One thing I should clarify: the definition of probability I propose here certainly isn't rigorous! That's probably why philosopher's prefer defining the probability in more defensible ways using decision theory. But I was looking for an understanding of probability that felt like probability even if it has flaws
Consider the following: Language, the very thing we utilize to think thoughts and convey ideas. Un-named Concepts -> Given a Name (could be a sound, symbol, etc) -> With an attached meaning -> And maybe even other meanings depending upon context -> And maybe even other names with the same meaning. (Basically a Dictionary and a Thesaurus for a language). BUT: a. How exactly do we know for 100% certainty that we have all the un-named concepts that could ever be named? b. How exactly do we know for 100% certainty that the meanings we give named concepts are 100% correct? We truly do not know what we do not know. This is a part of the 'Great Unknown'. Never stop learning.
I prefer to think of many worlds as being continuous rather than discrete. In your example you describe a branching of outcomes, but consider our current state as a ribbon that can be split at different proportions. You can consider the width of this ribbon to be related to our uncertainty of the world we inhabit. With more decisions we add another branching to the ribbon, and so on until we zoom out onto the entire map and see a tangle of threads branching and weaving together like string cheese.
In some sense our mathematical definition of probability is already a kind of many worlds definition as you have some probability measure over a set Omega and any omega is a "world" where random variables map to different properties of that world. Certain random variables can then be independent of some other, i.e. observing one does not tell you anything about the other, but for a fixed world of course the other one is fixed. But you don't know the world you are in
One thing that has always bothered me about many worlds and this explanation of probability as well is the following: According to many worlds, every possible event does in fact happen but only the probabilities of experiencing certain branches differ, right? If you look at a person's life then and map out a complete tree diagram of every single time they split into several different branches does that not imply that there is a version of that person that actually exists that has experienced all of the most unlikely events in their life? If we consider this world for a moment, would their empirical research and therefore some of their understanding of the world not be completely different from ours? Also, I'm not a physicist so I apologize if I misunderstood something but is entropy not a result of probability? Does that mean there is a world where energy reorganizes itself or at least works very differently?
Yeah, fantastic question. I think the answer is yes, and I oscillate on how bothered I am about it. On the one hand, if a person flips a coin all day, there's a chance that they flip 100 heads in a row. If that happens they'll also get entirely the wrong impression about coins. But on the other hand, this result only actually happens 1 in 2^100 times in the real world, but in MW there is definitely a person who experiences the equivalent scenario. You can't dismiss it by saying it's "low probability" either, because probability has a very different meaning in MW, and so just because it's low probability, it does not make that world any less real.
"There exists" is a bit of a strong word here. In MWI there exist many orders of magnitude more of the worlds where probability works as expected compared to these rare cases. You can still bring the probability back by saying that the chances of *you* being in one of those worlds are astronomically small (as with any other interpretation of QM), and since you probably aren't in one of those, then it doesn't matter if they exist or not since you can't really observe them either way. Even more so, you don't even need MWI for this. You can just have a universe with infinite time - since the time is infinite, every possible situation will happen infinitely many times, even the extremely unlikely ones. So in a universe with infinite time there eventually will be a person who experiences all the unlikely events happening
I think you only run into problems if you assert that the other worlds are _real_ in a sense. There's a kind of heuristic in physics that when two things are indistinguishable they should be treated as equivalent. And I think people treat the realness of alternate worlds too seriously, cause you can't distinguish a universe where the different worlds are real from one where the different worlds aren't and it's just a probabilities game. So I just sit with the thought of "for all intents and purposes, I can treat the world I am in as the only real one, without worry".
@@silentobserver3433 Infinite time doesn't necessarily mean that every conceivably event will happen. It's like how there are infinitely many real numbers between 1 and 2, but none of them is 3.
@@ericvilas I feel like that kind of defeats the entire purpose of _interpreting_ quantum mechanics though -- like, isn't the entire point to try to figure out what the math actually _means_ about reality? If we aren't treating the worlds as real, than what's even the point of many worlds in the first place? We might as well just "shut up and calculate" as Feynman supposedly said. To be clear, personally, I don't actually think many worlds is right, but I do think, in order for it to be _meaningful_ the worlds have to be thought of as real in some sense. I'm open to having my mind changed though, if you care to discuss it. Philosophy of quantum mechanics is fascinating and I enjoy discussing it.
Many comments here suggesting to split into 3 branches, where each has 1/3 probability. This doesn't work, because the words "world" and "branch" here actually refer to a precisely defined mathematical object -- a vector |v> in a Hilbert space. These objects by definition have to obey the linearity rule: a|v> + b|v> = (a+b)|v>. If we split into 3 branches where 2 of them represent the same measurement result with probability 2/3, then |a+b|² = 2/3. But |a+b|² > |a|² + |b|² for a, b ≠ 0. So the branches can't all have equal weights.
Even if you agree the universe splits into three branches, it doesn't work because it's circular. It is splitting up the branches specifically for the purpose of deriving the Born rule. All attempts to recover probability in MWI suffer from this problem, they are all just as arbitrary as assuming the Born rule from the get-go.
In David Deutsch's variant of MWI there are an infinite number of worlds that have the same state prior to the measurement, and in this model the probability of each outcome is the fraction of the infinite worlds that have the outcome. In Deutsch's model, the disproof that begins at 2:36 doesn't hold. In particular, the probability of measurement X where the electron energy is greater than energy A is 2/3, not 1/2, and the total number of worlds is infinity, not 2.
@@siarez Easy. If you run an experiment, and that experiment only creates two worlds with a version of you in each, then the probability must be 1/2. What would a 2/3 probability even mean in that scenario? You can only get probabilities that are not equal when you create enough outcomes so that the proportion of a specify outcome relative to all outcomes equals the probability of that outcome occurring. So in that case, there must be at least 3 worlds created. 2 for X and 1 for A. However most things wouldn't have such simple divisions. You'd quickly see that you'd need an infinite number of worlds created to be able to handle all possible probabilities. To me, the need for the many worlds theory to have an infinite number of worlds that can then be subdivided into an infinite number of other worlds in the correct proportions, defeats the whole point of the theory. What chooses that probability, and if you have such a chooser, you don't need many worlds. You can just have a single world with that chooser deciding the probabilities of future configurations. In that case, many worlds is actually more complex, because it adds an extra unnecessary step of creating the infinite number of other worlds you didn't experience.
@@siarez : I think she meant the two worlds, X and A, both exist with certainty, and no mechanism is understood to explain why you the observer are more likely to find yourself in the X world, while your other self would therefore be more likely to find him/herself in the less likely A world. But I too don't think that argument is clear.
Also there is actually a lot of problems with reducing quantum probabilities into self locating probabilities, you can look up the video on youtube "David Albert - "Worries About Accounts of Probability in Everettian Understandings of QM", once again this is a video by a philosopher of physics, and i still think the challenges he gives there are really unasnwered to the point when combined with Tim Maudlin ontological worries, really makes the Many Worlds interpretation as of now, not really a valid theory until these issues are answered.
Thank you. I just watched a video claiming to debunk many worlds theory due to the probability issue. I had a similar concept but you explain it much better than I could. 🙏
Excellent video and thought provoking too. So does this mean that in some experiments the same outcome will be found in both branches I.e. has 100% probability and the other has zero probability in that branch? And if so, doesn’t the branch stop there because there is no uncertainty at that point?
I feel like this answer was kind of unsatisfying, probably because it doesn't really answer what "our experience" means. We sit here with a 2/3 blue, 1/3 red particle in front of us, and we know that if we do the measurement, we will become two separate people in two non-interacting worlds. But, like, "our experience" travels into one of the worlds, with a 2/3 probability in the blue way and 1/3 probability in the red way. And that's what you kind of tried to define with probability at the end, but that definition still didn't define what it means for "our experience" to travel down one path and not the other; it kind of just assumes that we know what "our experience" is. And intuitively we do, of course, but it feels very handwavy and non-rigorous. I don't know if there is an answer to this, though. At some point it does go down the "what is consciousness?" issue that easily veers into the pseudoscientific philosophical talk that often surrounds quantum mechanics in pop culture. Maybe the next video about how to mathematically interpret "probability" will help, not sure.
With branch counting, what stops there from being an uncountable number of worlds in each branch? In other words, the fraction of branched worlds with each outcome is equal to the probability. From another perspective, there are an uncountable number of events happening in each instant across the universe. Discretely counting the branches doesn't make sense.
In any one instance or interaction event, there will only be a defined number of occurrences resulting in discrete worlds. But yes the number is *nearly* infinite overall in the universe.
I guess I don't understand the premise that an interaction with 2 outcomes only creates two worlds. if A has probability 1/3 and B has probability 2/3 why can't B just have two branches connecting to it assuming each branch as an equally likely chance to be "picked". My point being that there could only be 2 outcomes, but many different routes to get to those outcomes. Feyman diagrams come to mind.
