~ I wish I remember who said this.
I'm going away for a few days (until the Vernal Equinox), so today we're going to bite off more than we can probably chew in just one day. You might want to give the ideas presented here some time to sink in, because they may seem rather alien at first. We're going to grapple with the issue of openendedness and determinism, and we're going to talk about the fifth and sixth dimensions. Then we'll discuss two interpretations of quantum mechanics that pertain to these dimensions and find that each interpretation complements the other.
The Fifth Dimension
The fifth dimension is invisible but obvious. It may be that it seems to exist due to the way we think, or it may be real, but we'll get to that issue later. First let's talk about what the fifth dimension would be. In this post I am treating the fourth dimension as time, so what I'm calling the fifth dimension is really the second dimension of time. You've probably heard this story before:
One morning, you wake up late and rush out to your car, stressed and in a hurry to get to work, school, or whatever controls your time. You realize you've forgotten your keys and take a minute to step back inside and get them. As you drive to work, you get held up on your way by a terrible traffic accident.
One morning, you wake up late, grab your keys, and rush to your car, stressed and in a hurry to get to work, school, or whatever controls your time. You realize you're in the wrong lane and rush to get into the left one to turn without checking your blindspot, and a large SUV whose driver is on the phone smashes right into you. You are never able to move your legs again.
Often a version of this story is presented in order to encourage people to appreciate things like the butterfly effect, whereby small decisions or mistakes can have large unpredictable consequences. Here, however, we're looking at it because it's an example of where two timelines (i.e. lines in the fourth dimension) diverge from one another. One of the questions that has kept philosophers arguing with each other for thousands of years is how we end up in one timeline or the other.
Free Will and Determinism
Many philosophers believe in free will. This can lead to a variety of paradoxes that we won't be exploring here, but it has some nice features, too. First of all believing in free will means you believe humans to be responsible for their actions. Whether or not free will actually exists, believing that it does allows people to justify holding each other accountable for what they do. For people who believe in the agency of free will, we are fully responsible for our navigation through the fifth dimension.
Psychic determinism also has some good arguments for it, though. How far can we go from strict determinism before we get to an equally undesirable randomness? We want to believe that our past experiences and other factors don't control our current choices, but is a roll of the dice much better? Studying synchronicity and the way things are patterned definitely makes one wonder whether if we have any truly free choice in the matter. For psychic determinists, we are carried on particular currents through the fifth dimension, and sometimes our ability to perceive other paths through it is what ties us to the path we follow.
There are two resolutions to this opposition. The first is rather popular and is called compatibilism. As the name implies, compatibilism suggests that there isn't any real problem of free will. Free will requires that, all things being equal, we could have chosen otherwise than we did. Since we can't travel through time, this is an untestable proposition. So the people who argue that free will trumps determinism, or vice versa, are making free will up to be something more than it is, compatibilists say. In effect, they say that the fifth dimension doesn't exist because we cannot experience multiple paths through it in one lifetime.
Compatibilism is a nice way to tie the problem up and grin like a smart-ass at the folks arguing about it, but it reminds me of the idea that the Sun revolves around the Earth every day (and the stars and planets follow at different rates) because something as solid as our planet certainly could not be spinning. Certainly you can map out the positions of the stars and planets from a perspective like that, but imagining a spinning Earth revolving around the Sun allows for more information about the solar system to be communicated with less complexity in the actual message, especially when we're talking about how the planets sometimes appear to move backwards against the starry backdrop.
The resolution to the free will - psychic determinism question that I prefer is one I have not heard discussed much amongst most philosophers, but physicists of the very small might feel comfortable with it. In a simple quantum experiment, a stream of minuscule particles are fired through a single opening of comparable size at a detector. Using the best math and physics available to us, we cannot calculate precisely where each particle will land on the other side. However, we can, given the slit size and some information about the particle, calculate how many particles will land at each spot on the detector if we fire ten thousand of them. What is determined in this case is not the individual "choice" of each particle, but the set of options it has.
Since some of the choices we make involve coming up with options for other decisions, and our brains are slightly more complex than the experimental setup just described, we can have it the other way around, too. Peter Carroll says it best when he states that we sometimes have undetermined choices between determined options, and other times we have determined choices between undetermined options. So in this position, which has not been given a widely recognized name by philosophers yet, we have free will and psychic determinism working together just like we do in compatibilism. The advantage of this position over compatibilism is that it recognizes the synthesis between the two rather than simply implying that there is no real interplay between them. It also meshes much more nicely with modern ideas about physical determinism than compatibilism, which grew up around classical ideas of physical determinism, does. In this view, we are sometimes blown by the currents of fortune, and other times we swim through still waters of chance, but some degree of freedom plays a role at least most of the time.
