You say you want a revolution well, you know, we all want to change the world

https://www.historytoday.com/david-motadel/waves-revolution

Unlocking the "Mystery" of Consciousness

Explaining it requires neither supernatural intervention nor any new fundamental physics



https://blogs.scientificamerican.com/observations/unlocking-the-mystery-of-consciousness/

Why Math Is the Best Way to Make Sense of the World

To tell truth from fiction, start with quantitative thinking, argues the mathematician Rebecca Goldin.

https://www.quantamagazine.org/why-math-is-the-best-way-to-make-sense-of-the-world-20170911/

From New Scientist, 15th Sep 2018

Why creating a chemical brain will be how we understand consciousness

Rowan Hooper

Unorthodox chemist Lee Cronin is leading a radical quest to use chemistry to explain consciousness and create artificial life

“Consciousness will never be realised in silicon - we need to create chemical brains”

Robert Ormerod

WHEN Lee Cronin was 9 he was given a Sinclair ZX81 computer and a chemistry set. Unlike most children, Cronin imagined how great it would be if the two things could be combined to make a programmable chemical computer.

Now 45 and the Regius Chair of Chemistry at the University of Glasgow, Cronin leads a research team of more than 50 people, but his childhood obsessions remain. He is constructing chemical brains, and has ambitions to create artificial life – using a radical new approach.

What drives you?

Everything I'm doing now, I've wanted to do since I was a boy. I wanted to discover something new about the universe. It was stressful for my parents because anything they bought, I just took apart. Once I tried to build a carbon dioxide laser. When I was 7 or 8, I ripped the logic unit out of the washing machine and the cathode ray tube from the TV and tried to connect it all up and make my first computer.

Your poor parents. Were they scientists?

No, my father works in construction and my mother was a nurse but they separated when I was 9 and later divorced. I had learning difficulties and was in remedial class at school. I wasn't interested in what the teachers were doing. I taught myself the maths of relativity when I was 7. I'm determined to answer questions now because I was told I wasn't any good.

What are you doing to pursue those childhood dreams?

There are four missions in my lab: to build a robot that can do all of chemistry (and digitise it – we call it the "chemputer"), to create artificial life, to understand information and to make a chemical brain. They're all effectively about the same thing: understanding the interaction of information in chemistry.

What does "information in chemistry" mean?

It is another way of asking how chemical systems can process information, beyond information storage or logic operations or molecular electronics. It's asking how biological cells process information and what the physical principles are that allow this to happen.

And this can help with your ambition of creating artificial life?

Information as a concept refers to data about reality that is encoded and needs an encoder. So I think that information only exists if there is biology, though not everyone agrees with this approach. But, if we create new chemical systems that process information, perhaps that can be viewed as a new type of life form. Making a new type of life form is a vital endeavour if we are to start to understand the missing physics in biology and chemistry, and the missing rules of the universe that allowed the emergence of life in the first place.

Life is a slippery thing to define...

Here's an idea: let's think of living things as machines that can produce complex objects that could not have randomly formed – from DNA to iPhones, they require information to assemble them. By thinking about life in this way, we can design a way to measure whether something is alive and then use that to make a machine to discover the route to life.

I want to do for chemistry what the Large Hadron Collider has done for physics. They had a theory that predicted the existence of the Higgs boson, developed a model to find out what energy range to look in, then built the LHC to look for it. We are developing a new origin-of-life theory and model so we can work out what time is required, what resources are needed and what scale a machine needs to be to find the right route to a new life form.

How far have you got?

In my lab I'm creating a physical model of the world in which you have simple rocks and simple organic molecules and then develop a way of getting from there to genetics. I want to understand what the difference is between stuff that is just complicated to make, such as an arrangement of molecules, and stuff that requires information to make, such as basic cellular machinery.

We're looking for molecules that have high molecular weight, that are abundant and that require more information to make them than just a random mess. If we start to see such molecules forming, what does it mean? It can't be alive according to standard definitions of life, and it's happening through random chemistry, but if the selected molecules direct the creation of the next, increasingly complex molecules... isn't that like life? I don't have proof that this can happen yet, but my guess is that all matter wants to be Darwinian, and we'll get a selfish molecule that will try to convert all the other molecules to be it.

You say you want to make a chemical brain too. Why?

