Time Is An Illusion Born Out Of Our Ignorance

Imagine for a moment that you are having a conversation with a caveman. You tell him that the sun he sees in the sky every day is the same sun. A new sun does not emerge from beyond the hills every morning, and neither does it drown into the sea every evening.

“Oh, but it has to be a new sun. It comes up from here, and it goes down there!”

he retorts, his hands spread out pointing in opposite directions. You shake your head. Before explaining how the earth rotates around itself and revolves around the sun, you urge him: ‘Okay, just hear me out with an open mind…’

Here’s the thing about time: it is not real. There is nothing special about the present moment; in fact, a universal present moment does not even exist. The past and the future are equal in all respects. Our notion that time flows irreversibly from the past into the future is an illusion born out of our ignorance about the world. It exists only in our subjective perceptions and not as part of objective reality.

The distinction between past, present, and future is only a stubbornly persistent illusion.

— Albert Einstein

Modern physics makes these statements very convincingly and leaves little room to refute them. Let’s look at time and deconstruct it in this article. Let’s do it keeping an open mind.

Newton’s Absolute Time

We believe that time is universal; that it proceeds in a tick-tock fashion throughout the universe at the same speed.

We believe that time is independent and exists on its own regardless of everything else.

We believe that time is unidirectional; that things move from their past into their future but never the other way around.

Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration.

— Isaac Newton

Newton based his theory of mechanics on this notion of absolute time. Although this has arguably been one of the most successful theories ever proposed, chinks began to appear in it at the beginning of the twentieth century when time began to lose its absoluteness. In simple, easy to understand, bite-sized steps, we will proceed to examine time and deny it these three pillars one by one.

Spacetime Diagrams

Time is not absolute; it is relative. But what do we even mean by relative?

Alice and Bob are sitting in a cafe. Bob gets a call from his mother. He needs to go home, so he starts walking in a straight line towards his house at a constant speed. Alice remains sitting at the table.

If we assume for simplicity that Alice and Bob move only on a 1-D line, and we plot their locations on the X-axis and time on the Y-axis, we get a spacetime diagram like the one below.

Figure 1: What Alice sees from her frame of reference

This is how Alice will observe Bob from her frame of reference. But how will Bob observe Alice? We will use a piece of empirical evidence here: if I see you moving away from me at a speed v, you will see me moving away from you with the same speed v in the opposite direction.

To get the spacetime diagram from Bob’s frame of reference, we slide the X-axis towards the left progressively at each time interval while keeping the Y-axis the same. This is known as a shear transformation. Now, Bob appears to be stationary while Alice appears to be moving in the opposite direction. The lines that Alice and Bob make on the graph are called their worldlines.

Figure 2: What Bob sees from his frame of reference (in classical mechanics)

Simple enough. Let’s add another object there. Suppose there is a cat sitting with Alice and Bob at the table. As soon as Bob gets up, the cat also starts trotting in the direction of Bob’s house at a different speed. The two spacetime diagrams from Alice’s and Bob’s frames of reference would look like:

Figure 3: Alice, Bob, and the cat (in classical mechanics)

Note an important feature of this diagram: the cat appears to be moving at different speeds for different observers (the worldline of the cat is different in the two frames of reference). Since Alice is at the table and Bob is moving in the same direction as the cat, Alice will think the cat is moving faster than what Bob thinks. Our shear transformations work just fine in classical mechanics, but there’s a problem when we consider objects that move at speeds close to the speed of light.

Lorentz Transformations

In the late 1800s and early 1900s, physicists struggled to explain a strange phenomenon: regardless of whether you’re moving towards the source of light or away from it, the observed speed of light remains constant.

What happens then if our cat is moving at the speed of light? According to the classical spacetime diagrams we drew above, Alice should observe the cat moving at a speed faster than what Bob sees. In reality, both of them would measure the cat’s speed as 299,792,458 meters per second i.e. the speed of light.

To accommodate this thing about the speed of light, we need a different transformation in which the worldline of an object traveling at the speed of light (our cat) remains unchanged when we change the frame of reference from Alice’s to Bob’s. In other words, both Alice and Bob should see the cat moving at the same speed of light even if Alice and Bob are not at rest with respect to each other. If you have not followed this, read it again, and let it sink in — this is important.

Lorentz transformations do just this, and they are at the heart of Einstein’s special relativity. Before getting into them, eyeball the spacetime diagram below. According to special relativity, this is what Bob would see if we use Lorentz transformation to accommodate the phenomenon of constant speed of light instead of the classical shear transformation.

Figure 4: What Bob sees (in relativistic mechanics) Figure 5: Alice, Bob, and the cat (in relativistic mechanics)

Note what happens to the worldline of the cat moving at the speed of light. In the classical transformation of figure 3, it changes. In the relativistic transformation of figure 5, the worldline of the cat remains unchanged. Below are the equations that govern the transformation:

Figure 6: Lorentz transformations

If (t, x) are the time and location coordinates of an event in Alice’s frame of reference, they will become coordinates (t′, x′) in Bob’s frame of reference, where v is the speed with which Bob is moving with respect to Alice, and c is the speed of light.

Well, okay, so what’s the big deal? Here is where things get interesting. In the shear transformation, new time was the same as old time, and new location depended only on old location. Time and space were independent of each other. Movement through space and movement through time were two unrelated things.

Now, look at the equations that govern Lorentz transformation, and you will see that movement through time and movement through space influence each other. Time and space are no longer independent entities; they are relative and depend on each other!

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a union of the two will preserve an independent reality.

— Hermann Minkowski

Loss of Simultaneity

Imagine you are the chief spymaster of planet Earth, and you know that a hostile alien civilization from Andromeda is planning to attack Earth in the near future. You have invented a magical tablet, and you have given one tablet each to your two best spies, Adam and Eve. The tablet provides live coverage of whatever is happening inside the Andromedean military council building at that instant.

Your sources tell you that an important meeting is going to take place in Andromeda where the alien leadership will decide whether to attack Earth or not. You tell Adam and Eve to report to your office with their devices. You sit with Adam at the table with his tablet. Adam peers into the screen and tells you that the meeting is underway in Andromeda, and the alien military generals are arguing about the pros and cons of attacking earth. While thoughts swim in your head about what you should do, Eve bursts into the room. She checked the tablet while she was running in the corridor towards your office, and she saw that the alien spaceships have already departed for Earth!

Figure 7: Andromeda paradox: Adam and Eve see two different present moments since they are moving with respect to each other — Thanks, Deepti, for the illustration!

Neither Adam nor Eve nor their tablets are lying. The present moment in Andromeda is different for Adam and Eve because they are not at rest with respect to each other. This is described as the Andromeda paradox by Roger Penrose in his fascinating book The Emperor’s New Mind.

It’s worth taking a look at the equations in figure 6 again. In our daily lives, the velocities and distances (represented by v and x) are typically small. When x