We’ve all heard the phrase, “correlation does not imply causation”, but no one ever talks about what causation really is. Fundamental physics has an answer for us, and it might surprise you: It all comes back to correlation.
It’s a rainy day in the city, and everyone has their umbrellas out. Did the rain cause people to open up their umbrellas? Or did people opening up their umbrellas cause it to rain? While rain and umbrellas are highly correlated, only one of the two possible causal relationships is valid: Of course the rain caused people to open their umbrellas and not the other way around!
The answer feels intuitive. Indeed, humans are generally pretty good at making judgments about causation, as these judgements help us predict, plan, and justify our actions.
Beyond everyday life, human progress depends on us deciphering causes from effects. From practical questions like “did humans cause global warming?” to abstract thought-experiments such as “what caused the creation of the Universe?”, having a clear notion of causation is critically important for science and society.
If causation is so intuitive, surely there’s a simple definition for it, right? Perhaps the laws of nature can give us a straightforward answer.
Unfortunately, it turns out that our human notion of causation doesn’t really fundamentally exist. At best, this notion is an emergent phenomenon, rife with biases. Surprisingly, it turns out that the best we can do in terms of defining causation is to rely on a special form of correlation.
Curious? Read on.
Statistics has a multitude of methods to help us discern causes from effects — this is the study of causal inference. Making causal inferences relies on the idea of the controlled experiments: where we consider all the variables that may affect an outcome, systematically isolate each variable, and study how the outcome changes. Why does this method work?
It comes down to our laws of nature. Our world is governed by precise mathematical equations, many of which can be written (approximately) in the form:
As trivial as this equation may seem, it tells us that there is an unambiguous future, that can consistently be predicted by the present states — and that this prediction stays consistent over time. Controlled experiments take full advantage of this fact: controlled variables are always in the present, and the outcomes are always in the future. Thus, controlled experiments allow us to convert these physical equations into
This is the standard assumption for all causal inferences.
But equations alone are not enough to distinguish causes from effects, as even equations have ambiguities. For example, say I can predict 2 = 1+1, and conclude that 1 is the cause and 2 is the effect; we can rewrite the equation as 1 = 2−1, and flip the cause and effect around! The problem is that equations are just relationships, and there are multiple ways to write and interpret them. To separate causes and effects, there needs to be an extra disambiguating factor.
Going further, this sort of causal ambiguities run deep, all the way down to the fundamental laws of nature. The only way to resolve these ambiguities, is to accept that causation is not a fundamental clause of nature, but rather a complex emergent phenomenon that involves anthropogenic biases.
To illustrate further why causation is tricky to define, let’s play a game of billiards. Imagine I hit the ⚪ ️(white ball), which collides with the ⚫️ (black ball), and ⚫️ goes in a pocket. The question is: What causes the ⚫ to go into the pocket?
Many of us may jump to the following conclusion: ⚪ hits ️️⚫️, so obviously ⚪ causes the motion.
But let’s consider ⚪’s perspective. ⚪ sees ️⚫️ charging toward it, colliding with it head-on and swerving toward the hole (like a belligerent drunk driver!). While this perspective may be uncommon, it’s not entirely unreasonable to consider ⚫️ to be the causal agent. The only difference between ⚪ ️and ⚫️ is that the billiard player has more direct “control” over ⚪. But without the context of playing billiards, it’s difficult to determine what things we have “control” over.
Why is this billiard scenario relevant? Well, the real world is essentially made up of many tiny billiards: particles constantly colliding with each other. Every time two particles interact, we have the same causal conundrum. In the world of particles, there isn’t a notion of “stationary” or “actor” particle.
There is one solution to this conundrum: Perhaps we can include both billiards (⚪ and ️️⚫️) as causes for the outcome.
But are the billiards enough? Shouldn’t we include the person hitting the ball and the billiard table? But what about the air molecules in the room, aren’t they relevant? The Earth? The Solar System? And the entire Universe? If we include everything, how would such a notion of causation be useful?
In the language of controlled experiments, the issue is that there is no fundamental way to select out the control variables out of the myriad of possibilities.
By now, the key problems of defining causation should be clear.
- We need a way to separate objects and events unambiguously into either causes or effects.
- We need to figure out how to limit the number of objects/events we include in order to create a useful concept of causation.
These problems seem daunting. Luckily, physics has the answers. Due to the complexity of our discussions, I’ve decided to create two separate articles. This first article will focus on the limits of causation, and how the arrow of time comes in to distinguish causes from effects. The second article will focus on refinements of this raw idea of causation and explore how our intuitive sense of causation emerges.
Along our journey, we’ll stumble upon many profound topics in physics, including the Theory of Relativity, cosmology, quantum physics and chaos.
The ride is quite wild, so buckle up!
Let’s start with the basics, what are the tools at our disposal to define this notion of causation? Well, physics gives us equations on how particles interact with one another. The problem is, there isn’t any preferential treatment on any individual particle or component — there is no simple separation between cause and effect.
So what do equations give us? These equations are ultimately relationships between particles in space and time. In other words: correlations! (In fact, in fundamental physics, almost all calculations involve correlation functions). We are thus forced into a surprising conclusion:
There is no fundamental notion of causation — only correlations. Thus, our notion of causation must be a macroscopic emergent phenomenon derived from specific types of correlations.
This may be shocking for some, as we are often told that “correlation does not imply causation”. I’m not saying we should throw away this well-known adage; rather, we just need to add a stronger, secondary clause:
Causation must be derived from some specific form of correlation.
