The Gold Standard: Controlled Experiments

Statistics provides numerous methods to differentiate causes from effects, collectively known as causal inference. This process is rooted in controlled experiments, wherein all variables impacting an outcome are considered, isolated systematically, and their effects studied. Why is this methodology effective?

It hinges on the laws of nature. Our universe operates according to precise mathematical equations, many of which can be expressed (approximately) in the following form:

While this equation may appear simplistic, it signifies a definitive future that can be predicted consistently from the present states, remaining steady over time. Controlled experiments leverage this principle: controlled variables exist in the present while outcomes manifest in the future. Hence, these experiments enable the conversion of physical equations into

This serves as the fundamental assumption for all causal inferences.

However, equations alone cannot definitively separate causes from effects, as even equations harbor ambiguities. For instance, if I can determine that 2 = 1 + 1, I might conclude that 1 is the cause and 2 is the effect. Yet, we can rearrange the equation as 1 = 2, flipping the causal narrative. The challenge lies in the fact that equations merely represent relationships, which can be interpreted in multiple ways. To distinguish between causes and effects, an additional clarifying factor is necessary.

Moreover, these causal ambiguities extend deeply into the foundational laws of nature. The only resolution to these ambiguities is to acknowledge that causation is not a fundamental aspect of nature but a complex emergent phenomenon shaped by human biases.

The Causal Conundrum

To further illustrate the complexities of defining causation, let's consider a billiards scenario. Imagine striking the white ball, which collides with the black ball, causing it to drop into a pocket. The question arises: What causes the black ball to enter the pocket?

Many might hastily conclude that the white ball, being the one struck, causes the motion. However, let’s view it from the black ball's perspective. It might perceive the white ball as an incoming object colliding with it and diverting it towards the hole (akin to a reckless driver!). While this viewpoint may seem unusual, it's reasonable to consider the black ball as a causal agent. The only distinction between the two balls is that the player has more direct "control" over the white ball. Yet, without the context of billiards, discerning what we control becomes challenging.

Why is this billiards analogy significant? The real world is akin to a series of billiards: particles perpetually colliding. Each interaction among particles presents the same causal dilemma. In the realm of particles, there’s no notion of a "stationary" or "active" particle.

One potential resolution to this conundrum is to consider both billiards as contributors to the outcome.

But are those enough? Should we account for the player and the table as well? What of the air molecules in the room, the Earth, the Solar System, and the entire Universe? If we include everything, how can such a broad notion of causation be practical?

In the realm of controlled experiments, the problem lies in the absence of a fundamental method to isolate control variables from the myriad possibilities.

By now, the fundamental challenges in defining causation should be apparent:

1. We require a method to distinctly categorize objects and events as either causes or effects.
2. We must determine how to limit the objects/events involved to forge a practical concept of causation.

These challenges may seem overwhelming, but fortunately, physics provides solutions. Given the complexity of this discussion, I've opted to separate it into two articles. This initial piece will focus on the constraints of causation, while the subsequent one will refine this foundational idea and investigate how our intuitive sense of causation emerges.

Throughout this exploration, we will encounter profound topics in physics, including the Theory of Relativity, cosmology, quantum physics, and chaos.

Buckle up for an enlightening journey!

Causation is Correlation

Let's begin with the fundamentals: what tools do we have to define causation? Physics offers equations describing particle interactions. However, there is no inherent preference for any specific particle or element—no straightforward delineation exists between cause and effect.

So what do these equations provide? Ultimately, they depict relationships among particles over space and time. In simpler terms, they represent correlations! (In fundamental physics, nearly all calculations involve correlation functions). This leads us to a startling conclusion:

There is no inherent notion of causation—only correlations. Thus, our understanding of causation must be viewed as a macroscopic emergent phenomenon arising from specific correlations.

This revelation may be shocking for some, as we often hear that "correlation does not imply causation." I don't suggest we discard this well-known saying; rather, we must enhance it with a more robust secondary clause:

Causation must arise from specific forms of correlation.

The next question becomes: What are these unique correlations? Where do they commence and terminate? Human biases inevitably factor into this.

For now, we will defer our exploration of the types of correlations that lead to causation, as that discussion would require venturing into the quantum domain—a realm filled with unforeseen correlations.

To adequately discuss the initiation and termination of causation, we must involve the Universe, which necessitates assistance from Einstein.

The Causal Boundary: At the Speed of Light

The concept most closely related to our understanding of causation is causality. This idea stems directly from Einstein's Theory of Relativity.

(Side note: I will reserve the term "causation" for everyday use. The term "causality" in physics has a very specific technical definition, so in this article, when I refer to "causality," I am only discussing that technical meaning.)

To grasp the relationship between relativity and causality, consider Einstein's thought experiment: What would happen if the Sun were to vanish suddenly?

