The Most Misunderstood Concept in Physics

Summary

This video delves into entropy, a fundamental concept in physics that governs everything from molecular collisions to cosmic evolution. It explains how the Earth receives concentrated, low-entropy energy from the sun, which is crucial for life, contrasting it with the high-entropy energy radiated back into space. The script explores the historical development of thermodynamics, from Carnot's ideal heat engine to Clausius's entropy, and connects these principles to the arrow of time and the universe's ultimate fate. It also touches on the intriguing idea that life itself may be a consequence of the second law of thermodynamics, as it accelerates the natural tendency toward maximum entropy.

Takeaways

• 🌞 The Earth receives a certain amount of energy from the Sun and radiates a fraction of it back into space, maintaining a balance that prevents the Earth from overheating.
• 🔧 Sadi Carnot's work on heat engines led to the understanding of energy efficiency and the concept of an ideal, reversible engine with no energy loss.
• 🌡️ The efficiency of heat engines is determined by the temperatures of the hot and cold sides, and it is impossible to achieve 100% efficiency due to the inherent energy dispersal.
• 🔄 The second law of thermodynamics states that the entropy of the universe tends to a maximum, meaning energy naturally spreads out and becomes less usable over time.
• 🌿 Life on Earth is possible because the Sun provides a low entropy source of energy, which is used by plants and animals, and eventually spread out as entropy increases.
• 🌌 The universe's entropy was very low at the Big Bang, and it has been increasing ever since, providing the conditions for structures like stars and life to form.
• ☕️ Entropy can be thought of as the tendency of energy to disperse, and while high entropy is associated with disorder, low entropy does not necessarily mean high complexity.
• 🖥️ The concept of entropy is crucial for understanding various phenomena, from everyday occurrences like a cup of tea cooling down to the evolution of the universe.
• 🌐 The total entropy of the universe is largely contained in black holes, which have a vast amount of entropy proportional to their surface area.
• 🔮 The universe is expected to reach a state of maximum entropy, known as the heat death, where no interesting processes will occur and the arrow of time will disappear.

Q & A

What is the significance of the concept discussed in the video?

The concept discussed is entropy, which is significant because it governs a wide range of phenomena from molecular collisions to cosmic events. It's also suggested to influence the direction of time and possibly the existence of life.

What is the misconception people have about the Earth's energy exchange with the Sun according to the video?

People often believe that the Earth radiates less energy back into space than it receives from the Sun, but the video clarifies that, for most of Earth's history, the amount of energy in and out should be the same to maintain equilibrium.

Who is Sadi Carnot and why is he important in the context of the video?

Sadi Carnot was the son of a Napoleonic general and a physicist himself. He's important because he made key insights into the efficiency of heat engines, which laid the foundation for understanding the second law of thermodynamics.

What is an ideal heat engine as described by Sadi Carnot?

An ideal heat engine, according to Carnot, is one with no friction and no losses to the environment, operating between two temperature reservoirs, converting heat into work through a cycle of expansion and compression.

Why can't a heat engine be 100% efficient according to the video?

A heat engine can't be 100% efficient because to return the system to its original state, heat must be transferred to the cold reservoir, meaning not all energy can stay in the form of work.

What is entropy and how does it relate to the second law of thermodynamics?

Entropy is a measure of the spread or dispersion of energy. It relates to the second law of thermodynamics, which states that the entropy of the universe tends to a maximum, meaning energy naturally spreads out over time.

How does the video explain the irreversibility of certain processes?

The video explains that when energy spreads out, like heat dissipating, it becomes less usable for work. This spreading is irreversible because it's impossible to recapture the dispersed energy without additional input.

What role does the Sun play in the Earth's entropy according to the video?

The Sun provides a steady stream of low entropy energy to Earth, which is more usable than the energy radiated back into space. This concentrated energy is essential for life and the maintenance of Earth's structures.

How does life on Earth contribute to the increase of entropy?

