Today, we’re asking “why the arrow of time?”

it’s possible that you’re not quite sure what the arrow of time is

don’t worry, I’ll explain

but we need to be clear on something:

it is absolutely impossible to talk about the arrow of time

without talking about the course of time first.

And it’s impossible to talk about the course of time,

without talking about time itself first.

So then, what is time ?

“to expostulate why day is day,

“night night, and time is time,

were nothing but to waste night, day and time.”


Before explaining precisely what time is,

I’ll quote Aristotle (once doesn’t make a habit)

who said the following about time:

“Since the past is no more,

that the future is yet,

and the present is already gone as soon as it begun,

how can there be time ?”

To be honest, I have no jokes to make about this.

The real problem when you want to define time

is that it’s completely impossible – try it and you’ll see –

to define it without presuming the idea of time.

If you try to define time you automatically make a tautological definition.

One that refers to itself.

Most definitions of time revolve around the idea

that time is the phenomenon which enables us to witness transformations,

changes, mouvements, modifications…

The problem is that change, transformation, mouvement, modification,

are impossible to define without already having the notion of time.

This is why we’re not going to formally define time, since it’s impossible,

but considering that we all know what we’re talking about when talking about time

we’re simply going to distinguish 2 different types of time:

the physical time and the psychological time.

Time is a dimension made of a succession of moments.

In everyday life it’s quite easy to observe:

You just have to look at the second hand of a watch

and see that it is a succession of fixed moments.

For scientists, in all fields of physics, this definition works well,

because these moments can be made as short as you want

And as close to each other as you want.

Just like in mathematics with the dots that make up a straight line.

It should also be noted that the fact that time is one dimension,

means, among other things, that it can be defined exactly by a single number.

It happens that this number is called “the date”.

Psychological time, however, is a bit different.

Psychological time is each person’s perception of time passing by

more or less quickly depending on whether you’re active or not.

These 2 definitions are different in many aspects,

but still converge on the most important thing.

They’re different okay, but why? Because in physical time,

the present is the line between the past and the future.

But this line has duration which is null.

In psychological time, what makes the present, is not exactly the present.

In fact it’s what we would normally call the present

(meaning this same line between the past and the future)

BUT with a few seconds from the past.

Psychologically, the present is always a few seconds in the past.

This allows us, for instance, when we listen to a piece of music,

to keep the melody in our head.

This means that when we hear a note, we’ve still got the previous note in mind.

Because if the present was the physical present,

for everyone, Beethoven’s 9th would sound like this:

That would be a pity.

In the same way, these 2 definitions disagree about the fluidity of time:

physical time is a time which flows regularly,

one second after another,

while psychological time, as we all know,

flies by very quickly when you’re active

and seems to slow down when we’re bored to death.

In fact, it’s only when you are really, really bored

that psychological time matches physical time.

That’s when we start counting every second.

Still, both times – psychological and physical – have a huge similarity:

both times unfold from the past and towards the future.

And only this way.

This is what we call the course of time.

As soon as we talk about time as one single dimension

we need to compare it with a line

(which doesn’t need to be a straight line)

This line can be open, meaning it can have 2 ends,

which we’re going to call past and future

or it can be closed, like a loop,

which can have a direction

allowing it to define what is past and what is to come

but which repeats itself, continually circling back on itself.

And consequently, time: cyclic or not?

To answer this question, we need to account for a scientific principle

which has, for now, never been disproved by any experiments what so ever,

meaning that it’s considered as an axiom of science.

It’s called the causality principle.

But what does the causality principle state? Two things:

First: a cause always precedes its effects.

The effects of a cause cannot be witnessed before their cause has occured.

Second: an effect cannot affect its own cause.

That’s the reason why it’s theoretically impossible

to travel back in time.

But that’s the subject for an other video.

So as I said, causality is always true in science.

Therefore, time can only be linear

and cannot be cyclic

Because if time is cyclic: consider an event X which will have an effect Y.

This effect may, in the end,

affect X

which is the cause of Y.

And that violates the causality principle.

thus time is linear.

There’s a past, which may be finite or not,

a future, which may be finite or not,

and the direction of time, which is from the past to the future.

Let’s be precise on one thing:

time is often depicted as a straight line with an arrow.

Time doesn’t have to be a straight line.

It doesn’t have to be regular.

For instance, in general relativity, time doesn’t flow the same way

whether you are in movement

or whether you are subjected to more or less strong gravitational forces,

but it always flows in the same direction!

And that leaves us with one question. We have time, okay.

the course of time, all good, and time has a direction.

But why is there this direction?

There’s a reason for this question:

on the microscopic scale, for example, every phenomenon is reversible.

Reversible means that it can happen one way

or the opposite way.

Reversible doesn’t mean that it goes back in time.

There’s no phenomenon, at the microscopic scale, which can only happen one way.

