Electrons DO NOT Spin

Summary

量子力学には多くの奇妙な現象がありますが、量子自転という現象は特に理解が難しいとされています。この動画は、電子の量子自転がどのように物質の構造に影響を与え、またどのように量子力学の深遠な洞察につながるかを探求しています。実験と歴史的背景を交えて、量子自転の磁的性質、量子力学での自転の記述方法、そして自転がどのように粒子の相互作用と物質の構造に関わるかを解説しています。

Takeaways

• 量子力学には多くの奇妙な現象がありますが、量子自転という現象は誰も理解していません。
• 物理学の授業で行われる経典的なデモンストレーションは、角動量保存の説明に役立ちます。
• アイアンシリンダーが垂直方向の磁場に置かれ、急に定常速度で回転することを示す実験は、エインシュタイン・デハース効果と呼ばれます。
• 電子は自転していませんが、角動量を持っているようです。これは量子力学的なものであり、電子のような粒子の性質です。
• Stern-Gerlachの実験では、銀原子が磁場を通過し、原子内の電子が磁矩を与えるため、特定の方向に偏向します。
• 量子自転は、電子の性質として量子化されています。測定する方向に依存するため、古典的な回転とは異なります。
• 量子力学では、スピンを記述するために、特別な数学的对象であるスピンオルを使います。
• スピンオルは、360度の回転ではなく、720度の回転が必要とされます。これは、電子のような粒子がどのように振るうかを説明するのに役立ちます。
• 粒子の線形モメンタムは、その位置に根本的に関連しています。同様に、角動量は、粒子の方向性に関連しています。
• スピンは、粒子が持つ回転の自由度から生じるため、角動量は定義できます。
• 粒子はスピン数で区別され、半整数（fermion）または整数（boson）です。この違いは、粒子の相互作用に深い影響を与えます。
• fermionの「反社会的的な」性質は、物質の構造を形成するポアリンエクザル原理に責任があります。
• 量子統計学の定理は、スピンと粒子の性質に関連する現象を説明します。

Q & A

量子スピンとは何ですか？

量子スピンは、電子などの粒子が持つ非常に奇妙な種類の角動量です。これは、古典的な回転のように考えられがちですが、電子は古典的に回転しているわけではありません。量子スピンは、粒子の基礎的な量子力学的プロパティであり、质量や各種の電荷と同様に重要です。

アインシュタイン・デハアス効果とは何ですか？

アインシュタイン・デハアス効果は、1915年にアインシュタインとデハアスが行った実験によるものです。この実験では、鉄の円筒をスレッドからぶら下げ、垂直方向の磁場をかけることで、円筒がすぐに一定の速度で回転することを示しました。これは、角動量保存の原理に反するように見える現象です。しかし、実際には、外部の磁場が鉄を磁化し、鉄の外殻の電子が自らのスピンを整列させることで、角動量が保存されます。

Zeeman効果とは何ですか？

Zeeman効果は、原子が外部の磁場に置かれると、電子がエネルギーレベル間を跳躍させる際に放出されるフォトンの特定の波長が、磁場の存在によって分裂する現象を指します。この効果は、古典的な物理学の考え方で説明できますが、さらに複雑な分裂が観察されたことから、異常Zeeman効果と呼ばれる新たな現象が発見されました。

Stern-Gerlach実験とは何ですか？

Stern-Gerlach実験は、1921年にオットー・スターンが提案し、翌年ヴァルター・ゲルラークが行った実験です。この実験では、銀の原子が磁場のグラディエントを通過するように射出され、原子の外殻の単一電子が原子に磁矩を与えるため、外部の磁場によって原子に力が働き、それが原子を偏向させます。予想される乱反射の代わりに、銀の原子が2つの地点にのみ当たり、最も極端な偏向に対応する場所に現れます。

量子力学におけるスピンの数学的表現は何ですか？

量子力学において、スピンはスピンオブジェクトである特別な数学的オブジェクトとして表現されます。これは、一般的なベクトルとは異なり、360度の回転で元の状態に戻る代わりに、720度の回転が必要であるという、非常に奇妙な回転特性を持っています。

fermionsとbosonsの違いは何ですか？

fermionsは半整数のスピン量子数を持つ粒子で、電子、プロトン、中子などがそれに該当します。一方、bosonsは整数のスピン量子数を持つ粒子で、光子やグルーオンなどの力の媒介者粒子が該当します。fermionsはパウリ排他原理により、同じ量子状態を共有できず、bosonsは同じ量子状態に集積することができます。

