So, I recently read A Brief History of Time by Stephen Hawking. Given my interests, it's surprising it's taken me this long to get around to reading it. I have to say that I'm sorry I didn't read it sooner. It's quite fascinating, if a bit over my head at times. It's amazing to me how counter-intuitive physics becomes when you break it down to the quantum level or try to stretch it back to the beginning of time. It's even more amazing that we've managed to figure out any of the parts beyond Newtonian physics, which is, relatively speaking, pretty easy to observe.
I can't imagine the internal conflict for the first physicists to investigate these advanced concepts. Bohr, Schrödinger, Einstein, just to name a few, must have been stunned by the things they discovered. Indeed, Einstein's objections to some of the conclusions he and his colleagues were coming to are well documented. I'm reminded somewhat of Darwin's inner struggle with the reality he observed with evolution and natural selection versus what his lifelong faith told him about the origin of species.
Most interesting, though, is what these researches discovered about what we don't know and, indeed, perhaps can never know. The most significant of these, in my opinion, is Werner Heisenberg’s formulation of the uncertainty principle. I have to admit, this is one of those things that kind of goes over my head. I'm sure if I were a better mathematician, I might "get it" a bit more, but I'm not, so I don't.
I understand only the most basic concepts that come from uncertainty. Let me sum it up in my own words. Uncertainty basically tells us that there are certain variables that cannot be known to the same level of precision simultaneously. These variables seem to be somehow complementary to one another, or at least, the possible methods of measuring them seem to be complementary in such a fashion that the more precisely you know one, the less precisely you can know the other. For example, if you measure the position of some particle with high degree of precision, you will be unable to measure its momentum with much precision at all. Conversely, if you've measured its exact momentum, its position will be a mystery.
I've actually known this specific example of the uncertainty principle for quite some time, but I always thought that it was merely a matter of weakness in our measuring capabilities. According to Heisenberg's work, however, uncertainty is actually a feature of the universe. It wouldn't matter how advanced our instruments were, we could never measure these things simultaneously to the same level of precision.
I was thinking about this the other day, trying to figure out if I could come up with a macroscopic example that would demonstrate how this could possibly be true, and I think I came up with one. Please bear with me as I try to set it up...
Have you ever played Outburst? How about Password? In these games, and a few others, you have a card with some words written on them in light blue ink. Then, over the entire surface of the card, there are a bunch of small, randomly-shaped, and transparent red splotches. The purpose of this red pattern is to obscure the words written in blue so that they cannot be read at a glance. The only way to read them clearly is to insert the card into this little red plastic window that comes with the game. The clear red window cancels out the red on the card and the light blue ink of the words stand out as a dark purple.
Another example of this same concept is those old red and blue 3-D glasses. When I was a kid, I had this book with a bunch of drawings of dinosaurs in this blue and red ink. When you looked at it through the 3-D glasses, the dinosaurs seemed to jump off the page. I noticed that when I put the red eye of the glasses over a part of the drawing, the red lines would disappear. Similarly, when I put the blue eye of the glasses over the drawing, the blue lines would disappear.
Ok, going back to the Outburst example, say you wanted to read the words on the card as clearly as you possibly could. The best way to do that would be to slip the card into the red window. Now, say you wanted to see the random red splotches as clearly as you could. To do that, you'd put the card into a blue window. Now, it is true that green would contrast best with the red splotches, but you would still barely be able to see the word in blue ink, which might interfere with how well you were able to see the detailed shape of the red splotches over that word.
So, what if you wanted to be able to see both the words and the red splotches in the best detail possible simultaneously? One might suppose that a purple window might work, but probably not very well. I doubt you could see either the blue or the red ink any better than you could in regular light. Even if it was better, it still wouldn't be as good as seeing either one color or the other in the windows specifically designed to cancel out the color you wanted it to.
Wow, are you still with me?
So, translating this example to uncertainty, the words in blue ink represent a particle's position and the red splotches represent its momentum. To know its position with a high degree of precision, you have to put it in the red window. For its momentum, the blue window is best. There exists no window, however, that would reveal both simultaneously as nicely as the red and blue windows reveal the blue and red ink respectively.
Well, how do you like that? I've just reduced one of the most puzzling (to me) aspects of quantum physics to the simple pieces of a family game. Though I admit, this may just as well describe a lack of understanding as it does the basic concept of uncertainty. I'd be curious to know what a physicist thinks of it.
Ok, so what the hell does this have to do with determinism? Well, when I first read that uncertainty was "built in" to the universe and is something we are not likely to be able to overcome, my whole idea of a deterministic universe started crashing around me. Now, keep in mind that I was sleepily reading this on a flight to L.A., so my brain wasn't at its peak. What I later realized was that it still doesn't necessarily rule out determinism. All it does is solidify the idea that the universe is ultimately unpredictable. Uncertainty assures that we will never have all the information necessary to propagate the laws of physics out theoretically to some future moment.
