It’s been more than three weeks since I graced the internet with a post on this blog. That could be the longest time I’ve ever stayed away. The relatively encouraging results of last month’s election may have left me with the feeling that I should leave well enough alone. Plus, the urge to share thoughts — mine or somebody else’s — can come and go.
But to get going: There’s something that bothers me about time travel. When a fictional character travels through time, they always land standing up or sitting down in a relatively comfortable location. Arnold, for example, landed in an alley, naked, the first time we saw him. Time travelers never end up a mile deep in the earth’s crust or a million miles out in space.
One problem here is that the surface of the earth in the distant past or future is nowhere near wherever the time machine is. The earth, not a perfect sphere, is revolving on its axis and revolving around the sun; the sun and the rest of the solar system is going around the galaxy; the galaxy is moving quickly away from other galaxies as the universe expands. That means calculating the location of the traveler’s destination in space, not just in time, must be quite a challenge. A tiny mistake and Arnold lands six feet under or in the wrong solar system. Naked.
This detail concerning time travel came to mind because I’ve been skimming a TV series that makes use of time travel (in a surprising way) and because I read something that actually seems worth sharing.
Sean Carroll, famous physicist and now the Homewood Professor of Natural Philosophy at Johns Hopkins, has a new book out called The Biggest Ideas in the Universe: Space, Time and Motion. It’s the first volume in a planned trilogy that is supposed to make the fundamental equations of physics understandable to those of us who got through high school math (which may be a problem for me, since trigonometry convinced me to avoid calculus).
… In relativity, it’s no longer true that space and time have separate, objective meanings. What really exists is space-time, and slicing it up into space and time is merely a useful human convention.
One of the major reasons why relativity has a reputation for being difficult to understand is that our intuitions train us to think of space and time as separate things. We experience objects as having extent in “space,” and that seems like a pretty objective fact. Ultimately it suffices for us because we generally travel through space at velocities far lower than the speed of light, so pre-relativistic physics works.
But this mismatch between intuition and theory makes the leap to a space-time perspective somewhat intimidating. What’s worse, presentations of relativity often take a bottom-up approach — they start with our everyday conceptions of space and time and alter them in the new context of relativity.
We’re going to be a little different. Our route into special relativity might be thought of as top-down, taking the idea of a unified space-time seriously from the get-go and seeing what that implies. We’ll have to stretch our brains a bit, but the result will be a much deeper understanding of the relativistic perspective on our universe….
Einstein’s contribution in 1905 was to point out that [to] better understand the laws of physics … all we had to do was accept a completely new conception of space and time. (OK, that’s a lot, but it turned out to be totally worth it.)
Einstein’s theory came to be known as the special theory of relativity, or simply special relativity. [Einstein] argued for new ways of thinking about length and duration. He explained the special role of the speed of light by positing that there is an absolute speed limit in the universe — a speed at which light just happens to travel when moving through empty space — and that everyone would measure that speed to be the same, no matter how they were moving. To make that work out, he had to alter our conventional notions of time and space.
But he didn’t go quite so far as to advocate joining space and time into a single unified space-time. That step was left to his former university professor, Hermann Minkowski…. Once you have the idea of thinking of space-time as a unified four-dimensional continuum, you can start asking questions about its shape. Is space-time flat or curved, static or dynamic, finite or infinite? Minkowski space-time is flat, static and infinite.
Einstein worked for a decade to understand how the force of gravity could be incorporated into his theory. His eventual breakthrough was to realize that space-time could be dynamic and curved, and that the effects of that curvature are what you and I experience as “gravity”. The fruits of this inspiration are what we now call general relativity.
So special relativity is the theory of a fixed, flat space-time, without gravity; general relativity is the theory of dynamic, curved space-time, in which curvature gives rise to gravity….
We should be willing to let go of our pre-relativity fondness for the separateness of space and time, and allow them to dissolve into the unified arena of space-time. The best way to get there is to think even more carefully about what we mean by “time”. And the best way to do that is to hark back, once again, to how we think about space.
Consider two locations in space, such as your home and your favorite restaurant. What is the distance between them?
Well, that depends… There is the distance “as the crow flies”, if we could imagine taking a perfectly straight-line path between the two points. But there is also the distance you would travel on a real-world journey … avoiding buildings and other obstacles along the way. The route you take is always going to be longer than the distance as the crow flies, since a straight line is the shortest distance between two points.
Now consider two events in space-time. In the technical jargon of relativity theory, an “event” is just a single point in the universe, specified by locations in both space and time. One event, call it A, might be “at home at 6 p.m.” and event B might be “at the restaurant at 7 p.m.”
… We can ask ourselves, just as we did for the spatial distance between home and restaurant, how much time elapses between these two events…. If one event is at 6 p.m. and the other is at 7 p.m., there is one hour between them, right?
Not so fast, says Einstein. In an antiquated, Newtonian conception of the world, sure. Time is absolute and universal, and if the time between two events is one hour, that’s all there is to be said.
Relativity tells a different story. Now there are two distinct notions of what is meant by “time”. One notion of time is as a coordinate on space-time. Space-time is a four-dimensional continuum, and if we want to specify locations within it, it’s convenient to attach a number called “the time” to every point within it. That’s generally what we have in mind when we think of “6 p.m.” and “7 p.m.” Those are … labels that help us locate events….
But, says relativity, just as the distance as the crow flies is generally different from the distance you actually travel between two points in space, the duration of time you experience [on the journey between A and B] generally won’t be the same as the [one-hour difference between the universal coordinate times, A and B]. You experience an amount of time that can be measured by a clock that you carry with you on the journey. This is the proper time along the path. And the duration measured by a clock, just like the distance traveled as measured by the odometer on your car, will depend on the path you take.
That’s one aspect of what it means to say that “time is relative”. We can think both about a common time in terms of a [space-time coordinate] and about a personal time that we individually experience [or measure] along our path. And time is like space — those two notions need not coincide.
By a “straight path” in space-time, we mean both a straight line in space and a constant velocity of travel … with no acceleration. Fix two events in space-time — two locations in space and corresponding moments in time. A traveler could make the journey between them in a straight line at constant velocity … or they could zip back and forth. The back-and-forth route will always involve more spatial distance, but less proper time elapsed, than the straight version [i.e. a clock along for the ride will run more slowly on the back-and-forth route — really?].
Why is it like that? Because physics says so. Or, if you prefer, because that’s the way the universe is. Maybe we will eventually uncover some deeper reason why it had to be this way, but in our current state of knowledge it’s one of the bedrock assumptions upon which we build physics, not a conclusion we derive from deeper principles. Straight lines in space are the shortest possible distance; straight paths in space-time are the longest possible time. It might seem counterintuitive that paths of greater distance take less proper time. That’s OK. If it were intuitive, you wouldn’t have needed to be Einstein to come up with the idea.