For the second example, when we're looking for A or X and then C or B if X, shouldn't it be 1/3rd for A and 2/3rds for X, since X includes two options? Just because you're only testing for A or X initially doesn't give them equal weight in the probabilities because X is actually multiple things. Probabilities are so weird.
Yes, but this presupposes the probabilities are 1/3 and 2/3. At this point we're not assuming that and just counting branches regardless of their amplitudes in the superposition. This is kind of obviously wrong, but that's the point.
I've been waiting for this. Thank you! I must admit, I don't really see this as resolving the issue. My impression is the following: Looking forward, the current you will, indeed, see both outcomes; you can only say "you" only saw one outcome when speaking of the past. When looking to the future, there isn't a new other-you that spawns while the current-you continues along one branch. Both are what current-you will become. I don't see how looking forward toward expectations resolves the issue that current-you will see all outcomes as current-you splits into the countless future-yous. Or, to put it more succinctly, probability in other contexts is defined as much by what *doesn't* happen as upon what does happen. When you rolled a 6, you did not roll a 1, 2, etc. If everything always happens, how can you assign a weight to one outcome over another? In other contexts, probability is essentially a shorthand for permutations. But if MW permutations (i.e. world-counting) fail, I don't see what meaning probability can possibly hold. I love your videos, so I want to clarify my issue is not with your video (it was excellent, as always), but with the MW interpretation itself. I think you did as good a job as can be done trying to make sense of probability in this context, considering that, imo, there's no sense that can be salvaged from it. Or, at least, not that I've seen or thought of.
@@stevenjones8575 Well, how many real numbers are between 0 and 1? How many real numbers are between 1 and 3? I would say there are twice as many real numbers between 1 and 3 as between 0 and 1, despite dealing in infinities.
@@AkamiChannel Your intuition is likely failing you, as it does us all regarding infinities. For example, there are just as many even integers as there are integers in total. You could not salvage probabilities by trying to divide an infinite set of integers by an infinite set of even integers. They are the same size set: countably infinite.
A new video! I'm happy to see it. The way I've always thought about this (since reading David Wallace's book) is, when you figure branches happen 10^20 per second, and you're taking a random walk through that possibility space, which I think is what happens in MWI, then most path-ends are going to look back and see the Born Rule respected. But the finer you slice time, the more "random" the outcomes appear; the more likely you are to see very unlikely outcomes. And I think you can actually test that, and it's empirically grounded (i.e., the smaller the time-slice, the more probable are improbable events. But correct me if I'm wrong.) Then I thought for the really improbable branches on the bookends, it's going to appear really improbable for the people in those worlds as well compared with the rest of their history. So they'll be just as astonished to see it as we can predict, but they'd have predicted its possibility too. And then for the very, very improbable branches, where the classical world just breaks down completely, well, by definition humans simply wouldn't exist in such worlds to contemplate them. Anyway the punchline is, probability in MWI is about a long history of very many events. This is basically how you've presented it here; so it's nice to see I'm not the only one that figured this. ------------------- *** REQUEST: I have a request for a future video. Could you do an explanation of Entanglement (at a distance), the so-called EPR paradox, and Bell Inequalities from an MWI perspective? I get the idea that in MWI, what we call entangled particles are really all combinations of entanglements, but when we measure one, then the waves mediating that observation entangle with every other particle & drag the into their own decohered branch, which enforces a consistent history, so when the waves from Alice's observation arrive at Bob's observation of the entangled pair, only the proper pair can be measured for each respective Bob, and the other possibilities are lost to decoherence (from each Bob's perspective). But I'm still a little unclear about it and it'd be helpful I think to hear someone else try to explain it. I once thought about it like the branches are encrypted to each other, where a consistent history is the deencryption key. So the observation of A's entangled particle is carrying a deencryption key that will only deencrypt the proper property for B's particle. And all the other possibilities really in that space remain encrypted in decoherence. Is that a right way to think about it? ------------------ A related thing I'd really like to hear about is just how consistent histories are enforced generally. Take the case of light from a star 1 billion light years away. The last time the matter later mediating that light was in contact with matter later mediating earth was some 13 billion years ago, so when that light enters our solar system, does it interact with every branch of the Earth? That is, do they all see the "same light"? But as soon as that light starts scattering off the different branches, is it always the "latest branch" that constitutes the new branch? Like say in some branches the moon is between that star and the earth, and in other branches it's not. The light has to pass through empty space in one branch but be scattered by the moon in another branch... Does the incoming light respect every subsequent branch so it does both? Anyway, how do wave functions respect consistent histories? And is there a visualization like that to see it in action? This isn't necessarily a request for a video either, since I know how much work goes into them. If people would like to comment and give some guidance that'd be just as helpful, or anyway it's food for thought for everybody to think about. Cheers everybody!
There is another huge problem with the Many Worlds interpretation, i recommend you read the Chapter 4 "Can the World be Only Wavefunction? " in the book "Many Worlds? Everett, Quantum Theory, and Reality". In that chapter Tim maudlina argues that the wave function alone is insufficient to account for the result of any measurement. To do so, says Tim Maudlin in the chapter "Can the World Be Only Wavefunction?", one must add particles, i.e., localized objects in low-dimensional spacetime, into the ontology. Maudlin's conclusion is that Everett's interpretation, and similarly collapse alternatives in which nothing but the wave function exists, are epistemically incoherent: they do not make the connection between theory and the results of experiments comprehensible, and yet these results are presumably what serve to confirm these theories to begin with. The worry here seems to be that if, according to the Everettians, the wave function is all there is, and if, further, it 'lives' in an abstract, multidimensional space, then it is unclear how such an object can account for our experience which is, roughly put, the behavior of localized objects in the low-dimensional spacetime we inhabit. Bohmians can easily address this problem, says Maudlin, because they simply postulate such localized objects by adding them into the ontology. GRWf theory (collapse with flash ontology) has a similar solution. But Everettians (and first generation collapse theoreticians with them) face the serious challenge of coming up with a comprehensible link between the state of wave function (which is all there is) and what warrants our belief in the theory, namely, the behavior of localized objects in a low-dimensional spacetime, which is our experience. Decoherence, argues Maudlin convincingly, simply cannot meet this challenge. These kind of worries are unfortunately not appreciated by most physicists because they don't engage with the philosophy of physics, i recommend you read/watch Tim Maudlins work, he brings a lot of clarity on what a quantum theory has to have in order to be a satisfactory account of what the world is really like. One good lecture i recommend you listening to on youtube is " Tim Maudlin - The Metaphysics of Quantum Mechanics"
Once you start assigning probabilities to being in one of two worlds, the many worlds theory loses its elegance. What determines that probability, and what does that probability even mean since another version of you experienced the other outcome? If there is only one world for each outcome with one of you in each, then it would be impossible to for the probabilities to differ. Every time the experiment is run, all outcomes would happen exactly once, thus making them all equally likely. The only way to maintain the many worlds simplicity is to say a large number of worlds are created for each event, and the proportion of the worlds created for each outcome equals the likelihood of that outcome occurring. So if two outcomes could happen, with the probability 'A' being 1/3 and the probability 'B' being 2/3s, you'd have at least three worlds created. One world with event 'A' and two worlds with event 'B'. But that too gets extremely messy when the probability of an event happening is an irrational number that can't be represented like this. An infinite number of worlds would need to be created to get the proportions right.
The probability is "random", just as the probability in the Copenhagen "interpretation". But what is randomness truly is? Well, before, always that randomness appeared, was 'cause there were a "hidden mechanism" of some sort (or simply lack of (correct) understanding of the process, like missundertanding the extension of the process), so it's logical to think that probvably randomness is just an apparent thing.
@@ThePowerLover There is no randomness in many worlds. It is just an iteration of everything that can happen. As a result, it's extremely hard to get the required probabilities out of the theory, since there is no preferred point of view. Every outcome is equally valid, so if every outcome occurs only once, they must all have the same probability of happening.
@@ThePowerLover You've got that backwards. Copenhagen is a subset of Many Worlds. They both require some "chooser" to assign the configuration of a universe. The difference is that Copenhagen only requires that "chooser" to operate on one existing universe, while Many Worlds requires that "chooser" to do the exact same thing, but also create an infinite number of universes in the right proportions before assigning the proper configuration to each one.
💡Idea : In the Red / Blue ball case Because the probability distribution is 1/3 + 2/3, wouldn't it make more sense to split into 3 different worlds? 🤔 I mean, branching into 2 worlds where the ball is blue and 1 where the ball is red?
this would work but I feel there's an issue with it. Using this theory, the amount of worlds would basically be dependant on how "nice" the probabilities are. For example, 1/3 and 2/3 are "nice" probabilities and 3 worlds is enough. But consider the probabilities 33/100 and 67/100. It's almost the same as the previous case, but now you need 100 worlds. And you can keep getting arbitrarily close to the original example while requiring more and more worlds. I don't know, but it just doesn't feel right to me.
