The EPR Paradox & Bell's inequality explained simply

two of the biggest intellectual Giants of modern physics changed our view of reality and proposed their theories around the same time in the early 20th century yet their views about reality were completely different Niels Bohr one of the founders of modern quantum mechanics and the father of the Copenhagen interpretation argued that reality or the state of a particle at the fundamental level was not only unknown but was unknowable until it was measured Albert Einstein passionately disagreed with this idea and believed that reality was knowable and that probabilities could not completely define reality that there had to be an objective reality out there independent of measurement he famously said in his dramatic statement do you really believe the moon only exists when you look at it Bohr and Einstein argued passionately about their views on the essence of reality and for 30 years both views were considered equally valid and scientists chose sides then in 1964 Irish physicist John Bell devised a way to prove whether I Stan's view of a classical deterministic view of reality was correct and he put this in a simple elegant equation called the Bell inequality although the equation is simple understanding what it means is not so easy so how did this simple equation disprove the ideas of the most famous and powerful scientist of the 20th century and forced us to confront the unsettling truth that we may live in a fundamentally non deterministic universe the answer is coming up right now before I talk about the EPR paradox and bells inequality I want to point out that part of my inspiration for this video was from a documentary that I watched in Magellan TV by Jim al-khalili called Einsteins nightmare it's a fascinating show and the full story of quantum mechanics and the thought processes that led to it becoming the defining theory of reality this is just one of many eye-opening documentaries on Magellan TV Magellan is a streaming documentary service that I think you're gonna love it was founded by film makers and producers who bring premium in-depth documentary content you can watch it on any of your devices as well as your TV anytime without any disruptions and you can watch it in 4k my friends I'm delighted to tell you that Magellan TV has an exclusive offer right now for our vinash viewers if you use the link in the description you'll get one free month trial I highly recommend Magellan TV but be sure to use the link in the description the central weirdness of quantum mechanics can be demonstrated with the toss of the dice if the dice was a quantum system like a photon electron or atom it would be in superposition that is its position and other properties in a sense would be up in the air like a dice thrown before it hits the table it's a 1 2 3 4 5 & 6 all at the same time according to the most accepted interpretation of quantum mechanics the Copenhagen interpretation pioneered by Niels Bohr and Werner Heisenberg it's not only that the dices value is not known but that it is all values at once its value can only be known once it is measured the double slit experiment demonstrates this a single photon passing through the slit should not be thought of as a particle going through and interacting with itself rather it's like a three-dimensional wave or cloud of probability when it is emitted this wave can go through both slits at once and interfere with itself like a wave does before it is measured by the photosensitive screen in the back when it resolves to a specific location on the screen Einstein who is the most famous scientist at the time was bothered by this interpretation of quantum mechanics the idea that part of nature remains not only unknown but is unknowable unless measured that's why he famously said God does not play dice so Einstein along with two other scientists Boris Podolsky and Nathan Rosen EPR for short came up with what they thought disproved the Copenhagen interpretation the crux of their argument rested on the idea of a phenomenon predicted in quantum mechanics called entanglement let's say we have a quantum system that has zero angular momentum also known as spend zero and it emits two photons simultaneously since photons have spent and since angular momentum must be conserved if one photon has a spin up the other photon must have a spin down so the spin up and down cancel each other out this is entanglement the two photons are not independent if the spin of one of them is known the spin of the other becomes known instantaneously now let's separate these photons far apart let's say 300,000 kilometers which is about one light second away now according to quantum mechanics each of these photons is governed by a wave function and each photon is in a state of both spin up and down at the same time it is not up or down it is both up and down however the wave function of these photons is not independent they're really the same wave function governing both photons now if we measure the spin of one of them we have a 50% chance of detecting a spin up let's say we do detect spin up now let's measure the spin of the other photon in less than one second it should also have a 50% chance of having spin up or spin down but it doesn't it has a 100% chance of having a spin down this means that the information of the collapse of the wavefunction of one of the photons