Life on Earth contributes to entropy increase by converting low entropy energy into high entropy waste, such as through metabolic processes and other activities that dissipate energy.

What is the 'arrow of time' and how is it related to entropy?

The 'arrow of time' refers to the one-way direction or asymmetry of time from past to future. It is related to entropy because processes in the universe, like energy spreading, happen in a way that increases entropy, giving time its forward direction.

What is the heat death of the universe and how does it connect to entropy?

The heat death of the universe is a theoretical end state where all energy is evenly distributed, and no more work can be done. It connects to entropy because it represents a maximum entropy state where the universe has reached its most probable and uninteresting configuration.

Outlines

00:00

🌞 The Mystery of Energy Exchange with the Sun

This paragraph introduces the concept of energy balance between the Earth and the Sun. It discusses the common misconception that the Earth radiates less energy back into space than it receives from the Sun. The conversation highlights the idea that energy is conserved and should be balanced, leading to the question of what else, besides energy, the Earth might be receiving from the Sun. The paragraph ends with a historical note on Sadi Carnot, whose work on the efficiency of steam engines led to the discovery of the second law of thermodynamics.

05:02

🔧 The Ideal Heat Engine and Its Reversible Nature

The paragraph delves into Sadi Carnot's concept of an ideal heat engine, which is a theoretical model with no friction or energy loss. It describes how such an engine works by transferring heat between a hot and cold reservoir to perform work, and how it can be reversed to return to its initial state without additional energy input. The discussion includes the efficiency of this engine, which is not 100% due to the温差 between the hot and cold sides. The concept of absolute temperature scale, Kelvin, is introduced as a way to measure the efficiency of heat engines.

10:02

🌡️ Entropy and the Spread of Energy

This paragraph introduces the concept of entropy as a measure of energy dispersal, developed by Rudolf Clausius. It explains how energy naturally spreads out, leading to an increase in entropy, and how this is related to the irreversibility of processes. The paragraph also discusses the first and second laws of thermodynamics, emphasizing that energy tends to spread out over time, leading to a decrease in usable energy within a closed system. The example of a Rubik's cube is used to illustrate how systems naturally move from ordered states to disordered ones.

15:06

🏠 Entropy and the Role of the Sun in Supporting Life

The paragraph explores how the Earth is not a closed system due to the input of low entropy energy from the Sun. It explains how this energy is used by plants and animals, and how it becomes more dispersed at each step, leading to an increase in entropy. The discussion includes the idea that life on Earth is possible because of the Sun's concentrated energy input and the ability to radiate the dispersed energy back into space. The paragraph also touches on the concept that life may have evolved as a way to accelerate the natural tendency towards maximum entropy.

20:09

🌌 The Role of Gravity and Black Holes in Entropy

This paragraph discusses how gravity plays a crucial role in the early universe's low entropy state, as it tends to clump matter together, which is an unlikely and thus low entropy configuration. It explains how the universe's expansion and cooling led to the formation of structures like stars and galaxies, increasing entropy. The paragraph also covers Jacob Bekenstein's and Stephen Hawking's work on black holes, showing that they are significant contributors to the universe's entropy. It concludes with a reflection on the future of the universe, where entropy will continue to increase until the universe reaches a state of maximum entropy, known as the heat death.

25:10

🍵 The Complexity of Entropy and the Importance of Low Entropy

The final paragraph contrasts the simplicity of low and high entropy states with the complexity found in systems with intermediate entropy. It uses the analogy of tea and milk mixing to illustrate how complexity arises from the interaction of components. The paragraph emphasizes the importance of utilizing the low entropy available to us, as it is the driving force behind understanding and manipulating the world around us. It ends with a sponsorship note for Brilliant.org, an educational platform that helps users develop skills in various fields, connecting learning to real-world applications.