8:27 I know QM doesn't work like this, but so far this explanation seems to be along the lines of: I roll a dice. It comes up 6. I conclude that the probability of 6 is 1.
I appreciate you tackling this question, and I'm interested to see the other video you teased at the end of this one. I feel like you did a good job explaining the problem of probability in MWI. I think the 'explanation' in this video (e.g. the p(red)= expected proportion of red) was just a tautology, and therefore resolves into circular reasoning. This is why I'm interested in an explanation for MWI that deals with the problem of probability, because so far the only explanation is that if I ran an experiment under MWI I'm being told that I should expect to see the experimentally observed probabilities, but when I ask why MWI gives that outcome I'm hearing that it's because that's the probability I should expect. Okay why, when MWI doesn't appear to point to that outcome at all?
There are different probabilities associated with different results of experiments based on the proportion of universes that have a particular result vs other results.
What the MWI does to probability has, for me, always been a huge strike against it. The general notion that, contrary to our experience that rare events happen rarely, under the MWI _all_ events, no matter how rare, _always_ happen seems a strange and wasteful way to run a universe. I’ll have to see what your next video says about the Born rule, but here you’ve demonstrated nicely why branch counting doesn’t work. By branch counting, after three trials, your probability is 1/8 of seeing all three red when it should be (1/3)^3=1/27.
Can the many worlds interpretation be reconciled with bulk collection of infinite branes in M theory? Or are those completely independent and unrelated theories?
Do not confuse quantum physics theory and quantum physics interpretation. Theory makes accurate predictions of experiments and reasoning in theory can only be done by using mathematics. Interpretation is a useful but imperfect analogy that provides intuition. Common interpretations include analogies with classical physics and analogies with probability. An element of interpretation becomes theory only when the mathematics of this interpretation independently predicts an experimental outcome otherwise not explained by theory.
MWI makes mincemeat of Born's Rule. Consider one of the simplest branching worlds experiments: toss a coin eight times in a row. If every branched version of you completes the eight tosses, that will produce 64 branched worlds. According to MWI, you'll most likely end up in a world where you get about as many heads as tails, in accordance with Born's Rule. However, there's guaranteed to be one world where all tosses turned up heads (or conversely tails). For the branched version of you that wound up in that world, Born's Rule will have failed spectacularly. While it's true that such streaks of exceedingly unlikely outcomes would tend to average out over time, extreme exceptions will always remain, since every possible outcome is guaranteed to manifest in a branch somewhere in the multiverse.
Yep. This means that if I spend 8 hours a day flipping a coin for a year, there is a world out there where I get heads for every single flip, and another where I get tails for every single flip. Granted, the probability of finding yourself in that world is vanishingly small, but it's real. Many worlds implies that all vanishingly-small probability events happen. Which seems very susprect.
So one thing that bothers me with the many-worlds interpretation and this branch-counting idea is that branching is usually presented as binary decisions, which makes sense for something like spin. But what about for something like position? Surely when a particle's wave function collapses to a particular point in space from some interaction, there is a world for every possible value that its position could have, right? Which is presumably an uncountable infinity of branches created from a single collapse event (or a very large number if you think space is discrete). I'd love to know if you have any thoughts on this, though.
I'm far from an expert on many worlds or QM, but I don't think there has to be a binary decision, or any sort of _decision_ at all, actually, in order for the worlds to "split" -- just any sort interaction that would cause the "collapse" of the wavefunction. I presume the reason it's often presented in terms of binary decisions in pop-sci presentations is because it's just easier to explain that way. It's similar to how SR is often described in terms of different conscious observers, even though it's equally valid for inanimate objects, and all that actually matters is that we have different reference frames/coordinate systems, regardless of whether there's a conscious observers in either frame.
The whole idea of a "branch" is very pop-sci in the first place. A "world" in MWI is not a physical place you can go to, it's just a term in the wavefunction of the universe. Universal wavefunction evolves according to the regular Schrodinger equation and you can mentally split the wavefunction into non-overlapping parts according to their macroscopic state and call them "worlds". Then the entire wavefunction is just a sum of all these "worlds" that we've come up with for our own convenience, and since they are not overlapping in the wavefunction, they basically don't interact with each other. And there is no problem with uncountably infinite sums, that's just an integral
The binary I use in my modeling if the branching reality of all possible timelines is what I usually call contraction and expansion. Or stability and change. Or 0 and 1. What that binary means on a given level of reality's evolution is different, because it's a different kind of relationship. If you look at what Pascal's triangle represents geometrically, starting with -1D emptiness on the top, and one new dimension (on the right side) as you go down, you get all possible combinations of triangular geometric patterns, starting with a space (-1D), then a point (0D), then a line (1D), then a triangle (2D), then a tetrahedron (3D), and so on, adding one dimension per row, and generating complexity of relationships between spaces, points, lines, etc. I've recently started using a series of questions for each new dimension. It's usually Why?, When?, How?, and Where for the top 4 rows. Why? is a given, the singular (non-binary) category at the top of Pascal's triangle, which is answered "because" or with a definition of whatever we want to start with, such as a self (cogito ergo sum!). Then we ask where is it? It can either be in the past (contracted, unchanged), or the future (expanded, changed), in our binary split universe. Then we ask how is it? And the binary branching is either a familiar process (contracted, unchanged), or a novel process (expanded, changed). Then we ask where is it? And the binary branches are either here (internal, contracted, unchanged) or there (external, expanded, changed). And so on, with more specific kinds of questions as we get more detailed observations of the possible paths. (I have some nice diagrams of these, but alas, RUclips doesn't really like links and doesn't allow images in comments. You can find me on Twitter, though, with this username, where I share stuff like this.)
@@Lucky10279 "I presume the reason it's often presented in terms of binary decisions in pop-sci presentations is because it's just easier to explain that way. " That's a natural-enough presumption: if you don't understand a field deeply it's natural to imagine that, when experts give you a wordy description of something, that they're merely trying to make a complex concept relatable. It happens so often that it becomes expected. However, with the "many worlds interpretation", the wordy description is all there is, and when you scratch beneath the surface, you find there's nothing there at all! Despite many proponents' statements to the contrary, if you simply remove the collapse postulate from quantum mechanics, you do _not_ get many worlds. At least nobody has been able to show that you do. The project of actually obtaining the many worlds out without accidentally putting them in has been attempted since Everett himself, without success. A large part of the reason why the project has been a failure is precisely that there's no natural, consistent "measure" for an uncountable infinity of possible histories.
In David Wallace's book he talks about this. Yes many things like position are continua, not binary or discrete states. So how do you count branches in those cases? The way he describes it, think about a radial plane wave front in the position basis. Actually think about it in 2D so we're talking about circles. A wave front is continuous, so technically there are infinite branches or "points" in position. But events close to each other in Hilbert space (quantum possibility space) will stay close to each other, which is to say a vast number of points along the wavefront will be indistinguishable, so there's no sense calling them separate branches. His point was, counting a branch as "separate" has to do with our phenomenology of differences in physical events. It's not a property in whatever is mediating the wave; it's an emergent property about us (or whatever) in observing the thing. Then you can think about it like points along a circumference as a circle's radius grows. There are an infinite number of points along the circumference for both the small and large circle. But I think we'd say the large circle has "more branches" (in the position basis) because the separation in position is greater as you take proportional steps down the circumference, so the emergent phenomenology is going to have more countable differences in that sense. I think there is a mathematically clearer or more formal way to describe that, and Wallace does a better job explaining it than I did here. But I think you get the gist of it.
hey love your videos. I dont really get the problem here. at 5:28 why did you assign the "x" branch 1/2 and "a" branch 1/2. in mwt a quantum measurement causes an infinite number or large finite number of branches to split and 1/3 of those branches would split to "a" and 2/3 would split to "x".
It seems to me that once you accept Everett's original proposition, that the observer enters a superposition upon measuring, self locating uncertainty is a fairly obvious way to define the probability. You even get your own amplitude to work with.
Cool video! Counting the branches however still works when using the right branches. An experiment with chanes 1/3 (red) to 2/3 (blue) isn't splitting into two worlds, but three. There are now two people who measure blue and one red. Depending on what number the probabilities are represented in I guess we technically split into many many or even infinitely many worlds. Awesome food for thought though!
@@fg8557 only for some very weird irrational numbers. Any number that can be represented by a program can exist as a probability here, assuming we have countably infinitely many worlds. Numbers that do exist are n-th roots, eulerian, logarithm, technically complex ones (are there complex probabilities?)...all of which can be represented as a program 'creating' infinitely many worlds
@@ArvedRockt How many worlds do you get for a probability of root 2? For a probability of 0.5 do you get 2 worlds with 1 of each outcome or 4 worlds with 2 of each outcome (or 3/6 or 4/8, etc), or even infinitely many worlds at each wave function collapse? I mean, the real answer is you can make up whatever answer you want and the math will still work, which is the main problem with interpreting quantum mechanics.