スピンが物質の構造にどのように影響を与えるか？

スピンは物質の構造に根本的な影響を与えます。fermionsのスピンは、パウリ排他原理をもたらし、電子が独自のエネルギーレベルを持つことになり、これが元素の周期表や物質の構造を形成する基礎となります。また、bosonsのスピンは、宇宙の基本的な力の媒介者であり、物質間の相互作用に関与しています。

スピンが現実の構造にどのように関連しているか？

スピンは、物質の構造を決定するだけでなく、現実の構造にも深く関連している可能性があります。スピンオブジェクトは、空間時間の亜原子的な織物に沿って考えることができます。これらのオブジェクトは、奇妙な結び目のようなものです。スピンは、これらの結び目がどのように機能し、現実が形成されるかを理解する可能性のある手がかりです。

エントロピーと量子纠缠の関係は何ですか？

エントロピーは、システムの混乱度を測定する指標であり、量子纠缠は、システムの部分間の関連性です。エントロピーは、観察者の視点によって相対的であり、量子纠缠は、システム全体の情報含量を決定する要素の一つです。量子纠缠が低い場合、システムのvon Neumannエントロピーも低くなります。

宇宙の初期状態におけるエントロピーはどのようになっていたか？

宇宙の初期状態におけるエントロピーは、非常に低いとされています。これは、宇宙が非常に小型で高温で均一であったため、重力的な自由度がほとんど占有されておらず、低いエントロピーを有していたと考えられています。しかし、物質のエントロピーは非常に高かったため、重力エントロピーが物質エントロピーを圧倒していたのです。

電子が回転しているわけではないなぜスピンを如此く表現するのか？

電子が回転しているわけではないが、「スピン」という言葉を使用するのは、電子が持つ非常に奇妙な種類の角動量を説明するためです。この角動量は、古典的な物理学的な回転とは別の現象であり、量子力学的な性質を持っています。そのため、別の言葉で説明することが難しいため、「スピン」という言葉が使われることがあります。

スピンが電子の磁矩にどのように影響を与えるか？

スピンは、電子の磁矩に直接影響を与えます。電子はスピン量子数を持っているため、スピンが変化すると、電子の磁矩も変化します。これは、電子が磁场の中で力をを受けたり、銀の原子がStern-Gerlach実験で偏向するようにする現象の原因となります。

アインシュタイン・デハアス効果で観察された角動量保存は、どのようにして解明されたのか？

アインシュタイン・デハアス効果で観察された角動量保存は、外部の磁場が鉄を磁化し、電子のスピンが整列化することで解明されました。この整列化によって、鉄の円筒が角動量を得、円筒の回転が起こることで角動量が保存されると考えられています。

Outlines

00:00

🌀 量子自旋の神秘性と実験的検証

この段落では、量子自旋という量子力学における複雑で神秘的な現象について説明されています。量子自旋は、電子のような粒子が持つ非常に基本的な量子的角運動です。実験的な検証として、アインシュタイン・デ・ハアス効果が紹介されており、鉄の円筒が外部の磁場によって回転することを示しています。また、電子が自旋を持っていることを示すゼーマン効果も触れられています。電子の自旋は、古典的な回転ではなく、量子力学的なものであり、粒子の構造や物質の構成に深く関わることを強調しています。

05:03

🔬 スターン・ゲラフ実験と量子自旋の磁的性質

この段落では、スターン・ゲラフ実験について説明されています。この実験は、銀原子が磁場を通過する際に量子自旋が磁的モーメントを帯び、それがどのように影響を与えるかを示しています。実験の結果、原子が画面の2つの地点にしか当たりませんでした。これは、量子自旋が特定の方向を持つことが示されています。また、自旋は量子力学で非常に重要な役割を果たしており、保則と統計の原理に基づく粒子の性質と相互作用を決定します。

10:05

📐 量子自旋と角運動の関係性

この段落では、量子自旋と角運動の関係性に焦点を当てています。自旋は、粒子が持つ回転の自由度から生じる保存量であり、古典的な回転とは異なります。自旋は、粒子の位置と関連付けられた角位置の概念です。また、自旋は、粒子がどのように相互作用するかを定めるための鍵となる性質であり、フェルミオンとボーソンという2種類の粒子に分類されます。この違いは、物質の構造形成や宇宙の基本的な法則に影響を与えることになります。

