How can one not fall in love with math and physics while listening to him...man I wish I had a math / physics professor like him in high school. ... Thank you Sean ! I might not get all you are saying but even so I'm loving the struggle to be able to. You are amazing!
Thank you for the lectures, you make me feel as if I have my own personal physics professor. I'm sure most of us watching feel that they too have their own personal instructor. And he is freaking great.
I love the math part, please do not shy away from it :) Also, the way you present, you talk about it - these concepts look so easy. Please keep up this great work.
I have a degree in nuclear and electrical engineering and this is the best explanation of the double split experiment I have seen. Obviously nobody EVER bothered to teach me about how to conceptualize the wave function in graduate school. Thanks for this one Prof.
At 38:22 Sean speaks my favorite Physics idiom, "It turns out that …". I've heard that since high school, and it always makes me think there is something that I will never know--right before "It turns out!"
Strangely enough, as someone who left math back in high school, I really appreciated the math at the end to explain the wave function. The graphs help me put my brain in that way of thinking.
Thanks for the discussion on Planck units. They’re often referred to in popular physics talks in ways that I took to mean discrete, but this clears up that misconception
Yeah, Planck units tend to lead to a lot of misconceptions. I used to be absolutely astonished to almost a level of a "religious experience", feeling genuine awe and like I'd touched something truly fundamental and electrifying about the universe, at the fact that the speed of light is one Planck length per Planck time. I first heard that fact in relation to Simulation Theory, which stated it as something magical, and a gigantic clue about the nature of reality. Then I actually did some research into what Planck units actually are. The answer, that they are units that are defined such that the speed of light is one Planck length per Planck time, made me blush, laugh, and nearly cry all at once. XD In fact, it gets worse! Planck units are not even a _unique_ way of specifying units in terms of the fundamental constants. If you make different kinds of assumptions, you get quite a few different "fundamental" unit systems that all have their own way of simplifying certain aspects of the mathematics of physics, with each prevalent in its own field. So not only is it not mind-blowing, but rather simply tautological than the speed of light is one Planck length per Planck time, it's not even unique. Kinda shaky ground to base a hefty portion of a theory of reality on, eh?
I'm just an undergraduate, so most of my information come from science divulgation and journalism of some sort. But as far as I'm aware, there was actually one experiment in 2011 that showed that any granularity on space-time (if existent at all) should be at least 13 orders of magnitude smaller than the Plank Length (www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein). There's seem to be a lot of theorists trying to sell their pet theory or interpretation to the press as if it were "the truth", or the scientific consensus, that's (one of the things) that causes many of those misconceptions. Quantum mechanics says nothing about the Plank lenght, some quantum gravity theories suggest that there might be a minimum scale (but don't specify the value, actually, most quantum gravity now-a-days like string theory and some loop quantum gravity don't specify a lot, and you can always save the theory from observation). None of those theories predicted that granularity should be at the Plank level either, it's more like the plank scale seemed to be a nice place to put it, but they already know how to modify their theories. Theories that can predict any number or that you can always change so that they could match with new data are not good theories. I have nothing against people studying them, just like it's important to study pure math, I'm sure some useful things will come out of it, and maybe we even get lucky and it turns out to be right, but people should be more open about what we don't know and the problems in our understating, specially scientists. That's (one of the many reasons) I admire Sean Carroll (and Leonard Susskind and some others), they really draw the line on known, agreed upon, consensus, proved science and personal opinion or interesting and promissing ideas, speculations and interpretations. Sean specially seems to go to trouble of trying to explain other points of view he himself disagrees with.
best explanation of Hilbert space/wavefunction for a non- physics major I have ever come across. thank you so much . ( sad i'm late to the party as it would have been great to have had the opportunity to ask questions, what a privilege )
DAMN I love this series, Dr. Carroll. I'm a mechanical engineer and when I was in school (at ULL), my friend's grandfather offered a quantum mechanics elective for non-physics majors over a single fall semester. I unfortunately was not able to take it because it would have overlapped with my Machine Design lab. It's something I have always regretted; not only for the fact that those 3 credits would have given me enough for a physics minor. What you are doing with this and Mindscape is so hugely appreciated.
Best explanation of the double slit experiment I've run across. Others seem to suggest that the particle "somehow" goes through both slits and interferes with itself. The wave function explanation makes perfect sense.
5:00 - 15:00 is really good. Sean touches on how we think of probability as a tool for understanding and predicting physics, like the position of a gas molecule in a room, but we still believe that actually the molecules have a definite position, momentum etc, and statistics is more about our ignorance than the workings of universe. And so that touches on the issues I have with understanding physics - is it supposed to help us predicts or interact with physics at all, or is it just describing the laws of the universe that only the universe can follow. I’m still having trouble articulating that notion. Also, Sean says that with QM, statistics are not about our ignorance, not tools, but maybe something more fundamental. He then goes on to talk about the Double Split experiment, and tries to do so in a way that clears up the popsci misconceptions, and help us see what’s really going on there, necessarily biased towards what Sean thinks is relevant to talk about, in physics and in the context of this YT video, etc etc. Continuing on the notion I find hard to express; Sean also points out that it was useful to talk about the DSE and Schrödinger’s cat not just because they’re illuminating, but also to ‘correct’ (subject to all types of relevance realization) the readers previous misconceptions they’ve picked up from popsci, in a way that’s consistent with the implications the Author has made in their writings so far. I think this important to my idea of the pedagogy of physics, and how it is often presented with enthymemes about what you do and don’t know. Still having a hard time expressing that
Thank you, Sean. Your detailed explanation of how the wave function interferes with itself, in a way that a mere probability distribution can't, helped clarify several issues for me.
I have one particular way to see/explain wave function and would like to validate it here. It is the function that describes the path a particle take, from one interaction up to the next, and it is function of the particle's properties at start. The function is pretty much classical and deterministic from one interaction to the other. The problem is that we cannot access any sort of information during this interval in between interactions without creating a new interaction that would reset the wavefunction with new particle properties. That's what the slid barrier represents in the double slid experiment, a reset of the properties influenced by the shape and position of the slids, this reset configures the wavefunction to express the wave interference pattern. When added after the slids, the detectors interact with the particle, reseting the wavefunction with new properties, and this time without a doublle slid to re-interfere in the wavefunction, generating the "particle" pattern expected from two independent sources (each previous slid). Since we cannot set propper initial properties, is hard to see in experiments this deterministic aspect of the wave function, leading us to treat quantum mechanics as statistical. I would also consider this gap in between two interactions of a particle as the whole life of it, treating what it was past the first interaction and what it will be in after the second, as being other particles. The "story" told by this two-interaction-life-particle and its properties trough the wavefunction, generate the spacetime dimensions that connect all particle interactions in the Universe, no matter which set of dimensions they use to happen. And if we're talking about particles moving at the speed of light, that means the two interactions happen at the same moment and without a distance travelled in spacetime, indicating that spacetime is emergent from them and their interactions, and giving a hint that those particles have a special time dimension, the one that defines the order of interactions, and I have a strong feeling that this dimension is quantized and computable, since it's formed by a sequence of events.