Your brain is made of molecules and you can think. What is it about your brain that allows this? Instead of trying to image a brain to find out, why don't I just make one? There are 100 billion neurons in the brain, each with about 1000 connections. Overall, there are more potential configurations of the neurons and their connections in your brain than there are atoms in the universe. That's why consciousness will never be realised in silicon computers and why Elon Musk is foolish. He keeps going on about strong AI – machines that can think like humans. We'll have improved AI, but silicon doesn't allow enough available states for things to get really interesting. We'll need to create chemical brains to understand consciousness.

What about Google DeepMind? They're doing some amazing stuff.

DeepMind is brilliant, but I doubt they are ever going to understand what human intelligence really is unless they go beyond silicon-based computers. They are able to mimic some aspects, but ultimately I think it is more like a very good simulation tailored for specific jobs.

I don't think it is even possible to simulate the brain on a computer because we are missing so many rules, and the substrate is not complex enough. I want to make a chemical brain not to beat DeepMind, but to uncover the missing science, and perhaps make different types of non-biological or "inorganic" intelligence.

How would you go about making a chemical brain?

We are trying to see how a physical neural network, rather than an electronic circuit, can be used to physically compute and process information within a polymer, so we can make a physical, chemical, "wet" brain. We use a gel with conducting fibres on top of an electrode array. We tickle the bottom with random electrical inputs, or give it the output of a webcam: show it human faces and see if we can train the gel to recognise them. When we've got a brain gel that we've trained for one problem, we'll see if we can solve other ones with it.

Do you think this could affect how we see consciousness?

If we make a brain in the lab, and show that we can generate self-awareness in a certain chemical environment, that might change our view on consciousness. Take the chemical environment inside a jellyfish: they might be conscious on a basic level, or at least aware of their environment, but in a different way to whatever we imagine consciousness to be. That's if consciousness and free will really exist. I have my doubts.

This article appeared in print under the headline "'I want to make a chemical brain'"

Rowan Hooper is managing editor at New Scientist.

Hubble's Latest Jaw-Dropper Shows Where The Universe's Stars Come From

https://www.forbes.com/sites/startswithabang/2018/08/27/hubbles-latest-jaw-dropper-shows-where-the-universes-stars-come-from/#5e8c27e373c5

Judgments About Fact and Fiction by Children From Religious and Nonreligious Backgrounds

The results suggest that exposure to religious ideas has a powerful impact on children's differentiation between reality and fiction, not just for religious stories but also for fantastical stories.

https://onlinelibrary.wiley.com/doi/full/10.1111/cogs.12138

Why do the godless prosper?

Special edition of the American Psychological Association's journal Psychology of Religion and Spirituality


Paper can be found here

What was the universe like at its hottest?

Immediately after the Big Bang, the Universe was more energetic than ever. What was it like?

By Ethan Siegel

When we look out at the Universe today, we see that it’s full of stars and galaxies, in all directions and at all locations in space. The Universe isn’t static, though; the distant galaxies are bound together in groups and clusters, with those groups and clusters speeding away from one another as part of the expanding Universe. As the Universe expands, it gets not only sparser, but cooler, as the individual photons shift to redder wavelengths as they travel through space.

But this means if we look back in time, the Universe was not only denser, but also hotter. If we go all the way back to the earliest moments where this description applies, to the first moments of the Big Bang, we come to the Universe as it was at its absolute hottest. Here’s what it was like to live back then.

The quarks, antiquarks, and gluons of the standard model have a color charge, in addition to all the other properties like mass and electric charge. All of these particles, to the best we can tell, are truly point-like, and come in three generations. At higher energies, it is possible that still additional types of particles will exist. (E. SIEGEL / BEYOND THE GALAXY)

In today’s Universe, particles obey certain rules. Most of them have masses, corresponding to the total amount of internal energy inherent to that particle’s existence. They can either be matter (for the Fermions), antimatter (for the anti-Fermions), or neither (for the bosons). Some of the particles are massless, which demands they move at the speed of light.

Whenever corresponding matter/antimatter pairs collide with one another, they can spontaneously annihilate, generally producing two massless photons. And when you smash together any two particles at all with large enough amounts of energy, there’s a chance that you can spontaneously create new matter/antimatter particle pairs. So long as there’s enough energy, according to Einstein’s E = mc², we can turn energy into matter, and vice versa.

