Quantum Entanglement and the EPR Paradox

What is entanglement really? And why is it that it's a uniquely quantum phenomena?

Homework:

1 Explain why Alice can never send any messages through this set up.

2 This is one to practice working with wavefunctions of several objects. Prove mathematically that it’s impossible to write our state as two separate states for the electron and positron

3 This one is very relevant to quantum computing. If you have just one electron or positron, you only need 2 numbers to describe its state. Now suppose you have n of them. If they are not entangled, how many numbers to you need to describe the state? What about for a general state that is allowed to be entangled?

Bohmian mechanics stuff:
In Bohmian mechanics, you still have superpositions, they just mean something very different. A Bohmian mech particle only has one position, however, it still has a wavefunction that is a superposition of many possibilities. The difference is that the particle has one position but is influenced by other things in it's wavefunction. A particle like this behaves very differently to a classical particle that only has one position and is not at all influenced by it's other possibilities.

[SagaTympana]

This video was the first explanation that I came away feeling like I maybe understand a bit about how entanglement works. Your explanation of why the "state" has to describe both particles was really helpful. Thank you!

[ScienceAsylum]

Mixing quantum mechanics and relativity through entanglement makes me feel uneasy... but I guess someone has to do it eventually ;-)

[ucasvb]

Good video, but you made a big mistake: "photons never have any spin"

Photons have spin 1! You should have used |+, +〉 + |-, -〉 as the entanglement. :(

[michaelsommers]

You are quite right that no one paid any attention to this for the longest time. I was in school in the mid-80s, when EPR was just making itself felt, and it still had zero effect in the classroom or textbook.

[johanbriglia]

What I just love in your videos is that they do not only make me think afterward, but while I'm watching them also. I often pause your videos just to think about what you just said before resuming. Wondering about all of it sometimes gives me (approximate) answers, but mostly I get more questions about what I thought I knew, which is even more enjoyable. That is just a great way of popularizing a counter-intuitive topic like quantum mechanics. Keep going, you're doing great! ;)

[MichaelHarrisIreland]

Very well explained. It's beginning to come real for me. Feynman would have given you top marks I'm sure, because he said: Now, lets see what that looks like in reality, and that's what you are doing here.

[LoveDoctorNL]

These particles are so entangled, they're such a cute couple ❤️

[bogo]

Entanglement for Valentine's day. I get it ;)

[towseefrehman]

Nice interpretation
But the mistake spin of photon is 1 therefore net spin of electron n positron must be 1 which is actually coz of vector sum as both electron n positron have half spin
Anyways u explained it in a good way

[xero]

Just saw this, even with the mistake, it's the only video that's made entanglement click in my head!
Thank you :)

[bartholomeosphinx]

Another wonderful video. Your general state is certainly in a superposition of the basis states - apologising state and 100% dopamine-rush state What seems to be completely incomprehensible is why you always collapse to the apologetic state.

[sharpyd]

Loving this new wave of videos. I'm glad I stayed subscribed... It's good to have you back!

[chiepah]

1. Information can't be sent through entangled particles because the measurement will be the same regardless of which side does the measurement and there is no way to 'force' a result.

That's all I have, I can barely keep hold of the concept, they maths are beyond me; but this is why I love your videos, you explain the concepts so well that I don't feel (so) bad for not knowing the maths behind them.

[sionae]

I just discovered your channel and found it really great, although I have a doubt : your voice is extremely similar to the girl talking in the oxford website - physics. Is it you? Great video by the way, very clear explanations :)

[Hecatonicosachoron]

Relativity videos would be fun especially if they are mathematical.

[bryanchambers]

1. Alice can only send the message whether her particle is spin up or down but she can not predetermine it. She can't predict what she will measure so the only message she can send is random spin ups or spin downs.

2. That is easy, just multiply using binomial expansion.

3. For number 3, well if its a positron or electron then it is indistinguishable from all the others so each one can have the same a or b. You still only need to two numbers, a or b, they can be multiplied by a phase however.

If they are entangled you would only need one number by symmetry the only number could be 1/(sqrt(n))

Not sure I am right about the last one but I like that it got me thinking about it.

[mehlamfaizi]

we would love a few videoss on relativity. Explaining time dilation and other things. That would truly amazing. Please please dobit

[briteddy]

I love you :| thank you for the learning.

[khhnator]

I'm with Einstein on this one, is just much simpler to assume that the particles are already in a state inside the box all along

[AceNallawar]

1. Alice can't send any message, because no one can manipulate the result of superposition of the electron in a way that the message decrypted from positron makes sense.
2. Plus, since the particles needs to be entangled, they will have to be formed in a same location, and then separated, using normal snail mail like rocket. (basically it's impractical)