I think I missed something, but this felt like explaining the probability of an event by saying that the result is biased by a proportion determined by the expected outcome, but then saying that the expected outcome is based on the probability of the event. Isn't this circular?
There is no uncertainty before you do the experiment because both outcomes happen. After the experiment, you don't know which version of yourself you are, this is called indexical uncertainty. What I find interesting after repeating the experiment many times is that there will be a version of you which sees very unlikely results (e.g. red 100 times in a row).
Let's hope that there is a version of you who actually read Everett's thesis and who noticed the glaring mistake in the second sentence that renders all of MWI complete intellectual nonsense. Maybe not in this universe? :-)
@@martinkunev9911 Everett simply didn't know that quantum mechanics is an ensemble theory and that the wave function is NOT a description of an individual system. It's a description of a quantum mechanical ensemble, i.e. it describes an infinite repetition of the same experiment. He treats it as if it was the description of one system... and that logical error is what blows up one universe into an infinite number of parallel ones. MWI is a trivial counting mistake. ;-)
I have been thinking the same thing. Monty Hall problem, if we can compare it to MWI, is a branching problem. The player decides on a strategy of "always switch", the odds of winning are roughly 2/3. This is reported to match statistics when players use that strategy. And that player who decides on a strategy ahead of time, creats the branches for the worlds at the get-go. Players who adopt no strategy create their branches further along the branched tree of worlds. I realize it is maybe incorrect to say players "create branches" merely by deciding or not deciding on a strategy but I'm not sure how else to frame it. Some people make much of the host knowing which door has the car. The host has a branching also, but his is set by the game format. A robot could do it.
If we describe the universal wave function as | U > = | R > + | B > (two worlds where you either experienced Red or Blue). What is then the difference between |U> where you experience Red , and |U> where you experience Blue. Since the universal wave function is the same in both cases, there has to be something outside the wave function that is different. The universal wave function is supposed to represent the state of the universe. If the universal wave function describes everything in the universe, where does that leave thing not described by it?
Hallo there, my personal interpretation of the identity problem ("which world will you end up in?") is that it's wrong to think about you in terms of individual person. I think a change of paradigm is necessary, for which you are everyone. You experience being me and other people, separately, but simultaneously. This works the same of course for the many world identity problem: you experience all the branches simultaneously, not only one, though in each branch you think you perceive only that branch.
At 11:13, what if you just saw 3 reds in a row? What if you repeat the experiment another 3 times, and you get another 3 reds? What if every time you repeat the experiment 3 times in a row you get 3 reds? In that case, what would expect to get if you were to repeat the experiment another 3 times in a row?
Perhaps, if the many worlds already exist in a higher-dimensional multiverse (some kind of block-multiverse), the probability problem could be solved with some notion of distance. A metric relating probability to distance. Perhaps one outcome is more "likely" because that universe is closer and therefore "easier" to access. In this way, there could be some kind of law of least action to guarantee that the nearest universe is more likely than the most distant ones. Just maybe. It is an idea that is not clear to me. But it seems that the metric on Hilbert spaces for quantum states (and their components) could be related to this metric, because it is directly related to the probability of each state. I don't know, just that it's something that has given me a lot to think about. What do you think?
I don't see how MWI can accomodate correct probabilities of outcomes, except if it is regarded as a probability measure without "worlds", kind of like Copenhagen. The MWI is a philosophical concept, not a physics concept.
This experiment she does in the final part of the video would end up disconfirming the born rule in most but not all branches. So if one believes in MWI, then one must believe that one has ended up in a very rare world where the born rule is confirmed by simple 50/50 splitting.
Yes, it's the fact that most humans are incapable of learning even the most trivial facts about physics. To me, as a physicist, that is absolutely beyond comprehension because all of this stuff is trivial. There are hard physical problems, but this is not one of them. :-)
The quantum multiverse may be a bit like a landscape with many roads in it. That all the roads exists doesn't mean we actually drive along all of them.
Hmmm i always thought that the probabilities come from the rules of quantum mechanics and in many worlds all the expected outcome happen and we just happen to be one of it (so that the probabilities is independent of interpretation) maybe i'm missing something...
in all the counter examples, why does there need to only be 2 worlds? like for the red/blue example, why cant you just have 3 total words: 2 worlds with blue and 1 with red, or like 3k worlds (where k is huge)? in that case you'd get that the p(blue) = #worlds with blue/#worlds = 2/3 or =2k/3k as you'd expect. like sure the 2 blue worlds might be equivalent wrt the color, but might have other differences we don't care about.
I’m unsatisfied EVERY time I listen to a QM video, read a QM article or book, or THINK about QM. I’m pretty certain this state will continue until I go to my grave.
Why in the red vs blue, 1/3 vs 2/3 example, does the number of worlds have to correspond to the number of experience types? Why can't there be 1 world where you experience red and 2 where you experience blue?
7:20 Possible gibberish but potentially an interesting thought. While you were explaining this using your pictures, the original state with the particle seems to act as a "Let" statement whereby you are determining the probable exist of the particle without respect to its state being that the sun total is one, then working backwards from its existence where one would say Let particle P exist. You then say: Particle PsubR or P(R) [depending upon one's requirement for the variable use case] Plus PsubB or P(B) = 1P(1) Or, Let particle P exist as P(1) = P(R) + P(B) which == PsubR + PsubB = PsubRB = P Then, there's the recursive interaction of the original state pre-check as part of the branch for each succession as the check is done without respect to time. Furthermore, the theoretical system isn't restricted by a strict adherence to quantitative segments (strict branch probability) and could also lean towards the LIM to Probability of each approaching to true probability as the segments are defined as t -> 0 Because, there is a time requirement to perform the check that isn't taken into account through the illustration as shown. So that, it is taken to be that it occurs instantaneously as an unstated assumption. I suppose the biggest difference between math and physics is to say whether we assume time is instantaneous, taken into account or not relevant to values under consideration. Still, good video. Also, you seemed to hesitate with the connotation of 'expect' with its convention as a term in Statistics which may have been an instance of lacking a better word rather than any deficit of comprehension of either. More precisely, would did we expect from a random RUclips commenter regarding their knowledge of the statistical expectation given that the existence of the comment provides a non-zero until you get to the part where I then say: TL:DR OP doesn't know what they're talking about. But, which OP? OP(V) or OP(C)? XD
why not put randomness in between? like many universes of you drinking the same coffe but being served by a different person because of the universe that person is, which it might look different for them but not for you. idk if im explaining myself good lol
There is no randomness in quantum mechanics. Random physical processes cause dissipation and we have not been able to observe any dissipation in quantum mechanics (for one thing stable matter could not exist). The theory is simply based on statistical independence of individual experiments in an ensemble. Statistical independence is NOT the same as randomness. Most people simply don't understand the assumptions of the theory.
OK, now I know why you had that strange configuration in another video of your phone taped to 1 cardboard box sitting on top of another box. I didn't realize that you were filming a writing surface.
The certainty with which you state 'but I know there is another world...' is unbelieveble. I love the things are not as they seem part . However I am not convinced that there are mw, 'there are no worlds' makes more sense to me. We do see this world, so there is no obvious evidance that we actually dont. Similarly like we have no evidance about the other world. Though for both the argument can be made. Would be too long to make it here...
This reminds me a lot of the Sleeping Beauty Paradox. Is there a connection there? In the Sleeping Beauty Paradox, you are told that you will fall asleep for a number of days, and the prince will then flip a coin. The prince will wake you up on Monday and ask what side the coin landed on. Irrelevant of what you guess, if the coin landed on tails the prince will give you a pill that erases your memory and puts you back to sleep. He will then wake you up on Tuesday and ask what side the coin landed on. Whenever you are woken up, you have no way of knowing what day it is. Given you know the rules ahead of time, what is the probability that you will be correct if you guess tails?
If there two outcomes in MW one with near infinite possibility and the other with near zero possibility, this means nothing because both events will occur. The two versions of me will see both. Am I missing something.
Is it not true that quantum superposition implies that particles are not merely here or there, in one state or another, but actually in a combined state of possibilities? Hence explanations which look upon blue and red objects as wholly discrete (represented here by colour) seems misleading, in that it gives a false impression. Nor do the probability of all quantum events remain the same over time. Radioactive elements decay so, the probability of a cat being dead in the box increases over time. So the equations used to predict the outcome can never be exactly calculated.
So you define the probabilities with the word "expected proportion". But isn't this self-referential? Can you define what "expected" means without using the concept of probability of the outcomes in the first place?
Na, toss a coin, you expect half the outcomes to be heads. Probabilities will always be a ratio, and you can predict what that outcome will be. No circular reference at all. I think you've confused proportion with probability, they are not the same thing.