The production of matter/antimatter pairs (left) from pure energy is a completely reversible reaction (right), with matter/antimatter annihilating back to pure energy. This creation-and-annihilation process, which obeys E = mc², is the only known way to create and destroy matter or antimatter. (DMITRI POGOSYAN / UNIVERSITY OF ALBERTA)

Well, things sure were different early on! At the extremely high energies we find in the earliest stages of the Big Bang, every particle in the Standard Model was massless. The Higgs symmetry, which gives particles masses when it breaks, is completely restored at these temperatures. It’s too hot not only to form atoms and bound atomic nuclei, but even individual protons and neutrons are impossible; the Universe is a hot, dense plasma filled with all the particles and antiparticles that can exist.

Energies are so high that even the most ghostly known particles and antiparticles of all, neutrinos and antineutrinos, smash into other particles more frequently than at any other time. Every particle smacks into another countless trillions of times per microsecond, all moving at the speed of light.

The early Universe was full of matter and radiation, and was so hot and dense that it prevented protons and neutrons from stably forming for the first fraction-of-a-second. Once they do, however, and the antimatter annihilates away, we wind up with a sea of matter and radiation particles, zipping around close to the speed of light. (RHIC COLLABORATION, BROOKHAVEN)

In addition to the particles we know, there may well be additional particles (and antiparticles) that we don’t know about today. The Universe was far hotter and more energetic — a million times greater than the highest-energy cosmic rays and trillions of times stronger than the LHC’s energies — than anything we can view on Earth. If there are additional particles to produce in the Universe, including:

• supersymmetric particles,
• particles predicted by Grand Unified Theories,
• particles accessible via large or warped extra dimensions,
• smaller particles that make up the ones we now think are fundamental,
• heavy, right-handed neutrinos,
• or a great variety of dark matter candidate particles,

the young, post-Big Bang Universe would have created them.

The photons, particles and antiparticles of the early Universe. It was filled with both bosons and fermions at that time, plus all the antifermions you can dream up. If there are additional, high energy particles we haven’t yet discovered, they likely existed in these early stages, too. (BROOKHAVEN NATIONAL LABORATORY)

What’s remarkable is that despite these incredible energies and densities, there’s a limit. The Universe never was arbitrarily hot and dense, and we have the observational evidence to prove it. Today, we can observe the Cosmic Microwave Background: the leftover glow of radiation from the Big Bang. While this is a uniform 2.725 K everywhere and in all directions, there are tiny fluctuations in it: fluctuations of only tens or hundreds of microkelvin. Thanks to the Planck satellite, we’ve mapped this out to extraordinary precision, with an angular resolution that goes down to just 0.07 degrees.

The fluctuations in the Cosmic Microwave Background were first measured accurately by COBE in the 1990s, then more accurately by WMAP in the 2000s and Planck (above) in the 2010s. This image encodes a huge amount of information about the early Universe, including its composition, age, and history. The fluctuations are only tens to hundreds of microkelvin in magnitude. (ESA AND THE PLANCK COLLABORATION)

The spectrum and magnitude of these fluctuations teaches us something about the maximum temperature the Universe could have achieved during the earliest, hottest stages of the Big Bang: it has an upper limit. In physics, the highest possible energies of all are at the Planck scale, which is around 10¹⁹ GeV, where a GeV is the energy required to accelerate one electron to a potential of one billion volts. Beyond those energies, the laws of physics no longer make sense.

The objects we’ve interacted with in the Universe range from very large, cosmic scales down to about 10^-19 meters, with the newest record set by the LHC. There’s a long, long way down (in size) and up (in energy) to the Planck scale, however. (UNIVERSITY OF NEW SOUTH WALES / SCHOOL OF PHYSICS)

But given the map of the fluctuations we have in the Cosmic Microwave Background, we can conclude those temperatures were never achieved. The maximum temperature that our Universe ever could have achieved, as shown by the fluctuations in the cosmic microwave background, is only ~10¹⁶ GeV, or a factor of 1,000 smaller than the Planck scale. The Universe, in other words, had a maximum temperature it could have reached, and it’s significantly lower than the Planck scale.

