Not A Blog™

E=mc²

Einstein’s famous equation derived from his theory of special relativity has become so common and well known that it’s almost cliche. It is a consequence of special relativity being the way it is, namely the fact that all observers, regardless of their position and speed, will measure the speed of light as being the same velocity. This sets the speed limit of the physical world to c, the speed of light.

The equation specifies that matter and energy have an equivelence. In other words, what we actually measure when we measure mass is the object’s energy content. Mass is equivelent to energy proportionately based on c², which is a conversion factor between the units of energy (joules, or kg(m²/s²)) and mass, which is just kg of course, and the speed of light, which is, obviously, m/s.

With that in mind, I’d like to suggest an equivelence of a different sort. There is an equivelence between matter and information. In turn, this suggests an equivelence between information and energy. Unfortunately, it doesn’t follow in a nice proportional way, as the idea of information is not any sort of fundemental quantity. In fact, the amount of information we can pack into a space is growing smaller nearly every day so this number varies.

Two things sparked this line of thinking for me: the announcement by someone-or-the-other Futurist who said that we’ll have sugar-cube sized devices in twenty years that will be able to store HD video and audio of a person’s entire life. I’m not even going to touch that one. Suffice it to say that this’ll be a boon to the independent film industry, seeing as how college kids of the future won’t have to spend their last ten dollars on a DV tape so they can shoot their next project. The second thing is the idea that, in theory, one could predict the future if they had all the information about the past.

Astute readers have justed yelled “Uncertainty Principle!” in my ear. Yes, I’m getting to that. The uncertainty principal says that it’s impossible to know both the speed and position of any given subatomic particle for any given moment in time, because measuring one changes the other. However, even in light of this (and even more nebulous happenings with quantum physics), it would still seem possible to predict, on a macro scale, some happenings. After all, we can calculate the orbits of planets hundreds of years into the future and past, uncertainty notwithstanding.

Besides, it’s an interesting thought experiment to ignore the uncertainty principle for a second. Let’s suppose that we’re given all the information about the universe in the past and we have a supercomputer that can crunch the numbers and extrapolate things into the future. You’d have to agree that then, it would, theoretically, be possible to compute the future, right?

Wrong.

Here’s why. Even if we invoke our Heisenberg Compensators and get all the information possible about the past, we would still be unable to predict the future, for two reasons.

1. We can assume that the only way to 100% accurately predict everything about the universe, we’d have to know 100% of the information in the universe. The problem is that our computer and storage device that’s supposed to compute this information contains some of the information we need to know. So then we need to store information about that information, but then we need the information about that new storage device, too! We end up with an infinite regress. We can’t know all the information about the universe because this would entail us knowing the information about all the information—and then all the information about that, and so on. In essence, it’s a physical manifestation of Gödel’s Incompleteness Theorem. This is sufficient from ever being able to know all the information about the universe, however…

2. I don’t know that I’ve heard this postulated anywhere else, but I’m going to bet that someone else must have thought of this. I’m not going to take credit for it. I don’t know if I have any proof that this is true, but it is. The universe is the smallest presentation you can have of all the information in the universe. By extention, an atom is the smallest thing that can encode all the data about itself. In other words: Any time you attempt to store data about the universe, it must always take up more space than the thing itself that is the originator of that information. Generally speaking, the information will be incomplete, also. But induce the Heisenberg Compensators again. Even when you know (can record) all the information about an atom, the resulting information will always take up more space than the atom itself. All of this means that we could never know all the information about the universe (and, in turn, compute the future), because this information would take up more space than the universe itself.

Furthermore, Gödel’s Incompleteness Theorem applies here, too—so even if we started to record all the information about the universe, that would contain information that we’d have to record, too—which would contain information, etc, etc, and so on to infinity. It can’t be done.

Another way of looking at this is to realize that it takes matter to encode information. In this way, matter and energy and information share an equivelence as I mentioned at the beginning. When we determine the least amount of matter necessary to store information, then we can also calculate how much energy that information holds, via the matter that encodes it. Like I said, it’s not a proportionate ratio—at least not until we start encoding matter at the smallest size possible.