The next question, then, is what these special types of correlations are. Where do they begin and end? Somewhere along the way, human biases have to come into play.
For now, we’ll postpone our discussion on the types of correlations that lead to causation, as it will force us to detour into the quantum world — a realm filled with unexpected correlations.
Meanwhile, in order to describe the beginning and the end of causation, the Universe will need to get involved. For that, we’ll need some help from Einstein.
Probably the closest physics concept to our notion of causation is the notion of causality*. This concept is a direct consequence of Einstein’s Theory of Relativity.
(*Side note: I’ll reserve the word “causation” to refer to the everyday concept. The term “causality” in physics has a very special and technical meaning, so in this article when I use “causality” I am only referring to that technical meaning.)
To understand how relativity and causality are related, Einstein imagined a hypothetical scenario: The Sun suddenly disappears, what would happen to the Earth?
Before Einstein’s theory came along, the (wrong) answer would have come from Newton’s theory: That the Sun’s gravity would instantaneously disappear, and all the planets would instantly diverge from their paths.
Newton’s answer troubled Einstein deeply: How can the disappearance of something nearly 100 million miles away affect us immediately? That feels like spooky action at a distance!
To correct this conclusion, Einstein argued that at first, the Earth wouldn’t feel any change. It would only be after the massive gravitational disturbances (traveling at the speed-of-light) arrive at our planet that we would start to feel the effects. The essential point is that there needs to be a messenger (gravitational waves in this instance), that connects that we would consider as causes and effects. Einstein generalized this profound observation to everything in the Universe:
In order for one thing to meaningfully interact with another thing, there needs to be a messenger. Additionally, the messenger cannot travel faster than the speed of light.
These cosmic connections are the precursors of causation. Another profound realization is that these relationships are ultimately encoded in the geometry (or the shape) of the Universe. Anyway, digressions aside, we can now define causality in Einstein’s theory.
When two events can be connected by a messenger, they are said to be causally connected
What does this mean practically? It tells us that when considering events on earth, we can safely ignore what’s going on right “now” on the other end of our galaxy—ignoring subtleties in defining what “now” means. As a consequence, this means that there cannot possibly be a coordinated inter-galactic war (sorry Star Wars fans!).
Anyway, now that physics has given us this special causal relationship in the Universe (a causal correlation if you’d like), we are ready to define the most general form of causation.
Einstein’s Theory of Relativity brings another powerful notion: the time ordering of events. It can be mathematically proved that when two events are causally connected as defined above, there is a consistent time-ordering of events.
This consistency is something we take for granted everyday. For instance, we all agree that our parents are born before us, and that the year 2000 occurs before 2020. This is all thanks to the causal structure of our cosmos which gives us a consistent time-ordering of events!
Now, there are two choices for separating causes from effects: causes either come before or after effects. This is where human (or anthropogenic) biases come in. Due to the Big Bang, our Universe is structured such that we all experience the same flow of time. Because we can only manipulate conditions in the present to affect events in the future, there is only one natural way to define causation:
Events in the past cause events in the future
While this may sound completely tautological and self-evident, it is not at all obvious that it can be derived from Einstein’s mathematical description of the Universe. The fact that there is even a consistent general notion of causation is one of the great trumps of Einstein’s theory!
Another weird flip side of causality is that the time-ordering of causally disconnected events is ambiguous! Meaning that we can never answer questions like, “when did intelligent beings first evolve in the Universe?” unless these beings are able to meet-up (or come into causal contact).
Below is a summary of our discussions on causation:
- Physical laws only give correlations, not causation. So causation must be a subset of these correlations
- Einstein’s theory creates a notion of causality that is built into the structure of the Universe
- A consistent arrow of time, combined with Einstein’s causality, allow us to define the past as the cause and the future as the effect
All these above give us the most generally form of causation: every event that is happening now, from you reading this article in front of a screen, to the ebbs and flows of ocean waves in Hawaii, they are all caused by a similar set of events encompassing the entire causal history of the Earth and the Universe!
Coming back to our billiard game earlier, it means that we do in fact have to include part of the beginning of the Universe to fully capture the causation of the game. This reverberates one of Carl Sagan’s famous quote, that
“If you wish to make an apple pie from scratch, you must first invent the Universe”
So, it would seem like we did all this work for nothing, and still we don’t have a working definition of what it means for something to cause another thing in our daily lives.
In order to bridge these gaps, we will have to consider the magnitude of the correlations under discussions (which will be covered in the second part of this article). To judge whether something should be included as part of the cause, human biases would have to come in. For example, while the Big Bang is responsible for human’s existence on earth, we wouldn’t include it as a cause when searching for a cure for cancer. This is largely because we cannot control the Big Bang, and including it just wouldn’t help us cure cancer!
Still, does it mean that our approaches to causal inference and science is misguided or wrong? The answer is no. Causation is an incredibly useful concept that helps us extract information about the world. What fundamental physics reveals, is that we should treat causation as a complex phenomenon that emerges from a combination of fundamental laws and human intuitions. The lack of a fundamental definition only re-emphasize how we should stop being pedantic about how to define causation, and embrace its utility for extracting insights and helping us navigate the world.
Finally, our notion of causation also highlights our shared humanity, as it relies on our shared cosmological experience and senses of agency. I think we should all cherish that fact that we are all under the same causal umbrella, and rejoice how the laws of physics empower us to make sense of this Universe.