These fluctuations do more than tell us about the highest temperature the hot Big Bang achieved; they tell us what seeds were planted in the Universe to grow into the cosmic structure we have today.

Regions of space that are slightly denser than average will create larger gravitational potential wells to climb out of, meaning the light arising from those regions appears colder by time it arrives at our eyes. Vice versa, underdense regions will look like hot spots, while regions with perfectly average density will have perfectly average temperatures. (E. SIEGEL / BEYOND THE GALAXY)

The cold spots are cold because the light has a slightly greater gravitational potential well to climb out of, corresponding to a region of greater-than-average density. The hot spots, correspondingly, come from regions with below-average densities. Over time, the cold spots will grow into galaxies, groups and clusters of galaxies, and will help form the great cosmic web. The hot spots, on the other hand, will give up their matter to the denser regions, becoming great cosmic voids over billions of years. The seeds for structure were there from the Big Bang’s earliest, hottest stages.

As the fabric of the Universe expands, the wavelengths of any light/radiation sources will get stretched as well. Many high-energy processes occur spontaneously in the very early stages of the Universe, but will cease occurring when the temperature of the Universe drops below a critical value owing to the expansion of space.(E. SIEGEL / BEYOND THE GALAXY)

What’s more is that once you reach the maximum temperature achievable in the early Universe, it immediately begins to plummet. Just like a balloon expands when you fill it with hot air, because the molecules have lots of energy and push out against the balloon walls, the fabric of space expands when you fill it with hot particles, antiparticles, and radiation.

And whenever the Universe expands, it also cools. Radiation, remember, has its energy proportional to its wavelength: the amount of distance it takes a wave to complete one oscillation. As the fabric of space stretches, the wavelength stretches too, bringing that radiation to lower and lower energies. Lower energies correspond to lower temperatures, and hence the Universe gets not only less dense, but less hot, too, as time goes on.

There is a large suite of scientific evidence that supports the picture of the expanding Universe and the Big Bang. The entire mass-energy of the Universe was released in an event lasting less than 10^-30 seconds in duration; the most energetic thing ever to occur in our Universe’s history. (NASA / GSFC)

At the inception of the hot Big Bang, the Universe reaches its hottest, densest state, and is filled with matter, antimatter, and radiation. The imperfections in the Universe — nearly perfectly uniform but with inhomogeneities of 1-part-in-30,000 — tell us how hot it could have gotten, and also provide the seeds from which the large-scale structure of the Universe will grow. Immediately, the Universe begins expanding and cooling, becoming less hot and less dense, and making it more difficult to create anything requiring a large store of energy. E = mc² means that without enough energy, you can’t create a particle of a given mass.

Over time, the expanding and cooling Universe will drive an enormous number of changes. But for one brief moment, everything was symmetric, and as energetic as possible. Somehow, over time, these initial conditions created the entire Universe.

Dodge City Part 5

The latest in a series highlighting how apologists avoid subjects they can’t counter.


This statement of mine seems to have touched a raw nerve with an apologist: “It’s amazing to think that less than 100 years ago, the majority of Christians in the USA denounced evolution.”




(The statement specifically refers to the USA in the 1920s, which featured, for example, a movement led by William Jennings Bryan, “the leader of a full-fledged national crusade against evolution” and the Scopes trial in 1925.




The point is this: The majority of American Christians in the 1920s were strongly opposed to the teaching of a theory that had been established for sixty years. Some Christian leaders were so  strongly opposed, they would go so far as to take legal action against those who taught the theory.


The apologist tries to counter this information by turning the tables with a list of theories that were similarly opposed by atheists. Obviously, this strategy fails because there’s never been a scientific theory that a group of atheists have opposed or have tried to make illegal.  The apologist therefore provides a glaring example of avoiding the issue.


Here is his post:

"Less than 100 years ago, the majority of atheists argued for an eternally-extent, basically static universe--and built their beliefs around the assumption that the universe had no beginning or "creation" moment.

Less than 100 years ago the majority of atheists believed that the physical laws we observe perfectly accounted for the universe and its existence on their own terms, not as a one-in-ten-to-the-hundredth-power improbability that would allow for the eventual development for life as we know and observe it, not to mention almost certain other manifestations of life and consciousness that we have not directly observed yet.