I knew quantum mechanics was going to be where I depart from understanding, no matter how many times I've heard it explained and discussed and how the equations are reduced to symbolic simplicity. I appreciate some of the insight into the double-slit experiment, and it would be a cool supplement to explain some of the boundary parameters, i.e. width of the slits, distance between them, thickness of the material. For some reason, I've always thought it was on the scale of the "table top", in the sense that your "detectors" could be good old condensation chambers and you could have the slit inside a detector and watch the trails go through either slit and see the trails in the output detector all concentrate around two peaks. The basis vectors that Dirac was working out are new to me and I wish there was more history surrounding his insights as the "Dirac equation" was sort of a pre-cursor to the "Schroedinger equation". The thing that intrigues me about this "wave function" business, is that reality seems to be a field of probability as a component of space itself. As if there's the 4-D "points" of spacetime, yet attached to each is extra vectors or quantities of probability that, in conjunction with other "large mass observers" combine in a "measurement" so as to seem to produce particles from the vacuum where they satisfy the conditions of a certain "now". Hard to explain word-wise. Then again, it's the "square of the wave function", which is itself odd that it produces a "probability", which seems like a simple scalar number between 0 and 1. Which brings to mind, Higgs, and the mystery of how an electron can have no "size", yet still have mass, and a proton must have size, because there are a lot more components and forces interacting. So, I think these are important talks and definitely point to the lack of training in maths for the average American who made it through two semesters of undergraduate physics. Hopefully, you can add little primers to around these things for extra-interesting tidbits of history and insight. I never would've guessed at how astonishing the early 20th century was in terms of mathematical proficiency and physical insight, given the primitive technological landscape. It goes to show that brains are more valuable than apparatus when it comes to speculation, reasoning, and falsification.
Edifying, particularly regarding Planck discreetness and the role or rather the lack of a role of consciousness in the double slit experiment. The Dirac stuff at the end I sense is fundamental but very hard to grasp. Thank you so much for doing these. Can't wait for the next one.
Thank You for calling us that stayed til the end hardcore:D Perfect video, Something Deeply Hidden just arrived on my shelf for a week now cant wait to start it, hope it has some math as well?
Finally...Thanks Doc What it IS, is a wave, what it LOOKS like is a particle. I have been looking at this for over a year. Now I understand that bit. Not much else, but that bit is clear now.
"In one of Aesop's fables, a fox sees a juicy bunch of grapes and leaps to reach it, but can't quite jump high enough. In frustration, he declares that the grapes were probably sour, and he never really wanted them. The fox represents "physicists" and the grapes are "understanding quantum mechanics" - source Something Deeply Hidden, Sean Carroll; It's very hard to come and prove something new, we could ask Galileo, Giordano Bruno ... even Einstein how it was hard. You will succeed, you are the new Galileo's. Thank you Dr. Carroll for sharing your know-how, your intelligence, time ... I am very grateful for learning from you.
Thank you so much Sean! I guess some kind of a confusion when people ask "What is waving in psi?" is regarded to the observables, like energy _values_, spins, momentum, position (distance?) As you mentioned, the next video will be about measure and connection between QM and Measure theory (with Banach-Tarski paradox I hope?) but foreshadowing the answer to what's waving in psi and how outcomes of measuring things become positions and momentums. Thanks again!
This video series, plus your podcast, made me order ALL of your books on Amazon. I have always wanted to understand GR on a graduate level, so I hope your book is comprehensible for someone with a BS in engineering.
Indeed. Probably because it immediately raises the next question: why it doesn't entangle with a barier but does with a screen/observer? I think the similar experiment but with the Mach-Zehnder interferometer is also illustrative when one wants to show these quantum conundrum s.
How does quantum mechanics reconcile the fact that electrons have a measured mass yet seem to produce an interference in the double slit experiment?? Is it due to mass/energy equivalency?
It is extraordinarily tempting for people "in the know" about quantum mechanics to state it in the most confusing and mind-boggling language they can think of, because it is (unfortunately genuinely) quite fun to watch people's brains melt. Over the last few years, Sean Carroll has helped greatly with ending that tradition and instead explaining it in the most comprehensible language possible. I've had many of those "aha" moments thanks to him! :D
@@barefootalien Well, I think this is also because there is YT. The Leonard Susskind's Lectures are also enlightening. So are the Brian Greene's "festivals". BTW: This old quote is attributed to Bernard Shaw: "You have nothing to do but mention the quantum theory, and people will take your voice for the voice of science, and believe anything." ;)
The lectures are excellent--thanks for them. A phrase such as "The wave function is real" invites confusion. The wave function is, of course, a mathematical artifact, in this case, a core part of a model intended to describe quantum reality. In short, the wave function is a human construct. As such, it is 'real' but not in the sense intended. Your claim, I take it, is that this function describes an ontological reality--quite independent of a mathematical function designed to model this reality--that is wave-like in behavior.
At 3:15 - "The elctron wavefunction wants to be smooth and spread-out". Why does the electron prefer a spread-out wave function? (We can only know that by solving the Schrodinger equation)
Dustin, I took Modern Physics at the university this last semester. I love quantum mechanics, and so I've been trying to read up on Dirac notation (bra-ket notation) and Hilbert spaces. I've been looking into this stuff for roughly four months and it still makes my head explode.
@@donjuan6118 I'm also listening to a lecture in quantum mechanics right now and i can assure you that this really is just a matter of time and good teaching. But this is stuff from the third or fourth semester, therefore it's no wonder that it doesn't make much sense if you squizze it into 15 minutes or so. I honestly believe that everybody with motivation, enough time and a good teacher can understand this. This is not just for seldom geniuses.
34:08 "You might say, well, that's a little bit confusing..." No, _really?_ :) I love it, but this stuff is a whole _lot_ confusing to me! Luckily, I can just enjoy it, because I'm simply an old fart taking time out from playing computer games by watching this as I eat lunch. Heh, heh. Edit: 40:17 "This is why infinite vector dimensional spaces are hard." Oh, _that's_ why. Got it. :)
You can try Principles of Quantum Mechanics by Ramamurti Shankar along with Quantum Mechanics Demystified by David McMahon, both are great for beginners for basic QM math and notation.
Surely when the electron is approaching the barrier if the barrier is bumped the electron stops and if the barrier is not bumbed it does not stop. In that sense the electron is going to entangle with the barrier. I understood that part of the reason to say "no entanglements" would be that any "eye" that strongly correlates with which slit was used will trigger the particle-like outcome. But if you have a "detector" which beeps if both or one of the slits were used that would be in the same state regardless of which slit was used and would thus result in the wave-like outcome?
Listening to this whilst looking at the 'trending' videos on RUclips. Having said that - - and I get the irony - - I'd love a Craig vs Carroll round 2. And thank you for offering this, your expertise, for free. J
OH THANK YOU double slit!!!!! I appreciate you talking about it so much!! - Does the detector by the slits affect the outcome in the sense that it exerts some force on passing particles (like an induction coil or something)? - if we assume the slit detectors are powered (so have a power input), and a data output, does the interference pattern persist if the detectors are powered, but the data output is un-monitored (or maybe not plugged in)? if the data output is somehow recorded to a table that no-one can read (heavily encrypted, maybe) does that count as an observation, and affect the interference pattern? - if someone entirely un-related to the above experiment later manages to decrypt the above data table, does the initial data taken from the interference pattern suddenly change retroactively to non-interference somehow?, OR! does the initial experimenter NOT get an interference pattern, and can thereby determine/conclude that the encryption will some-day become breakable (or maybe "hey, someone must secretly be monitoring the slit detector data outputs!"). These are very round-about ways of me asking about the measurement problem, and my way of asking the (admittedly poorly phrased) question "how does the wave function/electron/photon KNOW that the data output of the slit detectors is actually monitored?" Thank you again so much!
Great video. I have been wondering wether measurements have anything to do with the asymmetry of time. I mean a classical observer is a system that can distinguish past and future that has a memory.
