Why is quantum mechanics non-local? (I wish someone had told me this 20 years ago.)

according to the headlines last year's Nobel Prize in physics was awarded for showing that the universe is not locally real or for spooky Quantum behavior and spooky action at a distance or for exploring Quantum weirdness what's that supposed to mean is the universe really not locally real or not really local or not really real that's what we'll talk about today my great plan for this video is that we'll first look at what locality means then we'll talk about quantum mechanics and then we'll combine both let's start with locality you'll know what locality means it means if you want to go to New York City you don't just disappear from Heathrow and reappear at JFK you must get on a plane fly in a seat through the sky and then drag yourself into the immigration Queue at U.S customs there is no instantaneous going anywhere it's not just travel it's generally any interaction you can only act on things next to you and it's not just you no really I swear anything can only interact with things right next to it this is what we mean by locality non-locality would basically be a portal something goes in and instantaneously appears I swear now if you could travel non-locally that might allow you to go faster than light but it doesn't necessarily have to Alice could go to Tokyo faster than light without taking a portal Bob could go through a lame portal that brings him to New York even later than our France and leaves his back in Paris again so non-locality and faster than light travel are two separate things but the two are related in that Expedia isn't offering either maybe more importantly though not unrelatedly neither of them is allowed in Einstein's theory Subspace and time yes that guy again we can make a little drawing to see what this means this is a space-time diagram the horizontal axis is one dimension of space say left or right the vertical axis is time if you don't move but sit still that's described by a vertical line in this diagram if you move at a constant velocity that makes a line at a fixed angle by convention a 45 degree angle is the speed of light according to Einstein nothing can go faster than light this means if an event happens here then anything that can be influenced by this event must lie within a region that's bounded by 45 degree lines emerging from the event this boundary is called the future light cone and the region that can be influenced from the event is that inside the future light cone likewise there's a region which contains everything that can influence the event which is the inside of the past light cone if something could go faster than the speed of light it could enter your light cone like this and if non-locality was possible it wouldn't have to respect those light cones either it could just jump into your nicone for the rest of this video we'll assume that faster than light travel can't happen and just look at non-locality if you'd rather hear me talk about faster than light travel I have another video on that our experience suggests that reality is local in that these jumps in space-time don't happen there's no action at a distance no portals however our descriptions of reality are not always local suppose I take two sheets of paper and write the number plus one on one 1 and -1 on the other I put them into identical envelopes then I send one to Alice in Tokyo and want to Bob a New York who is still waiting for Air France to deliver his bag Alison Bob both know what I did but not what's in their envelope either the plus one went to Bob and the miners one to Alice or the other way around it's a 50 50 chance but the moment Alice opens her envelope and finds plus one she knows that somewhere in New York there's an envelope with the number minus one you probably didn't find this particularly remarkable well what did you expect clicking on a video about locality only so much I can do to spice it up remarkable or not this simple example will be useful later thing is these numbers in these envelopes are correlated you don't know what either is but if you know one the other one is not random anymore and this correlation can stretch over a distance if you learn what one number in this correlated pair is you learned something about the other number elsewhere instantaneously you could call that a kind of non-locality but it's not an action at distance the only action that happens is an update of knowledge about something elsewhere the action itself is completely local it happens in Bob's brain or Alice's unless maybe they've become so bored by my number games there isn't anything left of their brains so the lesson of the first part is there are two types of non-locality the one is the physical non-locality an action at a distance which is like something going through a portal the other is a non-local correlation that allows us to acquire knowledge about what happens elsewhere but in this case the only physical changes are local let's then talk about quantum mechanics in quantum mechanics everything is described by a wave function usually denoted with the Greek letter PSI the wave function is a device that we use to calculate the probability of getting a particular measurement outcome but it doesn't predict the outcome with certainty we say that quantum mechanics is not deterministic imagine for example you have a single Quantum of light a photon and you send it through a semi-transparent plate if you still have the space-time diagram in your head please take it out and put it aside for now this illustration just shows two dimensions of space think tabletop the photon has a 50 probability of going through the plate and the 50 