Keywords

💡Entropy

Entropy, in the context of the video, refers to a thermodynamic property that represents the degree of disorder or randomness in a system. It is central to the second law of thermodynamics, which posits that natural processes tend to increase the total entropy of an isolated system. The video explains entropy as a measure of energy dispersal, where energy is most usable when it is concentrated and less usable when spread out. An example from the script is the process of energy transfer in Carnot's ideal engine, where the efficiency is not 100% because some energy is lost to the surroundings, increasing entropy.

💡Second Law of Thermodynamics

The second law of thermodynamics is a fundamental principle discussed in the video that states the entropy of an isolated system will either remain constant or increase over time. This law is illustrated through the concept of energy spreading out and becoming less usable, such as in the example of the engine where not all the energy input results in work output due to losses and energy dispersal.

💡Energy

Energy, as discussed in the video, is the capacity to do work. It is a fundamental concept in physics that governs various phenomena, from molecular collisions to cosmic events. The video emphasizes that while the total amount of energy remains constant (as per the first law of thermodynamics), the quality of energy changes as it spreads out, becoming less useful for doing work, which is directly related to the concept of entropy.

💡Carnot's Ideal Engine

Carnot's ideal engine is a theoretical model of a heat engine with perfect efficiency, introduced by Sadi Carnot in the early 19th century. The video uses this concept to explain the limitations of energy conversion and the role of temperature differences in determining the efficiency of heat engines. It is depicted as a system with no friction and no losses, where heat is converted into mechanical work, illustrating the concept of entropy and the direction of energy flow.

💡Heat Death of the Universe

The heat death of the universe is a theoretical endpoint of the universe where it reaches maximum entropy, leading to a state of uniform temperature and no further possibility for work to be done. The video suggests that this scenario arises from the relentless increase in entropy over time, where all energy becomes so dispersed that no structure or life can be sustained.

💡Low Entropy

Low entropy refers to a state where energy is concentrated and systems are more ordered. In the video, the concept is used to explain the initial conditions of the universe post-Big Bang, where entropy was low, and energy was more compact. This low entropy state allowed for the formation of structures and the eventual emergence of life, as energy could be harnessed and used more effectively.

💡Black Holes

Black holes are regions of spacetime with extremely strong gravitational effects from which nothing, not even particles or radiation such as light, can escape. The video discusses black holes in the context of entropy, mentioning that they contribute significantly to the universe's total entropy. It also touches upon the concept of Hawking radiation, which suggests that black holes are not entirely black but emit small amounts of radiation, contributing to the universe's entropy.

💡Arrow of Time

The arrow of time is the one-way direction or asymmetry of time that is experienced in the macroscopic world, where events cause other events but not vice versa. The video explains that the arrow of time is a result of the second law of thermodynamics, where entropy increases, giving time a direction from past to future. This is illustrated through the example of a Rubik's cube, which becomes more disordered with random moves, but never spontaneously solves itself.

💡Concentrated Energy

Concentrated energy refers to energy that is densely packed and thus more usable for work. The video explains how the sun provides the Earth with low entropy, concentrated energy, which is essential for life. This energy is used by plants and animals, and as it gets spread out through various processes, entropy increases.

💡Life and Entropy

The video suggests that life itself may be a consequence of the second law of thermodynamics, as living organisms are efficient at converting low entropy energy into high entropy waste. Life forms utilize concentrated energy from the sun to grow, reproduce, and carry out various biological processes, which in turn contribute to the overall increase in entropy of the universe.

Highlights

The concept of entropy governs everything from molecular collisions to cosmic evolution and may determine the direction of time.

The Earth receives energy from the sun and radiates a fraction of it back into space, maintaining a balance.

Sadi Carnot's discovery of the ideal heat engine and its efficiency, which is not 100% due to the irreversible nature of energy transfer.

Carnot's ideal engine is fully reversible, but real engines are not due to friction and energy losses.

Efficiency of an ideal heat engine depends on the temperatures of the hot and cold sides, not the materials or design.

Real engines have lower efficiency due to friction, heat dissipation, and non-constant temperature heat transfer.

Rudolf Clausius introduces entropy as a measure of energy spread, with higher entropy indicating less usable energy.

