Rules are bad?
When I was 20 years old, I was thinking about how incredible it was that the existence I inhabited followed such a well-behaved, consistent set of rules. This quickly became very worrying.
It starts with simple things. Think about flipping a coin. This appears to be a random event. But let’s propose that all the input variables are known. However, it is not just the mass of the coin, initial velocity of the toss, and other simplified quantities that are known. Let’s propose that the mass and position of every particle moving in and out of the system are initially known with perfect precision. In this case, the classical laws of physics could be applied to exactly determine the outcome of the coin toss. What initially appears to be random, is actually just the outcome of the input variables and the rules of the universe.
Our thoughts (such as your internal reaction to reading these words right now) are extremely complex. However, they are ultimately just the product of millions of processes that all follow the same consistent rules of physics and chemistry. If our thoughts and bodies follow these rules, then our actions also follow these rules. This concept could be further expanded to apply to computers, black holes, and everything else that exists in the universe.
Now, consider if everything about the state of the universe is known. Additionally, consider that everything in that universe follows the same set of consistent rules (our fundamental laws of physics). Then the state of the universe in the next moment can only have one outcome. And this is true for the next moment. And the next moment. And every moment after that. Everything is predetermined. We don’t actually have free will. Determinism.
Back when I was younger, I did some research and found that there were quantum events that are truly unpredictable. At the time, I was satisfied that this meant that the future wasn’t predetermined. These genuinely random events logically prevented that. However, I never did a deep dive into how “we” proved this. What if the reason that these events appear to be unpredictable is because we don’t understand what is going on? This could easily be the case via two mechanisms: 1) We aren’t capable of measuring at a small enough scale to have knowledge of smaller interactions. 2) The consistent set of rules that predict these (currently) unpredictable events are so complicated that it’s too difficult for humans to understand. The following article is a return to this idea of unpredictable events with a more rigorous approach and some discussion.
Proving Einstein wrong
In 1964, J. Bell publishes a response to a paper called “The paradox of Einstein, Podolsky and Rosen”. The important idea introduced here is an approach to challenge local hidden-variable theory. Local hidden-variable theory is essentially the idea that there are “hidden variables” that predetermine an outcome. There are two important, underlying assumptions that are being challenged:
-Locality: no faster than light influence
-Realism: measurement outcomes are predetermined
Bell proposed that quantum mechanics can violate these requirements which means that one of either locality or realism are false. It’s called Bell’s Theorem.
The Clauser–Horne–Shimony–Holt (CHSH) expression is used to mathematically explore this idea. The standard explanation for this concept is that you have two observers, Alice (station A) and Bob (station B), that can each detect either +1 or -1. They each have a choice of two settings: Alice can choose setting a or a′ and Bob can choose b or b′. The quantum correlation between the two observations is E(A,B). After a simple derivation, one can produce the CHSH expression which is S=E(a,b)+E(a,b′)+E(a′,b)−E(a′,b′). This is used in the CHSH inequality which requires ∣S∣≤2 for these observations to fall within the bounds of classical mechanics.
From the CHSH Inequality, we can construct a Bell’s test. This is an experiment that consists of many repeated measurements of pairs of entangled particles. The following steps are a simplification of the process:
Step 1: Prepare a pair of entangled particles
Step 2: Create two measurement stations (A and B) and randomly assign a measurement setting
Step 3: Perform measurements of the entangled particles at the separate stations (A and B) using the chosen setting
Step 4: Record the outcome of both measurements
This measurement is repeated thousands or millions of times. The purpose of this experiment is to determine if particles are:
a) Following classical laws. (∣S∣≤2 aka not violating Bell’s inequality)
b) Following quantum laws. (∣S∣>2 aka violating Bell’s inequality)
If the particles are violating Bell’s inequality, they are not following the previously discussed assumptions for the classical laws. When this theory is put to the test (Freedman-Clauser, Aspect et al., Hensen et al.), we find instances where ∣S∣>2. The scientific consensus is to reject local realism. This means that either locality or realism are violated. Rejecting local realism has extremely profound implications (and yes, Einstein appears to be wrong). These leaves two branches of interpretations where one can choose to either reject locality or realism. This is still a deeply debated topic.