Thanks so much for this amazing series, @Sean Carroll! Wish I'd found this back when we were in lockdown... May I ask for clarity on one small matter that's raised in this video? At approximately 28:30 you say that, when the electron is observed at the slits, the observer "...will see it either as a particle going through one slit or as a particle going through the other slit. Therefore, when it eventually hits the screen, it will have behaved like a particle." Perhaps my understanding of QM is wrong, but I thought that observation at the slits would result in the particle behaving not strictly as a particle per se, but rather as a wave, albeit one that passes through a single slit only. That is, I would expect the pattern formed by a stream of individual particles that are observed at the slits to form a diffraction pattern typical of a wave passing through each of the single slits, as opposed to the pair of blobs that would be expected were the particles to not exhibit any wave-like behaviour at all. Am I actually completely mistaken about this?!
The Dirac delta function figures prominently in circuit analysis in electrical engineering. I think a similar technique is used in mechanical engineering, as well.
Whatever the wave-function 'IS' and/or whatever reality it represents, is a mystery that, as you say, may be beyond our ability to perceive. But, one thing that emerges for me from your presentation is that it interacts (as a wavy, undefined thing) with the 'real' edges of the double slit and allows us to experience its behaviour. For me , this offers a little window into its true 'nature'... (Not that I am trying to avoid getting to know Hilbert space entirely :)
HMMMMM! Another Wonderful video! If sound waves travel linearly they are expressed as a wavy line with frequency and amplitude. But we know that the birds song is heard no mater where you are relative to the bird. Left, right, above, below or some combination. The sound propagates in concentric spheres and not in linear vectors. Using X, Y coordinates or even X, Y, Z coordinates is confusing because reality happens in concentric spheres and not concentric circles except when a human looks at them and only "sees" the 2 or 3 dimensional cross section of wave reality. Reality is in concentric sphere waves because all of human observable reality occurs due to electrons revolving around a nucleus that is traveling through space. We do not see the entire "sphere" of reality but only a cross section of the surface of it. Similar to the sine wave "signal" of an electric motor; but, more dynamic, because an electric motor actually comprises a linear reality as the armature has a definite length. I think.
Thanks Sean. How to interpret a statement like "The wave function of the electron passes through both the splits" given that a wave function is a function in Hilbert space? In particular, given that the wave function has ordinary spacetime as its domain, does that constrain the Hilbert space in some interesting way?
Somewhat ironically, one of the reasons to reject Sean's preferred interpretation of QM is that the domain of the "wave function" is configuration space (and time) - *not* ordinary spacetime.
I begin to suspect that the fields we should consider are not electron fields, proton fields, etc. but rather electric charge fields, strong color fields, etc... the character of particles. "Particles" are then the points where these fields interact to conserve and to exchange physical quantities. In this picture an "electron/positron" is a specific stable interaction among these fields and a "top/anti-top" is another specific stable interaction among these fields.
Good morning Sean. Thanks for the vid. :-) Time for my mental exercise. This helps my understanding of this quite a lot. (but I have a long way to go).
If there is electrical field which influences magnetic field ten why there is no gravitational field which influences time field, then those could be influenced by other fields which manifest themselves to us as particles. I guess hence quantum fields theory. Also when measurement is done some energy should be used to trigger that but if one action gets opposite reaction then some energy goes also to the opposite side. I guess even smallest amount can collapse a particle function to make it appear at the coordinates where energy was excreted. Right? :)
What happens at the Minimum and maximum of the wave function? Why does the wave function is waveving--more specifically . What tells the wave function not to wave anymore after it has reach the min/max, and just change back and forth from min to max then max and min ? Why does it have to wave?
Measuring things involves interacting with the "field" in some way. I don't think we can assume it is purely passive. We are measuring "wave functions" with tools that are orders of magnitude larger than the size of the effect. This is akin to measuring a red blood cell with a yard stick. We don't know what is going on on the scale of what is going on. I don't think it is fair to say that there is nothing "more fundamental" than a "wave function" when we don't really know what is going on here yet.
I understand what Sean is saying about the Dirac delta function and yet there seems to be a more fundamental deeper layer to the wave functions. If we are to assume, similar to the Pilot Wave theory, that all objects are "particles", in a specific pin-point location, and these wave functions, an observation of our observation of reality, are describing the wave-like movements of these pin-point particles. So, what is creating these wave-like movements of these particles? A universal force at all points in space and at all moments in time. The universal force is the force that moves everything. An analogy is similar to a magnetic field that only affects particles with certain properties. The universal force affects all particles with all range of properties.
After I watched video 7, I had the question. What is between 2 plank points and 2 plank moments? And the three answers I could think of were 1 nothing 2 another universe 3 we don’t know. Thank you for answering my question . I also realize that the question “between 2 points” may be meaningless.
But when does the wavefunction uncollapse? I mean, does it stay collapsed forever, and if so will we eventually run out of quantum weirdness? I thought when you shine light through a series of polarizing filters, you need QM to explain what happens at each filter, it doesn't start behaving like a particle after the first one, even though the first one measures it, right? Does it somehow get reset from having a definite property to being uncertain again?
Why do we pose that the observables such as electrons or photons are acting like a wave but then a particle with the collapse of a wave function instead of posing that the electrons or photons act/are like particles interacting in a 'wavey' like background medium or some extra dimension(s) or 'partial dimension' that force corpuscles into appearing to have interference? Alternately asked, is there a reason to believe that space-time could not be causing the interference patterns observed in the double slit experiment?
In short, we can say that the iconic name Quantum Mechanics doesn't refer to a theory of quanta, but to one of smooth functions. So what's the point? The point is that the theory measurements do help going forward. So we really have to care about reality and not to overstate the fancy part of measurements.
Excellent video Sean as always. Question: In "what is waving" - I kept thinking if this is a 'new' way of looking at the concept of "Ether" ? (which was long discredited)
What if movement is an illusion? Particles are just a wave in the matter field and just appear and disappear as the wave passes. Every spot in the universe has the intrinsic quality to create matter if the surrounding area promotes it. Time dilation is just a change in how fast or slow this appearances and disappearances occur. It makes sense that if your moving fast it is harder to these changes occur. Also if you have a lot of mass that tries to keep bodies together it would be harder to make those changes from spot to spot
Guess - Assume Psi(x,t) is not inf. smooth. in reality because of various calculation difficulties in causality. I assume information in the form of extra decimals are prohibited. Some function could jump on this as causality for iterating an answer faster or more accurate. So no it Must be discrete. A simple choise of crafted decimals would be enough. idx = f.argmin((x[i]-d)**2) and then x[i] = d[idx]. Where d is a list of approved decimals. If quantum mechanics has some logic to it. So could the decimals belonging to it. Its simple. Theorem guess - Since the universe is large assume eveything that can make it larger without any sacrifice is considered. Security by engineering is one such thing.
35:00 is it that helpful to say that Ψ is a vector in Hilbert space? I think you're saying there's an abstract domain, perhaps with infinite points, and Ψ maps that domain to the range of complex numbers. Also you can do linear operations on Ψ like add them or scale by a number. So far nothing new. Where it might get interesting is if you define what is the domain of Hilbert space (real spacetime, or something else?) and how vector operations produce things like persistent particles or localized scattering. I'm sure that'll get technical. So far I feel like I've been following an audio course for Japanese and it has been awesome. So now I can go to Japan and book hotel rooms and talk to shopkeepers or ask simple questions. But at some point the accessible audio course stops and you have to go to a real school or read grammar books or go and live in Japan if you want to become fluent. Still, getting this far on Sean's free public outreach is totally awesome!
All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954). Does this statement still hold true? What did he mean?
If I give you a function like f(x)=x^2, it is defined for all real numbers x and takes on an infinite number of values. Does that mean the function contains an infinite amount of information? If it does, how is it that I can transmit to you an infinite amount of information just by saying x^2?