The first law of thermodynamics states that energy in the universe is constant, while the second law says entropy tends to a maximum.

Energy spreads out over time, leading to phenomena like heat transfer from hot to cold objects and the inability to create perpetual motion machines.

Entropy can be thought of as the tendency of energy to spread out, rather than just disorder.

Heat flowing from cold to hot is improbable but not impossible, as explained by Ludwig Boltzmann's statistical interpretation of entropy.

The decrease in entropy in systems like air conditioning is counterbalanced by an increase in entropy elsewhere, such as in power plants.

Life on Earth is possible due to the sun's low entropy energy, which is more usable than the energy radiated back into space.

Life may be a consequence of the second law of thermodynamics, as it accelerates the natural tendency of energy to spread out.

The universe's low entropy at the Big Bang allowed for the formation of structures like stars, planets, and life.

Gravity plays a crucial role in the early universe's low entropy, as matter clumping together increases entropy.

Black holes are a significant source of entropy in the universe, with their entropy proportional to their surface area.

The arrow of time is a result of increasing entropy, giving a clear direction from past to future in the universe.

The universe is expected to reach a heat death where energy is so spread out that no interesting events occur, erasing the arrow of time.

Complex structures like life thrive in the middle range of entropy, where there is a balance between order and disorder.

Transcripts

- This is a video about one of the most important,

yet least understood concepts in all of physics.

It governs everything from molecular collisions

to humongous storms.

From the beginning of the universe

through its entire evolution, to its inevitable end.

It may, in fact, determine the direction of time

and even be the reason that life exists.

To see the confusion around this topic,

you need to ask only one simple question.

What does the Earth get from the sun?

- What does the earth get from sun?

- Well, it's light rays?

- What do we get from the sun? - Heat.

- Warmth.

- Warmth, light.

- Vitamin D, we get vitamin D from-

- We do get vitamin D from the ultraviolet rays.

- Well, a lot of energy.

- What does the earth get from this, energy?

- Yeah, energy.

- Energy.

- Nailed it.

Every day, the earth gets a certain amount of energy

from the sun.

And then how much energy does the earth radiate back

into space relative to that amount

that it gets from the sun?

- Probably not as much, I, you know,

I don't believe it's just radiating right back.

- I'd say less.

- Less.

- Less. - I say less.

- I guess about 70%?

- It is a fraction.

- I'd say 20%.

- Because... - Because we use some of it.

- We use some of the energy. - Mm-hmm.

- We consume a lot, right?

- But the thing about energy is it never really goes away.

You can't really use it up.

- It would have to break even, wouldn't it?

Same amount, yeah.

- You know, cause and effect.

It'd be equal in some ways, right?

- For most of the earth's history,

it should be exactly the same amount of energy

in from the sun as earth radiates into space.

- Wow.

- Because if we didn't do that,

then the earth would get a lot hotter, that'd be a problem.

- That'd be a big problem.

- So, if that is the case...

- Yeah.

- Then what are we really getting from the sun?

- That's a good question.

- Hmm.

- It gives us a nice tan.

- It gives us a nice tan, I love it.

We're getting something special from the sun.

- I don't know, what do we get without the energy?

- But nobody talks about it.

To answer that, we have to go back to a discovery

made two centuries ago.

In the winter of 1813, France was being invaded

by the armies of Austria, Prussia, and Russia.

The son of one of Napoleon's generals

was Sadi Carnot, a 17-year-old student.

On December 29th, he writes a letter to Napoleon

to request to join in the fight.

Napoleon preoccupied in battle, never replies.

but Carnot gets his wish a few months later

when Paris is attacked.

The students defend a chateau just east of the city,

but there're no match for the advancing armies,

and Paris falls after only a day of fighting.

Forced to retreat, Carnot is devastated.

Seven years later, he goes to visit his father

who's fled to Prussia after Napoleon's downfall.

His father was not only a general, but also a physicist.