What if observing the red/blue state does not create two worlds but 3? Two worlds where you see the blue and one where you see red. This makes it so we can keep the relatively intuitive idea that P of red= worlds with red/all worlds.
I mean, this is a problem with probability even without many worlds or quantum mechanics, right? What does it really mean to say there's a 50% chance of rain? Conventional intuition is like you conclude here -- if you experience this day 100 times, you will expect to experience rain 50 of those days. Likewise, if you run a quantum experiment 100 times, you will expect to experience a certain result 50 of those times. You mention that this idea applies equally to all QM interpretations, but I think it's even broader than that.
The diagram at 11:07 is incomplete… in some universes the experiment will be conducted only once, in other universes the experiment will be conducted only twice, etc
I think the problem with branch counting is simplification. It's more like for all the outcomes there are 100 worlds, in 33 of them you get red in 67 you get blue, 2 outcome with correct probability. The simplistic branch counting is like saying it's 50% for any outcome because it either happens or it doesn't.
The whole idea of branches is that you have a superposition of a couple of states, each of which are orthogonal to each other, and you wanna say that each term represents a branch that exists physically. If you measure a two level system, you only have two orthogonal terms, so only two branches.
@@jezer8325 sure, but the branches are not equal, so treating them as if they are is like saying every outcome has a 50% chance of happening. If you had 3 branches with 2 being blue and 1 being red that would actually give you the correct distribution of probability. If the model doesn't match actual reality you can't get mad at reality for being wrong.
@@chiepah2 It would give you the results you expect but that's because you reverse engineered a definition of 'branch' that's consistent with the 'branch counting' method but is not a relevant in any other way. The change you made that fits reality doesn't fit with the rest of the model. Your idea has as much explaining power as simply stating that the probability of being in each branch follows Born's rule. And maybe that's fine, but either way you're going to need to fit that into an extra postulate in place of the one we removed when moving from the Copenhagen interpretation to the MW interpretation. Hopefully the next video will explain how you can derive the rule without having to simply assert it.
@@jezer8325 ah, I see, thanks for the explanation, that makes sense. You don't really know what the probability is until you calculate it, so you wouldn't know how many versions of the same branch to add until after you calculate probability. If you know the probability you aren't adding anything by including additional branches of the same kind.
I find the feature of many worlds that you mentioned "it's really important that *you* only experience one world in many worlds" problematic. What definition of *you* are you using? The person you were before measurement of a particle's state is now gone, survived only by the two *you's* that measured the particle. I argue that *you* still actually experience both branches, the only thing to do is to let go of the traditional notion of *you* and see that both measurers are you: *you* who measured outcome 1 and *you* who measured outcome two. Isn't this what it means for an organism to have a life tree? Isn't this why it doesn't even make sense to ask "what is the probability that *you* end up one one branch or the other?"?
With the branch counting why are you assuming only 2 worlds, 1 for blue and 1 for red? How do we know there aren't 4 worlds where red are experienced and 8 worlds where blue is experienced? Then the # of branches where red is experienced / # of total branches would be 1/3 as needed.
perhaps the "world" splits into all probabilities. Two blue and one red. You get two blue worlds and one red world. If the probability is fifty four to forty six you create fifty four blue and forty six red. Is there some force stopping the creation of multiple identical worlds? I dont see why there should be.
Now you've just created a separate black box entity that can determine which outcome happens in a universe. It literally has to be able to create a universe with a specific configuration. But if you've done that, what is the point of a many worlds theory? Occam's razor would insist that that black box would be used to determine the evolution of a single universe than to do the exact same thing to a potentially infinite number of newly created ones. So instead of that black box creating exactly 44 identical universes for outcome blue and 46 identical universes for outcome red, it simply would allow the existing universe to evolve with outcome blue 44/90 percent of the time and outcome red 46/90 percent of the time. This black box would be doing the exact same type _hand wavium_ as many worlds, just with much less of it and without the need to create entire new universes.
in any branch in a timeline, say you want 2 choices, thinking if i do it, other me has no choice in the matter. well, a whole lot of conditions existed before that determine which branch you are on that have these yes/no forks. there is not only your Personal yes/no fork but so many branches up stream that also came to this fork. across ALL of these, the probability can approach a statistical value. there is unknown # of you's arriving at this choice
The branch counting argument feels silly Things can have only 2 possible outcomes without those outcomes necessarily being equally weighted. For example, you either will be struck by lightning tomorrow or you won't. But that doesn't mean the probability is 50/50 This argument is very unconvincing compared to the arguments for MW.
I really have a problem w Many Worlds for the very reason you made this video, but between time 10:40 and 11:30 you glossed over the crux of the problem w Expected experience....if red being 1/3 of the time.... in your diagram there were 8 observers that had each observed the experiment 3 times, and each one had a different observed probability. If u expand the experiment a million more times, there is no way that all observers end up seeing the same expected value of 1/3 red. I have no idea why many worlds is always a binary split (into 2 worlds) but it makes it impossible to get probabilities other than 50/50. Your original intuition was correct, I think. I have not heard an explanation that properly shows otherwise. Note I did watch your next referenced vídeo on the born rule, it didn't help. Thanks.
This just proves that the many worlds doesn't exist....not just on probabilities being wrong, but the very basics of energy dispersion not matching field draw under an observed event collapsing. There MIGHT be other universes, but it has nothing to do with ours splitting.
About 01:10 Your basic assumption that an experiment with n possible outcomes will get reality split into exactly n realities, here n being 2,... _...there will be one version of yourself who sees the outcome A and another who sees the outcome B._ ...might be false to begin with. It might split into a huge number N words instead, in p(A)∙N of them the outcome will be A and in p(B)∙N of them it will be B.
The thing with the many worlds theory is that it’s based on your actions. The probability of me choosing the red or blue is based off of my opinion and which I like better. It’s every time you make a decision you split off.
human choice has absolutely no impact on many worlds. humans are not magical beings, we are made out of atoms following the rules of physics. there is no such thing as free will.
The thing I don't understand is why people would bother discrediting certain branches from existing. If you believe in the many worlds theory, then you know that everything can happen somewhere in those branches... The branch might not relate closely to your universe, but you have to understand the conundrum that multiple branching universes cause. If you go backwards and start branching forward, are you sure there isn't a universe where this becomes more likely? It seems to me that its not that it is impossible. but rather you lack the ability to ever come across that possbility in your mind. There's alot of questions left to answer. Is the universe existence itself or is their many layers to this existence that we don't know. Is Quantum mechanics a small example of the chaotic nature that helped create existence? If we believe in the chaotic mess that is quantum probability. Then its not too farfetched into believing existence is governed by more chaotic ???? that we could never hope to wrap our heads around. I think many of us question why existence happens the way it does. Why did existence decide to shape in the way it did. I think we all agree that before existence there was no rules. So why would each existence come about with the same fundamental logic and rules. Can't it think of something better or is it really unoriginal. No pressure. I mean it has no time at all to decide something. Perhaps it did. I like this idea because I find it proposterous that existence would shape itself like this and this alone. There are no rules and yet unlimited rules to try out. It would be a creative shame to stick to just one rule set. So if you take that into account, the many worlds theory more than supports the impossible branches out there.... It also helps explain where the possible end point for these branches might exist. Since the fundamentals can be altered infinitely, then the many world branches may stop at universes where Quantum mechanics are different from our own. Making a universe that does not support the many world theory. The best part of this may be the fact that if you genuinely consider this, you may conclude that this world is that very same world. Meaning I just made a religion on the idea that the many world theory is right, but just false in this one. Which sounds like absolute nonsense, but Its impossible to disprove it. All this just to say... I f'd your mom.
I think people misunderstand probability. If a random experiment has two possible outcomes, that does not necessarily mean that their probability is 50-50. Or 33% in case of 3 possible outcomes. Probabilities can be different based on actual experimental data or some other properties. Say I have put two balls inside a box and you have to pick one up randomly. But Ball 1 is twice the size of Ball 2, so may be you will pick Ball 1 more often than Ball 2. Just because you pick up the balls randomly and it has two possible outcomes do not mean both the outcomes are equally probable. We can see that say after 100 times, you picked up Ball 1: 75% and Ball 2: 25% of the times.
You're A vs. X is incorrect. A is 1/3rd since X = B or C. For example if it is known that people live to 100 years old and every age group is equally represented, then choosing a 1 year vs. any other age group is not 50% for a year old and 50% for all ages over 1. That is just bad math.