The relation between spacetime and the amount of information it contains is interesting. I am not a physicist and don't claim to understand the details. But I think it was found, at least in some theoretical settings, that the maximum amount of information in 3d space is proportional not to the volume but to the area.(This is the basis for the so-called holographic principle) I don't know how these calculations in terms of discrete bits were made on top of a smooth spacetime (perhaps they assume discrete spacetime in these calculations?), but perhaps Sean would kind enough to explain the chain of argument?
I do not know if it helps but you can characterize any continuous function be defining its values only on a set of rational numbers. And they are countable...
@@trucid2 if you give the algebraic definition, it's compact. But if you give a list of samples at arbitrary real x, f(x) pairs the samples would require infinite digits to conclude they're exactly consistent with f(x) = x^2. By the same token if a particle can be literally anywhere in continuous spacetime, either we need infinite digits to simulate it, or there's some constraint: algebraic, discrete, or fuzzy. I think quantum mechanics leans on saying the universe is continuous and fuzzy, the uncertainty principle, but it's not completely clear how that might map to bounded information.
Hi Sean. Great job from you. I am a great admirer and seen many documentaries from you. I have an idea about nature of light a vacuum. So please how can i contact you to discuss it. It very interesting and if you consider it powerful enough it can be published why not. I have something to tell...
How often was this experiment of monitoring Quantum Electrons been done? Does the electrons accumulated in that same pattern every time? What is your explanation for it?
@Sean Carroll I think that you could change the way mathematics is presented in schools, reorganizing it and making it easier to understand. This way more of us would understand it and our civilization would progress much faster. What is your opinion about the way mathematics is presented in schools? Would you try to do something at a great scale regarding that? Thanks for sharing your passion with us. RUclips is becoming a smarter and more enjoyable platform through the presence of people like you!
What does the math say if you consider the electron as entangling with both slits and the wall (to whatever extent) before going on to interact with the screen? So long as there isn't a detector there to entangle with it, perhaps it entangles with the whole system and it comes off like waves do in "regular" waves.
As much as we are exploring the quantum world it is also exploring us. It is not like we have a box of toys or a sandbox to play with where we are the masters in control of it -- quite the converse. We are being monitored and measured, things are done on our behalf to see how we react. We have our formulas and measurements, but the quantum world has its own too -- measurement sizing up measurement. You think you are sizing up a bug in a sandbox but it is sizing you up too. How do I know this? It is logical that if the quantum world reacts to the observers then it observes as well. The bigger experiment includes our attempts at experimentation, we are part of the its bigger experiment. If you think aliens are out in space at the macro level... think again.
Dr Carroll, the 4th system you discribed in double slit experiment i.e with monitoring, is this experiment performed in lab?? Or it is just a thought experiment.
Not sure if somebody still reads comments here, with the last one being 4 years ago, but I'll ask my question anyway. What happens in the double slit experiment when you have a detector at only one of the slits, not both? Will the fact that I have a detector at one of the slits affect all electrons that made it to the screen, or only the ones that were detected at the slit? What kind of pattern will I see on the screen?
It never doesn't work. In principle you could calculate anything you like using Schrodinger's Equation. The only thing stopping you is the fact that for increasingly complex systems you rapidly approach a point at which the math becomes absolutely nightmarish, and then even impossible to do computationally. Lucky for us, in that ultra complex regime, decoherence assures that uniquely quantum effects are extremely rare, and thus classical mechanics is "good enough" and vastly easier to use. It is absolutely no different from when you use General Relativity instead of Newtonian/Keplerian: when the relativistic term is small enough that you no longer feel a need to use its more complex math to attain a sufficiently accurate prediction for your purposes. Similar transitions exist between classical physics, statistical physics, chemistry, and biology. In principle you could (and indeed people have) model every detail of a biological system like photosynthesis purely with QM. If your goal is to tease out minute details about how individual particles are transported within chlorophyll via quantum tunneling, you actually do need that. If you just want to understand the bonds between atoms in the resultant fructose molecule, the Bohr model of the atom is enough, and vastly easier. If you want to analyze the chain of chemistry an animal then uses to metabolize that fructose into glucose and then ATP, then both QM and Bohr style chemical bond analysis are vast overkill and you would instead use chemical equations. If you want to track the overall metabolism of an entire animal and understand how it is similar or different from other organisms, then chemistry is too detailed to be very helpful and you use molecular biology, etc. In principle you could determine the difference between a giraffe and a turtle just with QM. In practice, it would take a stellar-scale computer longer than the heat death of the universe to do, so it's not recommended, but "when does Psi no longer work?" Never. (Okay, not never... It doesn't work inside black holes or before about 10^-34 seconds after the Big Bang, but that's the opposite sense from the implication of your question). A better way to phrase this might be "When does Classical Mechanics stop working, forcing us to use Quantum Mechanics?" QM (or precisely Quantum Field Theory) is the more fundamental theory and in principle can reduce to Special Relativity, Newtonian Mechanics, Lagrangian Mechanics, etc with 100% fidelity (but not General Relativity)
10:00 - There was an observation (www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein) that showed if there's some granularity in spacetime it can't be bigger than 10^-13 times the Plank length. So I don't think the Plank length is such a big deal.
If something is real (like the wave-function), it must be instantiated in the real world by some 'stuff'. What represents physically the wave function before the measurement? The particles of the parallel worlds should be there already to do that.
hi i am really grateful that you have put your time and energy into this series of videos. my questions are 2. if the wave function is a function of space and time, where does it sit in theories where space and time emerge rather than being presupposed? second, re the measurement problem in QM i see that some experiments comment on an ability to 'measure' without collapsing the wave function. can you comment onn that? again my great thanks for you doing all this.
I like actualized leos videos about spirituality in a non religious way. He has videos about quantum mechanics. He quoted you in there too. I really would like to know what your current opinion about this stuff. The Allan Wallace video was clear. You may changed ever since.
How can one not fall in love with math and physics while listening to him...man I wish I had a math / physics professor like him in high school. ... Thank you Sean ! I might not get all you are saying but even so I'm loving the struggle to be able to. You are amazing!
Thanks, Dr Carroll for the energy, effort and enthusiasm you put into this series of videos. It's very much appreciated.
What is the formula for Sean Carroll's energy?
Thank you for the lectures, you make me feel as if I have my own personal physics professor. I'm sure most of us watching feel that they too have their own personal instructor. And he is freaking great.
I love the math part, please do not shy away from it :) Also, the way you present, you talk about it - these concepts look so easy. Please keep up this great work.
Sean singing at 27:35 is literally the best part of the video
Dum dum dum dum dum dum dum dum Dum dum dum dum dum. Dum dum dum dum dum dum dum
I have a degree in nuclear and electrical engineering and this is the best explanation of the double split experiment I have seen. Obviously nobody EVER bothered to teach me about how to conceptualize the wave function in graduate school. Thanks for this one Prof.
At 38:22 Sean speaks my favorite Physics idiom, "It turns out that …". I've heard that since high school, and it always makes me think there is something that I will never know--right before "It turns out!"
Dr. Carrol, thank you for taking the time to explain things on the discrete/granularity issue. Your explanation helped a great deal.
Strangely enough, as someone who left math back in high school, I really appreciated the math at the end to explain the wave function. The graphs help me put my brain in that way of thinking.
Holy cow, what an amazing 45 minutes 👏🏽
Thanks for the discussion on Planck units. They’re often referred to in popular physics talks in ways that I took to mean discrete, but this clears up that misconception
Yeah, Planck units tend to lead to a lot of misconceptions. I used to be absolutely astonished to almost a level of a "religious experience", feeling genuine awe and like I'd touched something truly fundamental and electrifying about the universe, at the fact that the speed of light is one Planck length per Planck time. I first heard that fact in relation to Simulation Theory, which stated it as something magical, and a gigantic clue about the nature of reality.