He wrote an essay on how energy

is most efficiently transferred in mechanical systems.

When his son comes to visit, they talk at length

about the big breakthrough of the time, steam engines.

Steam engines were already being used to power ships,

mine ore, and excavate ports.

And it was clear that the future industrial

and military might of nations

depended on having the best steam engines.

But French designs were falling behind

those of other countries like Britain.

So, Sadi Carnot took it upon himself to figure out why.

At the time, even the best steam engines

only converted around 3% of thermal energy

into useful mechanical work.

If he could improve on that, he could give France

a huge advantage and restore its place in the world.

So he spends the next three years studying heat engines,

and one of his key insights

involves how an ideal heat engine would work,

one with no friction and no losses to the environment.

It looks something like this.

Take two really big metal bars, one hot and one cold.

The engine consists of a chamber filled with air,

where heat can only flow in or out through the bottom.

Inside the chamber is a piston,

which is connected to a flywheel.

The air starts at a temperature just below that

of the hot bar.

So first, the hot bar is brought into contact

with the chamber.

The air inside expands with heat flowing into it

to maintain its temperature.

This pushes the piston up, turning the flywheel.

Next, the hot bar is removed,

but the air in the chamber continues to expand,

except now without heat entering, the temperature decreases.

In the ideal case,

until it is the temperature of the cold bar.

The cold bar is brought into contact with the chamber

and the flywheel pushes the piston down.

And as the air is compressed,

heat is transferred into the cold bar.

The cold bar is removed.

The flywheel compresses the gas further

increasing its temperature until it is just below that

of the hot bar.

Then the hot bar is connected again and the cycle repeats.

Through this process, heat from the hot bar is converted

into the energy of the flywheel.

And what's interesting to note about Carnot's ideal engine

is that it is completely reversible.

If you ran the engine in reverse,

first the air expands lowering the temperature,

then the chamber is brought into contact with the cold bar,

the air expands more, drawing in heat from the cold bar.

Next, the air is compressed, increasing its temperature.

The chamber is placed on top of the hot bar

and the energy of the flywheel is used to return the heat

back into the hot bar.

However many cycles were run in the forward direction,

you could run the same number in reverse, and at the end,

everything would return to its original state

with no additional input of energy required.

So by running an ideal engine, nothing really changes.

You can always undo what you did.

So what is the efficiency of this engine?

Since it's fully reversible,

you might expect the efficiency to be 100%,

but that is not the case.

Each cycle, the energy of the flywheel increases

by the amount of heat flowing

into the chamber from the hot bar,

minus the heat flowing out of the chamber at the cold bar.

So to calculate the efficiency, we divide this energy

by the heat input from the hot bar.

Now the heat in on the hot side is equal to the work done

by the gas on the piston,

and this will always be greater than the work done

by the piston on the gas on the cold side,

which equals the heat out.

And this is because on the hot side,

the hot gas exerts a greater pressure

on the piston than that same gas when cold.

To increase the efficiency of the engine,

you could increase the temperature of the hot side,

or decrease the temperature of the cold side, or both.

Lord Kelvin learns of Carnot's ideal heat engine

and realizes it could form the basis

for an absolute temperature scale.

Imagine that the gas is allowed to expand an extreme amount,

so much that it cools to the point

where all the gas particles effectively stop moving.

Then they would exert no pressure on the piston,

and it would take no work to compress it

on the cold side, so no heat would be lost.

This is the idea of absolute zero,

and it would make for a 100% efficient engine.

Using this absolute temperature scale, the Kelvin scale,

we can replace the amount of heat in and out

with the temperature of the hot and cold side respectively,

because they are directly proportional.

So we can express efficiency like this,

which we can rewrite like this.

What we have learned is that the efficiency

of an ideal heat engine doesn't depend on the materials

or the design of the engine,

but fundamentally on the temperatures

of the hot and cold sides.

To reach 100% efficiency, you'd need infinite temperature

on the hot side or absolute zero on the cold side,

both of which are impossible in practice.

