I'm not just talking about digital watches, mp3 players, CD's, DVDs, Blu-Ray, and the internet; I'm talking about all the way down at the most fundamental level of reality, we live in a digital universe. That idea has some very interesting implications for us in a number of ways, but before we explore those ideas, let's make sure we all know what we're talking about first.
What does "digital" mean? Merriam Webster says:
1: of or relating to the fingers or toes (digital dexterity)
2: done with a finger (a digital rectal examination) (Eeeww.)
3: of, relating to, or using calculation by numerical methods or by discrete units
4: of, relating to, or being data in the form of especially binary digits (digital images) (a digital readout) ; especially : of, relating to, or employing digital communications signals (a digital broadcast) compare analog 2
5: providing a readout in numerical digits (a digital voltmeter)
6: relating to an audio recording method in which sound waves are represented digitally (as on magnetic tape) so that in the recording wow and flutter are eliminated and background noise is reduced
7: electronic (digital devices) ; also : characterized by electronic and especially computerized technology
We're going to go with definition 4 for right now because it comes closest to the physics definition. To help our understanding, let's follow the reference it gives and look up the second definition of "analog."
2 a: of, relating to, or being a mechanism in which data is represented by continuously variable physical quantities
So, what does that mean to you and me? Well, let's look at this picture.
Here we have two numbered lines. The bottom one is a digital line going from 1 to 10. Each digit stands alone, and there is nothing in between them. In a digital world, there is no 1.5, only 1 or 2. The top line is analog. You have an infinite number of points between 1 and 2, and between 2 and 3 and so on. Instead of only having ten choices of positions, you have an infinite number of choices. The analog number line is much more powerful than the digital because of its infinite variability.
Let's look at another example, a sine wave. Here again, you see a smoothly varying line with an infinite number of possible points all along the signal. Compare that to the digitized sine wave seen in the next picture.
The gray boxes are a digital representation of the smoothly curving sine wave, and you can see that the discrete nature of the digital representation creates a very jagged wave form. It simply cannot carry the same amount of information that an analog signal can.
For example, we've all heard YouTube videos where it sounds like the microphone is under a raging surf. That roaring echoing noise is the result of digitizing the original audio. Each of those jagged steps in the digital sine wave introduce distortion.
So how does a CD sound so good, if digital introduces so much distortion? Well, let's take a look back at our digital sine wave. The accuracy of our sine wave is directly related to the size of the blocks we use to build it. Bigger blocks, as shown in this drawing will result in a less accurate reproduction of the sine wave. On the other hand, if we make our blocks smaller, we get a much better reproduction of the original wave, as seen in the earlier example. So, when a CD is made, the blocks used to build the sine wave are very small, resulting in a sound that is nearly indistinguishable from the original.
And that begs the question, if we have to work so hard to get our digital signal to equal the original analog in quality, why bother? Stick with the analog. As it turns out, there are some significant advantages to digitizing information like music. Editing and noise reduction become much easier and more effective, and controlling playback quality becomes a snap. The fidelity of the playback is always identical to the recording, a feat no analog system can match.
It turns out that as we look into things, our world is made up of analog systems. Sound is analog. Electromagnetic radiation is analog. Light is analog (sort of, sometimes, but we'll get to that another time.) And that makes sense because as you look around, the world is a continuous place. There are no real gaps between here and there, or between 1:00 and 2:00, or between freezing and boiling temperatures. Everything follows a continuously varying path.
But I started out by saying we live in a digital universe, and that doesn't make sense with what I just said, does it? The truth of the matter is that just as a CD is a digital representation of an analog signal, i.e. music, sounding to our ears nearly identical to the analog original but missing tons of information, our universe may be a digital representation of some far greater reality, looking real to our limited senses but missing tons of information.
What makes me say this? Actually, I'm not the one saying it. Max Planck, Neils Bohr, Albert Einstein, Werner Heisenberg, and others said it first, they just said it in mathematics, not English. Let's start with quantum mechanics and then we'll dig into the really tricky stuff. (How's that for a scary sentence?)
Keeping things very simple, a mathematician named Max Planck noticed that he could predict the energy of a photon by an equation that related its frequency to a constant. This constant had no real physical reason to exist, except that it made the equations work. The fact that it did so told physicists that energy was not transmitted smoothly and in an infinitely variable way, but was broken up into discrete bundles or packets that they called quanta.
Does that sound familiar to anyone?
Boiled down to its simplest form, quantum mechanics says that energy is not an analog system, but a digital one. Now that doesn't surprise most of us because we have heard this before in high school or college, particularly when we're talking about light particles, AKA photons. But it did surprise the crap out of the physicists who had no idea why energy should be quantized. All they knew was that it worked when they used it, so they set out to figure out why it worked.
Along the way, a guy named Werner Heisenberg made another interesting discovery. He found out that when you get down to things that are smaller than the constant Plank discovered, you could no longer know their position and momentum. Going further, he discovered that it had nothing to do with an inability to measure such small quantities, or an inability to measure one without affecting the other, but that it was a property inherent in sub atomic particles. If their position was known, their momentum was mathematically undefined.
This was called the uncertainty principle, and the fact that it centered round Planck's Constant was no coincidence.
A few years earlier, Einstein had released his theories of relativity, and he realized that there were some fundamental incompatibilities between his theories of the super big and fast and quantum mechanics descriptions of the super small. He was unable to reconcile those incompatibilities, partly because he spent so much time trying to refute quantum mechanics because the implications were so strange. A couple of decades later, some bright boys came up with a startling idea that shows promise in reconciling the quantum world with the relativistic world.
In a way, their idea is derived from the quantum, Again, very simply, the theorized that the reason that energy wwas quantized, and why the Heisenberg uncertainty existed, and that they were all tied to Plank's Constant was that Plank's Constant was actually the smallest anything could be, or put another way, not only is energy quantized, but space is as well. We're used to thinking of moving through space in a smooth, continuous manner, but at the subatomic level, string theory says that, just like our earliest example of ten numbers with no line, we are actually moving from place to place without traveling through the distance between.
OK, that went too far too fast. Let's take it a bit slower. If space is quantized, as string theory suggests, and if we put 0 and Plank's Constant (h) on a number line, it would look like the bottom line in our first drawing. There would be no line between them. And there would be no line between 1h and 2(h). We're back in familiar territory now, aren't we? Because if string theory is correct, then our universe, at its most fundamental level, is not analog at all, but digital.
So, besides being a neat thing to think about, what does this all mean for you and me? Maybe nothing. Maybe a digital universe really is the ultimate answer. But I can't help thinking about all the information we lose when we take an analog signal and digitize it. I can't help but wonder what we're missing in our digital universe that might be present in the analog original, if it exists. I can't help but think that maybe, just maybe, I have some small understanding of Genesis 1:6-7.
Gen 1:6 And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.
Gen 1:7 And God made the firmament, and divided the waters which [were] under the firmament from the waters which [were] above the firmament: and it was so.
Was God creating a digital copy of the real universe, and preparing it for us? Is the firmament, which God called heaven, the analog original?
I don't know, and science will never answer that particular question.
But it is intriguing.