15:10

🌌 宇宙の初期状態とエンタングルメント

最後の段落では、宇宙の初期状態とエンタングルメントの関係性について議論されています。宇宙の初期状態における低いエントロピーと量子自旋の役割が説明されています。宇宙の非常に早期段階で、粒子がすでにエンタングルメントであった可能性や、宇宙の膨張がエンタングルメントな地域を永遠に分離した可能性についても触れられています。また、情報理論の創始者であるクロード・シャノン博士にちなんで「The Cloud」という言葉の由来についても言及されています。

Keywords

💡量子スピン

量子スピンは、電子などの素粒子が持つ固有の角運動量であり、古典的な回転運動とは異なる量子力学的な性質です。このビデオスクリプトでは、量子スピンがどのようにして物質の構造や磁場に影響を与えるかを探求しています。例えば、アインシュタイン・デハース効果やシュテルン＝ゲルラッハの実験が挙げられ、これらの現象を通じて量子スピンの奇妙な特性が示されています。

💡角運動量の保存

角運動量の保存は物理学の基本原則の一つで、閉じた系では角運動量の総和が変わらないという法則です。スクリプトでは、自転椅子に座った教授が自転車の車輪を持ち上げて反対方向に回転するデモンストレーションを通じて、この原則が説明されています。これは量子スピンを理解するためのアナロジーとして用いられ、量子スピンもまた角運動量の形態の一つとして機能することが示されています。

💡アインシュタイン・デハース効果

アインシュタイン・デハース効果は、鉄のシリンダーが磁場内で回転を始める現象です。

Highlights

Quantum spin is a fundamental property of particles that has deep insights into the nature of the quantum world.

The conservation of angular momentum is demonstrated in a classic physics experiment involving a spinning wheel and a rotating professor.

The Einstein de-Haas effect shows that an iron cylinder starts rotating in a magnetic field due to the alignment of electron spins.

Electrons are not spinning like bicycle wheels, but they possess a strange type of angular momentum without classical rotation.

Quantum spin is a manifestation of a deeper property of particles responsible for the structure of all matter.

The Zeeman effect and the anomalous Zeeman effect led to the understanding of electron spin and its magnetic properties.

The Stern-Gerlach experiment revealed the quantized nature of electron spin, showing that it can only take on specific directions.

Electron spin is an intrinsic angular momentum that is a quantum mechanical property, not explainable by classical physics.

Pauli's work on the two-valuedness of electrons led to the development of the concept of spinors in quantum mechanics.

Dirac's equation, which incorporates special relativity, also includes spinors, revealing the importance of spin in quantum theory.

Spinors describe particles with strange rotation properties, requiring a 720-degree rotation to return to their original state.

The concept of spin is related to the orientation of particles and their rotational degree of freedom in quantum mechanics.

Fermions, particles with half-integer spins, and bosons, with integer spins, exhibit different behaviors and interactions.

The Pauli Exclusion Principle, a result of fermion behavior, is responsible for the structure of matter and the periodic table.

Spin statistics theorem explains the fundamental differences between fermions and bosons and their interactions.

The nature of quantum spin and its implications for the structure of reality are still being explored and understood.

Entropy and quantum entanglement are interconnected, with the former being relative and dependent on the context of observation.

The low entropy at the Big Bang suggests a highly ordered early universe, which may have implications for understanding quantum entanglement.

The concept of 'The Cloud' in information theory is mistakenly named and mispronounced, originally referring to Dr. Shannon.

Transcripts

Quantum mechanics has a lot of weird stuff  - but there’s one thing that everyone agrees

that no one understands. I’m talking about quantum spin. Let’s find out how chasing

this elusive little behavior of the electron led us to some of the deepest insights into

the nature of the quantum world.

There’s a classic demonstration done in undergraduate physics courses - the physics

professor sits on a swivel stool and holds a spinning bicycle wheel. They flip the wheel

over and suddenly begin to rotate on the  chair. It’s a demonstration of the conservation

of angular momentum. The angular momentum  of the wheel is changed in one direction,

so the angular momentum of the professor has  to increase in the other direction to leave

the total angular momentum the same.

Believe it or not, this is basically the same experiment - suspend a cylinder of iron from

a thread and switch on a vertical magnetic field. The cylinder immediately starts rotating

with a constant speed. At first glance this appears to violate conservation of angular

momentum because there was nothing spinning  to start with. Except there was - or at least

there sort of was. The external magnetic field  magnetized the iron, causing the electrons

in the iron’s outer shells to align their spins. Those electrons are acting like tiny

bicycle wheels, and their shifted angular momenta is compensated by the rotation of

the cylinder.