In relativity, may it be special or general

physical phenomena can also be reversible.

Which means they can happen one way and the opposite way.

At this point it seems like all physical phenomena

governed by the laws of nature

are reversible.

Meaning there’s no reason for time to run only in one direction.

The reason is that I haven’t exactly been honest with you

when I told you that every phenomenon is reversible.

There are phenomena which are irreversible.

These are the phenomena that can be experienced on a daily basis.

Take a glass, drop it, it will shatter on the floor.

This phenomenon is theoretically irreversible.

And when a physical phenomenon is irreversible,

time has an arrow.

The arrow of time is the irreversibility of certain physical phenomena.

At the macroscopic scale can emerge something different

which doesn’t exist at the microscopic scale.

And that’s exactly the question that poses the arrow of time:

How can it be that at some point, seemingly out of nowhere,

an irreversibility occurs?

To answer this question I’ll be needing a prop.

A deck of cards. It’s perfectly in organised.

We have all the spades, the hearts, the clubs and the diamonds

in order.

Now, if I take this deck and I shuffle it…

I shuffle it…

And I shuffle it again…

Can it still be organised?

In reality, it’s absolutely impossible for the deck to be in order.

Unless you’re cheating.

Because if you take this deck there are 52 cards.

There’s only 1 combination in which the deck is in order.

For all the other shuffles, the deck is not in order.

And there are many, many, different shuffles when I say “all the other suffles”.

8 × 10⁶⁷ shuffles.

That’s an 8 followed by 67 zeros!

I looked it up and it has a name:

It’s called 80 unvigintillion. I didn’t even know it existed!

And that’s only 52 cards. The reality of every daily life is much more complex.

A glass of water holds millions of billions of billions of molecules.

And in each of these molecules, there are atoms.

In each of these atoms, there are particles…

This gives us an insane amount of combinations!

So if you take a glass of water and you put an ice-cube in it,

we all know what’s going to happen:

the ice-cube will melt.

But what does that mean?

It means that the ice-cube will go from an organised state, like this,

– these are ice crystals,

ice crystals are beautiful,

they’re all symmetric,

neatly packed, it’s nice and clean –

and when it melts it’s going to become water.

This thing here.

Hydrogen, Oxygen, Hydrogen.

And it is going to move around in every direction

Not too fast, otherwise it’s going to become water vapour,

and it’s going to move, and move, and move.

There are others like this one, you just can’t see them because I’m only holding one.

There are a hole lot of them moving around.

And the question I’m asking is the same:

what are the odds for these molecules to rearrange themselves

in order to form ice crystals again, spontaneously?

It’s just impossible.

What statistics tell us is that

these water molecules can only get more disorganised.

Well in science we have a mean to measure that and it’s called “entropy”

Entropy is what allows us to measure the amount of chaos in a system

of thermodynamic particles.

In thermodynamics, there are laws. And the second law of thermodynamics

says exactly what I just said, except better.

It says that a system of particles, if left alone,

at best doesn’t change, but if it does,

it can only get more disorganised.

To be precise this law states that in an isolated system,

entropy can only increase.

And this law establishes the fact that certain phenomena are irreversible.

I’ll give you a very simple example: take an empty 2 litre cistern.

You pour in 1 litre of hot water

and 1 litre of cold water

You wait

and after a while you’ll get 2 litres of warm water.

It’s absolutely impossible that, spontaneously,

provided there are no outside interferences on the cistern,

that you end up with 1 litre of hot water on one side of the cistern

and 1 litre of cold water on the other side.

It’s impossible.

It’s an irreversible phenomenon because chaos can only increase.

Entropy proves the existence of the arrow of time.

But it doesn’t explain where this arrow comes from.

But in a sense, we’re half way through already.

At the microscopic scale, the equations remain reversible.

So there’s no arrow of time.

And in both cases – macroscopic and microscopic – there are people who disagree.

For the macroscopic, you’re going to have people saying:

“Actually, it’s perfectly reversible, but it’s just so complex

that we’re not capable of creating an equation

to properly describe what’s happening and which is actually reversible.

But if we could have an equation taking in account, in our 2 litres of water,

every particle, factor, etc,

we could build an equation that’s reversible.”

And after all, maybe! It does make sense.

In the same way, on the microscopic scale, we can say that

if the equations do seem reversible,

as soon as we measure or observe the particles

we cause a reduction of the wave functions,

we modify the state of the particles we’re observing

and thus we “force” a state

which induces an irreversibility.

This irreversibility can be due to the obeserver

or it can be due to decoherence.

Decoherence is a theory explaining how we can go from

the quantum scale, where particles can exist in different states at the same time

with probabilities of a particle being at a given place, with a given speed, etc.

How we can go from that scale

to a larger one where things are fixed.

Decoherence is the theory that explains all that, but it remains only a theory.

Just as everything else in quantum physics,

there are many equations that work fine but are still problematic.