Before Einstein's theory, the erroneous answer would have stemmed from Newtonian physics: that the Sun's gravitational pull would instantly cease, causing planets to diverge from their orbits immediately.

Einstein found this conclusion troubling: How could the disappearance of an object nearly 100 million miles away affect us instantaneously? That seemed like "spooky action at a distance"!

To rectify this misconception, Einstein posited that initially, the Earth would feel no change. It would only be after the gravitational disturbances—traveling at light speed—reach our planet that we would begin to notice the effects. The crux of his argument is that for any two events to be meaningfully connected, a messenger is necessary (in this case, gravitational waves). Einstein generalized this profound insight to encompass everything in the universe:

For one event to interact meaningfully with another, there must be a messenger, and this messenger cannot exceed the speed of light.

These cosmic connections form the foundation of causation. Another significant realization is that these relationships are fundamentally encoded in the Universe's geometry. With that aside, we can now define causality within Einstein's framework:

When two events can be linked by a messenger, they are deemed causally connected.

What does this imply in practical terms? It indicates that when examining events on Earth, we can disregard what is occurring "now" on the opposite side of our galaxy—ignoring the intricacies of defining "now." Consequently, this suggests that an intergalactic war could not possibly be coordinated (sorry, Star Wars enthusiasts!).

Now that physics has provided us with this special causal relationship within the universe (a causal correlation, if you will), we are prepared to outline the most general form of causation.

The Causal Arrow of Time

Einstein's Theory of Relativity introduces another compelling concept: the temporal ordering of events. It can be mathematically demonstrated that when two events are causally connected as previously defined, a consistent time-ordering of events exists.

This consistency is something we often take for granted. For instance, we universally agree that our parents precede us in birth, and that the year 2000 comes before 2020. This coherence arises from the causal structure of our universe, which provides a consistent temporal ordering of events!

Now, we face two options for distinguishing causes from effects: causes either precede or follow effects. This is where human (or anthropogenic) biases enter the fray. Due to the Big Bang, our universe is structured so that we all share the same temporal flow. Since we can only manipulate present conditions to influence future events, there is only one logical way to define causation:

Events in the past lead to events in the future.

While this assertion may seem tautological and self-evident, deriving it from Einstein's mathematical description of the universe is not immediately obvious. The mere existence of a consistent general definition of causation stands as one of the significant achievements of Einstein's theory!

An intriguing aspect of causality is that the temporal ordering of causally disconnected events can be ambiguous! Thus, questions like "When did intelligent life first emerge in the universe?" become technically observer-dependent. Consequently, if extraterrestrial visitors were to arrive, there may be an unresolvable debate regarding which civilization came first!

From Correlation to Causation

To summarize our discussion on causation:

• Physical laws yield correlations, not causation. Hence, causation must be a subset of these correlations.
• Einstein's theory establishes a notion of causality embedded within the universe's structure.
• A consistent arrow of time, combined with Einstein's causality, allows us to define the past as the cause and the future as the effect.

All of this culminates in the most generalized form of causation: every current event, whether it's you reading this article on a screen or the rhythmic ebb and flow of ocean waves in Hawaii, is a result of a similar series of events that encompass the entire causal history of the Earth and the universe!

Reflecting on our earlier billiards analogy, we indeed must consider aspects of the universe's inception to fully understand the causation of the game. This resonates with Carl Sagan's famous assertion:

> "If you wish to make an apple pie from scratch, you must first invent the Universe."

Thus, despite our efforts, we still lack a straightforward definition of causation in our daily lives.

To bridge these gaps, we will need to consider the magnitude of the correlations we discuss (which will be addressed in the next article). In determining whether something should be deemed a cause, human biases will come into play. For instance, while the Big Bang is integral to human existence on Earth, we wouldn't consider it a relevant cause when seeking a cancer cure. This is largely because we cannot control the Big Bang, and including it wouldn't contribute to our goal of curing cancer!

Nonetheless, does this imply that our methods of causal inference and scientific inquiry are flawed? The answer is no. Causation is an invaluable concept that aids us in gathering insights about the world. What fundamental physics reveals is that we should regard causation as a complex phenomenon that emerges from a blend of fundamental laws and human intuitions. The absence of a straightforward definition merely underscores the importance of not being overly pedantic in defining causation while appreciating its utility in extracting insights and guiding our navigation through the world.

Ultimately, our understanding of causation highlights our shared humanity, as it relies on our collective cosmological experiences and sense of agency. We should embrace the fact that we are all under the same causal umbrella and celebrate how the laws of physics empower us to comprehend this universe.

If you found this article insightful, you might enjoy my other pieces linked below. Feel free to reach out if you want to hear a physicist's perspective on another topic—I'm eager to share more insights with you!