Less than 100 years ago the majority of atheists argued for "light" being the irreducable component of "reality," not for quantum phenomena which demonstrated that photons behaved differently from the time they were observed and measured, affecting even their state and actions prior to that observation.

Less than 100 years ago the majority of atheists were unaware of quantum entanglement, causing even particles separated by vast distances to act in tandem at the same instant, suggesting interaction with a matrix which may be the manifestation of hyperconsciousness and the source of such. 

Most atheists today probably are oblivious to their own a priori philosophical assumptions and presumptions and the resulting limited lens through which they filter their perceptions of "reality" by only referencing that which conforms to such--i.e., engaging in an endless cycle of circular reasoning.

I could go on, but..."

 

Hmmm… Let’s look at those statements one at a time.

“Less than 100 years ago, the majority of atheists argued for an eternally-extent, basically static universe--and built their beliefs around the assumption that the universe had no beginning or "creation" moment.”

Did they? I can find no evidence to support that idea. The earliest reference I can find to a steady state universe is by a 13th century maverick catholic philosopher called Siger of Brabant.  As far as I can tell, both atheists and theists had no idea the universe was flying apart at unimaginable speeds until Einstein predicted the universe was not static in 1917 and Hubble verified the theory in 1925. There is no evidence of atheists subsequently taking court action to prevent the teaching of the Big Bang theory in schools. (It’s interesting to consider why).  The only thing we know for sure is that atheists do not believe God exists and so they would obviously not believe that God created the universe, whether it be static, expanding or contracting.  So this statement is factually incorrect, and off topic. Next…

"Less than 100 years ago the majority of atheists believed that the physical laws we observe perfectly accounted for the universe and its existence on their own terms, not as a one-in-ten-to-the-hundredth-power improbability that would allow for the eventual development for life as we know and observe it, not to mention almost certain other manifestations of life and consciousness that we have not directly observed yet."

Again, there is no evidence as to what the majority of atheists thought about cosmology in the 1920s. The idea that the laws of nature can explain the origin of the universe itself is very recent and there’s certainly no evidence that the majority of atheists believed what the apologist says they believed. It might be more accurate to say that some atheists believed physics would eventually explain the origin of the universe.   The only thing we can be sure of is that atheists didn’t believe God was responsible for the existence of our universe.


The “one in ten to the hundredth power improbability” comment is presumably the fine tuning trope, debunked long ago. The apologist apparently believes it to be true, which implies he’s never read the counter arguments.  In short, the “improbability” argument is based on a set of assumptions which are then multiplied together. This idea fails because the assumptions are either demonstrably wrong or purely speculative. The overall approach is wrong because it assumes each physical constant stands alone. For example, creationists will argue that if a physical constant (such as the atomic strong force) was to vary by the tiniest fraction, a universe capable of supporting life would not result.  This is a false assumption - a different universe may be the result of such tinkering, but the value could change significantly and still result in a universe that can support life.  Fine tuning/improbability also ignores the interdependencies between the various physical constants which hints at an underlying relationship, hence fundamental constants simply can’t be changed stand alone.  So the true position is that the probability of our universe existing is unknown. It could be 0.000000001% or 99.9999999% or any number in between. No one knows because we don’t know the exact mechanism responsible. For the same reason,  we don’t know the probability of God existing despite His apparent fine tuning.  A different set of assumptions will provide a completely different result.  


With regard to the topic, the apologist’s entire paragraph is yet another example of theories that atheists have not tried to ban and so again, avoids the issue.   Next…

"Less than 100 years ago the majority of atheists argued for "light" being the irreducable [sic] component of "reality," not for quantum phenomena which demonstrated that photons behaved differently from the time they were observed and measured, affecting even their state and actions prior to that observation."

This reveals a misunderstanding of quantum physics which I will explain in a minute. But the point here is that for thousands of years, there were varying beliefs regarding the nature of light. Sometimes it behaved like a wave, sometimes like a particle, depending on the type of experiment. There was no difference of opinion on religious grounds. It was just as likely for a theist to believe light was a particle (or a wave) as it was for an atheist.  It wasn't until 1905 that the truth emerged when Einstein suggested light exists not as waves or particles, but as tiny packets (photons) in other words, quanta, which are ripples in a quantum field. And again - there is no contention to this idea on religious grounds.