probability of being reflected so long as we don't observe the photon its wave function changes locally from one place to the next by spreading into these two directions but once we make a measurement we know where the photon went then the probability jumps to 100 on the one side way of measured it and drops to zero percent on the other side this is like when Alice opens her envelope and sees the number plus one now she knows that the probability that Bob had plus one is zero and like Alice adjusts her probability for Bob when she opens the envelope once we measure the photon on one side we have to update the wave function to reflect this change in probability on the other side why because otherwise it doesn't agree with our observations this update is also sometimes referred to as the collapse or reduction of the wave function and its non-local you make a measurement in one place and the wave function changes elsewhere so quantum mechanics is non-local in some sense the question is in which sense as we saw previously just because you gain knowledge about something that happened elsewhere doesn't mean there wasn't a local action maybe the wave function just describes knowledge rather than being real itself maybe the photon really went one way or the other you just didn't know it and the measurement revealed its real State being a wave function isn't easy not only do people reduce and collapse you they also then argue that it doesn't matter because you aren't real the quantum mechanical version of the envelope example gives like this imagine you have a particle with spin zero that decays into two particles that can each either have spin value plus or minus one one flies to the left the other one to the right the total spin is conserved in the Decay so you know that either the particle going left has spin Value Plus one and the one going right has minus one or the other way around but you don't know which has which spin these two particles are entangled entanglement is a correlation like the correlation between the numbers in the envelopes and like the correlation between the envelopes it can stretch over a distance the difference between the two cases is that if you think that quantum mechanics describes all there is then before you make a measurement the particles really are in both States at once and then the update is really physically non-local the idea that this update is physically real is what Einstein called a spooky action at a distance he thought that can't be right Einstein believed that the real process must be local and that the update just revealed something you didn't previously know that's something you revealed in the measurement is usually called The Hidden variable it could be for example the value of the spin that the particle really had before you did the measurement and found out what it is boar held against that he said there are no hidden variables and no underlying information that you can reveal the wave function is all there is and the collapse is really non-local bore seems to have like quantum mechanics because he thought that its indeterminism makes place for free will though that's rather questionable we just talked about that a few weeks ago Einstein did not use the phrase spooky action at a distance to refer to entanglement to begin with the example in which he coined the phrase didn't use entangled particles I went through the history in the previous video but more importantly entanglement has no action it's just a correlation that stretches over a distance like the correlation between the envelopes when I read the headlines about last year's Nobel Prize I got the impression that some science writers believe entangled particles are somehow mysteriously linked to each other they seem to think that if you do something to one particle in an entangled pair then that'll immediately affect the other one but this isn't so it's only when you measure one particle then you have to update the wave function of both so long as you don't measure them doing something to one particle won't affect the other one you could for example flip the spin of one of the particles in an entangled pair so that one becomes -1 and the other way around you can do that without measuring the spin like you can do this in reality in the laboratory not just with mathematics if you flip the spin of one particle without measuring it this will not do anything to the particle it's entangled with it's not as weird as they made you believe it is is it okay so entanglement is just a correlation over long distances but does it at least allow us to send signals faster than light unfortunately not it doesn't work because you can't force the outcome of your measurement on one of the entangled particles to be a particular value it'll just be randomly distributed according to the probability given by the wave function this means that on the other end they won't know whether you have made a measurement any more than Bob knows whether Alice has opened her envelope if quantum mechanics is correct then no information can be sent faster than light one can mathematically prove that this is the case not just for this experiment but for any possible experiment it's called the no signaling theorem but because of this randomness of quantum mechanics it's also rather unclear in which sense the collapse is even non-local if making the measurement on one of the pair of entangled particles doesn't change the measurement outcome on the other one then what is non-local in the first place enter John bell bell try to find a way to pin down what it means that quantum mechanics is non-local please put the space-time diagram back into your hand because we need it again we