So even with no friction or losses to the environment,

it's impossible to make a heat engine 100% efficient.

And that's because to return the piston

to its original position,

you need to dump heat into the cold bar.

So not all the energy stays in the flywheel.

Now, in Carnot's time, high pressure steam engines

could only reach temperatures up to 160 degrees Celsius.

So their theoretical maximum efficiency was 32%,

but their real efficiency was more like 3%.

That's because real engines experience friction,

dissipate heat to the environment,

and they don't transfer heat at constant temperatures.

So for just as much heat going in,

less energy ends up in the flywheel.

The rest is spread out over the walls of the cylinder,

the axle of the flywheel,

and is radiated out into the environment.

When energy spreads out like this,

it is impossible to get it back.

So this process is irreversible.

The total amount of energy didn't change,

but it became less usable.

Energy is most usable when it is concentrated

and less usable when it's spread out.

Decades later, German physicist, Rudolf Clausius,

studies Carnot's engine, and he comes up with a way

to measure how spread out the energy is.

He calls this quantity, entropy.

When all the energy is concentrated in the hot bar,

that is low entropy,

but as the energy spreads to the surroundings,

the walls of the chamber and the axle

will entropy increases.

This means the same amount of energy is present,

but in this more dispersed form,

it is less available to do work.

In 1865, Clausius summarizes the first two laws

of thermodynamics like this.

First, the energy of the universe is constant.

And second, the entropy of the universe tends to a maximum.

In other words, energy spreads out over time.

The second law is core to so many phenomena in the world.

It's why hot things cool down and cool things heat up,

why gas expands to fill a container,

why you can't have a perpetual motion machine,

because the amount of usable energy in a closed system

is always decreasing.

The most common way to describe entropy is as disorder,

which makes sense because it is associated with things

becoming more mixed, random, and less ordered.

But I think the best way to think about entropy

is as the tendency of energy to spread out.

So why does energy spread out over time?

I mean, most of the laws of physics

work exactly the same way forwards or backwards in time.

So how does this clear time dependence arise?

Well, let's consider two small metal bars,

one hot and one cold.

For this simple model,

we'll consider only eight atoms per bar.

Each atom vibrates according to the number

of energy packets it has.

The more packets, the more it vibrates.

So let's start with seven packets of energy

in the left bar and three in the right.

The number of energy packets in each bar

is what we'll call a state.

First, let's consider just the left bar.

It has seven energy packets,

which are free to move around the lattice.

This happens nonstop.

The energy packets hop randomly from atom to atom

giving different configurations of energy,

but the total energy stays the same the whole time.

Now, let's bring the cold bar back in

with only three packets and touch them together.

The energy packets can now hop around

between both bars creating different configurations.

Each unique configuration is equally likely.

So what happens if we take a snapshot at one instant in time

and see where all the energy packets are?

So stop, look at this.

Now there are nine energy packets in the left bar,

and only one in the right bar.

So heat has flowed from cold to hot.

Shouldn't that be impossible because it decreases entropy?

Well, this is where Ludwig Boltzmann

made an important insight.

Heat flowing from cold to hot is not impossible,

it's just improbable.

There are 91,520 configurations

with nine energy packets in the left bar,

but 627,264 with five energy packets in each bar.

That is the energy is more than six times

as likely to be evenly spread between the bars.

But if you add up all the possibilities,

you find there's still a 10.5% chance that the left bar

ends up with more energy packets than it started.

So, why don't we observe this happening around us?

Well, watch what happens as we increase the number of atoms

to 80 per bar and the energy packets to 100,

with 70 in the left bar and 30 in the right.

There is now only a 0.05% chance that the left solid

ends up hotter than it started.

And this trend continues as we keep scaling up the system.

In everyday solids, there are around 100 trillion,

trillion atoms and even more energy packets.

So heat flowing from cold to hot is just so unlikely

that it never happens.

Think of it like this Rubik's cube.

Right now, it is completely solved,

but I'm gonna close my eyes and make some turns at random.