had to travel faster than light to affect the other photon EPR argued that since nothing can travel faster than light according to the rules of special relativity this should invalidate the Copenhagen interpretation the theorized violation is the EPR paradox EPR proposed instead that there is likely another theory which which showed that the two entangled photons were in cahoots from the very beginning that their states were predetermined from their creation in other words their states contained the information locally so that when they were moved apart no communication had to take place the information that we were measuring was hidden inside the two particles this is called local hidden variables so for example it's as if the two particles were a pair of gloves one was a left-handed pair and the other was a right-handed pair once we found the left-handed pair we knew immediately that the other pair no matter where it was in the universe must be a right-handed pair this was a valid interpretation of quantum mechanics for almost 30 years from 1935 to 1964 this could not be disproven this is where Irish physicist John Bell comes in and in 1964 he proposed an experiment that could show whether the local hidden variable theory was correct or incorrect now Bell's equation is remarkably simple but it's one of the most difficult to understand and simplify so I'll present a highly simplified idea of how it works then also show you the simplified version of the mathematical underpinnings later in this video now we're going to play a game and our opponent is going to be the universe and the game is guess the color of the checkers pieces now I want to give a big shout out to Jim al-khalili who shows a similar simplified illustration in a documentary available on Magellan TV I encourage you to check it out because it's fascinating if I guess the color correctly I win if I'm incorrect the universe wins in the first game I declare that if the colors match I went the universe picks the pieces now in play after play I find that I'd lose every time so in the next round I change the rules this time I declare that if the colors are different I went the universe picks the pieces in play after play I find that I lose every time again so I conclude that perhaps the universe has rigged the game against me this is what Einstein suspected was happening that the checkers pieces were rigged he believed that the colors of the pieces were predetermined and that this information had been known from the very beginning when the two pieces work together Niels Bohr's ID on the other hand was that the red and black don't even exist until the piece is turned over so I changed the rules of the game again this time I do not tell the universe whether matching colors or different colors will win the game until after the universe has already picked the checker pieces if after revealing the checker pieces I find that I win 50% of the time and lose 50% of the time then my conclusion is that indeed the checker pieces were rigged from the very beginning because my chances of winning would be 50% if the red and black pieces were already picked by the universe but if I continue to lose then I have to conclude that somehow the colors of the checker pieces were not chosen ahead of time let's look at how Bell's elegant equation proves my conclusion to do this let's look at a universe where local hidden variables are correct in other words entangled particles have predetermined properties which are complementary to each other at the moment of their creation note that this is not an interpretation of quantum mechanics it's an alternative to quantum mechanics so in this system when two entangled particles are produced from a process that conserves linear and angular momentum we will get two particles that go off in opposite directions and they will have opposite spins as well as opposite directions let's say Alice makes the measurement and particle 1 in her laboratory and Bob makes the measurement on particle 2 in his laboratory and let's say that 2 labs are very far apart and are not in communication with each other if Alice measures the particles spin in the Z direction as positive Bob will measure the spin as negative in the Z direction if they measure the spin in the X direction which is orthogonal to the Z direction or 90 degrees apart the same type of complimentary opposite spins will be measured because as I said earlier angular momentum is always conserved what bells inequality does is it says now let's make a third measurement that is somewhere in between the Z and x axis in our example who use 45-degree angles to the Z and X direction we'll call this the Q direction so 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 eight combinations or possibilities of Spense that each particle could have so for Alice and Bob these eight combinations will be the following the event one could be where the spin in the Z Direction is positive the spin in the X Direction is positive and the spin in the Q Direction is positive e 2 is when Z is positive x is positive and Q is negative the three is when Z is positive x is negative and Q is positive V four is when Z is positive x is negative and Q is negative V five is when Z is negative x is positive and Q is positive he's six z is negative x is positive Q is negative e 7 Z is negative x is negative and Q is positive e 8 z