That explanation makes sense if we imagine  electrons like spinning bicycle wheels - or

spinning anything. Which might sound fine because electrons do have this property that

we call spin. But there’s a huge problem: electrons are definitely NOT spinning like

bicycle wheels. And yet they do seem to possess  a very strange type of angular momentum that

somehow exists without classical rotation. In fact the spin of an electron is far more

fundamental than simple rotation - it’s a quantum property of particles, like mass

or the various charges. But it doesn’t just cause magnets to move in funny ways - it turns

out that quantum spin is a manifestation of a  much deeper property of particles - a property

that is responsible for the structure of all matter. We’ll unravel all of that over a

couple of episodes - but today we’re going to

Today we’re going to talk about what  spin really is and get a little closer to

understanding what this weird property of nature.

The experiment with the iron cylinder is called  the Einstein de-Haas effect, first performed

by, well, Einstein and de-Haas in 1915. It wasn’t the first indication of the spin-like

properties of electrons. That came from looking  at the specific wavelengths of photons emitted

when electrons jump between energy levels  in atoms. Peiter Zeeman, working under the

great Hendrik Lorenz in the Netherlands, found  that these energy levels tend to split when

atoms are put in an external magnetic field.  This Zeeman effect was explained by Lorentz

himself with the ideas of classical physics. If you think of an electron as a ball of charge

moving in circles around the atom, that motion  leads to a magnetic moment - a dipole magnetic

field like a tiny bar magnet. The different alignments of that orbital magnetic field

relative to the external field turns one energy level into three.

Sounds reasonable. But then came the anomalous  Zeeman effect. In some cases, the magnetic

field causes energy levels to split even further  - for reasons that were, at the time, a complete

mystery. One explanation that sort of works is  to say that each electron has its own magnetic

moment - by itself it acts like a tiny bar magnet. So you have the alignment of both

the orbital magnetic moment and the electron’s  internal moment contributing new energy levels.

But for that to make sense, we really need to think of electrons as balls of spinning

charge - but that has huge problems. For example, in order to produce the observed

magnetic moment they’d need to be spinning  faster than the speed of light. This was first

pointed out by the Austrian physicist Wolfgang  Pauli. He showed that, if you assume electrons

have a maximum possible size given by the best  measurements of the day, then their surfaces

would have to be moving faster than light to give the required angular momentum. And

that’s assuming that electrons even have a size - as far as we know they are point-like

- they have zero size, which would make the  idea of classical angular momentum even more

nonsensical. Pauli rejected  the idea of associating such  

a classical property like rotation to

the electron, instead insisting on calling it a “classically non-describable two-valuedness”.

OK, so electrons aren’t spinning, but somehow  they act like they have angular momentum. And this

is how we think about quantum spin now. It’s  an intrinsic angular momentum that plays into

the conservation of angular momentum like  in the Einstein de-Haas effect, and it also

gives electrons a magnetic field. An electron’s  spin is an entirely quantum mechanical property,

and has all the weirdness you’d expect from  the weirdest of theories. But before we dive

into that weirdness, let me give you one more  experiment that reveals the magnetic properties

that result from spin.

This is the Stern-Gerlach experiment - proposed  by Otto Stern in 1921 and performed by Walther

Gerlach a year later. In it silver atoms are fired through a magnetic field with a gradient

- in this example stronger towards the north  pole above and getting weaker going down.

A lone electron in the outer shell of the silver atoms grants the atom a magnetic moment.

That means the external magnetic field induces a  force on the atoms that depends on the direction

that these little magnetic moments are pointing  relative to that field. Those that are perfectly

aligned with the field will be deflected by the most - either up or down. If these were

classical dipole fields - like actual tiny bar magnets - then the ones that were only

partially aligned with the external field should be deflected by less. So a stream of

silver atoms with randomly aligned magnetic  moments is sent through the magnetic field.

You might expect a blur of points where the  silver atoms hit the detector screen - some

deflected up or down by the maximum, but most  deflected somewhere in between due to all

the random orientations. But that's not what’s  observed. Instead, the atoms hit the screen

in only two spots corresponding  to the most extreme deflections.

Let’s keep going. What if we remove the screen and bring the beam of atoms back together.