What if, when the measurement is made, there were not two worlds where each of the states of the particle is measured, but three worlds where one measures one state and the other two measure the other state? Could that solve the contradiction? If we consider that after a measurement two worlds appear without any possibility of empirical verification, what difference would it make to consider that more than two worlds are created? Assuming this were true, the different probabilities of measuring different properties would be an indication of how many worlds are being created when making each measurement. I hope I'm not talking nonsense :S
This doesn't really work, but in a more complicated way. In quantum mechanics some parts of the wavefunction are allowed to cancel each other out, since it's just regular mathematical sums. However, branches can't really cancel each other out, and if you say they can, they you'd have to provide exact formulas for when they do and which branches do, which is even more complicated than just using QM with amplitudes instead of probabilities
Actually mathematically when the probability of a state A is bigger than state B, it means number of world where A happens is more than B. So the branch counting is clearly valid, but you're doing it wrongly. Because there are many worlds where A happens it's not just 1. For example if you have a fair dice, clearly your probability of getting 6 is 1/6 since the you only have one 6 in a dice. But if you hava a fair dice where you change number 5 to 6 such that there are 2 number 6 in your new dice. The probability of getting number six now is 2/6=1/3. That's because the number of world where number 6 happen is more than others.
You've made a mistake sorry, you have the branch with X and A each with probablity 1/2, thats not correct, X has a probablity of 2/3 and A of 1/3, so this mistake is what lead to the calculations being incorrect. You say "our rule tells us they should both be a half" what? No, not all measurements must be 50, 50 outomes... when meausuring position for example, it takes on a continuum of values. I just don't understand why you assign equal probablity to both A and x just because we are not sure which it will be, thats not correct at all, you can't just assume that of two possible measurement results the odds are always 50/50, thats defintely not true.
The conclusion at 5:35 is incorrect… the probability of each outcome is exactly 1. The probability of any past event is always 1, no matter how unlikely that event might be, ie what is the probability that someone is struck by lightning 10 times in 1 day and survive, given that they been struck by lightning 10 times in 1 day and survived? The answer is 1!
I have never been all that convinced by the many worlds interpretation of quantum mechanics or by the spontaneous collapse theories but you can't just assign an equal probability to all the worlds happening and expect that to make any sense because when dealing with infinites things are a little more complicated, I said infinities because there would be an infinite number of outcomes that all happen due to a measurement but you can group those into worlds that are not statistically dissimilar enough from each other to be considered different. Some worlds are going to be more likely than other worlds and the probability in those theories would be the probability that you find yourself in a world where x happened and not y rather than what the probability is of x happening instead of y. This is the basic understanding you have to have when dealing with this interpretation of quantum mechanics. When you use the branch counting method you are classifying two types of world with the properties you are looking for and as such you can't just assign a probability to the 2 groupings of the worlds from the fact that you made 2 groupings because that destroys probability entirely.
In first explanation, what if there were 3 worlds, 2 of them with blue and 1 with red ... But then the number of total worlds would be different for every situation (probability). One solution of this could be the infinite world interpretation where we have infinity many worlds. Can we explain it this way? Im not a physicist so please correct me if I'm wrong about anything
Instead of each branch being equally likely, I like to think of the branches as having a thickness to them that is proportional to the probability of the corresponding event. Almost as if you are flowing through a pipe, you are more likely to end up in the world at the end of the thicker branch. As time progresses, each world gets smaller and smaller, but at each event or 'intersection', we describe the probability of going to another, smaller world based on the proportion of the cross sectional area of each path.
@@negativevariance1363 if a water company were to supply two houses, it wouldn’t use two separate pipes. There would be a water main that would branch off to each of the houses. This could be drawn to show two separate branches, making it appear that each house would get equal amounts of water. However, if the pipe for house A had a cross-sectional area that was twice as large as the pipe to house B, house A would receive twice as much water as house B. The junction where 2 parts of water goes to house A and one part of water goes to house B is the ‘event’ such as when a quantum measurement is taken. Both houses get water just as both states composing the particle’s superposition is observed albeit in different worlds instead of different houses. If we were to think of ourselves as the water, we split into the two worlds just as water splits into the two houses, but just as any one particle of water is twice as likely to go to house A as house B, we are twice as likely of ending up in the world where state A is observed rather than state B. I believe the line-thickness model is used by RUclipsr Minutephysics if I am remembering correctly.
@@negativevariance1363 not really, just like a Markov chain that doesn't loop back to itself ever, where you end up depends purely on the probability of events at your current state. They just want to reflect the probability with thickness rather than a number. Perfectly fine if that helps them visualise it.
One thing I should clarify: the definition of probability I propose here certainly isn't rigorous! That's probably why philosopher's prefer defining the probability in more defensible ways using decision theory. But I was looking for an understanding of probability that felt like probability even if it has flaws
Consider the following: Language, the very thing we utilize to think thoughts and convey ideas.
Un-named Concepts -> Given a Name (could be a sound, symbol, etc) -> With an attached meaning -> And maybe even other meanings depending upon context -> And maybe even other names with the same meaning.
(Basically a Dictionary and a Thesaurus for a language).
BUT:
a. How exactly do we know for 100% certainty that we have all the un-named concepts that could ever be named?
b. How exactly do we know for 100% certainty that the meanings we give named concepts are 100% correct?
We truly do not know what we do not know.
This is a part of the 'Great Unknown'. Never stop learning.
I prefer to think of many worlds as being continuous rather than discrete. In your example you describe a branching of outcomes, but consider our current state as a ribbon that can be split at different proportions. You can consider the width of this ribbon to be related to our uncertainty of the world we inhabit.
With more decisions we add another branching to the ribbon, and so on until we zoom out onto the entire map and see a tangle of threads branching and weaving together like string cheese.
In some sense our mathematical definition of probability is already a kind of many worlds definition as you have some probability measure over a set Omega and any omega is a "world" where random variables map to different properties of that world.
Certain random variables can then be independent of some other, i.e. observing one does not tell you anything about the other, but for a fixed world of course the other one is fixed. But you don't know the world you are in
@@trulyUnAssuming "But you don't know the world you are in" -> hi! shouldn't have a continuation of your comment? ;)
One thing that has always bothered me about many worlds and this explanation of probability as well is the following:
According to many worlds, every possible event does in fact happen but only the probabilities of experiencing certain branches differ, right?
If you look at a person's life then and map out a complete tree diagram of every single time they split into several different branches does that not imply that there is a version of that person that actually exists that has experienced all of the most unlikely events in their life?
If we consider this world for a moment, would their empirical research and therefore some of their understanding of the world not be completely different from ours?
Also, I'm not a physicist so I apologize if I misunderstood something but is entropy not a result of probability? Does that mean there is a world where energy reorganizes itself or at least works very differently?
Yeah, fantastic question. I think the answer is yes, and I oscillate on how bothered I am about it. On the one hand, if a person flips a coin all day, there's a chance that they flip 100 heads in a row. If that happens they'll also get entirely the wrong impression about coins. But on the other hand, this result only actually happens 1 in 2^100 times in the real world, but in MW there is definitely a person who experiences the equivalent scenario. You can't dismiss it by saying it's "low probability" either, because probability has a very different meaning in MW, and so just because it's low probability, it does not make that world any less real.
"There exists" is a bit of a strong word here. In MWI there exist many orders of magnitude more of the worlds where probability works as expected compared to these rare cases. You can still bring the probability back by saying that the chances of *you* being in one of those worlds are astronomically small (as with any other interpretation of QM), and since you probably aren't in one of those, then it doesn't matter if they exist or not since you can't really observe them either way.
Even more so, you don't even need MWI for this. You can just have a universe with infinite time - since the time is infinite, every possible situation will happen infinitely many times, even the extremely unlikely ones. So in a universe with infinite time there eventually will be a person who experiences all the unlikely events happening
I think you only run into problems if you assert that the other worlds are _real_ in a sense. There's a kind of heuristic in physics that when two things are indistinguishable they should be treated as equivalent. And I think people treat the realness of alternate worlds too seriously, cause you can't distinguish a universe where the different worlds are real from one where the different worlds aren't and it's just a probabilities game. So I just sit with the thought of "for all intents and purposes, I can treat the world I am in as the only real one, without worry".
@@silentobserver3433 Infinite time doesn't necessarily mean that every conceivably event will happen. It's like how there are infinitely many real numbers between 1 and 2, but none of them is 3.
@@ericvilas I feel like that kind of defeats the entire purpose of _interpreting_ quantum mechanics though -- like, isn't the entire point to try to figure out what the math actually _means_ about reality? If we aren't treating the worlds as real, than what's even the point of many worlds in the first place? We might as well just "shut up and calculate" as Feynman supposedly said.
To be clear, personally, I don't actually think many worlds is right, but I do think, in order for it to be _meaningful_ the worlds have to be thought of as real in some sense. I'm open to having my mind changed though, if you care to discuss it. Philosophy of quantum mechanics is fascinating and I enjoy discussing it.