We'll get back to classical and modern determinism in a moment, but first let's go one dimension further.
The Sixth Dimension
We're quite familiar with the sixth dimension (the third dimension of time), too, though we don't call it that. If the fifth dimension is where the branching occurs between the timeline where we forgot our keys and the timeline where we lost use of our legs, the sixth dimension is the one that allows us to be glad we forgot our keys when we see the accident, thinking, 'that could've been me,' or alternately to wish we'd either forgotten them, woken up earlier, or checked our blindspot before changing lanes.
It may be worth watching this clip to see why this is the sixth dimension.
If the fifth dimension is what lets us make decisions about what timeline to follow from here, looking through the sixth dimension allows us to think about where we would be if we had acted differently. Again, compatibilists say that we can't do this. The process is called counterfactual thinking. Just like with the fifth dimension, it's somewhat arguable whether this dimension objectively exists or exists only as a way of thinking to help us understand our choices.
The question, "Could it really have happened otherwise?" has plagued not only philosophers but people trying to make sense of quantum mechanics. While there are many interpretations of quantum mechanics (such as the Copenhagen interpretation, which is said by some to mean that quantum mechanics is just the way you have to think in order to make fairly accurate predictions about the world at the subatomic scale, and by others to say that the act of observing something causes it to collapse out of flux and into definition), we're going to focus on just two of them today - the two that I think are the least implausible without saying nothing at all about what quantum mechanics (hereafter Q.M.) means, and the two which are most relevant to the questions we're exploring.
The first is hidden variable theory. This line of thought was pursued by Albert Einstein and revived in a more robust form by David Bohm. As you may know, Einstein is famously paraphrased as saying, "God does not play dice." He believed that the indeterminacy of the behavior of individual particles found in Q.M. resulted not from their movement being fundamentally undetermined, but from things affecting their behavior which we were unable to observe. They were, after all, very small. Perhaps the statistical tendencies in the behavior of small particles reflected statistical tendencies of the hidden variables affecting each. The hidden variable interpretation did not catch on for awhile, because for awhile nobody found anything in the experimental setup or in the properties of the particles that looked the way the hidden variables ought to. Saying that they were completely hidden from us was a cop-out that convinced no one in the sciences.
Then came quantum entanglement. Particles which come into contact with one another appear to have a correlation between them that extends beyond time and space. Imagine if Alice and Bob, stand-ins for two particles, shared a secret handshake one day, becoming entangled, then Alice took off on a spaceship going at near the speed of light and Bob stayed on Earth. The entanglement established a peculiar relationship so that whenever Bob wore white socks, Alice was wearing black socks, and whenever Alice wore white socks, Bob was wearing black socks. This effect was instantaneous rather than moving by signal at the speed of light, so the physicists monitoring Bob's socks (if they knew about Alice and Bob's entanglement) knew instantly when Alice changed the color of her socks, faster than the communication from the departing spaceship could tell them. Similarly, the physicists on the spaceship knew what was happening with Bob's socks before they received a signal from Earth. That's what I mean when I say the effect extends beyond space. When I say the effect extends beyond time, I mean that Alice's and Bob's socks had this relationship even before they shook hands. (In a real analogue to this paragraph, the directions of spin for particles A and B would be perpetually opposite due to entanglement.)
Particles in your eyes (as well as other parts of you) are entangled with light from Sirius, Betelgeuse, and Aldebaran, and all the other stars you've seen. Perhaps the scientists who were looking for hidden variables were looking in the wrong place for them. Maybe they could be seen through their quantum effects before they could be seen in any other way, due to the vast distance to the things entangled with them. As Natalie Drest (a fictional character) aptly puts it, "You mean the whole universe will decide what we're gonna do next?"
This interpretation (sometimes called the non-local hidden variable interpretation) gives us a very simple answer to the question, "Could [event N] have happened otherwise?": "No." That's not to say that the experience of free will is irrelevant to the universe, though. Just as you depend on the universe to be who you are, the universe depends upon you - without you and without everything that's culminating right now in your existence, it would be a quite different place. Lamenting the lack of indeterminism in a universe like this would be like lamenting the fact that J.S. Bach never wrote, "Improvise for this part," in any of his fugues. Rather than autonomy, we have holonomy (same word root as holism) in this view. With this interpretation of the universe, the fifth and sixth dimensions exist in the minds of beings that perceive that way, and affect reality by affecting the behavior of those beings.