Because of this, any time we introduce information into a system, we change it. This realization isn’t really anything new. One problem with quantum physics seems to be that it requires an observer to actually do anything. Otherwise, it’s nothing more than moving probabilities around, but nothing can ever be said to actually happen. When you finally observe the event, then you see it being one way or the other, and the probability collapses to a point of happening. Quantum physics requires an observer, but observing the experiment “changes” it.

There is debate as to what “collapsing a probability waveform” actually means. Some say it’s a mathematical construct only; it’s just the way we “see” the quantum world. Others say that it corresponds to a very real event, specifically the observation of the result. I agree with the second hypothesis in that it corresponds to a real event, but in light of the previous information, I don’t think it is the observer that makes the difference.

The quantum physics probability waveform collapses when information is recorded. This serves to disturb the quantum state, which then becomes an absolute. The interesting consequence about this wholly unsubstantiated claim (which could be wrong) is that, since information is recorded in matter—any quantum interaction with matter records information, and therefore collapses the waveform. That’s what matter is: it’s the interaction of quantum particles. Matter itself is evidence of a collapsed quantum waveform because information has been encoded there.

It appears to fit the experiments that have been done so far. My favorite is the double-slit experiment. Really quick: everyone knows that if you shine light through two slits, you get a stripped pattern. That’s because light is a wave. But light is also a particle, because you can break it down to a single piece known as the photon. We have the ability to generate single photons. When we do this, and fire them at just one of the two slits in a double-slit setup, we find that the resulting photons (fired one at a time, a few seconds apart) build up a pattern exactly like what we should see if we were flooding the area with light. However, if we cover up one hole, the light doesn’t do this, exactly as we expect. In other words, the photons are interacting with their own probability waveforms and creating—each independently—a striped pattern when taken collectively.

This is crazy. But it’s exactly what’s predicted by quantum physics, contrariwise as it may be to our sensibilities. So where is the waveform collapsing? I would argue that it collapses as soon as information is introduced into the system—that is, at the exact moment that it strikes the photographic plate. This records it’s path and the waveform (the number of probable paths it could have taken and where it ended up) collapses.

But what if the plate wasn’t there? Simple. The waveform still collapses—only now it happens when the photon hits the wall, or a tree out the window, or it escapes the Earth’s atmosphere untouched and, five billion years later, ends up on the planet Broxar 7. Whatever. The point is that in all of these cases, the information is still recorded, we just can’t access it. Since the information was recorded, the waveform collapsed. Also notice that while the photon is en route to another planet (or the tree, or the photographic plate for that matter), the waveform hasn’t collapsed yet, and so can still interfere with itself depending on the surrounding environs (such as the other slit).

Well, how about that observer? Practically speaking, even if the information is recorded somewhere, shouldn’t we still treat the waveform as uncollapsed because, after all, we can’t observe that it collapsed. True, and mathematically, there is no difference. But let’s take the observer to its ultimate, reductionist conclusion.

In order to “observe” the information encoded in the photographic plate, we have to, no kidding, look at it. The plate is developed, and then (more) photons are emitted from the lab lights, bounce off the light and dark spots on the emulsion, and ultimately end up in our eyes. These collective photons all have probability waveforms, too. So when do they collapse? Well, necessarily, it would be when they strike the rods and cones in the retina, and convert their energy into electrical pulses.

Stop. At this point, the waveform is collapsed—but not yet observed. We can’t actually see photons. We “see” them with our eyes, but the eye then takes that information and converts it to an entirely different piece of information! Now there’s an electrical pulse. This races around in our brains for a few milliseconds, or however long it takes, and then we make some mental connections—which have nothing to do, not really, with the photon hitting our eyeball—and arrive at the conclusion that the waveform must have collapsed at some point because of the striped pattern. But in order for us to observe the collapsing of the waveform (which, after all, is only conveying to us information about an entirely different waveform that, necessarily, collapsed some hours previously), it must have happened before we thought this thought, seeing as how it set off a cascade of other reactions, and it is the sum of these reactions that got us the information that the waveform collapsed.

So I’ll say it again: a quantum waveform collapsing is the result of encoding information via matter. The waveform collapses the instant the information is recorded. The observer, while allowing us to know about quantum physics and photons, is largely incidental to the waveform collapsing. That fact that we can observe it, well—that’s just helpful, but not necessary for the universe to exist.

-Ted