The EPR Paradox & Bell's inequality explained simply

Two of the greatest intellectual giants of modern physics changed our view of reality and proposed their theories almost at the same time in the early 20th century, but their views on reality were completely different. Niels Bohr, one of the founders of modern quantum mechanics and father of the The Copenhagen Interpretation held that the reality or 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 fully define the reality that had existed. be an objective reality independent of measurement, he said in his famous dramatic statement: Do you really believe that 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 then, in 1964, Irish physicist John Bell devised a way to demonstrate whether Stan's view of a classical deterministic view of reality was correct and expressed it in a simple and elegant equation called Bell's

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 force us to face the disturbing truth that we can live in a fundamentally non-deterministic universe?

Right now, before I talk about the EPR

paradox

and

bell

inequality

, I want to point out that part of my inspiration for this video came from a documentary I saw on Magellan TV by Jim al-khalili called Einstein's Nightmare. It is a fascinating program and the complete history 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 from Magellan TV. Magellan is a documentary streaming service that I think you'll love. It was founded by filmmakers and producers who offer premium in-depth documentary content, you can watch it on any of your devices and on your TV at any time without interruptions and you can watch it in 4k, my friends, I am 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 will get a free month trial. I highly recommend Magellan TV, but be sure to use the link in the description. The central oddity of quantum mechanics can be demonstrated by the rolling of the dice, if the dice were a quantum system like a photon, an electron or an atom, it would be in superposition, that is its position and other properties would in some sense be in the air like a dice thrown before touching the table, is a 1 2 3 4 5 and 6 all at the same time according to the most accepted interpretation of quantum mechanics the Copenhagen interpretation initiated by Niels Bohr and Werner Heisenberg is not only that it does not the value of the dice is not known but all the values ​​are known at the same time.

Value can only be known once it is measured. The double slit experiment demonstrates that a single photon passing through the slit should not be considered as a particle passing through the slit and interacting with itself, but rather is like a three-dimensional wave or probability cloud when measured. This wave is emitted which can pass through both slits at once and interfere with itself like a wave does before being measured by the photosensitive screen on the back when resolved at a specific location on the screen Einstein, who is the most scientific famous at that time. He was bothered by this interpretation of quantum mechanics, the idea that part of nature not only remains unknown but is unknowable unless measured, which is why he said that God does not play dice, which is why Einstein along with two others Scientists, Boris Podolsky and Nathan Rosen, EPR for short, proposed With what they thought refuted 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 zero expenditure, and emits two photons simultaneously since the photons have been spent and since angular momentum must be conserved, if one photon has an upward spin, the other photon must have a downward spin, so the up and down spin cancel each other, this is entanglement, the two photons are not independent if the spin of one of is known the spin of the other is known instantaneously now let's separate these photons very far away, say 300,000 kilometers, which is about a light second away now, according to quantum mechanics, each of these photons is governed by a wave function and each photon is in a spin up state. and down at the same time is not up or down, it is up and down, however the wave function of these photons is not independent, they are actually the same wave function that governs both photons now if we measure the turn.

From one of them we have a 50% chance of detecting a turn. Let's say we detect a turn. Now let's measure the spin of the other photon in less than a second. You should also have a 50% chance of having a spin. downward but it is not, it has a 100% chance of having a downward spin, this means that the information from the collapse of the wave function 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 probably exists another theory that shows that the two entangled photons were colluded from the beginning, that their states were predetermined from their creation;

In other words, their states contained the information locally, so when they were separated there had to be no communication. The information we were measuring was hidden within the two particles. This is called local hidden variables, so for example, 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 immediately knew 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 was not true. was able to refute 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 the Bell equation is remarkably simple, but it is one of the most difficult to understand and simplify, so I will present a very simplified idea of ​​how it works and then I will also show you the simplified version of the mathematical fundamentals later in this article. video now we are going to play a game and our opponent will be the universe and the game is to guess the color of the checkers pieces.

Now I want to thank Jim al-khalili, who shows a similar simplified illustration. in a documentary available on Magellan TV I encourage you to watch it because it is fascinating if I guess the color correctly I win if I am wrong the universe wins in the first game I declare that if the colors match I was the universe chooses the pieces now in game after game encounter that I would lose every time so in the next round I change the rules this time I declare that if the colors are different it was the universe choosing the pieces in game after game I find that I lose more and more 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 was known from the beginning when the two pieces work together, Niels Bohr's identification, On the other hand, it was that 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 don't tell the universe if the colors match. or different colors will win the game until the universe has already chosen the checkers pieces, if after revealing the checkers pieces I find that I win 50% of the time and lose 50% of the time, then my conclusion is that indeed The checkers pieces were rigged from the beginning because my chances of winning would be 50% if the red and black pieces had already been chosen by the universe, but if I keep losing then I have to conclude that somehow the colors of the checkers pieces ladies were not chosen before.