There's another very interesting interpretation of quantum mechanics. It takes the math used in Q.M. very literally. For the slit arrangement we talked about above, the math of Q.M. generates what's called a "wave function." The wave function is highest in the area directly behind the slit, and it tapers off to the sides. What's 'higher' or 'lower' in the wave function is the probability a particle landing there. The many worlds interpretation says that the universe splits into multiple timelines each time something happens where quantum indeterminacy is involved. In most of the universes, the particle lands in the middle where the wave function is highest, but in many of them it lands to one of the sides. In other words, probability actually exists.
Under the many worlds interpretation, we are constantly and, typically, unconsciously navigating the fifth dimension. Each time the worlds split, multiple copies of ourselves are created, one for each world. So with the many worlds interpretation and the car accident mentioned at the beginning of this post, there's at least one world where you just arrived late to work because of the traffic the accident caused and one where you are now a paraplegic, as well as worlds where you stopped working years ago when you won the lottery, where your parents met but you were never born because another sperm won the race or they conceived at a different time, where your parents never met, where they never existed, and where you're sitting at your computer right now but you're reading a blog post about how the Copenhagen interpretation is used to justify both skeptical non-realism and New Age solipsism instead of about free will and determinism. And many more. There are at least a googol (one followed by a hundred zeros) of worlds like this if the universe is around as old as Big Bang theorists think it is, and there are infinitely many worlds like this if the universe has always existed.
In the many worlds interpretation, the fifth and sixth dimensions are a bona fide objective part of the universe rather than simply ideas that become apparently objective through the actions of conscious beings. In fact, with this interpretation our capability to pay attention to other timelines is as limited as our ability to pay attention to our other senses is. Just as we're much more likely to pay attention to a scrumptious smell if we're hungry, we're more likely to pay attention to the reality that could have been where we have what we wish we did, or where we lost what we're glad we didn't.
Now, you may be wondering why I said that our navigation of the fifth dimension is 'typically' unconscious rather than always that way. I say 'typically' because of the rather large pile of studies that have seemingly found that simple intention on the part of the experimenter can affect the outcome of quantum experiments. The many-worlds interpretation provides a nice vehicle for this supposed influence to be expressed - through our decisions of which universe to experience ourselves in. This goes beyond the orthodox many worlds interpretation, and creates some paradoxes, though.
For instance, if this influence is real and can be learned as a skill, what happens to the copies of us that go on to undesirable timelines? Are they never experienced, due to our ability to avoid their fates?
It's worth noting that the non-local hidden variables interpretation also may allow this sort of influence via entanglement between brain cells and particles in the experiment. This avoids the problem of unlived timelines that shows up when the many worlds interpretation is coupled with intention, but it creates some interesting effects of its own. After all, what can influence is also susceptible to influence. If our brains affect the tangled quantum fabric in subtle ways, they are also prone to being affected by it with equal subtlety.
This provides an even more interesting solution to the free will problem. Recall that in the hidden variable interpretation, the universe could be said to decide what we do by instantaneous committee vote. Now consider the possibility that certain structures in the brain (most likely in glial cells) exist to amplify quantum indeterminacy. This would provide the undetermined half mentioned above of the balance between determined and undetermined functions to create human choice. It would also mean that there's really no difference between our will as it manifests and the will of the universe for us.
An interesting consequence of pushing consciousness back from the individual to the quantum probability matrices is the way the fifth and sixth dimensions change, and the way they don't. If the mind arises in part out of quantum amplification, then these dimensions exist not only as a part of our own minds but as a part of the universal mind. They need not all be actualized like they are in the many worlds interpretation in order to exist in this way, but there's nothing to prevent an infinite subset of them from existing. (Yes, you can have an infinite set that's part of a bigger infinite set, just like the set of all odd numbers is part of the set of all whole numbers.) And thus the problem of unactualized timelines becomes no longer a problem.
It's possible that both world-splitting and non-local hidden variables play a part in the world as it is. Every quantum particle could be influenced by entanglement but still have some freedom to its behavior.
Anyway, I hope you enjoyed the read. If you're interested in learning more about quantum mechanics without using differential equations, linear algebra, and operators, I can recommend a few books. The first is Quantum Psychology by Robert Anton Wilson for an exploration of how psychology and quantum mechanics are reflective of each other. The same author also wrote the Schroedinger's Cat Trilogy, a hilarious and multilayered sci-fi novel that explores the interpretations of quantum mechanics which I would describe as Finnegan's Wake for your brain's left hemisphere. I'd also recommend Wholeness and the Implicate Order by David Bohm for its clarity and brilliance. There are a lot of books on the market full of New Age fluff that bandy terms from quantum mechanics about, but these three are worth noting for their avoidance of wishful thinking.
Hope to see you back next week, I'll be writing about infinity and how the many-worlds view leads to some truly mind-boggling consequences. I'll also discuss an album that you'll probably enjoy if you liked this post.