have seen earlier that without faster than light travel everything that an event might be influenced by has to be in the past light cone but if the theory is also local then you don't need the entire inside of the light cone this is because if you know what happens at One Moment In Time you can calculate what happens later if the theory is deterministic you can calculate it exactly if it's not deterministic probabilistically this means all you need is the information at one particular moment in time for anyone's notion of time in one dimension that moment is a line going through the inside of the past light cone in three dimensions it's what's called a space like hypersurface just so you don't go away disappointed about the lack of incomprehensible terminology the point is that the information at One Moment In the past light cone of the event is all you need to calculate what happens at the event if the theory is local if the theory isn't local then that doesn't work because information could jump into your icon later burst Insight was now that you can use this to decide whether the theory is local and it works even if the theory has a random element suppose you have all available information on this slice here and you use that to make your best prediction for what happened here then the theory is local if information from over here doesn't tell you anything new about what happened at a bell called this property local causality if on the other hand the theory is not locally causal then information can jump into the light cone after your slice and that can tell you something about what happens at that event quantum mechanics is not locally causal think back of the earlier example with the entangled particles let's say they are created here one goes left one goes right in the space-time diagram this means they go diagonally no less than a 45 degree angle you make two measurements here and here let's call them A and B we want to know what happens at measurement a all the information you could have about it is down here in the wave function this wave function as we've seen earlier does not allow you to predict the measurement outcome at a just the probability of a measurement outcome it's either spin minus one or plus one with 50 probability each here's the thing if you make a measurement over here at B and you find it's plus one then you know the spin at a is minus one so what happens that b does add information to the inside of the past light cone and quantum mechanics is not locally causal the important thing is now that local causality is a property of a model in this case a property of quantum mechanics the relevant question is whether it's also a property of reality if quantum mechanics was all there is then that would be the case the wave function would be how the word really works and it would have a spooky action as a distance but if quantum mechanics was not all there is then the wave function down here was not the entire information that be a hidden variable there from which the outcome followed and if you had had the entire information then adding the measurement outcome from B would not provide any further information quantum mechanics would still not be locally causal but reality would be so which one's right that's what John Bell was trying to figure out wow you're still with me that's lovely I really appreciate the company let's look again at that semi-transparent plate because it can teach us something very important we'll now try to build a simple hidden variables model that explains what happens at that semi-transparent plate also called a beam splitter we want to do this with hidden variables and we want to do it locally so no action at a distance the hidden variables are usually called Lambda so we'll say if Lambda is one then the photon goes that way if Lambda is 3 then it goes the other way Y3 and not two because I know what's coming next and you don't now we put two mirrors here and here so that the photons don't run off our screen and another two semi-transparent plates there okay so now we have four different paths each with 25 probability we'll give those the numbers 1 2 3 4. and now we'll combine these two paths by directing both towards the same beam splitter if our hidden variable explanation was correct then we should get half of the photons here in detector a and half here in detector B but this isn't what happens indeed you have probably noticed that this setup is what's called a marsender interferometer if the paths are the same length then the photon will always go to detector B you can measure it and all it's definitely real the interference in these detectors is exquisitely sensitive to the length of the path which is why one can use this type of interferometer to measure tiny deformations this is how a gravitational wave interferometer works but how does it work well in quantum mechanics the photon is described by a wave function and waves can interfere with themselves either constructively or destructively in quantum mechanics the photo tone goes over both paths and on this output the wave interferes destructively with itself so no signal and all photons go the other way but the price you have to pay for this is that if you measure which path the photon went you need the non-local collapse how can we use hidden variables to get this done locally well no one ever said that we can't have waves that go to paths in a local hidden variable model all we need to do is say if we measure which path the photon goes then we use these variables one two three four and the photon behaves like a particle if we measure the interference between the paths then that's hidden variable number five the photon behaves