Then I actually did some research into what Planck units actually are.
The answer, that they are units that are defined such that the speed of light is one Planck length per Planck time, made me blush, laugh, and nearly cry all at once. XD
In fact, it gets worse! Planck units are not even a _unique_ way of specifying units in terms of the fundamental constants. If you make different kinds of assumptions, you get quite a few different "fundamental" unit systems that all have their own way of simplifying certain aspects of the mathematics of physics, with each prevalent in its own field.
So not only is it not mind-blowing, but rather simply tautological than the speed of light is one Planck length per Planck time, it's not even unique. Kinda shaky ground to base a hefty portion of a theory of reality on, eh?
I'm just an undergraduate, so most of my information come from science divulgation and journalism of some sort. But as far as I'm aware, there was actually one experiment in 2011 that showed that any granularity on space-time (if existent at all) should be at least 13 orders of magnitude smaller than the Plank Length (www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein).
There's seem to be a lot of theorists trying to sell their pet theory or interpretation to the press as if it were "the truth", or the scientific consensus, that's (one of the things) that causes many of those misconceptions. Quantum mechanics says nothing about the Plank lenght, some quantum gravity theories suggest that there might be a minimum scale (but don't specify the value, actually, most quantum gravity now-a-days like string theory and some loop quantum gravity don't specify a lot, and you can always save the theory from observation).
None of those theories predicted that granularity should be at the Plank level either, it's more like the plank scale seemed to be a nice place to put it, but they already know how to modify their theories. Theories that can predict any number or that you can always change so that they could match with new data are not good theories. I have nothing against people studying them, just like it's important to study pure math, I'm sure some useful things will come out of it, and maybe we even get lucky and it turns out to be right, but people should be more open about what we don't know and the problems in our understating, specially scientists.
That's (one of the many reasons) I admire Sean Carroll (and Leonard Susskind and some others), they really draw the line on known, agreed upon, consensus, proved science and personal opinion or interesting and promissing ideas, speculations and interpretations. Sean specially seems to go to trouble of trying to explain other points of view he himself disagrees with.
best explanation of Hilbert space/wavefunction for a non- physics major I have ever come across. thank you so much . ( sad i'm late to the party as it would have been great to have had the opportunity to ask questions, what a privilege )
DAMN I love this series, Dr. Carroll. I'm a mechanical engineer and when I was in school (at ULL), my friend's grandfather offered a quantum mechanics elective for non-physics majors over a single fall semester. I unfortunately was not able to take it because it would have overlapped with my Machine Design lab. It's something I have always regretted; not only for the fact that those 3 credits would have given me enough for a physics minor. What you are doing with this and Mindscape is so hugely appreciated.
Best explanation of the double slit experiment I've run across. Others seem to suggest that the particle "somehow" goes through both slits and interferes with itself. The wave function explanation makes perfect sense.
Love to hear Sean say "well... we have no idea" There's still much to discover!
Really neat pedagogical device, to emphasize what we don't know
We are so lucky to get to watch these videos ♥
5:00 - 15:00 is really good. Sean touches on how we think of probability as a tool for understanding and predicting physics, like the position of a gas molecule in a room, but we still believe that actually the molecules have a definite position, momentum etc, and statistics is more about our ignorance than the workings of universe. And so that touches on the issues I have with understanding physics - is it supposed to help us predicts or interact with physics at all, or is it just describing the laws of the universe that only the universe can follow. I’m still having trouble articulating that notion.
Also, Sean says that with QM, statistics are not about our ignorance, not tools, but maybe something more fundamental.
He then goes on to talk about the Double Split experiment, and tries to do so in a way that clears up the popsci misconceptions, and help us see what’s really going on there, necessarily biased towards what Sean thinks is relevant to talk about, in physics and in the context of this YT video, etc etc.
Continuing on the notion I find hard to express; Sean also points out that it was useful to talk about the DSE and Schrödinger’s cat not just because they’re illuminating, but also to ‘correct’ (subject to all types of relevance realization) the readers previous misconceptions they’ve picked up from popsci, in a way that’s consistent with the implications the Author has made in their writings so far.
I think this important to my idea of the pedagogy of physics, and how it is often presented with enthymemes about what you do and don’t know. Still having a hard time expressing that
Thank you, Sean. Your detailed explanation of how the wave function interferes with itself, in a way that a mere probability distribution can't, helped clarify several issues for me.
I have one particular way to see/explain wave function and would like to validate it here. It is the function that describes the path a particle take, from one interaction up to the next, and it is function of the particle's properties at start. The function is pretty much classical and deterministic from one interaction to the other. The problem is that we cannot access any sort of information during this interval in between interactions without creating a new interaction that would reset the wavefunction with new particle properties. That's what the slid barrier represents in the double slid experiment, a reset of the properties influenced by the shape and position of the slids, this reset configures the wavefunction to express the wave interference pattern. When added after the slids, the detectors interact with the particle, reseting the wavefunction with new properties, and this time without a doublle slid to re-interfere in the wavefunction, generating the "particle" pattern expected from two independent sources (each previous slid). Since we cannot set propper initial properties, is hard to see in experiments this deterministic aspect of the wave function, leading us to treat quantum mechanics as statistical. I would also consider this gap in between two interactions of a particle as the whole life of it, treating what it was past the first interaction and what it will be in after the second, as being other particles. The "story" told by this two-interaction-life-particle and its properties trough the wavefunction, generate the spacetime dimensions that connect all particle interactions in the Universe, no matter which set of dimensions they use to happen. And if we're talking about particles moving at the speed of light, that means the two interactions happen at the same moment and without a distance travelled in spacetime, indicating that spacetime is emergent from them and their interactions, and giving a hint that those particles have a special time dimension, the one that defines the order of interactions, and I have a strong feeling that this dimension is quantized and computable, since it's formed by a sequence of events.
I knew quantum mechanics was going to be where I depart from understanding, no matter how many times I've heard it explained and discussed and how the equations are reduced to symbolic simplicity.
I appreciate some of the insight into the double-slit experiment, and it would be a cool supplement to explain some of the boundary parameters, i.e. width of the slits, distance between them, thickness of the material. For some reason, I've always thought it was on the scale of the "table top", in the sense that your "detectors" could be good old condensation chambers and you could have the slit inside a detector and watch the trails go through either slit and see the trails in the output detector all concentrate around two peaks.
The basis vectors that Dirac was working out are new to me and I wish there was more history surrounding his insights as the "Dirac equation" was sort of a pre-cursor to the "Schroedinger equation".
The thing that intrigues me about this "wave function" business, is that reality seems to be a field of probability as a component of space itself. As if there's the 4-D "points" of spacetime, yet attached to each is extra vectors or quantities of probability that, in conjunction with other "large mass observers" combine in a "measurement" so as to seem to produce particles from the vacuum where they satisfy the conditions of a certain "now". Hard to explain word-wise.
Then again, it's the "square of the wave function", which is itself odd that it produces a "probability", which seems like a simple scalar number between 0 and 1. Which brings to mind, Higgs, and the mystery of how an electron can have no "size", yet still have mass, and a proton must have size, because there are a lot more components and forces interacting.
So, I think these are important talks and definitely point to the lack of training in maths for the average American who made it through two semesters of undergraduate physics. Hopefully, you can add little primers to around these things for extra-interesting tidbits of history and insight. I never would've guessed at how astonishing the early 20th century was in terms of mathematical proficiency and physical insight, given the primitive technological landscape. It goes to show that brains are more valuable than apparatus when it comes to speculation, reasoning, and falsification.
Edifying, particularly regarding Planck discreetness and the role or rather the lack of a role of consciousness in the double slit experiment. The Dirac stuff at the end I sense is fundamental but very hard to grasp. Thank you so much for doing these. Can't wait for the next one.
