREDICTIONS AND WHIMSY
Some of our understanding of time is based on logic and the known laws of physics, but some of it is based purely on convenience and reasonable-sounding assumptions. We think that the ability to uniquely determine the future from knowledge of our present state is important, but the real world might end up having other ideas.
If closed timelike curves could exist, we would have a definitive answer to the debate between eternalism and presentism: The eternalist block universe would win hands down, for the straightforward reason that the universe can’t be nicely divided into a series of “presents” if there are closed timelike curves lurking around.
The ultimate answer to the puzzles raised by closed timelike curves is probably that they sim...
This highlight has been truncated due to consecutive passage length restrictions.
FLATLAND
The real question is, can we make closed timelike curves in a local region of spacetime?
STUDYING TIME MACHINES IN FLATLAND (AND IN CAMBRIDGE)
right. But it was very clear that general relativity was trying to tell us something: It doesn’t like closed timelike curves. You can try to make them, but something always seems to go wrong.
WORMHOLES
TIME MACHINE CONSTRUCTION MADE EASY
PROTECTION AGAINST TIME MACHINES
But even if you were lucky enough to stumble across a wormhole, you’d be faced with the problem of keeping it open. Indeed, this difficulty is recognized as the single biggest obstacle to the plausibility of the wormhole time machine idea.
The problem is that keeping a wormhole open requires negative energies.
Do negative energies exist in Nature? Probably not, at least not in the ways necessary to sustain a macroscopic wormhole—but we can’t say for sure.
As if that weren’t enough to worry about, even if we found a wormhole and knew a way to keep it open, chances are that it would be unstable—the slightest disturbance would send it collapsing into a black hole.
Nature, it seems, tries very hard to stop us from building a time machine. The accumulated circumstantial evidence prompted Stephen Hawking to propose what he calls the “Chronology Protection Conjecture”: The laws of physics (whatever they may be) prohibit the creation of closed timelike curves.
The arrow of time, on the other hand, is indisputably a feature of the real world, and the problems it presents demand an explanation. The two phenomena are related; there can be a consistent arrow of time throughout the observable universe only because there are no closed timelike curves, and many of the disconcerting properties of closed timelike curves arise from their incompatibility with the arrow of time.
PART THREE
ENTROPY AND TIME’S ARROW
7
RUNNING TIME BACKWARD
CHECKERBOARD WORLD
All we’ve done is describe what real scientists do to understand nature, albeit in a highly idealized context. In the case of physics, a good theory has three ingredients: a specification of the stuff that makes up the universe, the arena through which the stuff is distributed, and a set of rules that the stuff obeys.
FLIPPING TIME UPSIDE DOWN
As we’ve discussed, the real world is also invariant under time shifts; the laws of physics don’t seem to be changing as time passes.
The idea behind time reversal is relatively straightforward—just make time run backward. If the result “looks the same”—that is, looks like it’s obeying the same laws of physics as the original setup—then we say that the rules are time-reversal invariant.
THROUGH THE LOOKING GLASS
It is often the case that a certain theory of physics would not be invariant under “naïve time reversal,” which reverses the direction of time but does nothing else, and yet the theory is invariant under an appropriately generalized symmetry transformation that reverses the direction of time and also does some other things.
THE STATE-OF-THE-SYSTEM ADDRESS
The theories that physicists often use to describe the real world share the underlying framework of a “state” that “evolves with time.”
In different approaches to real-world physics, what counts as a “state” will be different. But in each case we can ask an analogous set of questions about time reversal and other possible symmetries.
