The EPR Paradox & Bell's inequality explained simply
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Published 2020-02-14
This video is on Quantum entanglement, Bell’s inequality, EPR paradox, nonlocality, determinism vs nondeterminism and probability. Bohr and Einstein argued passionately about their views on the essence of reality. And for 30 years, both views were considered equally valid. Then in 1964, Irish physicist John Bell devised a way to prove whether Einstein’s view of a classical, deterministic view of reality was correct, and he put this in a simple elegant equation – called the Bell Inequality.
The weirdness of quantum mechanics can be demonstrated with a dice. If the dice was a quantum system, it would be in superposition. It would be a 1, 2, 3, 4, 5, and 6 all at the same time. It’s value can only be known once it is measured. Einstein, was bothered by this interpretation of quantum mechanics. Einstein along with Boris Podolsky and Nathan Rosen came up with what they thought disproved the Copenhagen interpretation. The crux of their argument rested on the idea of a phenomenon in quantum mechanics called entanglement. EPR argued that since nothing can travel faster than light according to special relativity, this should invalidate the Copenhagen interpretation. This was the EPR paradox.
in 1964, John bell proposed an equation to determine who was right. In a universe where local hidden variables are true, when the two particles are emitted, they know what their state is going to be in all three directions, Z, X, and Q from birth. And there are only 8 possibilities of spins that each particle could have.
what is the probability that Alice measures in the z direction, gets a positive spin, and Bob measures in the X direction and gets a positive spin? Well, if the above case is for Alice, there are 4 events where Z is positive. In order for Bob to get X positive, Alice would have to have measured X as negative. So these would be in event 3 and event 4. To get the probability we have to divide by the total number of events, 8.
Let’s do this for two more scenarios. What is the probability that Alice measures positive in the Z direction, and Bob measures positive in the Q direction? In this scenario, it would be event 2 and event 4. Again we divide by 8 to get the probability.
And the third case is: What is the probability that Alice measures positive in the Q direction, and Bob measures positive in the X direction? This would be event 3 and event 7, divided by 8 for probability.
P: Z+, X+ = E3 + E4/8
P: Z+, Q+ = E2 + E4/8
P: Q+, X+ = E3 + E7/8
So these are the three probabilities given the hidden variables theory. Now here is big insight that John Bell had:
If I take the total number of Events, and multiply that by the probability that Alice measures Z positive and Bob measures X positive, this has to be less than or equal to the total number of events times the probability that Alice measures Z positive, and bob measures Q positive, plus the probability that Alice measures Q positive, and bob measures X positive.
P:Z+,X+ less than or equal to P:Z+,Q+ + P:Q+,X+
I can prove this is true by doing simple math:
E3 + E4 is less than or equal to E3 + E4 + E2 + E7
This makes total sense, because E3 and E4 are on both sides of the equation. And E2 and E7 have to be positive. So this inequality absolutely HAS to be true for any hidden variables theory to be true.
But what happens in a universe where the laws of quantum mechanics are correct, and not hidden variables theory?
And that probability of Bob measuring Q to be positive, after Alice has measured Z to be positive, is given by the following equation:
P: Z+,Q+ = sin^2 of 45 degrees/2
This is the critical difference between quantum mechanics and hidden variables theory. The probability is not linear but looks like sine wave. When you plot this out, this is what the probabilities look like: So you can see from the graph that at 0, and multiples of 90 degrees, the two systems are in agreement. But in between, like at 45 degrees, the probability is 25% for hidden variables, and about 14.6% for quantum mechanics.
#bellsinequality
#eprparadox
#bellstheorem
But the proof is in the pudding, because in test after test, the sine function correlation has been confirmed. The particle does not behave linearly, and so the hidden variables theory cannot be correct.
So most theorist do not think special relativity is violated, because we can’t communicate using this seemingly faster than light phenomenon.
All Comments (21)
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The understanding of this material doesn't really come from one video, it comes from watching a whole bunch of them, listening to all their perspectives, and then slowly merging together a coherent interpretation. It's very exciting! Thank you for producing your videos and adding perspective to this problem.
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The most outstanding thing about this video by Arvin Ash is throwing in the explanation of the Mathematics in a way for the Layman to understand ...no other big media company Science show has ventured into this realm..not even the BBC .Congratulations!
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"The universe has rigged the game against me." I've known this all my life... SIGH.
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continually stunned at his ability to take incredibly complex concepts and topics and make them accessible in a conversational and layman-friendly way. truly setting the standard for content in these genres.
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This is far and away the best explanation of Bell's inequality I have ever seen/read. Arvin has truly hit the nail on the head, not too hot, not too cold, just right. I actually think I understand exactly what Bell's inequality is all about. Thank you Arvin!!!
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I have no idea what he said but I enjoyed listening to him.
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Bravo to the actors playing Alice and Bob. It’s very difficult to stand motionless in front of a camera for a long period of time and not lose focus / concentration.
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good teachers make a huge difference, thank you!
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I have seen many of these explanations but this is the best. You hit a few key points that are always overlooked and those key points made it very clear. The meat that most explanations don't explain is at 14:47. That was the missing part that you nailed! Good Job!!!!!
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I can tell Arvin takes his role of teacher quite seriously. Loved this video and the subject matter is always edgy. That is Arvin explains current accepted science as simply as possible with mysterious difficult to comprehend topics.
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I repeatedly ignored your videos in search results and recommendations, but from now on you will be among the first ones I click. Great job!
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Dear Arvin, i have seen so many videos on the topic but i must say that you have nailed the explanation at its best and not only in this video but in lots of other videos of yours. Thanks for putting your brilliant efforts to let us understand the topics that we are not much familiar with in our institutes.
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A really good video. I liked Jimi Alkalili’s explanation on the episode Einstein’s Nightmare (obviously simplified similar reasoning). However I love this modern era we live in where we can get videos like these - offering clear explanations of the actual theory. Very well made in my view.
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This is by far the best explanation of quantum entanglement
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Best video ever made about Bell's theory and the meaning of Epr-Kopenhag combat.
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you are my favorite youtuber explaining quantum theories, cause you never use equations nor complicate, you always find ways to explain it to the everyday people out there. But this video wanst one of those :(
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Best video about entanglement I've seen .
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you make some of the best videos, i like the way you present info, you're an entertaining person to listen to! thanks for all these and keep up the great work!
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I really loved this video. Your explanation was amazing and very easy to understand. The part I loved the most was the math and the way you simplified it so that Bell's inequality made sense. Please do more videos with maths like this. Keep up the good work👍
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Lovely Arvin. It's a delight to hear you explain physics, real world, warped universe, Quantum world and the macrocosm. You not only fire my imagination, but also enlighten me to relate the magnificent forces of nature, their effects and affects. It is a chancy chancy universe or.... Keep it up!
