Excerpted with permission from The Island of Knowledge: The Limits of Science and the Search for Meaning by Marcelo Gleiser. Available from Basic Books, a member of The Perseus Books Group. Copyright © 2014.
What goes on when you see something, say, this book you are reading? Leaving aside the whole business of how the brain processes visual information, let’s just focus on the information travel time. To make life simple, let’s also just consider the classical propagation of light, ignoring for now how atoms absorb and reemit light. Light is bouncing around the room because either the window is open or the lamp is on, or both. This bouncing light hits the surface of the book, and some of it is absorbed, while some is reflected outwards in different directions. The page and the ink used for printing absorb and emit light in different ways, and these differences are encoded in the reflected light. A fraction of this reflected light then travels from the book to your eyes, and thanks to the brain’s wondrous ability to decode sensorial information, you see the words on the book’s page.
It all looks instantaneous to you. You say, “I’m reading this word now.” In reality, you aren’t. Since light travels at a finite speed, it takes time for it to bounce from the book to your eye. When you see a word, you are seeing it as it looked some time in the past. To be precise, if you are holding the book at one foot from your eye, the light travel time from the book to your eye is about one nanosecond, or one billionth of a second. The same with every object you see or person you talk to. Take a look around. You may think that you are seeing all these objects at once, or “now,” even if they are at different distances from you. But you really aren’t, as light bouncing from each one of them will take a different time to catch your eye. The brain integrates the different sources of visual information, and since the differences in arrival time are much smaller than what your eyes can discern and your brain process, you don’t see a difference. The “present”—the sum total of the sensorial input we say is happening “now”—is nothing but a convincing illusion.
Even if nerve impulses propagate fast along nerve fibers, their traveling times are still much slower than the speed of light. Although there are variations for different types of nerves and for different people, the speed is around 60 feet per second. That is, nerve impulses travel about 1 foot in sixteen milliseconds. (A millisecond is one thousandth of a second.) For comparison, light travels 2,980 miles in the same amount of time, a little more than the driving distance from New York to San Diego.
Here is an imaginary experiment that illustrates the implication of these time differences. Imagine two lights programmed to flash simultaneously every second. One of the lights is fixed at 10 yards from an observer, and the other can be moved away on a straight rail. Imagine separating them by increasing distances as they flash together every second. An observer will start perceiving a difference in the flashing times when the distance between the two lights is larger than about 2,980 miles. Since we can’t see this far, our perception of the simultaneous now seems very credible for huge separations. An alternative, and more realistic, experiment could be set up to test this theory: have two lights flashing at slightly different times, and check when observers notice a difference. If my conjecture is correct, observers will start to notice differences when the timing interval is larger than about twenty milliseconds or so. This timescale sets the limit of visual simultaneity in humans.
The arguments above lead to a startling conclusion: the present exists because our brain blurs reality. To put it another way, a hypothetical brain endowed with ultrafast visual perception would catch the difference between the two flashing lights much earlier. For this brain, “now” would be a much narrower experience, distinctive from the human “now.” So in addition to Einstein’s relativity of simultaneity involving two or more moving observers, there is also a relativity of simultaneity at the cognitive level resulting from the subjective perception of simultaneity or “now” for the individual or, more generally, for every kind of brain or apparatus capable of detecting light.
Each one of us is an island of perception. Just as when we look out into the ocean and call the line where water and sky meet the horizon—a limit to how far we see—our perceptual horizons comprise all the phenomena that our brains compute as happening simultaneously even if they are not: the perceptual horizon delineates the boundary of our “sphere of now.” Since light is the fastest speed in Nature, that’s the one I’m using to define our sphere of now. (Had we used the speed of sound, of only 1,126 feet per second in dry air and at 68 degrees Fahrenheit, the sphere of now would have a much smaller radius. Two lightning strikes miles apart look simultaneous but wouldn’t sound simultaneous.)
To summarize: given that the speed of light is fast but finite, information from any object takes time to hit us, even if the time is tiny. We never see something as it is “now.” However, the brain takes time to process information and can’t distinguish (or time-order) two events that happen sufficiently close to one another. The fact that we see many things happening now is an illusion, a blurring of time perception. Since no brain is the same, every person will have their own limits of time perception and their own sphere of now. In fact, every brain, be it biological or mechanical (light-sensitive detecting device), has a different processing time and will have its own sphere of now; each one will have a distinctive perception of reality. From current neurocognitive experiments, it seems reasonable to suppose that on average a human’s time perception is on the order of tens of milliseconds. The distance light travels in this time interval is the approximate radius of an individual’s sphere of now—a few thousand miles.
“Now” is not only a cognitive illusion but also a mathematical trick, related to how we define space and time quantitatively. One way of seeing this is to recognize that the notion of “present,” as sandwiched between past and future, is simply a useful hoax. After all, if the present is a moment in time without duration, it can’t exist. What does exist is the recent memory of the immediate past and the expectation of the near future. We link past and future through the conceptual notion of a present, of “now.” But all that we have is the accumulated memory of the past—stored in biological or various recording devices—and the expectation of the future.
The notion of time is related to change, and the passage of time is simply a tool to track change. When we see something moving in space, we can follow how its position changes in time. Say it’s a ball; as the ball moves, it will describe a curve in space, an imagined sequence of points from initial position A to final position B. We can tell where the ball is between A and B by ordering its location sequentially in time: at zero it is leaving the soccer player’s foot—point A; at one second it is hitting the upper-left-hand corner of the goal—point B. The curve in between A and B links the position of the ball at the intermediate times between zero and one second. A ball, however, never occupies a single point in space, and time can never be measured with infinite precision. (The most accurate locks use electronic transitions in atoms to achieve a precision of about one billionth of a second per day.) Mathematically, though, we brush all this aside and compute how the position of the ball changes in time instantaneously: for every moment of time we claim to know its position. Clearly, this is only an approximation, albeit a very good one.
We represent the flow of time continuously so that each instant of time has a (real) number attached to it. In our example of the soccer ball, time will cover the number line from zero to one. How many instants of time are there between zero and one second? Mathematically, there is an infinite number of them, since there are infinite numbers between zero and one. (You can keep subdividing intervals into smaller and smaller bits: a tenth of a second, a hundredth of a second, a thousandth of a second, and so on.) But even the most accurate clocks have limited precision. We may represent time continuously, but we measure it in discrete chunks. As a consequence, the notion of “now,” a time interval of zero duration, is only a mathematical convenience having nothing to do with the reality of how we measure time, let alone perceive it. I will have more to say about this and what it means about our notion of reality when we get to quantum physics, where nothing is ever continuous.