Many comments here suggesting to split into 3 branches, where each has 1/3 probability. This doesn't work, because the words "world" and "branch" here actually refer to a precisely defined mathematical object -- a vector |v> in a Hilbert space. These objects by definition have to obey the linearity rule: a|v> + b|v> = (a+b)|v>. If we split into 3 branches where 2 of them represent the same measurement result with probability 2/3, then |a+b|² = 2/3. But |a+b|² > |a|² + |b|² for a, b ≠ 0. So the branches can't all have equal weights.
Yess. Thank you
Even if you agree the universe splits into three branches, it doesn't work because it's circular. It is splitting up the branches specifically for the purpose of deriving the Born rule. All attempts to recover probability in MWI suffer from this problem, they are all just as arbitrary as assuming the Born rule from the get-go.
I love your explanations. Great video!
Love your videos!!! And I missed you ! Thank you for your content
In David Deutsch's variant of MWI there are an infinite number of worlds that have the same state prior to the measurement, and in this model the probability of each outcome is the fraction of the infinite worlds that have the outcome. In Deutsch's model, the disproof that begins at 2:36 doesn't hold. In particular, the probability of measurement X where the electron energy is greater than energy A is 2/3, not 1/2, and the total number of worlds is infinity, not 2.
I don't know about Deutsch, but I didn't get why she said the probability of measurement X is 1/2. Why not 2/3?
@@siarez Easy. If you run an experiment, and that experiment only creates two worlds with a version of you in each, then the probability must be 1/2. What would a 2/3 probability even mean in that scenario?
You can only get probabilities that are not equal when you create enough outcomes so that the proportion of a specify outcome relative to all outcomes equals the probability of that outcome occurring. So in that case, there must be at least 3 worlds created. 2 for X and 1 for A. However most things wouldn't have such simple divisions. You'd quickly see that you'd need an infinite number of worlds created to be able to handle all possible probabilities.
To me, the need for the many worlds theory to have an infinite number of worlds that can then be subdivided into an infinite number of other worlds in the correct proportions, defeats the whole point of the theory. What chooses that probability, and if you have such a chooser, you don't need many worlds. You can just have a single world with that chooser deciding the probabilities of future configurations. In that case, many worlds is actually more complex, because it adds an extra unnecessary step of creating the infinite number of other worlds you didn't experience.
@@siarez : I think she meant the two worlds, X and A, both exist with certainty, and no mechanism is understood to explain why you the observer are more likely to find yourself in the X world, while your other self would therefore be more likely to find him/herself in the less likely A world. But I too don't think that argument is clear.
I’ve been looking for an explanation for this for really long. Can’t wait for your next video!
Also there is actually a lot of problems with reducing quantum probabilities into self locating probabilities, you can look up the video on youtube "David Albert - "Worries About Accounts of Probability in Everettian Understandings of QM", once again this is a video by a philosopher of physics, and i still think the challenges he gives there are really unasnwered to the point when combined with Tim Maudlin ontological worries, really makes the Many Worlds interpretation as of now, not really a valid theory until these issues are answered.
Please make some non-MW videos! You are so insightful I would love to hear your thoughts on more grounded subjects in QM!
I've been struggling to understand these things for years now. I very much look forward to your next video!
Thank you. I just watched a video claiming to debunk many worlds theory due to the probability issue. I had a similar concept but you explain it much better than I could. 🙏
Really enjoy these thought provoking videos. Eagerly await the follow up to this.
the day superposition was explained to me was the day I first thought "oh, I live in a computer simulation" and I haven't shook it since
Excellent video and thought provoking too.
So does this mean that in some experiments the same outcome will be found in both branches I.e. has 100% probability and the other has zero probability in that branch? And if so, doesn’t the branch stop there because there is no uncertainty at that point?
I feel like this answer was kind of unsatisfying, probably because it doesn't really answer what "our experience" means. We sit here with a 2/3 blue, 1/3 red particle in front of us, and we know that if we do the measurement, we will become two separate people in two non-interacting worlds. But, like, "our experience" travels into one of the worlds, with a 2/3 probability in the blue way and 1/3 probability in the red way. And that's what you kind of tried to define with probability at the end, but that definition still didn't define what it means for "our experience" to travel down one path and not the other; it kind of just assumes that we know what "our experience" is. And intuitively we do, of course, but it feels very handwavy and non-rigorous.
I don't know if there is an answer to this, though. At some point it does go down the "what is consciousness?" issue that easily veers into the pseudoscientific philosophical talk that often surrounds quantum mechanics in pop culture. Maybe the next video about how to mathematically interpret "probability" will help, not sure.
With branch counting, what stops there from being an uncountable number of worlds in each branch? In other words, the fraction of branched worlds with each outcome is equal to the probability.
From another perspective, there are an uncountable number of events happening in each instant across the universe. Discretely counting the branches doesn't make sense.
In any one instance or interaction event, there will only be a defined number of occurrences resulting in discrete worlds. But yes the number is *nearly* infinite overall in the universe.
I guess I don't understand the premise that an interaction with 2 outcomes only creates two worlds. if A has probability 1/3 and B has probability 2/3 why can't B just have two branches connecting to it assuming each branch as an equally likely chance to be "picked". My point being that there could only be 2 outcomes, but many different routes to get to those outcomes. Feyman diagrams come to mind.
I came here with the speed of light.
Love it when you upload a video.
;)
That was really fast!
So you must be a very thin person then. Good for you, xD
@@LookingGlassUniverse
I honestly learnt a lot from you.
Next year I'll be in college .
By the way ,my field of interest is Nonlinear Dynamics.
@@traywor1615 I'm quite obese 🤣(due to pandemic)
fantastic stuff. keep up the great work
For the second example, when we're looking for A or X and then C or B if X, shouldn't it be 1/3rd for A and 2/3rds for X, since X includes two options? Just because you're only testing for A or X initially doesn't give them equal weight in the probabilities because X is actually multiple things. Probabilities are so weird.
Yes, but this presupposes the probabilities are 1/3 and 2/3. At this point we're not assuming that and just counting branches regardless of their amplitudes in the superposition. This is kind of obviously wrong, but that's the point.
I've been waiting for this. Thank you!
I must admit, I don't really see this as resolving the issue. My impression is the following: Looking forward, the current you will, indeed, see both outcomes; you can only say "you" only saw one outcome when speaking of the past. When looking to the future, there isn't a new other-you that spawns while the current-you continues along one branch. Both are what current-you will become. I don't see how looking forward toward expectations resolves the issue that current-you will see all outcomes as current-you splits into the countless future-yous.
Or, to put it more succinctly, probability in other contexts is defined as much by what *doesn't* happen as upon what does happen. When you rolled a 6, you did not roll a 1, 2, etc. If everything always happens, how can you assign a weight to one outcome over another? In other contexts, probability is essentially a shorthand for permutations. But if MW permutations (i.e. world-counting) fail, I don't see what meaning probability can possibly hold.
I love your videos, so I want to clarify my issue is not with your video (it was excellent, as always), but with the MW interpretation itself. I think you did as good a job as can be done trying to make sense of probability in this context, considering that, imo, there's no sense that can be salvaged from it. Or, at least, not that I've seen or thought of.
Why does it have to split? They are completely separate universes.
@@AkamiChannel How many? And if you say infinite, how can you get probability out of it?
@@stevenjones8575 Well, how many real numbers are between 0 and 1? How many real numbers are between 1 and 3? I would say there are twice as many real numbers between 1 and 3 as between 0 and 1, despite dealing in infinities.
@@AkamiChannel Your intuition is likely failing you, as it does us all regarding infinities. For example, there are just as many even integers as there are integers in total. You could not salvage probabilities by trying to divide an infinite set of integers by an infinite set of even integers. They are the same size set: countably infinite.
A new video! I'm happy to see it.
The way I've always thought about this (since reading David Wallace's book) is, when you figure branches happen 10^20 per second, and you're taking a random walk through that possibility space, which I think is what happens in MWI, then most path-ends are going to look back and see the Born Rule respected. But the finer you slice time, the more "random" the outcomes appear; the more likely you are to see very unlikely outcomes. And I think you can actually test that, and it's empirically grounded (i.e., the smaller the time-slice, the more probable are improbable events. But correct me if I'm wrong.) Then I thought for the really improbable branches on the bookends, it's going to appear really improbable for the people in those worlds as well compared with the rest of their history. So they'll be just as astonished to see it as we can predict, but they'd have predicted its possibility too. And then for the very, very improbable branches, where the classical world just breaks down completely, well, by definition humans simply wouldn't exist in such worlds to contemplate them.
Anyway the punchline is, probability in MWI is about a long history of very many events. This is basically how you've presented it here; so it's nice to see I'm not the only one that figured this.
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*** REQUEST: I have a request for a future video. Could you do an explanation of Entanglement (at a distance), the so-called EPR paradox, and Bell Inequalities from an MWI perspective?
