THE ONE WITH CAUSALITY

Shantanu Lokhande
6 min readOct 15, 2020
Photo by Sergey Pesterev on Unsplash

So causality huh?

A very basic concept of physics that turns out to be “not” so basic after all. It has been debated over time and time again. Causality as the name itself suggests deals with cause and effect. Not karma, I am talking about physics. Causality is so important that it proved out to be one of the major motivations behind the Quantum Feild Theory. Don’t worry I won’t go into that much detail. I’ll try to put it in the most simple way possible.

Without any further ado let’s get started.

In layman’s terms, one can understand causality as 2 different events in which one is the CAUSE and the other one is the EFFECT. Cause gives birth to the effect. To be more specific causality means an active relationship that brings to life something new and thereby turning possibility into actuality. For example, the falling of dominoes arranged in a specific way so that one fall triggers a sequence of other falls.

A LIGHT CONE REPRESENTING THE “SPHERE OF INFLUENCE” AROUND A POINT IN SPACETIME. IMG SRC: https://archive.briankoberlein.com/2015/08/24/could-we-ever-build-a-time-machine/index.html

Causal events can be divided into 3 major parts with respect to time. Firstly the events in the past light cone. Secondly the events in the future light cone. Thirdly the events that are currently happening (here/now). Now you must be thinking if it is so simple to classify the events then why don’t we retrace the steps of cause and effect and find the so-called “First cause”? The answer is no, it’s not that easy. Each cause results in a primary phenomenon as well as many secondary phenomena. These phenomenons when combined produce the effect. When you try to retrace them they get lost in the infinite distances of universal interactions.

In classical physics, it was assumed that all events are caused by earlier ones and they obey the laws of physics. This gave birth to the principle of determinism. The principle of determinism basically tells us that any state of an object or event is completely determined by its previous states. For example, with the help of Newton’s Laws of Motion, one can precisely determine the future states of the object like position, velocity, etc. Here is a famous quotation from Pierre Simon Laplace which would give a clear understanding of determinism.

“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual position of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes.”

This quotation is also referred to as “Laplace’s Demon”.

Determinism sounds well and good as long as we are talking about classical physics. But what’s the fun in that?

Let’s look at some complications that arise due to determinism in quantum mechanics and Einstein’s Special Relativity. No no, don’t worry we won’t get into ugly details. As promised, I would keep it simple.

Quantum Mechanics provide a description of the physical behavior of particles at the sub-atomic and atomic levels. But the problem with quantum mechanics is that it’s mostly acausal. In many cases, it fails to identify the cause of the actually observed effects. But when it comes to Einstein’s special relativity it more or less confirmed causality, but binding it into strict boundaries by stating that cause MUST precede its EFFECT according to all “inertial” observers.

Here is a mind boggler for you. Wanna know why Einstein’s Special Relativity never allows communication faster than the speed of light?

The answer is that the cause and the effect are separated by a “timelike”(1) interval and the effect belongs to the future of its cause. If a timelike interval separates these two events, this means that a signal could be sent in between them at less than the speed of light. But on the other hand, let’s assume that the signals could move faster than the speed of light. Then it would allow a signal to be sent across “spacelike”(1) intervals which means that at least to some inertial observer the signal would travel backward in time. This backward flow of time caused problems and so communications faster than the speed of light were never allowed in Special Relativity. Yeah, let that sink in.

(1)Timelike & Spacelike = 4-D Manifold containing 3 dimensions of space and 1 dimension of time fused together into space-time. Basically timelike means it takes more time to traverse through less space and spacelike means it takes less time to traverse through more space. We can understand this using a simple equation

G(λ) = w² — (x² + y² + z²)

Where G(λ) = resulting worldline

W = time component

x,y,z = space components(directions)

Now the worldline is

Timelike when G(λ) > 0,

Spacelike when G(λ) < 0,

Lightlike when G(λ) = 0.

Now you must be thinking what was all that about? We were dealing with just cause and effect then why complicate it with all these worldlines, timelike, spacelike stuff? It was necessary so that you have a strong basic foundation so that it would be easy for you to understand the Causality Principle. The heart of causality theory. It explains why in the 4-D manifold only the time changes and the space remains intact, why can we only see the past/ present state of an object, not it's future. We will look at it with the help of an example and then we will wrap up.

The causality principle states that only timelike or lightlike worldlines could represent the history of a physical object.

Imagine you are standing at a particular distance from a bucket that is being filled with water. Now a “timelike” worldline will explain the history as “at a particular instance in time the water was 2 Liters then 3 Liters etc”. A “lightlike” worldline will explain the history as “when the light carries information to you from the bucket, by the time the information reaches you (maybe in a billionth of a second)the actual state of bucket changed because even light takes some time to travel. So you are seeing the history of the bucket”. This “lightlike” will become more clear if you take things to the celestial level i.e. light from stars, red-shift, etc. But when it comes to “spacelike” worldline the concept of “proper time” is undefined. Yes, the flow of time itself is not defined clearly in such a worldline. Physical objects cannot move according to such a worldline, so we shouldn’t expect to have any notion of the progression of time.

Imagine living in such a “spacelike” worldline. A world in which time won’t be defined. FUN!

If viewed retrospectively the theory of causality came a long way. Over the years it got divided into various parts such as Distributed Causality(the famous butterfly effect), Causal Dynamical Triangulation(how the fabric of space-time itself evolves), and Causal Set(mapping surfaces without changing space-time curves. But let’s not talk about that.

Well with this, we come to an end of our discussion on the basics of causality. I hope that this sparked a bit of your interest in physics. If you made it all the way down till this point then thanks for reading it.

See you soon.

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Shantanu Lokhande

I am a second year student pursuing my BTech in IT department. Also a AI minor student. Trying to spark interest in physics and stuff like....yeah physics.