Now let's see how the elegant Bell equation proves my conclusion. To do this, let's look at a universe where the hidden local variables are correct; In other words, entangled particles have predetermined properties that are complementary to each other at the time of their creation; Please note that this is not the case. An interpretation of quantum mechanics is 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 shoot in opposite directions and They will have opposite spins as well as opposite directions, let's say that Alice makes the measurement and particle 1 in her laboratory and Bob makes the measurement of particle 2 in his laboratory and let's say that 2 laboratories are far apart and are not in communication with each other if Alice measures particles spinning in the Z direction as positive Bob will measure spin as negative in the Z direction if they measure spin in the X direction which is orthogonal to the Z direction or 90 degrees away the same type of spins will be measured complementary opposites because, like I said The angular momentum above is always conserved, what Bell's inequality does is it says: now let's make a third measurement that is somewhere between the Z and x axes in our example, which use 45 degree angles with respect to the Z and birth and there are only eight combinations or spending possibilities that each particle could So for Alice and Bob, these eight combinations will be the following: the event that one could be where the spin in the Z direction is positive, the spin in the X is positive and the turn in the Q direction is positive e 2 is when Z is positive x is positive and Q is negative three is when Z is positive and Q is negative V five is when Z is negative x is positive and Q is positive he has six z is negative x is positive Q is negative e 7 Z is negative x is negative y 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.

If the above case is for Alice, there are four events in which Z is positive for Bob to get positive X. Alice should have measured X as negative. So these would be in events three and four to get the probability that 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 the event. 3 and 7/8 for probability, so these are the three probabilities given the hidden variables. Third, here's the great idea that John Bell hat if I take the total number of events and multiply it by the probability that Alice measures z+ and Bob measures positive X. this has to be less than or equal to the total number of events multiplied by the probability that Alice measures positive e and Bob measures positive q plus the probability that Alice measures positive q and Bob measures positive X. When we write this the eight cancel out and we are left with just the probabilities this is Bell's inequality now I can prove this to be true by doing simple math III plus B 4 divided by 8 equals e 2 plus e 4 plus e 3 plus e 7 divided by 8 the eights cancel and we rearrange the order of the addition and we are 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 a lot of sense because III and E 4 are on both sides of the equations e 2 and E 7 have to be positive, so this inequality has to be absolutely true for any hidden variable theory to be true.

Now remember that these probabilities are for a universe with hidden variables, but what happens in a universe where the laws of quantum mechanics are valid? is correct and not the theory of hidden variables, 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 she would get a spin. that is negative however Bob does not measure in the Z direction but in the Q direction whichwill be the spin of this particle in hidden variables there was a 50% probability that it was positive and a 50% probability that it was negative but This is not what happens in quantum mechanics because the measurement of the particle follows the laws of probability of the wave function for a particle rotated 45 degrees and that probability of Bob measuring Q being positive after Alice has measured C as positive if the angle between them is 45 degrees is given by the following equation sin squared of 45 degrees divided by 2 this comes from the mathematics of quantum mechanics this is the critical difference between quantum mechanics and hidden variable theory the probability that Bob measures the same spin as Alice depending on the The difference and the measured angle are not linear, but they look like a sine wave when you plot this.

This is what the probabilities look like you can see in this graph which is 0 and multiples of 90 degrees, the two systems agree, but in the middle, like at 45 degrees, the probability is 25% for hidden variables and approximately 14.6% for quantum mechanics, but the proof is clear because, test after test, the correlation of the sine function has been confirmed, the particle does not behave linearly and, therefore, the theory of hidden variables can't be correct. The

bell

inequality is violated, so we can write and compare the bell inequality in both cases. For the 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 is valid for quantum mechanics the equation would be sine squared 90 degrees divided by 2 is less than or equal to sin squared of 45 degrees divided by 2 plus sin 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 Bell's inequality in quantum mechanics is violated, which is exactly what we observe experiment after experiment now proves that the two entangled particles are communicating faster than light.

There are different opinions about this on the surface. It appears that superluminal communications are occurring, but my personal opinion is that no communication is occurring. In reality, two particles are just part of a wave function and since the wave function can theoretically be as wide as the universe, when this wave function collapses, both particles collapse and since the collapse is random, they do not can be used to communicate this way, so most theorists don't think special relativity is violated because we can't communicate using this apparently faster-than-light phenomenon, but our knowledge of quantum mechanics and entanglement is incomplete to say the least, why is there overlap?

What is the mechanism of wave collapse between two particles? separated by space and time. It occurs to me that I think the scientist is going to reveal the mystery of quantum mechanics that 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 see you in the next video friend