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"Quantum entanglement- An "easy" explanation from Quora" Topic


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158 hits since 10 May 2017
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Personal logo Bowman Supporting Member of TMP11 May 2017 6:06 a.m. PST

I'll be on a cruise for the next week and a bit and will be without internet usage while on the ship (the rates are too high).

So I left a nice question and answer from Quora about quantum entanglement. Hopefully it is of some interest, especially to GWA who likes these esoteric things


"What is quantum entanglement?

Barak Shoshany
Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics

Answered Jan 14, 2015 · Upvoted by Abhijeet Borkar, PhD in Physics (Astrophysics) and Jess H. Brewer, Professor Emeritus, Dept. of Physics & Astronomy, Univ. of British Columbia

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⟩. This is just a fancy way of writing a vector. I could have just written ψ⃗ but physicists like to write things in a fancy way.

The thing inside the |⟩ can be anything; the letter ψ (psi) is commonly used for historical purposes, but |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⟩ is the linear combination of the states |A⟩ and |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⟩
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⟩. This is just a fancy way of saying that particle 1 is in the state |A⟩ and particle 2 is in the state |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√|↓⟩|↓⟩

The arrows are meant to represent spin up |↑⟩ and spin down |↓⟩. 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 |↑⟩|↑⟩ (i.e. both particles have spin up) and a probability of 1/2 to get |↓⟩|↓⟩ (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."
Reader: "I see. So… How is quantum entanglement explained in <insert interpretation here>?"
Me: "Ask me in the comments, or better yet, ask the entire Quora community in a separate question!""

Now I'm not ashamed to say that this doesn't make a lot of sense to me, but apparently, that puts me in good company. Anyone want to tackle this and make comments?

Winston Smith Supporting Member of TMP11 May 2017 8:18 a.m. PST

Magic? grin
I could explain it better, but the Magician's Union has a very good Hit Squad.
"We laugh at your puny equations!"

Personal logo Bowman Supporting Member of TMP11 May 2017 8:22 a.m. PST

I could explain it better, but the Magician's Union has a very good Hit Squad.

Lol. They could lock you in a box and have you sawn in half by an apprentice Magician.

My Calculus Professor (Bruno Gerhardt Wilhelm Muller….still remember his name) was an expert in Hilbert Spaces. I barely understood that either.

Personal logo Andrew Walters Supporting Member of TMP11 May 2017 9:46 a.m. PST

Let me zoom the lens out and make things worse.

We can think of "understanding" in two sense. I can understand "2+2=4" in the sense that I can understand the math, the equation, and the phenomenon of actually taking two beans and putting them with two other beans and counting four beans. Let's call this practical understanding, but I'm pretty sure you know exactly what I mean.

But when I look over this, I have a *sensation* in my mind of understanding it. It "makes sense", its implications are clear, no questions are left, I am comfortable with it. This sensation of comprehension is *independent* of practical understanding.

By independent we mean this: somethings you feel you understand something, but when the time comes to take the test, make the soufflé, help your kid with their homework, or actually play the game it turns out you do not understand it and have to go back to the book, get bad results, embarrass yourself, etc. We've all been there. We had the sensation of understanding, but we didn't understand it in practice.

Alternately, we often we run into a situation where we study a procedure or some academic material or something and we don't feel like we understand it, but when the time comes we take the test, carry out the procedure, etc, feeling very unsure of ourselves, but everything turns out fine. Turns out we had a perfectly functional understanding of whatever, but not the sensation of understanding.

This is also the explanation for deja vû: you have the sensation of remembering something, but there was no remembering happening, only the sensation thereof.

At the quantum level our intuition quits working. When you're talking about galaxies or molecules we grasp things pretty well using our physical experiences in life either directly or as metaphors. The Earth orbits the Sun like a rock tied to a string that you swing around your head, etc. There are some weird things in astronomy and chemistry, but there are weird things in every day life, too, so we manage. At the quantum level our intuition, derived from our human scale of interacting with physics, is of no use. So we can, through very technically complicated observations and involved theory reach conclusions that we have great confidence in, but while we have the first kind of understanding of them we never get the sensation of understanding them. They are describable in words we know, but their implications are so inconsistent with our personal experiences that we just never feel right about them.

And surely this shouldn't surprise us. Obviously some ideas are more complicated than others. Most likely you can understand some things that some people could not understand. And most likely there are some other people who can understand things you cannot. It's obviously possible for an idea to be so complicated that no person could understand it, and there probably are such ideas, maybe this is one of them. Maybe the human mind just can't have a sensation of understanding quantum entanglement, even if our tools give us a practical understanding of it.

Or maybe the scientists are making it all up. I have my suspicions.

Personal logo Bowman Supporting Member of TMP11 May 2017 11:16 a.m. PST

We evolved in an environment that didn't require us to understand very, very large things, very,very small things and events that happen on an huge time scale and things that happen on a very, very short time scale.

I think phenomena that happen on these extremes do not make intuitive sense, as you are alluding to above. But I don't think the scientists are making this all up. I think they are trying to get their heads around very difficult observations and concepts. It's weird for them too.

Personal logo Parzival Supporting Member of TMP11 May 2017 12:22 p.m. PST

That was as clear as an over-saturated suspension of clay particles in water.

huh?grin

JSchutt11 May 2017 1:24 p.m. PST

Sometimes while shaving I try to implore my quantum entangled twin in the mirror to take my place for a few days while I cool my heals wherever he goes when I'm not looking at him….assuming he is not thinking the same thoughts of me…..

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