There is a further misunderstanding in the second half where the apologist suggests the behaviour of a photon can be affected by a measurement in the future. This is a misunderstanding of the “delayed choice quantum eraser” experiment. There is no “backwards in time” effect as implied by the apologist. The state of a particle before it was measured is not affected by the measurement. The state of a particle (or system of particles)  before it is measured, is unknown and not determinate. Measurement causes the wave function to collapse, revealing its state.


So again - no evidence of a religious controversy with theories of light, no difference of opinion between atheists and theists on the quantum nature of photons. We have a misunderstanding of the subject and avoidance of the issue. Next…

"Less than 100 years ago the majority of atheists were unaware of quantum entanglement, causing even particles separated by vast distances to act in tandem at the same instant, suggesting interaction with a matrix which may be the manifestation of hyperconsciousness and the source of such."

Same issues as before. No one (be they atheist or theist) was aware of quantum entanglement until 1935 when Einstein realised it was a prediction of quantum mechanics and Erwin Schrödinger formalised the theory. Einstein assumed the ides was silly and sadly didn't live to see it verified by experiment forty years later. The concept is accepted equally by theists and atheists – there is no opposition to this idea on religious grounds.


The pointlessness of the apologist's argument is compounded by a major misunderstanding of the concept. Entangled particles do not “act in tandem”. There is a sort of “interaction with a matrix” if we consider quantum fields to be “a matrix” but it's this "matrix" that manifests the particles in the first place.  There is certainly no evidence to suggest that entanglement is the “manifestation of hyperconsciousness” whatever that means, because there is no communication between entangled particles.  If two particles are entangled they form a single system, the measurement of the state of each particle is correlated but as with any quanta, the states are unknown until measured. If particle A is measured and appears “left handed” then we know the other particle is “right handed” even if it’s a trillion miles away, and vice versa. And when we measure the state of one of the particles, they are no longer entangled.


Even if the apologist understood what entanglement was, atheists and theists are comfortable with entanglement being taught in school, there is no dispute between atheists and theists regarding the concept of entanglement so again, not relevant to the issue.

Quantum Entanglement in a nutshell

As well as the article below, check this...
https://www.sciencenews.org/blog/context/entanglement-spooky-not-action-distance
Part 2 here https://www.sciencenews.org/blog/context/quantum-spookiness-survives-its-toughest-tests?mode=blog&context=117

Plus this paper on string theory https://arxiv.org/pdf/1512.02477v5.pdf

An excellent overview of Quantum Entanglement by Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics

For my next trick I will explain quantum entanglement in 5 minutes to anyone with basic knowledge of linear algebra (no prior knowledge of physics or quantum mechanics necessary), as I promised elsewhere on Quora.

Let's say I have a physical system (a particle, for example). This system has some properties (position, momentum, spin and so on). In quantum mechanics we write the quantum state of a system as |ψ⟩$|\psi ⟩$. This is just a fancy way of writing a vector. I could have just written ψ⃗$\overrightarrow{\psi }$ but physicists like to write things in a fancy way.

The thing inside the |⟩$|⟩$ can be anything; the letter ψ$\psi$(psi) is commonly used for historical purposes, but |cat\ is\ alive⟩$|\text{cat is alive}⟩$ is also a perfectly good quantum state.

These quantum states live in a vector space. We call this a Hilbert space and we say that all the possible states of the system are vectors in this space. Now, as you know, if you have some vectors in a vector space you can always write a linear combination of them. For example, |A⟩+|B⟩$|A⟩+|B⟩$ is the linear combination of the states |A⟩$|A⟩$ and |B⟩$|B⟩$. (Again, in quantum mechanics we like to use fancy language so we call this a superposition of states. But it's just a linear combination of vectors.)

In quantum mechanics the coefficients of each state in the superposition are called probability amplitudes, and in general they are complex numbers (since our Hilbert space is a complex vector space).

Roughly speaking, if we perform a measurement on the superposition (assuming that it's in the right basis, etc., but I don't want to get into too much detail since we only have 5 minutes) we will measure only one of the states in the superposition, with the probability given by the absolute value squared of the amplitude.