Now we know that the electrons have to be aligned up or down only. Let’s send them

through a second set of Stern-Gerlach magnets,  but now they’re oriented horizontally. Classical

dipoles that are at 90 degrees to the field would experience no force whatsoever. But

if we put our detector screen we see that the atoms again land in two spots - now also

oriented horizontally.

So not only do electrons have this magnetic  moment without rotation, but the direction

of the underlying magnetic  momentum is fundamentally quantum.  

The direction of this "spin" property

is quantized - it can only take on specific values. And that direction depends on the

direction in which you choose to measure it.  Here we see an example of Pauli's two-valuedness

manifesting as something like the direction  of a rotation axis, or the north-south pole

of the magnetic dipole.

But actually this two-valuedness is far deeper  than that. To understand why we need to see

how spin is described in quantum mechanics. It  was again Pauli who had the first big success

here. By the mid 1920s physicists were very  excited about a brand new tool they’d been

given - the Schrodinger equation. This equation  describes how quantum objects behave as evolving

distributions of probability - as wavefunctions.It  was proving amazingly successful at describing

some aspects of the subatomic world. But the  equation as Schrodinger first conceived it

did not include spin. Pauli managed to fix this by forcing the wavefunction to have two

components - motivated by this  ambiguous two-valuedness of electrons.  

The wavefunction became a very

strange mathematical object called a spinor,  which had been invented just a decade prior.

And just one year after Pauli’s discovery,  Paul Dirac found his own even more complete fix

of the Schrodinger equation - in this case to make it work with Einstein’s special

theory of relativity - something we’ve discussed  before. Dirac wasn’t even trying to incorporate

spin, but the only way the equation could be derived was by using spinors.

Now spinors are exceptionally weird and cool,  and really deserve their own episode. But

let me say a couple of things to give you a taste. They describe particles that have

very strange rotation properties. For familiar  objects, a rotation of 360 degrees gets it

back to its starting point. That’s also true of vectors - which are just arrows pointing

in some space. But for a spinor you need to  rotate it twice - or 720 degrees - to get

back to its starting state.

Here’s an example of spinor-like behavior. If I rotate this mug without letting go my

arm gets a twist. A second rotation untwists me.

We can also visualize this with a cube attached  to nearby walls with ribbons. If we rotate

the cube by 360 degrees, the cube itself is back to the starting point, but the ribbons

have a twist compared to how they started.  Amazingly, if we rotate another 360 - not

backwards but in the same direction - we get  the whole system back to the original state.

Another thing to notice is that the cube can  rotate any number of times, with any number

of ribbons attached, and it never gets tangled.

So think of electrons as being connected to  all other points in the universe by invisible

strands. One rotation causes a twist, two brings it back to normal. To get a little

more technical - the spinor wavefunction has  a phase that changes with orientation angle

- and a 360 rotation pulls it out of  phase compared to its starting point.

To get some insight into what spin really is,  

think not about angular momentum,  but regular or linear momentum.

A particle's momentum is fundamentally  connected to its position.

By Noter's theorem, the invariance  of the laws of motion to changes in

coordinate location gives us the law of the  conservation of momentum. For related reasons

in quantum mechanics position and  momentum are conjugate variables.

Meaning you can represent a particle wavefunction  in terms of either of these properties.

And by Heisenberg's uncertainty principle  

increasing your knowledge of one, means  increasing the unknowability of the other.

If position is the companion variable of momentum,  what's the companion of angular momentum?

Well it's angular position. In other  words the orientation of the particle.

So one way to think about the  angular momentum of an electron

is not from classical rotation,  

but rather from the fact that they  have a rotational degree of freedom

which leads to a conserved  quantity associated with that.

They have undefined orientation, but  perfectly defined angular momentum.

Some physicists think that spin is  more physical than this. Han Ohanian,  

author of one of the most used quantum textbooks.

shows that you can derive the right values of the  electron spin angular momentum and magnetic moment

by looking at the energy and charge  currents in the so called Dirac field.

That's the quantum field surrounding  the Dirac spinor aka the electron,  

imply that even if the electron

is point like, it's angular momentum can arise  from an extended though still tiny region.

However you explain it, we have an excellent  working definition of how spin works.

We say that particles described by spinors have spin quantum numbers that are half-integers

- ½, 3/2, 5/2, etc. The electron itself has spin ½ - so does the proton and neutron.