is negative x is negative and Q is negative now let's ask the question 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 four 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 events three and four to get the probability we have to divide by the total number of events which is eight 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 would be event two and four again we divide by eight 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 7/8 for probability so these are the three probabilities given the hidden variables third now here's the big insight that john bell hat if i take the total number of events and multiply that by the probability that alice measures z+ 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 e positive and Bob measures q positive plus the probability that alice measures q positive and Bob measures X positive when we write this out the eight cancels out and we are left with just the probabilities this is bell's inequality now I can prove this is true by doing simple math III plus B 4 divided by 8 is equal to e 2 plus e 4 plus e 3 plus e 7 divided by 8 the eights cancel out and we rearrange the order of addition and we're left with this III plus e 4 is less than or equal to e 3 plus e 4 plus C 2 plus C 7 this makes total sense because III and E 4 are on both sides of the equation e 2 and E 7 have to be positive so this inequality absolutely has to be true for any hidden variables theory to be true now remember these probabilities are for a universe with hidden variables but what happens in a universe where the laws of quantum mechanics are correct and not the hidden variables theory well this inequality is violated in quantum mechanics how is it violated let's say Alice measures the spin to be positive in the Z direction then we know that if Bob measured the particle in the Z direction he would get a spin that is negative however Bob doesn't measure in the Z direction but in the Q direction what will the spin of this particle be in hidden variables there was a 50% chance that it would be positive and a 50% chance that it was negative but this is not what happens in quantum mechanics because the measurement of the particle follows the probability laws of the wavefunction for a particle rotated 45 degrees and that probability of Bob measuring Q to be positive after Alice has measured C to be positive if the angle between them is 45 degrees is given by the following equation sine squared of 45 degrees divided by 2 this comes from the math of quantum mechanics this is the critical difference between quantum mechanics and hidden variables theory the probability that Bob measures the same spin as Alice depending on the difference and angle measured is not linear but looks like a sine wave when you plot this out this is what the probabilities look like you can see from this graph that it's 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 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 bells inequality is violated so we can write out and compare bells inequality for both cases for hidden variables the equation would be e 3 plus e 4 is less than or equal to e 3 plus e 4 plus e 2 plus e 7 2 is less than or equal to 4 the inequality holds true for quantum mechanics the equation would be sine squared of 90 degrees divided by 2 is less than or equal to the sine squared of 45 degrees divided by 2 plus the sine squared of 45 degrees divided by 2 and when you solve this you get 0.5 is less than or equal to 0.2 93 which of course is not true so bells inequality is violated in quantum mechanics which is exactly what we observe in experiment after experiment now does this prove that the two entangled particles are communicating faster than light there is differing opinion on this on the surface it does appear that superluminal communications is taking place but my personal is that no communication is happening the two particles are really just part of one wave function and since the wave function can theoretically be as wide as the universe when this one wave function collapses both particles collapse and since the collapse is random it cannot be used to communicate in this way so most theorists do not think special relativity is violated because we can't communicate using this seemingly faster-than-light phenomenon but our knowledge of quantum mechanics and entanglement is incomplete to say the least why is there superposition what is the mechanism of wave collapse between two particles separated by space and time I happen to think that the scientist is going to reveal the mystery of quantum mechanics is alive right now in the world and I can't wait for him or her to explain this and like Copernicus Newton and Einstein completely change our paradigm I'll see you in the next video my friend [Music]

Channel: Arvin Ash

Views: 503,722

Keywords: epr paradox, quantum mechanics, quantum entanglement, bells theorem, quantum physics, spooky action at a distance, bells inequality, bell experiment, epr paradox and quantum entanglement, epr paradox meaning, bells theorem simplified, bells theorem easily explained, epr paradox and bells inequality, bells theorem simple, bells theorem youtube, niels bohr, albert einstein, bells theorem explained, bells inequality explained, yt:cc=on, hidden variable, hidden variable theory

Id: f72whGQ31Wg

Length: 18min 17sec (1097 seconds)

Published: Fri Feb 14 2020