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.

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.

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:

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.

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:

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!

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<<c and v<<c, t′ is almost equal to t; therefore, if something happens in your present, it happens in my present too. But in our example above, Andromeda is far far away from earth, and our equations come into full play. What is happening in Andromeda now simultaneously with Adam’s present moment has already happened a week ago according to Eve’s. Put in some arbitrary value for v (the speed with which Eve runs in the corridor), and find out the difference in the number of days between what your two spies see. Two events that are simultaneous in one frame of reference may not be simultaneous in a different frame of reference.

Simultaneous means nothing. There is no single now.

Time is Not Universal

Let’s take down the first pillar of Newton’s absolute time. Time is not universal. What is happening in your present may lie in my past or my future. It may also lie neither in my past nor in my future but in an inaccessible region of spacetime called elsewhere — that is a story for another day.

There is no tick-tock-tick-tock that can be heard in the same rhythm throughout the universe. Something that you think will happen in the future may have already happened in my past. The order in which different observers witness two unrelated events is not fixed; Adam may say that event P happened before event Q, while Eve might argue that P happened after Q. In this scenario, a nice and clear relationship where the past causes the present, and the present causes the future breaks down. Indeed, causality itself breaks down.

Time has no Independent Existence

The year 1905 was really special for physics. Einstein showed in special relativity the dependence between space and time and also between mass and energy. In 1915, as a part of general relativity, Einstein further combined spacetime with mass-energy equivalence.

It’s not just speed that slows time. Gravity slows it too. Actually, mass slows down time, and gravity is nothing but the slowing down of time. If things fall down, it is because Earth is a massive object, and it slows down time in its vicinity. In the absence of gravity, time passes uniformly, and things just float without falling down, like they do in outer space.

Time is nothing other than the measurement of change.

— Aristotle

In his enchanting book The Order of Time, physicist Carlo Rovelli describes how Aristotle and Newton disagreed on the nature of time and space. If nothing changes, does time exist? Aristotle would say no, while Newton would say yes. In absolute emptiness where there is nothing, does space exist? Again, Aristotle would say no, while Newton would say yes. Rovelli then tells us that the synthesis between Aristotle’s and Newton’s views is the most valuable contribution Einstein has made towards physics.

Einstein says that time and space do exist even in the absence of tangible matter, but they are not absolute; they are made of the same stuff that other things like tables, chairs, protons, and electrons are made of. Spacetime is a gravitational field. Like other fields, it is neither absolute nor uniform. It influences other fields and, in turn, gets influenced by them.

Thus, we strike down the second pillar. Time does not exist independently on its own.

Past and Future

We believe there is a fundamental distinction between the past and the future. The past has already happened. We may not remember all the details exactly, but we know pretty much what happened. We cannot change the past. The milk has been spilled, and we should not cry about it.

The future, on the other hand, is yet to happen. All possibilities are open. Planning finances, talking to our spouses, negotiating with our employers, self-introspecting, exercising, learning — all these things we do to influence and shape the future into what we want.

In the fundamental laws of physics that describe reality, however, there is no distinction between the past and the future. The equations given in Newton’s laws of motion, Einstein’s relativity, Maxwell’s electromagnetism, or Schrödinger’s quantum mechanics are all reversible; they treat the past and the future as if they were equal in all respects. The equation that governs the motion of a ball rolling down a slope also governs the ball rolling up the slope — and it doesn’t care whether the ball is moving from up to down or from down to up. If there is no difference between the past and the future, why do we remember the past but not the future?

Entropy

There is only one law of physics that distinguishes the past from the future, the second law of thermodynamics, which states that the total entropy of an isolated system can only increase or remain the same, but it can never decrease. So what is entropy, and what does it have to do with time?

Entropy is a measure of disorder in the system. Consider the arrangement of gold molecules in a ring. They have more structure and order than the molecules in a chunk of gold of the same weight. Hence, we say that the ring has lower entropy than the chunk. If the configuration of a system is structured, peculiar, or special, we say that the system has more order and lower entropy. If it is random, shuffled, or disordered, it has higher entropy.

Mathematically, entropy is given by the below formula:

where k stands for the Boltzmann constant, and W is the total number of possible micro-configurations for the given macro-state.

If a system begins in a state of low entropy, it is obvious why its entropy can only increase: because any random movement of molecules will most likely take the system to a more disordered configuration. If a teacup falls down and breaks, its molecules can scatter in a near-infinite number of ways. The number of possible micro-configurations W for the macro-state of a broken cup is far larger than the number of micro-configurations for the macro-state of an intact cup. Hence, we often see a teacup shatter into innumerable pieces leading to an increase in its entropy, but we never see broken pieces of glass spontaneously rearrange themselves to form a teacup.

Let’s take another example. Gently pour some milk into a mug of black coffee. The milk forms a distinct layer at the top. Now, leave this system alone. As the molecules in the mug zip-zap around randomly, the two layers slowly mix up leading to an increase in entropy. But nothing really prevents the reverse from happening. Molecules swishing around randomly in a mug of mixed-up brown coffee can, just out of plain chance, get rearranged in neat layers of milk and black coffee. It’s just that this is highly improbable!

The Arrow of Time

A physical system always evolves from a low-entropy configuration towards a high-entropy one. This unidirectional tendency of entropy to always increase is what gives us the perception of time flowing from the past into the future. This is what introduces irreversibility in our experience of everyday lives where eggs scramble, milk mixes into coffee, glass breaks, hot water cools down, and it is easy to squeeze toothpaste out of the tube but not back into it.

Entropy is order leading to disorder, structure giving way to randomness. The universe started in a state of low entropy, and that is why life is at all possible. Entropy has since then been increasing. Our sun will eventually die. All the stars in the Milky Way will eventually die. The entire universe will slowly crumble leading to an eventual state of maximum entropy or thermal equilibrium where energy and matter will be spread out in a diffused manner throughout the universe making it a cold, dark, bleak place.

But think about this: if the universe had started in a state of high entropy, stars would never have been created, there would be no Earth, and no us. Why the universe started in a state of exceptionally low entropy is a mystery, but its inexorable evolution since then towards states of higher entropy is what creates the perception of time.

Time Arises out of Ignorance

We said that an intact teacup is more special or peculiar than a shattered teacup. But, if you decide to list down the exact location of each molecule that forms the teacup, you will find that every possible configuration is equally special and can occur with the same probability as any other configuration. The sense of order and disorder emerges because we differentiate between a teacup on one hand and all broken configurations on the other. If we were to individually differentiate between every possible configuration in which the cup can shatter, we would find each configuration to be special and peculiar and equiprobable. In such a case, entropy has no meaning.

[Trying to understand time] is like holding a snowflake in your hands: gradually, as you study it, it melts between your fingers and vanishes.

— Carlo Rovelli

Entropy is not a fundamental property. It is, like temperature and pressure, a statistical one. If you isolate a single particle, it has no entropy of its own. Entropy exists because we see reality in a blurred and approximate fashion. It exists because we cannot distinguish between the innumerable micro-configurations of the macro-states we observe. If you assimilate complete information about the exact microscopic subatomic state of the world around you, will the flow of time disappear?

Yes! With complete information about the state of the world, the difference between the past and the future vanishes. The passage of time is a distortion of reality that emerges due to our imperfect knowledge. Time thus is born out of our ignorance.

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