Thank you! what you and Brian Greene are doing is historic
Thank You for calling us that stayed til the end hardcore:D Perfect video, Something Deeply Hidden just arrived on my shelf for a week now cant wait to start it, hope it has some math as well?
Thank you Dr. Carrol for your double slit explanation. I had heard most of it in bits and pieces before. All of it at one time is much better.
Also, I believe the first piece of Quantum Mechanics should be pi not psi. Pi belongs here.
I appreciated the math at the end. Reminded me of Brian Greene's daily equation videos.
Finally...Thanks Doc What it IS, is a wave, what it LOOKS like is a particle. I have been looking at this for over a year. Now I understand that bit. Not much else, but that bit is clear now.
I stayed to the end even if my brain didn’t. What’s waving again?
"In one of Aesop's fables, a fox sees a juicy bunch of grapes and leaps to reach it, but can't quite jump high enough. In frustration, he declares that the grapes were probably sour, and he never really wanted them. The fox represents "physicists" and the grapes are "understanding quantum mechanics" - source Something Deeply Hidden, Sean Carroll; It's very hard to come and prove something new, we could ask Galileo, Giordano Bruno ... even Einstein how it was hard. You will succeed, you are the new Galileo's. Thank you Dr. Carroll for sharing your know-how, your intelligence, time ... I am very grateful for learning from you.
This challenges me so much! Thank you! It is good to explore areas of study that are very different from ours
Thank you so much Sean! I guess some kind of a confusion when people ask "What is waving in psi?" is regarded to the observables, like energy _values_, spins, momentum, position (distance?) As you mentioned, the next video will be about measure and connection between QM and Measure theory (with Banach-Tarski paradox I hope?) but foreshadowing the answer to what's waving in psi and how outcomes of measuring things become positions and momentums. Thanks again!
This is amazing! Thank you Dr. Carroll!
Thank you for this series, it is very enjoyable and much appreciated. Have bought 'Something Deeply Hidden' to continue the fun!
This video series, plus your podcast, made me order ALL of your books on Amazon. I have always wanted to understand GR on a graduate level, so I hope your book is comprehensible for someone with a BS in engineering.
Between this and Brian Greene's daily equation, my evenings are full of mathematical wonder (and confusion)!
Started listening: "...hoping that this video will be short and sweet". Looking at the length: 46.05. Great, let's continue listening! ;)
"The wave function of the electron goes through both slits" - aha moment. I've never heard anyone say that exact language before.
Indeed. Probably because it immediately raises the next question: why it doesn't entangle with a barier but does with a screen/observer? I think the similar experiment but with the Mach-Zehnder interferometer is also illustrative when one wants to show these quantum conundrum
s.
@@PrzemyslawSliwinski i guess because the barrier doesn't interact with the EM field, whereas a detector does?
How does quantum mechanics reconcile the fact that electrons have a measured mass yet seem to produce an interference in the double slit experiment?? Is it due to mass/energy equivalency?
It is extraordinarily tempting for people "in the know" about quantum mechanics to state it in the most confusing and mind-boggling language they can think of, because it is (unfortunately genuinely) quite fun to watch people's brains melt. Over the last few years, Sean Carroll has helped greatly with ending that tradition and instead explaining it in the most comprehensible language possible. I've had many of those "aha" moments thanks to him! :D
@@barefootalien Well, I think this is also because there is YT. The Leonard Susskind's Lectures are also enlightening. So are the Brian Greene's "festivals".
BTW: This old quote is attributed to Bernard Shaw: "You have nothing to do but mention the quantum theory, and people will take your voice for the voice of science, and believe anything." ;)
Great addition to the last video. Thanks! Can't wait for the follow-ups.
The lectures are excellent--thanks for them. A phrase such as "The wave function is real" invites confusion. The wave function is, of course, a mathematical artifact, in this case, a core part of a model intended to describe quantum reality. In short, the wave function is a human construct. As such, it is 'real' but not in the sense intended. Your claim, I take it, is that this function describes an ontological reality--quite independent of a mathematical function designed to model this reality--that is wave-like in behavior.
I'm looking forward to your video about measurement/observation, and any explanation on how or why that collapses the wave function. Thanks
At 3:15 - "The elctron wavefunction wants to be smooth and spread-out". Why does the electron prefer a spread-out wave function? (We can only know that by solving the Schrodinger equation)
Your explanation is the best!! Thank you. Kisses from Brazil.
The Dirac math made my brain a little wavy.
Dustin, I took Modern Physics at the university this last semester. I love quantum mechanics, and so I've been trying to read up on Dirac notation (bra-ket notation) and Hilbert spaces. I've been looking into this stuff for roughly four months and it still makes my head explode.
@@donjuan6118 I'm also listening to a lecture in quantum mechanics right now and i can assure you that this really is just a matter of time and good teaching. But this is stuff from the third or fourth semester, therefore it's no wonder that it doesn't make much sense if you squizze it into 15 minutes or so. I honestly believe that everybody with motivation, enough time and a good teacher can understand this. This is not just for seldom geniuses.
34:08 "You might say, well, that's a little bit confusing..."
No, _really?_ :) I love it, but this stuff is a whole _lot_ confusing to me!
Luckily, I can just enjoy it, because I'm simply an old fart taking time out from playing computer games by watching this as I eat lunch. Heh, heh.
Edit: 40:17 "This is why infinite vector dimensional spaces are hard." Oh, _that's_ why. Got it. :)
Glad it's not just me :)
You can try Principles of Quantum Mechanics by Ramamurti Shankar along with Quantum Mechanics Demystified by David McMahon, both are great for beginners for basic QM math and notation.
Newton and other pre quantum physicists continue to dislike this video. Science can not be stopped!
I liked the Monad comment. Reminded me of Moleeds (old school funny stuff). Thanks for the refresh.
Surely when the electron is approaching the barrier if the barrier is bumped the electron stops and if the barrier is not bumbed it does not stop. In that sense the electron is going to entangle with the barrier. I understood that part of the reason to say "no entanglements" would be that any "eye" that strongly correlates with which slit was used will trigger the particle-like outcome. But if you have a "detector" which beeps if both or one of the slits were used that would be in the same state regardless of which slit was used and would thus result in the wave-like outcome?
Listening to this whilst looking at the 'trending' videos on RUclips.
Having said that - - and I get the irony - - I'd love a Craig vs Carroll round 2.
And thank you for offering this, your expertise, for free.
J
You mean the Craig the creationist?
@@rage9715 Yep.
OH THANK YOU double slit!!!!! I appreciate you talking about it so much!!
- Does the detector by the slits affect the outcome in the sense that it exerts some force on passing particles (like an induction coil or something)?
- if we assume the slit detectors are powered (so have a power input), and a data output, does the interference pattern persist if the detectors are powered, but the data output is un-monitored (or maybe not plugged in)? if the data output is somehow recorded to a table that no-one can read (heavily encrypted, maybe) does that count as an observation, and affect the interference pattern?
- if someone entirely un-related to the above experiment later manages to decrypt the above data table, does the initial data taken from the interference pattern suddenly change retroactively to non-interference somehow?, OR! does the initial experimenter NOT get an interference pattern, and can thereby determine/conclude that the encryption will some-day become breakable (or maybe "hey, someone must secretly be monitoring the slit detector data outputs!").
These are very round-about ways of me asking about the measurement problem, and my way of asking the (admittedly poorly phrased) question "how does the wave function/electron/photon KNOW that the data output of the slit detectors is actually monitored?"
Thank you again so much!
He doesn´t answer questions in the comment section. Next Q&A is for lesson 8 and the questions asked in the comments to that video.
@@lennarthedlund9783 ok thanks. Dang it!