So we’ve seen that on the macroscopic scale and on the microscopic one

there can be an arrow of time or not, depending on how you see things.

So the question is: arrow or no arrow ?

I’m not talking from a human point of view.

Of course, in what we perceive as humans

it’s easy to understand the idea

that things go from past to future

and that this is the way it is.

The question is : “In reality,

without taking us, observers, into account,

is there an arrow to time or not?

Here we’re going to need another principle other than the causality principle,

but one that’s still tightly linked to the causality principle,

and which derives naturally from the equations of the standard model.

To recap, the “standard model” is the model that we use today

to describe all that happens in the universe,

from quantum mechanics to the laws of gravity on a cosmic scale.

You could say that it’s the “standard” model to talk about the universe.

It’s the model just before we start getting into string theory,

superstrings theory, the M system and things like that.

It’s not these.

It’s the standard model.

In the standard model every physical phenomenon

has to work accordingly to the so called CPT symmetry.

That’s what’s known as the CPT invariance principle.

It’s going to be a rough ride but we’ll get there.

CPT… C stands for “charge conjugation”

P stands for “parity”

and T stands for “time”.

What this means is that when any physical phenomenon occurs,

if you increment a C symmetry, meaning a charge symmetry [matter anti-matter]

Meaning you take all the particles involved in that phenomenon

and you replace them with their anti-matter equivalent…

and if you have anti-matter, you change it into matter

meaning all matter becomes anti-matter and all anti-matter become matter.

I won’t be explaining what anti-matter is right now.

I’ll talk about it… but some other time.

Then, to this same physical phenomenon already with a C symmetry…

you also apply a P symmetry, of Parity.

P symmetry is the “mirror” symmetry, meaning that left becomes right,

you simply invert the phenomenon [left right]

And if you also apply the T symmetry, meaning that you invert the time

Let me be clear one one thing, when I say “invert time”

it doesn’t mean that you go back in time.

It simply means that the physical phenomenon

is going to unfold normally in time, but in reverse.

For instance, if you have an object falling down in 2 seconds,

it’s going to go up in 2 seconds.

It doesn’t go back in time.

When you apply these 3 transformations to any physical phenomenon

what you get is a phenomenon respecting all the laws of physics

and which is symmetric with the first one.

And that is the CPT invariance principle.

That always holds true in the standard model.

If it doesn’t it either means that the standard model is wrong

or that the causality principle (because this is all highly linked to the causality principle)

that the causality principle is violated.

And the causality principle cannot be violated. That’s impossible.

By definition.

There are some cases where one of these transformations

seems to go against the CPT invariance principle.

But there will always be another transformation which will also

go against this principle and compensate the difference.

Which means that the global result will be symmetric and will obey this principle.

There are certain cases of beta decay where,

if you try to apply the CPT transformations,

they don’t respect the P transformation.

But they don’t respect C either, they compensate one another and it’s okay.

But no matter what, T…

T is perfectly symmetric, so no problem there.

And then comes the kaon. [The neutral kaon]

There is a strange particle called the neutral kaon.

An experiment in 1964 has left the entire scientific world a bit confused.

They found out that when you put

this neutral kaon through a whole lot of different tests

the double CP transformation didn’t fit with the CPT symmetry.

This means that for the invariance principle to be respected

T needs to compensate.

And if T needs to compensate

it means that T also needs to violate this system

and that T is no longer symmetric.

Later, it’s been figured out by other expermiments

that, when a neutral kaon moves, it transforms into anti-matter,

into a neutral anti-kaon and then it transforms back into a neutral kaon and so on.

But the transformation kaon -> antikaon is slower

– a tiny bit slower –

than the anti-kaon -> kaon transformation.

Therefore, T is indeed not perfectly symmetric

and can compensate the asymmetry that we had with C and P.

Thus the CPT invariance principle holds true.

But THIS is the proof that there are instances where T is not symmetric.

Furthermore, what this experiment shows is that, at a given moment,

there are more neutral kaons than there are neutral anti-kaons.

And it would seem – I’m using the word “seem” because this is very high-level stuff

which still probably needs some more verifications –

that this asymmetry with kaons,

that may be also present with other particles,

is enough to explain the presence of matter in the universe

and the fact that the laws governing matter

promote the existence of an arrow of time.

I’d like to thank you all. There is always more of you willing to e-penser (think about it)

You’ve noticed that today’s episode was a lot more complicated than usual.

it was a bit hard, I’m experimenting,

so don’t hesitate to leave a comment and tell me if you like it better this way,

if it’s too complicated, if it’s not clear enough…

just tell me what you think so I know if in the future I can,

in addition to the videos I usually make, start to get into more complicated topics

about things that can be really fundamental.

And as usual, stay curious

and take some time to e-penser (think about it)

English subtitles: Antn Grlkn / 3D

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