Tag: reality

The speed of light, we know, is the universe’s speed limit. Nothing can move faster than that through space.

Are we missing the point? Maybe it’s not so much that that’s the top speed through space; maybe that’s the only speed through spacetime, and everything is moving at it — you, me, light, trains, turtles, mountains, everything, always. “Slower” things are moving at the speed of light more in the time direction of spacetime than in the space direction. “Faster” things are moving at the speed of light more in the space direction of spacetime than in the time direction. What we call “acceleration” is (I speculate) nothing other than changing the direction of your constant motion, more timeward or more spaceward. Non-spaceward motion (i.e., standing still) is what we experience as the ordinary passage of time.

If this is anything like right, then it supplies an intuitive foundation for thinking about all kinds of weird mysteries: why the speed of light is a constant in all reference frames (the paradox that got Einstein thinking about relativity in the first place); what’s special about acceleration; and time dilation and the physical basis of the Lorentz transformation.

Every now and then, however, I get a flash of insight that seems to put the nature of reality just nearly within my grasp. The feeling is brief and tantalizing, like trying to recall the details of a dream as they evaporate on waking. But it’s thrilling.

My latest one came while pondering the odd fact that there is no discernible difference between gravity and the acceleration due to motion.

When you’re sitting in a parked car, there is a force pressing your butt down into the seat. That’s gravity acting on your mass. (I’ll refrain from making comments about the mass of your butt.) When you peel out of that parking space and go from zero to sixty in 6.2 seconds, there is another force pressing your back against the seat. That’s acceleration. Science says that if you didn’t already know which force was acting on you, and the only clue you had was how it felt (not how it looks out the window, not the roar of the engine, not that you remember the Earth being beneath your feet when you got into the car, etc.), you couldn’t tell whether you were sitting still in a gravity field or accelerating through space, or some combination of both.

This turns out to be useful for sending humans on long interplanetary journeys in the future. If we invent a propulsion system that can sustain enough power continuously, then the spaceship can accelerate at 1g halfway to its destination, then turn around and decelerate (which is just accelerating in the other direction) at 1g the rest of the way. The humans on board will avoid the many health hazards of prolonged weightlessness; they’ll experience “gravity” holding them to the spaceship’s floors.

But what accounts for the fact that gravity and acceleration are the same thing? When you’re accelerating, your velocity is changing from moment to moment. And your velocity is nothing more than a measure of how your position changes from moment to moment. If your velocity is constant, you experience no acceleration. That is, you can be changing your position, but as long as it changes at a steady rate, you’re not accelerating. On the other hand, as soon as there is a change in the rate at which your position changes, the force due to acceleration appears.

• Velocity: rate of change of position
• Acceleration: rate of change of velocity

You can have lots of velocity and still have zero acceleration. If you plot your position over time on a graph, anything that’s a straight line means your velocity is constant and you’re not accelerating. To get acceleration, the graph needs to curve. (Any curve will do, but if the acceleration happens to be constant, then the curve is a parabola.)

Unchanging velocity; no acceleration, no force.

Velocity changing at a constant rate; produces a parabolic curve and a steady force.

When you’re standing still on the ground and experiencing the pull of the Earth’s gravity, what’s changing to make that feel like acceleration? Not your position (with respect to the Earth). Not the rate of change of your position. But time is passing, and thanks to Dr. Einstein we know that space and time are mysteriously bundled together into something called spacetime. So even if you’re not moving through space, you’re always moving through spacetime.

But as I pointed out above, it’s not enough to be moving to experience acceleration. The rate at which you’re moving must itself be changing. When you’re standing still on the Earth, you’re moving through spacetime, yes; but the rate at which you’re moving through spacetime stays the same. So again: what’s changing that can give rise to a force like acceleration?

Standing still in space…

…is still moving through spacetime.

Well, hang on. We know (also from Einstein) that the presence of a large mass like the Earth causes spacetime to curve — whatever that means. So maybe it’s wrong to draw our spacetime axis as a straight line.

Suppose spacetime happens to curve just like this:

Standing still in curved spacetime.

Straightening the axis again forces the plot into a curve. (In fact, in this [manufactured] case it forces it into the shape of our old friend the parabola.)

Standing still in curved spacetime.

So. I’ve managed to convince myself that just standing still in a region of curved spacetime can look exactly like accelerating in a region of flat spacetime. Spacetime itself remains a difficult idea to internalize, to say nothing of it being curved, and even if I’ve managed to make one graph look like another in a hand-wavy way, still none of it makes any intuitive sense.

But I observe that moving at a constant velocity requires no energy. You need energy to change your velocity — i.e., to accelerate. And you need mass to curve spacetime. And as we know (thank you once again, Dr. Einstein), energy and mass are the same. Somehow it’s all down to the interactions between space, time, and energy. But what are they?

See what I mean? I can almost feel what real understanding would be like. It’s maddening.

[Update: followup thoughts added here.]