Great video. I have been wondering wether measurements have anything to do with the asymmetry of time. I mean a classical observer is a system that can distinguish past and future that has a memory.
Thanks so much for this amazing series, @Sean Carroll! Wish I'd found this back when we were in lockdown...
May I ask for clarity on one small matter that's raised in this video? At approximately 28:30 you say that, when the electron is observed at the slits, the observer "...will see it either as a particle going through one slit or as a particle going through the other slit. Therefore, when it eventually hits the screen, it will have behaved like a particle."
Perhaps my understanding of QM is wrong, but I thought that observation at the slits would result in the particle behaving not strictly as a particle per se, but rather as a wave, albeit one that passes through a single slit only.
That is, I would expect the pattern formed by a stream of individual particles that are observed at the slits to form a diffraction pattern typical of a wave passing through each of the single slits, as opposed to the pair of blobs that would be expected were the particles to not exhibit any wave-like behaviour at all.
Am I actually completely mistaken about this?!
The Dirac delta function figures prominently in circuit analysis in electrical engineering. I think a similar technique is used in mechanical engineering, as well.
27:35 best part of the whole video
Whatever the wave-function 'IS' and/or whatever reality it represents, is a mystery that, as you say, may be beyond our ability to perceive. But, one thing that emerges for me from your presentation is that it interacts (as a wavy, undefined thing) with the 'real' edges of the double slit and allows us to experience its behaviour. For me , this offers a little window into its true 'nature'... (Not that I am trying to avoid getting to know Hilbert space entirely :)
What is the wave function made out of? Chalk, if you're writing it on a chalk board, and ink if you're writing it on paper.
Thank you! So glad you are doing these videos.
Sean "the wave situation" Carroll
Sean 'my hair is wavy' carroll
I know you favor the many worlds interpretation, but have you looked into superdeterminism?
HMMMMM! Another Wonderful video! If sound waves travel linearly they are expressed as a wavy line with frequency and amplitude. But we know that the birds song is heard no mater where you are relative to the bird. Left, right, above, below or some combination. The sound propagates in concentric spheres and not in linear vectors. Using X, Y coordinates or even X, Y, Z coordinates is confusing because reality happens in concentric spheres and not concentric circles except when a human looks at them and only "sees" the 2 or 3 dimensional cross section of wave reality. Reality is in concentric sphere waves because all of human observable reality occurs due to electrons revolving around a nucleus that is traveling through space. We do not see the entire "sphere" of reality but only a cross section of the surface of it. Similar to the sine wave "signal" of an electric motor; but, more dynamic, because an electric motor actually comprises a linear reality as the armature has a definite length. I think.
Love the explanation Sean. Thank you
Thanks Sean. How to interpret a statement like "The wave function of the electron passes through both the splits" given that a wave function is a function in Hilbert space? In particular, given that the wave function has ordinary spacetime as its domain, does that constrain the Hilbert space in some interesting way?
Somewhat ironically, one of the reasons to reject Sean's preferred interpretation of QM is that the domain of the "wave function" is configuration space (and time) - *not* ordinary spacetime.
I begin to suspect that the fields we should consider are not electron fields, proton fields, etc. but rather electric charge fields, strong color fields, etc... the character of particles. "Particles" are then the points where these fields interact to conserve and to exchange physical quantities. In this picture an "electron/positron" is a specific stable interaction among these fields and a "top/anti-top" is another specific stable interaction among these fields.
Good morning Sean. Thanks for the vid. :-) Time for my mental exercise. This helps my understanding of this quite a lot. (but I have a long way to go).
If there is electrical field which influences magnetic field ten why there is no gravitational field which influences time field, then those could be influenced by other fields which manifest themselves to us as particles. I guess hence quantum fields theory. Also when measurement is done some energy should be used to trigger that but if one action gets opposite reaction then some energy goes also to the opposite side. I guess even smallest amount can collapse a particle function to make it appear at the coordinates where energy was excreted. Right? :)
What happens at the Minimum and maximum of the wave function? Why does the wave function is waveving--more specifically . What tells the wave function not to wave anymore after it has reach the min/max, and just change back and forth from min to max then max and min ? Why does it have to wave?
Measuring things involves interacting with the "field" in some way. I don't think we can assume it is purely passive. We are measuring "wave functions" with tools that are orders of magnitude larger than the size of the effect. This is akin to measuring a red blood cell with a yard stick. We don't know what is going on on the scale of what is going on. I don't think it is fair to say that there is nothing "more fundamental" than a "wave function" when we don't really know what is going on here yet.
I understand what Sean is saying about the Dirac delta function and yet there seems to be a more fundamental deeper layer to the wave functions. If we are to assume, similar to the Pilot Wave theory, that all objects are "particles", in a specific pin-point location, and these wave functions, an observation of our observation of reality, are describing the wave-like movements of these pin-point particles. So, what is creating these wave-like movements of these particles? A universal force at all points in space and at all moments in time. The universal force is the force that moves everything. An analogy is similar to a magnetic field that only affects particles with certain properties. The universal force affects all particles with all range of properties.
After I watched video 7, I had the question. What is between 2 plank points and 2 plank moments? And the three answers I could think of were 1 nothing 2 another universe 3 we don’t know. Thank you for answering my question . I also realize that the question “between 2 points” may be meaningless.
But when does the wavefunction uncollapse? I mean, does it stay collapsed forever, and if so will we eventually run out of quantum weirdness? I thought when you shine light through a series of polarizing filters, you need QM to explain what happens at each filter, it doesn't start behaving like a particle after the first one, even though the first one measures it, right? Does it somehow get reset from having a definite property to being uncertain again?
Why do we pose that the observables such as electrons or photons are acting like a wave but then a particle with the collapse of a wave function instead of posing that the electrons or photons act/are like particles interacting in a 'wavey' like background medium or some extra dimension(s) or 'partial dimension' that force corpuscles into appearing to have interference? Alternately asked, is there a reason to believe that space-time could not be causing the interference patterns observed in the double slit experiment?
In short, we can say that the iconic name Quantum Mechanics doesn't refer to a theory of quanta, but to one of smooth functions.
So what's the point? The point is that the theory measurements do help going forward. So we really have to care about reality and not to overstate the fancy part of measurements.
I think I will watch this regularly now :)
Excellent video Sean as always. Question: In "what is waving" - I kept thinking if this is a 'new' way of looking at the concept of "Ether" ? (which was long discredited)
Thank you once again Sean.
What if movement is an illusion? Particles are just a wave in the matter field and just appear and disappear as the wave passes. Every spot in the universe has the intrinsic quality to create matter if the surrounding area promotes it. Time dilation is just a change in how fast or slow this appearances and disappearances occur. It makes sense that if your moving fast it is harder to these changes occur. Also if you have a lot of mass that tries to keep bodies together it would be harder to make those changes from spot to spot
Guess - Assume Psi(x,t) is not inf. smooth. in reality because of various calculation difficulties in causality. I assume information in the form of extra decimals are prohibited. Some function could jump on this as causality for iterating an answer faster or more accurate. So no it Must be discrete. A simple choise of crafted decimals would be enough. idx = f.argmin((x[i]-d)**2) and then x[i] = d[idx]. Where d is a list of approved decimals. If quantum mechanics has some logic to it. So could the decimals belonging to it. Its simple. Theorem guess - Since the universe is large assume eveything that can make it larger without any sacrifice is considered. Security by engineering is one such thing.
If the Universe is a wave function, with what "environment" does it entangle/interact/decoherence ???
Two years later relistening I think I’m slowly starting to get the gist.