If I keep doing this, it will get further and further

from being solved.

But how can I be confident that I'm really messing

this cube up?

Well, because there's only one way for it to be solved,

a few ways for it to be almost solved,

and quintillions of ways

for it to be almost entirely random.

Without thought and effort,

every turn moves the Rubik's cube

from a highly unlikely state that of it being solved

to a more likely state, a total mess.

So if the natural tendency of energy is to spread out

and for things to get messier,

then how is it possible to have something

like air conditioning where the cold interior of a house

gets cooler and the hot exterior gets hotter?

Energy is going from cold to hot,

decreasing the entropy of the house.

Well, this decrease in entropy is only possible

by increasing the entropy a greater amount somewhere else.

In this case, at a power plant,

the concentrated chemical energy and coal is being released,

heating up the power plant in its environment,

spreading to the turbine the electric generators,

heating the wires all the way to the house,

and producing waste heat in the fans and compressor.

Whatever decrease in entropy is achieved at the house

is more than paid for by an increase in entropy required

to make that happen.

But if total entropy is constantly increasing

and anything we do only accelerates that increase,

then how is there any structure left on earth?

How are there hot parts separate from cold parts?

How does life exist?

Well, if the earth were a closed system,

the energy would spread out completely,

meaning, all life would cease,

everything would decay and mix,

and eventually, reach the same temperature.

But luckily, earth is not a closed system,

because we have the sun.

What the sun really gives us is a steady stream

of low entropy that is concentrated bundled up energy.

The energy that we get from the sun is more useful

than the energy we give back.

It's more compact, it's more clumped together.

Plants capture this energy and use it to grow

and create sugars.

Then animals eat plants and use that energy

to maintain their bodies and move around.

Bigger animals get their energy

by eating smaller animals and so on.

And each step of the way,

the energy becomes more spread out.

- Okay, interesting.

- Yeah.

- Oh wow, I did not know that.

- There you go.

Ultimately, all the energy that reaches earth from the sun

is converted into thermal energy,

and then it's radiated back into space.

But in fact, it's the same amount.

I know this is a- - You do know this is...

- I'm a PhD physicist.

- Oh, okay, but anyway, so... - I trust you.

The increase in entropy can be seen

in the relative number of photons arriving at

and leaving the earth.

For each photon received from the sun,

20 photons are emitted,

and everything that happens on earth,

plants growing, trees falling, herds stampeding,

hurricanes and tornadoes, people eating,

sleeping, and breathing.

All of it happens in the process of converting fewer,

higher energy photons

into 20 times as many lower energy photons.

Without a source of concentrated energy

and a way to discard the spread out energy,

life on earth would not be possible.

It has even been suggested that life itself

may be a consequence of the second law of thermodynamics.

If the universe tends toward maximum entropy,

then life offers a way to accelerate that natural tendency,

because life is spectacularly good

at converting low entropy into high entropy.

For example, the surface layer of seawater produces

between 30 to 680% more entropy when cyanobacteria

and other organic matter is present than when it's not.

Jeremy England takes this one step further.

He's proposed that if there is a constant stream

of clumped up energy, this could favor structures

that dissipate that energy.

And over time, this results

in better and better energy dissipators,

eventually resulting in life.

Or in his own words,

"You start with a random clump of atoms,

and if you shine light on it for long enough,

it should not be so surprising that you get a plant."

So life on earth survives on the low entropy from the sun,

but then where did the sun get its low entropy?

The answer is the universe.

If we know that the total entropy of the universe

is increasing with time, then it was lower entropy yesterday

and even lower entropy the day before that,

and so on, all the way back to the Big Bang.

So right after the Big Bang,

that is when the entropy was lowest.

This is known as the past hypothesis.

It doesn't explain why the entropy was low,

just that it must have been that way for the universe

to unfold as it has.

But the early universe was hot, dense,

and almost completely uniform.

I mean, everything was mixed and the temperature

was basically the same everywhere,

varying by at most 0.001%.