It’s as if I decided to write an elaborate computer program to simulate a universe, complete with its own laws of nature and its own intelligent life. In time those beings might figure out all the rules of their universe, but what chance would they ever have of guessing what I’m like, or the nature of the computing hardware in which they are abstractions? The copper and silicon and tiny electrical charges of which they’re really composed would appear nowhere at all inside the simulation. The rules by which their universe operates would bear no resemblance to the rules of the programming language in which I expressed them.

Nevertheless, physicists (human ones) are making attempts at guessing at the nature of the computing hardware in which our reality is an abstraction (if we can agree to think about it that way for now). One of the more well-known guesses is a very complicated idea called string theory. Famously it declares that our universe is not merely three-dimensional, it’s actually ten-dimensional. The hell?

To understand what ten-dimensional space can possibly mean, and how it jibes with the universe-is-just-a-computer-program metaphor, let’s first make sure we understand three-dimensional space.

What does it mean to say that space is three-dimensional? Put simply, it means that three numbers are necessary to identify your location — for example, latitude, longitude, and altitude. Two numbers won’t do it.

It also means that three numbers are sufficient to identify your location (if you choose the right three). You don’t need more. You could tell someone, “I’m at the corner of 34th Street and 5th Avenue on the 57th floor where the ZIP code is 10118 and there are 28 days left before my next birthday,” but some of those numbers will be redundant and/or irrelevant for locating purposes.

Finally, the three numbers that are necessary and sufficient for locating you are also independent of each other. You can change your latitude without changing your altitude. You can change your longitude without changing your latitude. You can change your altitude without changing your latitude or your longitude. (For that you probably need a helicopter. Or to be plummeting out of the sky.) Of course you can also change the numbers together in any combination — e.g., changing both your latitude and longitude at the same time by going northwest instead of due north or due west. You can, but the point is that you don’t have to.

Back to ten-dimensional space. If our space is really ten-dimensional, like string theorists say it is, wouldn’t that mean that three numbers don’t suffice to describe our position? Well, yes, it would; we’d need ten numbers. But this contradicts our everyday experience, which tells us that three numbers really do suffice.

String theorists counter this by saying that seven of the ten dimensions are really really small. The hell? Small dimensions? Isn’t a dimension the same as a direction? (E.g., north/south; east/west; up/down.) How can a direction be small?

To understand what a small dimension is, let’s switch to computer programming for a moment. A big part of programming is modeling objects, which means representing something in terms of numbers and other kinds of digital data. Suppose, for instance, that I’m writing a weather-predicting program and that among the things I need to model is a cloud. What are the essential properties of a cloud that my program would have to model?

• Its height above the ground;
• Its latitude and longitude;
• Its volume (how big it is);
• Its moisture content (thin and wispy, or dense and puffy?);
• Its temperature;
• Its electrical charge (for predicting lightning);
• Size change: currently growing, shrinking, or stable.

(Disclaimer: I’m no meteorologist, I don’t really know how you’d model a cloud in software, but this looks good for our purposes.)

A cloud’s latitude and longitude can vary enormously — the cloud can be situated over any point on earth! But its height above the ground can range only from 0 to a few miles. And its “size change” property can contain only one of three values. If you think of each of these properties as a dimension, then it’s easy to see how latitude and longitude are “big” dimensions, height is smaller, and “size change” is really tiny.

What? You can’t think of those properties as dimensions? Why not? Each one is arguably necessary for describing the cloud; collectively they are sufficient for describing the cloud (let’s assume); and each property is independent of the others, able to vary on its own. As we agreed earlier, those are the requirements for calling something a dimension. So by that definition, this cloud is eight-dimensional.

Even so, if you omitted the smaller dimensions — the ones that can’t vary much, such as “size change” and “temperature,” say — you’d still know a lot about the cloud. You’d have a six-dimensional approximation to what’s really an eight-dimensional object. Most of what you usually need to know about a cloud can be discerned from that approximation — where the cloud is, roughly what it looks like, and so on. There are some things that would be harder to predict about it, such as whether it will rain on you and whether flying through it will cause ice to form on your wings. A fuller description of the cloud would make those things clearer. But you can still do a lot with just six of those eight dimensions.

That’s my analogy to ten-dimensional space, where seven of the dimensions are really small. The three big dimensions are enough to describe everything in our ordinary experience, but there are details of reality that only become clear when you add in the others. (That’s assuming that space is ten-dimensional — string theory is just an unproven hypothesis, after all, and other competing theories have other things to say about the number of dimensions we inhabit.)

If string theory’s right, and if our universe really is running as a simulation inside some sort of computer — two enormous “ifs” — then the cosmic computer programmer who invented our universe found it necessary to use ten numbers to model the position of each fundamental particle. That ten-dimensional machinery gives rise to what we perceive as three-dimensional reality. That’s not such a strange thought, after all. Haven’t you ever used three-dimensional machinery to create a two-dimensional reality?