like a wave and goes only into detector B problem solved it's local because the photon goes on one continuous path into the detector where it's measured for this to work the value of the Hidden variable that determines what the photon does must depend on what you measure it's called a violation of measurement Independence so the lesson is if we want a local hidden variable model that reproduces quantum mechanics correctly then it needs to violate measurement Independence this finally brings us to Belle's theorem I'm not going to explain both theorem because you've already watched 20 videos about it and it didn't help I'll just tell you what it says Bell's theorem says if you want a local hidden variables model that reproduces quantum mechanics correctly then it needs to violate measurement Independence isn't that what we just concluded from this little example with the interferometer yes Pearl's theorem says the same thing you see what happened is that Bell originally just assumed that measurement Independence is fulfilled he then proved that any local hidden variable Theory which fulfills this assumption will obey an inequality for the correlations of certain measurement outcomes it's now called Bell's inequality quantum mechanics can violate this inequality what the Nobel Prize was awarded for is experimentally demonstrating that these inequalities are indeed violated by observed measurement outcomes this means that either reality respects measurement Independence but is not locally causal or its locally causal and violates measurement Independence just logically it could be a combination of both but I don't know why you'd want to do that since Bell had forgotten about this Assumption of measurement Independence he mistakenly thought that demonstrating an experimental relation of his inequality would rule out all local hidden variables models and thereby show that spooky action at a distance is real indeed most physicists still seem to believe this at this point you might think zabina is talking complete rubbish because of that's right why doesn't anyone ever mention this well first of all you don't have to take my word for it it's all in the published literature and easy to check in fact one of the people who pointed out that Bell had forgotten this assumption was John clauser who was one of the recipients of the 2022 Nobel Prize why physicists refuse to mention it is a very interesting question to which I don't have an answer my best guess is that they want reality to be weird because they like the mystery there are several hidden variables models that are local and that reproduce the predictions of quantum mechanics by violating measurement Independence I'll leave you links in the info below and yes a violation of measurement Independence has also been called super determinism though this term is extremely misleading I talked about this in an earlier video in summary quantum mechanics is not local what makes it non-local is the collapse of the wave function the question is whether this non-locality is physically real if the collapse of the wave function was a physical process it would be what Einstein called a spooky action at the distance and reality would be non-local it has not been shown that this is indeed the case no matter how many headlines say otherwise lies entanglement is a non-local correlation that can stretch over long distances but it's not what Einstein meant by action at a distance because there is no action in it if you're a fan of the many worlds interpretation of quantum mechanics you probably took issue with some things I said but this video is already too long so I'll talk about this some other time if you want to hear me complain about many words don't forget to subscribe yes I admit there's a lot going on in this video that I only touched on very briefly what is a wave function how do you get probabilities out of it how does interference work and why is it important if you want to understand this in more depth you can do this with my course on quantum mechanics at brilliant.org who have been sponsoring this video brilliant offers courses on a large variety of subjects in Science and Mathematics the great thing about their courses is that they are all interactive with visualizations and follow-up questions so you can check your understanding right away this is why I like to look things up on brilliant it's fast it's easy and it tells me what I need to know my course on quantum mechanics gives you an introduction to interference superpositions and entanglement the uncertainty principle and bars theorem it begins from the very Basics so you don't need to bring any background knowledge and after that you can continue maybe with their course on Quantum objects or Quantum Computing or wherever your curiosity drives you if you're interested in trying brilliant out use our link brilliant.org Sabina and sign up for a free trial where you'll get to try out everything brilliant has to offer for 30 days the first 200 subscribers using this link will also get 20 off the annual premium subscription thanks for watching see you next week

Channel: Sabine Hossenfelder

Views: 1,015,072

Keywords: science without the gobbledygoook, hossenfelder, Quantum Mechanics, Locality, Einstein, Physics, Non-Locality, Local Causality, Bell's Theorem, Local causality, what is nonlocality, is quantum mechanics nonlocal, is quantum mechanics locally real, local realism, quantum mechanics faster than light, quantum physics faster than speed of light, nonlocality, nonlocality and entanglement, entanglement, what is entanglement, is entanglement faster than light

Id: hpkgPJo_z6Y

Length: 25min 8sec (1508 seconds)

Published: Sat Jul 08 2023