In my last post about determinism, I hypothesized about a computer that was powerful enough to hold all the information and perform all the calculations necessary to predict the future. I reasoned that such a computer could not be built because it would require infinite resources. Thinking about it now, I realize I may have been wrong about not only the reason it was impossible, but also its requirements. The reason it would be impossible is because uncertainty guarantees that we will never have all the information necessary to load into the computer. So, even if we had infinite memory, we wouldn't be able to fill it with the necessary information to perform our calculations.
Which brings me to its requirements. Would it really need infinite memory? My reasoning was that such a computer would have to include a simulation of itself resident in memory, which would set up an infinitely recursive situation. If we're talking about building a computer in the sense of a modern-day computer, that might not be far off. In A Brief History of Time, Hawking talks about the laws of thermodynamics and entropy. He says that in the process of storing data in memory or processing that data, a computer generates heat, which increases the overall entropy in the universe by a much higher degree than the order that is created by the memory storage or processing. So, my future-gazing computer would have to at least include in its simulation the amount of heat it outputs into the universe, which would require more memory and processing, which would increase the heat further...etc.
But, let's say we don't build the computer like a modern-day computer. Instead, we'll let the universe run the simulation itself. Or, at least, we'll have half the universe run the simulation. So, let's ignore uncertainty for a moment. All we have to do is freeze time and build a huge partition that splits the universe exactly in half and prevents any energy transfer between the two. Then, we arrange every particle in one half in exactly the same position as the particles in the other half. Once that's done, we use the laws of physics to manipulate one half as it will appear at some arbitrary point in the future. Now the only thing left is to start up time again. If you want to know what's going to happen in the future of the one half, you just have to look at the other half. Simple, no?
Actually, it's not simple. In fact, it's ridiculous. You have to throw out so many physical laws to accomplish this, in the end you're just dealing with fantasy. Ignore uncertainty? Freeze time? Build a perfect barrier between two halves of the universe? Even if you could do these things, what do you then do to calculate out the future of each particle in the half that's going to be your future universe? You can't use a computer, because that's what you're building. It's the whole reason for this insane project! The only option that leaves is to do it by hand or incrementally using weaker computers. Even so, if you could freeze time, you could take the preposterously ponderous amount of time required to calculate the future incrementally using your weaker computers.
I could go on, but it doesn't serve my point, which is that even if the universe is deterministic, which I believe it to be, it may as well not be. Daunting does not even begin to describe the most trivial of steps in calculating the exact future of the universe, and that's even ignoring uncertainty. Throw uncertainty into the picture and your nearly infinitely difficult task literally becomes impossible.
Now, let me propose a thought experiment to you. I'm not sure what conclusions you might draw from it, but I think its purpose is more to evaluate how you think about time (and time travel) than to determine whether or not the universe is deterministic. However, if any definite conclusions could be reached with this experiment, they might have some interesting implications about determinism. So, here goes:
Suppose I approached you and asked you at some specific moment to choose a random number between 1 and 100. If there are truly random events in the universe and human free will is a consequence of that randomness, then there is a 1 in 100 chance that you will pick a particular number within that range, regardless of any events that occurred in all of the universe's history before I asked you to choose.
Now, suppose at some arbitrary point in the future I traveled back in time to a point before I asked you to choose a number and, taking the place of my past self, I approach you at the same moment I did previously and ask you in exactly the same way to choose a random number between 1 and 100. Again, we are assuming that there are truly random events and our free will is a consequence of them. It shouldn't matter, then, that this already happened in the past I know. There should still be a 1 in 100 chance that you will pick a specific number in that range, which means that the number you choose this time might not be the same as the number you chose last time.
Think about how time travel is represented in science fiction. Does this thought experiment agree with that representation? Consider the hypothetical "what if you could go back and kill Hitler?" question. Well, what if you went back far enough that enough events that depended upon the random elements of a non-deterministic universe played out differently and maybe Hitler wasn't even born, or maybe he made different decisions that led to a different history than the one we know? In this hypothetical universe where random events truly happen and have noticeable effects, you wouldn't necessarily have to do anything to stop Hitler. It might just work out that Hitler never ends up doing what he did in our history, if he even exists at all.
There is, of course, one minor kink in this experiment. If the universe is deterministic, then the amount of entropy you inject into the past universe by arriving there via time travel might have a significant effect on future events as well. Just by being there, the energy your body gives off as it metabolizes calories might change how history plays out. Unless you can figure out how to travel to the past without adding more entropy to the past universe, you'd never be able to completely rely upon your observations to prove randomness. But to talk about figuring out how to prevent contamination of your experiment while traveling to the past, you have to figure out how to travel to the past in the first place.
Ultimately, we're no further along in figuring out whether or not the universe is deterministic. I still believe that it is, but I also still believe that it doesn't matter. And it seems like the more we know, the more we're starting to understand that we'll never know it all. We may end up knowing a lot of it, but some things in the universe will still remain a mystery. I'm ok with that.
* * * * *
No comments:
Post a Comment