Further experiments (Groblacherr et al.) have shown strong evidence that “maintaining realism as a fundamental concept would therefore necessitate the introduction of ’spooky’ actions that defy locality”. When realism is rejected (and locality retained: information cannot travel faster than the speed of light), the measurement outcome could not have been determined before the measurement was made. Therefore, the observed unpredictability is not caused by ignorance, it is intrinsic. In other words, we are measuring a fundamentally unpredictable quantity.
Microscopic effects, larger consequences
For these unpredictable events to actually matter, they need to have a tangible effect on the state of a larger, macroscopic scale. There are two important things to consider here: the frequency and total impact of these events. An example: Imagine an unpredictable event is a single grain of sand on a beach magically disappearing. Does this actually impact the rest of the beach? It depends.
It’s important to consider that these tiny unpredictable events are probabilistic in nature. When this is a symmetrical effect, then the net effect will “average out” to nothing. Going back to our grains of sand on the beach analogy, it’s like there is an equal chance for a grain of sand to appear or disappear. Even if these events happen very often, from a faraway perspective, the amount of sand on the beach effectively isn’t changing at all. However, what if a single grain of sand disappears and an entire sand dune topples over? When quantum effects occur around a threshold, then it is possible to trigger a macroscopic, one-sided outcome. A single event can cause a cascade of effects that propagate to the macroscopic scale.
There are also asymmetrical effects that can build up over time. Then the rate of occurrence of this asymmetric effect would determine the outcome. The relevant example is that our grains of sand are disappearing and appearing at different rates. If this event happens extremely often, then all of the beach’s sand would disappear in minutes. This occurs in processes like radioactive decay, avalanche breakdown (semiconductors), and other unstable situations. When there is a process with a tiny fluctuation that interacts with small thresholds, nonlinear behavior, or irreversible effects, then these unpredictable quantum events have a real effect on the macroscopic world.
The focus on unpredictable quantum events does not tell the full story. Although macroscopic randomness was initially discarded as not “truly” random, this is an oversimplification. Even on this macroscopic scale, events are often required to be described using statistical mechanics. Thermal fluctuations, chaos, and low-resolution observations can create results that appear random to a human observer. However, this “Randomness” at the macroscopic scale is a consequence of unknown information, not a direct effect of indeterminism.
Random thought: Are random thoughts random?
If these unpredictable quantum events only matter in radiative decay and p-n junctions, then this is pretty underwhelming for anyone that wants free will to exist. The best case scenario would be to have unpredictable quantum events with a direct impact on how we think. Human thoughts are the result of many large networks of neurons that transmit electrical signals. Each of these neurons contains thousands of ion channels which can directly affect the transmission of those signals through the brain. It would be great if microscopic randomness played a part in this mechanism.
When these ion channels are observed, measurements reveal noise, spontaneous spikes, and missing spikes. There are many papers that report these experimental measurements (Schneidman et al., Yu et al., Moezzi et al., McDonnell et al.). The behavior of these ions have only been modeled using a stochastic approach which uses probability distributions to predict outcomes. Stochastic models incorporate randomness and uncertainty. However, these models could just be a description of observed variance with underlying effects that are deterministic. There is currently no evidence of quantum effects having relevant influence on the macroscopic systems in the brain.
A Bell’s test requires two spatially separated measurement systems and binary measurement results (typically either -1 or +1). Each individual ion channel has significant complexity that makes it essentially impossible to isolate if the randomness is caused by quantum events. There are other neural processes that also are modeled stochastically but they all have the same limitation as the stochastic ion channels. It’s not currently possible to design an experiment to determine if the origin of this randomness is from the quantum level. Until this is accomplished, it’s not clear if the mechanisms behind our thoughts are influenced by quantum unpredictability.
What now?
Let us return to the initial problem of determinism (none of us is actually in control of thoughts, emotions, and actions because everything in the universe is following a consistent set of rules). Ultimately, I was hoping for true randomness to be the solution that elegantly defeats determinism. If locality is rejected, then measurement outcomes are not predetermined. If realism is rejected, then measurements may still be deterministic. Even once this question has been answered, it will be difficult to verify if the observed randomness in our brains is intrinsically unpredictable. Science is far away from resolving whether our thoughts are predetermined.
However, even if our thoughts are influenced by true randomness, is that even a desirable outcome? I don’t actually believe that it’s more reassuring that a brain’s response follows a strict set of rules that are influenced by consistent dice rolls. Randomness is different from free will. Quantum unpredictability isn’t just an incomplete answer, it’s not a good answer at all.
So, what now? It’s your turn to think about it.
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