35:00 is it that helpful to say that Ψ is a vector in Hilbert space? I think you're saying there's an abstract domain, perhaps with infinite points, and Ψ maps that domain to the range of complex numbers. Also you can do linear operations on Ψ like add them or scale by a number. So far nothing new. Where it might get interesting is if you define what is the domain of Hilbert space (real spacetime, or something else?) and how vector operations produce things like persistent particles or localized scattering.
I'm sure that'll get technical. So far I feel like I've been following an audio course for Japanese and it has been awesome. So now I can go to Japan and book hotel rooms and talk to shopkeepers or ask simple questions. But at some point the accessible audio course stops and you have to go to a real school or read grammar books or go and live in Japan if you want to become fluent. Still, getting this far on Sean's free public outreach is totally awesome!
All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954).
Does this statement still hold true?
What did he mean?
10:00 If spacetime is completely smooth doesn't that imply the universe contains an infinite number of (classical) bits of information?
If I give you a function like f(x)=x^2, it is defined for all real numbers x and takes on an infinite number of values. Does that mean the function contains an infinite amount of information? If it does, how is it that I can transmit to you an infinite amount of information just by saying x^2?
The relation between spacetime and the amount of information it contains is interesting. I am not a physicist and don't claim to understand the details. But I think it was found, at least in some theoretical settings, that the maximum amount of information in 3d space is proportional not to the volume but to the area.(This is the basis for the so-called holographic principle) I don't know how these calculations in terms of discrete bits were made on top of a smooth spacetime (perhaps they assume discrete spacetime in these calculations?), but perhaps Sean would kind enough to explain the chain of argument?
@@aman3133 But it likely refers to the Planck area as a single bit container.
I do not know if it helps but you can characterize any continuous function be defining its values only on a set of rational numbers. And they are countable...
@@trucid2 if you give the algebraic definition, it's compact. But if you give a list of samples at arbitrary real x, f(x) pairs the samples would require infinite digits to conclude they're exactly consistent with f(x) = x^2. By the same token if a particle can be literally anywhere in continuous spacetime, either we need infinite digits to simulate it, or there's some constraint: algebraic, discrete, or fuzzy. I think quantum mechanics leans on saying the universe is continuous and fuzzy, the uncertainty principle, but it's not completely clear how that might map to bounded information.
Hi Sean. Great job from you. I am a great admirer and seen many documentaries from you. I have an idea about nature of light a vacuum. So please how can i contact you to discuss it. It very interesting and if you consider it powerful enough it can be published why not. I have something to tell...
Thanks Sean! Great stuff.
Not waving but drowning...(but enjoying trying to keep up!)
How often was this experiment of monitoring Quantum Electrons been done? Does the electrons accumulated in that same pattern every time? What is your explanation for it?
@Sean Carroll I think that you could change the way mathematics is presented in schools, reorganizing it and making it easier to understand. This way more of us would understand it and our civilization would progress much faster. What is your opinion about the way mathematics is presented in schools? Would you try to do something at a great scale regarding that?
Thanks for sharing your passion with us. RUclips is becoming a smarter and more enjoyable platform through the presence of people like you!
What does the math say if you consider the electron as entangling with both slits and the wall (to whatever extent) before going on to interact with the screen? So long as there isn't a detector there to entangle with it, perhaps it entangles with the whole system and it comes off like waves do in "regular" waves.
As much as we are exploring the quantum world it is also exploring us. It is not like we have a box of toys or a sandbox to play with where we are the masters in control of it -- quite the converse. We are being monitored and measured, things are done on our behalf to see how we react. We have our formulas and measurements, but the quantum world has its own too -- measurement sizing up measurement. You think you are sizing up a bug in a sandbox but it is sizing you up too. How do I know this? It is logical that if the quantum world reacts to the observers then it observes as well. The bigger experiment includes our attempts at experimentation, we are part of the its bigger experiment. If you think aliens are out in space at the macro level... think again.
Oh time went fast, now I have to face reality.
Dr Carroll, the 4th system you discribed in double slit experiment i.e with monitoring, is this experiment performed in lab?? Or it is just a thought experiment.
Not sure if somebody still reads comments here, with the last one being 4 years ago, but I'll ask my question anyway. What happens in the double slit experiment when you have a detector at only one of the slits, not both? Will the fact that I have a detector at one of the slits affect all electrons that made it to the screen, or only the ones that were detected at the slit? What kind of pattern will I see on the screen?
When does the psi function no longer work? i.e when do we switch to Newtonian physics, and why do we do that?
It never doesn't work. In principle you could calculate anything you like using Schrodinger's Equation.
The only thing stopping you is the fact that for increasingly complex systems you rapidly approach a point at which the math becomes absolutely nightmarish, and then even impossible to do computationally. Lucky for us, in that ultra complex regime, decoherence assures that uniquely quantum effects are extremely rare, and thus classical mechanics is "good enough" and vastly easier to use.
It is absolutely no different from when you use General Relativity instead of Newtonian/Keplerian: when the relativistic term is small enough that you no longer feel a need to use its more complex math to attain a sufficiently accurate prediction for your purposes.
Similar transitions exist between classical physics, statistical physics, chemistry, and biology.
In principle you could (and indeed people have) model every detail of a biological system like photosynthesis purely with QM. If your goal is to tease out minute details about how individual particles are transported within chlorophyll via quantum tunneling, you actually do need that. If you just want to understand the bonds between atoms in the resultant fructose molecule, the Bohr model of the atom is enough, and vastly easier. If you want to analyze the chain of chemistry an animal then uses to metabolize that fructose into glucose and then ATP, then both QM and Bohr style chemical bond analysis are vast overkill and you would instead use chemical equations. If you want to track the overall metabolism of an entire animal and understand how it is similar or different from other organisms, then chemistry is too detailed to be very helpful and you use molecular biology, etc.
In principle you could determine the difference between a giraffe and a turtle just with QM. In practice, it would take a stellar-scale computer longer than the heat death of the universe to do, so it's not recommended, but "when does Psi no longer work?" Never. (Okay, not never... It doesn't work inside black holes or before about 10^-34 seconds after the Big Bang, but that's the opposite sense from the implication of your question).
A better way to phrase this might be "When does Classical Mechanics stop working, forcing us to use Quantum Mechanics?" QM (or precisely Quantum Field Theory) is the more fundamental theory and in principle can reduce to Special Relativity, Newtonian Mechanics, Lagrangian Mechanics, etc with 100% fidelity (but not General Relativity)
@@barefootalien Good answer. Thank you. I put my trust in your answer.
Top of the morning Sean
10:00 - There was an observation (www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein) that showed if there's some granularity in spacetime it can't be bigger than 10^-13 times the Plank length. So I don't think the Plank length is such a big deal.
If something is real (like the wave-function), it must be instantiated in the real world by some 'stuff'. What represents physically the wave function before the measurement? The particles of the parallel worlds should be there already to do that.
How far can one go relating this to computer science ? Could we say a function takes vectors as inputs and does operations on them ?
Good intro, enjoyed. But where does cohomology come in? And is qm an axiomatic theory?
hi i am really grateful that you have put your time and energy into this series of videos. my questions are 2. if the wave function is a function of space and time, where does it sit in theories where space and time emerge rather than being presupposed? second, re the measurement problem in QM i see that some experiments comment on an ability to 'measure' without collapsing the wave function. can you comment onn that? again my great thanks for you doing all this.
I wonder what Sean thinks of Stephen Wolfram's newest work...
If the wave function is one element of the hilbert space, I wonder what the other elements are?
I like actualized leos videos about spirituality in a non religious way. He has videos about quantum mechanics. He quoted you in there too. I really would like to know what your current opinion about this stuff. The Allan Wallace video was clear. You may changed ever since.
At what size particle do we start to see a more classical pattern of impacts on the detector?