So how is this low entropy?

Well, the thing we've left out is gravity.

Gravity tends to clump matter together.

So taking gravity into account,

having matter all spread out like this,

would be an extremely unlikely state,

and that is why it's low entropy.

Over time, as the universe expanded and cooled,

matter started to clump together in more dense regions.

And in doing so, enormous amounts of potential energy

were turned into kinetic energy.

And this energy could also be used

like how water flowing downhill can power a turbine.

But as bits of matter started hitting each other,

some of their kinetic energy was converted into heat.

So the amount of useful energy decreased.

Thereby, increasing entropy.

Over time, the useful energy was used.

In doing so, stars, planets, galaxies, and life were formed,

increasing entropy all along.

The universe started with around 10

to the 88 Boltzmann constants worth of entropy.

Nowadays, all the stars in the observable universe

have about 9.5 times 10 to the 80.

The interstellar and intergalactic medium combined

have almost 10 times more,

but still only a fraction of the early universe.

A lot more is contained in neutrinos

and in photons of the cosmic microwave background.

In 1972, Jacob Bekenstein proposed

another source of entropy, black holes.

He suggested that the entropy of a black hole

should be proportional to its surface area.

So as a black hole grows, its entropy increases.

Famous physicists thought the idea was nonsense

and for good reason.

According to classical thermodynamics,

if black holes have entropy,

then they should also have a temperature.

But if they have temperatures, they should emit radiation

and not be black after all.

The person who set out to prove Bekenstein wrong

was Stephen Hawking.

But to his surprise, his results showed that black holes

do emit radiation, now known as Hawking radiation,

and they do have a temperature.

The black hole at the center of the Milky Way

has a temperature of about a hundred trillionth of a Kelvin,

emitting radiation that is far too weak to detect.

So still pretty black.

But Hawking confirmed that black holes have entropy

and Bekenstein was right.

Hawking was able to refine Bekenstein's proposal

and determine just how much entropy they have.

The super massive black hole at the center of the Milky Way

has about 10 to the 91 Boltzmann constants of entropy.

That is 1,000 times as much

as the early observable universe,

and 10 times more than all the other particles combined.

And that is just one black hole.

All black holes together account for 3 times 10

to the 104 Boltzmann constants worth of entropy.

So almost all the entropy of the universe

is tied up in black holes.

That means, the early universe

only had about 0.000000000000003% of the entropy it has now.

So the entropy was low, and everything that happens

in the universe like planetary systems forming,

galaxies merging, asteroids crashing,

stars dying, to life itself flourishing,

all of that can happen because the entropy

of the universe was low and it has been increasing,

and it all happens only in one direction.

We never see an asteroid uncrash

or a planetary system unmix

into the cloud of dust and gas that made it up.

There is a clear difference between going to the past

and the future, and that difference comes from entropy.

The fact that we are going from unlikely

to more likely states is why there is an arrow of time.

This is expected to continue until eventually,

the energy gets spread out so completely

that nothing interesting will ever happen again.

This is the heat death of the universe.

In the distant future,

more than 10 to the 100 years from now,

after the last black hole has evaporated,

the universe will be in its most probable state.

Now, even on large scales, you would not be able to tell

the difference between time moving forwards or backwards,

and the arrow of time itself would disappear.

So it sounds like entropy is this awful thing

that leads us inevitably

towards the dullest outcome imaginable.

But just because maximum entropy has low complexity

does not mean that low entropy has maximum complexity.

It's actually more like this tea and milk.

I mean, holding it like this is not very interesting.

But as I pour the milk in, the two start to mix

and these beautiful patterns emerge.

They arise in an instant and before you know it,

they're gone back to being featureless.

Both low and high entropy are low in complexity.

It's in the middle where complex structures

appear and thrive.

And since that's where we find ourselves,

let's make use of the low entropy we've got while we can.

With the right tools, we can understand just about anything,

from a cup of tea cooling down

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