Their intrinsic angular momenta can only be observed as plus or minus a half times

the reduced Planck constant,  

projected onto whichever direction  you try to measure it. We call these

particles fermions. Particles that have integer  spin - 0, 1, 2, etc. are called bosons, and

include the force-carrying particles like the photon, gluons, etc. These are not described

by spinors but instead by vectors, and behave  more intuitively - a 360 degree rotation brings

them back to their original state.

This difference in the rotational  properties of fermions and bosons  

results in profound differences

in their behavior - it defines how they interact  with each other. Bosons, for example, are

able to pile up in the same quantum states, while fermions can never occupy the same state.

This anti-social behavior of fermions  

manifested as the Pauli Exclusion  Principle and is responsible

for us having a periodic table, for electrons  living in their own energy levels and for matter  

actually having structure. It’s the reason

you don’t fall through the floor right now. But why should this obscure rotational property

lead to such fundamental behavior? Well this  is all part of what we call the spin statistics

theorem - which we’ll come back to in an episode very soon.

Electrons aren’t spinning - they’re doing something far more interesting. The thing

we call spin is a clue to the structure of matter - and maybe to the structure of reality

itself through these things we call spinors - strange little knots in the subatomic fabric of

spacetime.

Last time we talked about the connection between  quantum entanglement and entropy - this was

a heady topic to say the least, but you guys had such incredibly insightful comments and

questions.

Joseph Paul Duffey asks whether entropy is  an illusion created by our observation of

isolated components within a "larger"  entangled system? Well the answer

is that entropy is sort of relative.  It's high or low depending on context. 

The air in a room may be perfectly mixed and

so considered “high” entropy. But if that room  is warm compared to a cold environment outside,

then the total room + environment is at a relatively low entropy compared to the maximum

- if you opened the doors and  let the temperature equalize.

Von Neumann entropy is different to thermodynamic  entropy in that it represents the information

contained in the system and extractable in principle, versus information that’s lost

to the system by entanglement with the  environment with the environment. On  

the other hand, classical or  thermodynamic entropy represents

information that is hidden beneath the crude  properties of the system, but may in principle

be extracted. And yet von Neumann entropy has  a similar contextual nature. If your system

has no entanglement with the environment then  its von Neumann entropy is zero. But if you

consider a subsystem within that  system then that entropy rises.

Randomaited asks the following: If entropy only increased over time, which implies it

was at its minimum at the Big Bang, does that  mean there was no quantum entanglement at

the Big Bang? To answer this we’d need to know why entropy is so low at the Big Bang - and

that’s one of the central mysteries of the universe. But, I’ll give it a shot anyway.

So we can’t really talk about the t=0 beginning  of time, because that moment lost in our ignorance

about quantum gravity and inflation and whatever  other crazy theory we haven’t figure out

yet. But what we do know is that at some very,  very small amount of time after t=0, the universe

was extremely compact - which meant hot and  dense, and it was also extremely smooth. The

compact part is where the low entropy comes  from. The “gravitational degrees of freedom”

were almost entirely unoccupied. On the other  hand, the extreme smoothness meant that the

entropy associated with matter was extremely  high. Energy was as spread out as it could

get between all of the particles and the different  ways they could move. The low gravitational

entropy massively outweighed the matter entropy,  so entropy was low. That smoothness seems

to suggest the particles of the early universe  were already entangled - otherwise how did

they spread out their energy?

Chris Hansen makes the same point, asking if  the conditions of the Big Bang meant everything

started out entangled. You’d think so - but  that’s not necessarily the case. Remember

that von Neumann entropy is relative to the 

system you’re talking about,  and so is entanglement.

Let’s say you have a bunch of particles that are not entangled with each other but

are all entangled with another bunch of particles  somewhere else. If you ignore those other

particles then it seems like there’s no entanglement in the particles of the first

system.  

And yet those particles may have correlated  thermodynamic properties due to their mutual

connection to the outside. In the early universe, the extreme expansion of cosmic

inflation may have permanently separated entangled  regions, but left those regions with an internal

thermal equilibrium which does NOT require maximal  entanglement within the regions themselves.

In other words, the universe - or our patch of it - may have started out unentangled and

at low entropy, even if it was at thermal equilibrium.

Lincoln Mwangi also dropped some knowledge,  informing us that “The Cloud” - is actually

named after Dr, Shannon, the founder of the  field of information theory. As with many

of these things, the word has been corrupted  over time and is now routinely mispronounced.

This is very disrespectful, and I intend to write a series of op-eds to correct the matter.

Right after we upload this video to the Claude.