Here's an example. If my superposition is
15‾‾√|A⟩+25‾‾√|B⟩+25‾‾√|C⟩$\sqrt{\frac{1}{5}}|A⟩+\sqrt{\frac{2}{5}}|B⟩+\sqrt{\frac{2}{5}}|C⟩$
Then I will measure A with probability 1/5, B with probability 2/5 or C with probability 2/5. (Again, the probabilities are the squares of the coefficients.)

(For more information about quantum states and measurements see for example my answer to In layman's term, what is a quantum state? and my answer to What are the postulates of quantum mechanics?)

Are you still with me? Great! Now, every 7 year old can tell you that if you want quantum entanglement you need to have more than one particle, right? So let's say I have two particles. Now my system is a so-called composite system of two separate systems. It's still a vector space, just a bigger one.

In this bigger Hilbert space, I can write a quantum state like so: |A⟩|B⟩$|A⟩|B⟩$. This is just a fancy way of saying that particle 1 is in the state |A⟩$|A⟩$ and particle 2 is in the state |B⟩$|B⟩$. (The order matters! The state on the left or right is always that of particle 1 or 2 respectively.)

So, we had 1-particle states, then we had superpositions of them, then we had 2-particle states. The next step is, of course, superpositions of 2-particle states. And this is where quantum entanglement happens.

Let's say I have the following superposition:

12‾‾√|↑⟩|↑⟩+12‾‾√|↓⟩|↓⟩$\sqrt{\frac{1}{2}}|\uparrow ⟩|\uparrow ⟩+\sqrt{\frac{1}{2}}|\downarrow ⟩|\downarrow ⟩$

The arrows are meant to represent spin up |↑⟩$|\uparrow ⟩$ and spin down |↓⟩$|\downarrow ⟩$. But the states can be anything, they don't have to be spin states.

The above superposition means that, if I measure the spin of the 2-particle system, I have a probability of 1/2 to get |↑⟩|↑⟩$|\uparrow ⟩|\uparrow ⟩$ (i.e. both particles have spin up) and a probability of 1/2 to get |↓⟩|↓⟩$|\downarrow ⟩|\downarrow ⟩$ (i.e. both particles have "spin down").

And that, folks, is quantum entanglement! (Or at least, a very simple example of it.)

Reader: "Wait, what? That's it?"

Me: "Yes, that's it."

Reader: "What do you mean, that's it? Where is the faster-than-light communication?"

Me: "It's nowhere. There is no such thing. It's just a common misconception. There is no communication of any kind taking place, not in any speed and certainly not faster than light."

Reader: "What about time travel? And parallel universes? And wormholes?"

Me: "Completely unrelated. You've been watching too many sci-fi movies."

Reader: "Well, that is disappointing."

Me: "I'm sorry. But hey, at least now you know how quantum entanglement works!"

Reader (after some time): "Aha! Wait a minute! What if I take one particle to the Andromeda galaxy, 2.5 million light years from Earth, and then measure its spin? How will the particle on Earth instantly know to have the same spin? They must communicate somehow. Surely something fishy is going on here!"

Me: "Nope. The entangled state I defined above simply says that the measurements of the spins of the two particles are correlated. It doesn't matter what the distance between them is. If one is measured to have spin up, then the other will also have spin up simply because they were entangled in such a way that their spins are correlated."

Reader (after reviewing the math): "Okay, I get that this is what the math says, but it still doesn't make sense to me."

Me: "Congratulations; you're in good company. Great minds such as Einstein also thought it doesn't make sense. Physicists and philosophers of physics have been debating the meaning of quantum mechanics in general, and quantum entanglement in particular, ever since quantum mechanics was first formulated, and are still debating it today, almost 100 years later."

Reader: "Surely they have reached some conclusions after 100 years..."

Me: "Sort of. They have come up with a very long list of interpretations of quantum mechanics which attempt to make sense of weird quantum phenomena, such as entanglement. An interpretation of quantum mechanics is an attempt to explain what is "really" going on behind the math."

Reader (after some time): "I clicked on the link. There are so many different interpretations... Which is the correct one?"

Me: "Unfortunately, since the experimental predictions are unchanged by the interpretations, it's impossible to determine which interpretation is the correct one, or if there even is a correct one! The only thing we know for sure is that all experiments ever performed have supported the validity of quantum mechanics. It's true independently of how you interpret it."