I get the idea that in MWI, what we call entangled particles are really all combinations of entanglements, but when we measure one, then the waves mediating that observation entangle with every other particle & drag the into their own decohered branch, which enforces a consistent history, so when the waves from Alice's observation arrive at Bob's observation of the entangled pair, only the proper pair can be measured for each respective Bob, and the other possibilities are lost to decoherence (from each Bob's perspective). But I'm still a little unclear about it and it'd be helpful I think to hear someone else try to explain it. I once thought about it like the branches are encrypted to each other, where a consistent history is the deencryption key. So the observation of A's entangled particle is carrying a deencryption key that will only deencrypt the proper property for B's particle. And all the other possibilities really in that space remain encrypted in decoherence. Is that a right way to think about it?
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A related thing I'd really like to hear about is just how consistent histories are enforced generally. Take the case of light from a star 1 billion light years away. The last time the matter later mediating that light was in contact with matter later mediating earth was some 13 billion years ago, so when that light enters our solar system, does it interact with every branch of the Earth? That is, do they all see the "same light"? But as soon as that light starts scattering off the different branches, is it always the "latest branch" that constitutes the new branch? Like say in some branches the moon is between that star and the earth, and in other branches it's not. The light has to pass through empty space in one branch but be scattered by the moon in another branch... Does the incoming light respect every subsequent branch so it does both? Anyway, how do wave functions respect consistent histories? And is there a visualization like that to see it in action?
This isn't necessarily a request for a video either, since I know how much work goes into them. If people would like to comment and give some guidance that'd be just as helpful, or anyway it's food for thought for everybody to think about. Cheers everybody!
There is another huge problem with the Many Worlds interpretation, i recommend you read the Chapter 4 "Can the World be Only Wavefunction? " in the book "Many Worlds? Everett, Quantum Theory, and Reality".
In that chapter Tim maudlina argues that the wave function alone is insufficient to account for the result of any measurement. To do so, says Tim Maudlin in the chapter "Can the World Be Only Wavefunction?", one must add particles, i.e., localized objects in low-dimensional spacetime, into the ontology. Maudlin's conclusion is that Everett's interpretation, and similarly collapse alternatives in which nothing but the wave function exists, are epistemically incoherent: they do not make the connection between theory and the results of experiments comprehensible, and yet these results are presumably what serve to confirm these theories to begin with.
The worry here seems to be that if, according to the Everettians, the wave function is all there is, and if, further, it 'lives' in an abstract, multidimensional space, then it is unclear how such an object can account for our experience which is, roughly put, the behavior of localized objects in the low-dimensional spacetime we inhabit. Bohmians can easily address this problem, says Maudlin, because they simply postulate such localized objects by adding them into the ontology. GRWf theory (collapse with flash ontology) has a similar solution. But Everettians (and first generation collapse theoreticians with them) face the serious challenge of coming up with a comprehensible link between the state of wave function (which is all there is) and what warrants our belief in the theory, namely, the behavior of localized objects in a low-dimensional spacetime, which is our experience. Decoherence, argues Maudlin convincingly, simply cannot meet this challenge.
These kind of worries are unfortunately not appreciated by most physicists because they don't engage with the philosophy of physics, i recommend you read/watch Tim Maudlins work, he brings a lot of clarity on what a quantum theory has to have in order to be a satisfactory account of what the world is really like.
One good lecture i recommend you listening to on youtube is " Tim Maudlin - The Metaphysics of Quantum Mechanics"
Once you start assigning probabilities to being in one of two worlds, the many worlds theory loses its elegance. What determines that probability, and what does that probability even mean since another version of you experienced the other outcome? If there is only one world for each outcome with one of you in each, then it would be impossible to for the probabilities to differ. Every time the experiment is run, all outcomes would happen exactly once, thus making them all equally likely.
The only way to maintain the many worlds simplicity is to say a large number of worlds are created for each event, and the proportion of the worlds created for each outcome equals the likelihood of that outcome occurring. So if two outcomes could happen, with the probability 'A' being 1/3 and the probability 'B' being 2/3s, you'd have at least three worlds created. One world with event 'A' and two worlds with event 'B'. But that too gets extremely messy when the probability of an event happening is an irrational number that can't be represented like this. An infinite number of worlds would need to be created to get the proportions right.
This comment right here nails the difficulty MWI proponents still face.
The probability is "random", just as the probability in the Copenhagen "interpretation".
But what is randomness truly is? Well, before, always that randomness appeared, was 'cause there were a "hidden mechanism" of some sort (or simply lack of (correct) understanding of the process, like missundertanding the extension of the process), so it's logical to think that probvably randomness is just an apparent thing.
@@a.hardin620 But the Copenhagen "interpretation" have the same problem and more.
@@ThePowerLover There is no randomness in many worlds. It is just an iteration of everything that can happen. As a result, it's extremely hard to get the required probabilities out of the theory, since there is no preferred point of view. Every outcome is equally valid, so if every outcome occurs only once, they must all have the same probability of happening.
@@ThePowerLover You've got that backwards. Copenhagen is a subset of Many Worlds. They both require some "chooser" to assign the configuration of a universe. The difference is that Copenhagen only requires that "chooser" to operate on one existing universe, while Many Worlds requires that "chooser" to do the exact same thing, but also create an infinite number of universes in the right proportions before assigning the proper configuration to each one.
💡Idea :
In the Red / Blue ball case
Because the probability distribution is 1/3 + 2/3, wouldn't it make more sense to split into 3 different worlds? 🤔
I mean, branching into 2 worlds where the ball is blue and 1 where the ball is red?
this would work but I feel there's an issue with it. Using this theory, the amount of worlds would basically be dependant on how "nice" the probabilities are. For example, 1/3 and 2/3 are "nice" probabilities and 3 worlds is enough. But consider the probabilities 33/100 and 67/100. It's almost the same as the previous case, but now you need 100 worlds. And you can keep getting arbitrarily close to the original example while requiring more and more worlds. I don't know, but it just doesn't feel right to me.
8:27 I know QM doesn't work like this, but so far this explanation seems to be along the lines of: I roll a dice. It comes up 6. I conclude that the probability of 6 is 1.
Ok. Now it's being repeated it makes more sense that there *might* be an issue here.
But she wrote sqrt of 1/3 and 2/3, which tell you the probabilities right there.
I appreciate you tackling this question, and I'm interested to see the other video you teased at the end of this one. I feel like you did a good job explaining the problem of probability in MWI. I think the 'explanation' in this video (e.g. the p(red)= expected proportion of red) was just a tautology, and therefore resolves into circular reasoning. This is why I'm interested in an explanation for MWI that deals with the problem of probability, because so far the only explanation is that if I ran an experiment under MWI I'm being told that I should expect to see the experimentally observed probabilities, but when I ask why MWI gives that outcome I'm hearing that it's because that's the probability I should expect. Okay why, when MWI doesn't appear to point to that outcome at all?
There are different probabilities associated with different results of experiments based on the proportion of universes that have a particular result vs other results.
That doesn’t solve the problem of probability in mwi
What the MWI does to probability has, for me, always been a huge strike against it. The general notion that, contrary to our experience that rare events happen rarely, under the MWI _all_ events, no matter how rare, _always_ happen seems a strange and wasteful way to run a universe. I’ll have to see what your next video says about the Born rule, but here you’ve demonstrated nicely why branch counting doesn’t work. By branch counting, after three trials, your probability is 1/8 of seeing all three red when it should be (1/3)^3=1/27.
Can the many worlds interpretation be reconciled with bulk collection of infinite branes in M theory? Or are those completely independent and unrelated theories?
Do not confuse quantum physics theory and quantum physics interpretation. Theory makes accurate predictions of experiments and reasoning in theory can only be done by using mathematics. Interpretation is a useful but imperfect analogy that provides intuition. Common interpretations include analogies with classical physics and analogies with probability. An element of interpretation becomes theory only when the mathematics of this interpretation independently predicts an experimental outcome otherwise not explained by theory.
MWI makes mincemeat of Born's Rule. Consider one of the simplest branching worlds experiments: toss a coin eight times in a row. If every branched version of you completes the eight tosses, that will produce 64 branched worlds. According to MWI, you'll most likely end up in a world where you get about as many heads as tails, in accordance with Born's Rule. However, there's guaranteed to be one world where all tosses turned up heads (or conversely tails). For the branched version of you that wound up in that world, Born's Rule will have failed spectacularly. While it's true that such streaks of exceedingly unlikely outcomes would tend to average out over time, extreme exceptions will always remain, since every possible outcome is guaranteed to manifest in a branch somewhere in the multiverse.
Yep. This means that if I spend 8 hours a day flipping a coin for a year, there is a world out there where I get heads for every single flip, and another where I get tails for every single flip. Granted, the probability of finding yourself in that world is vanishingly small, but it's real. Many worlds implies that all vanishingly-small probability events happen. Which seems very susprect.
So one thing that bothers me with the many-worlds interpretation and this branch-counting idea is that branching is usually presented as binary decisions, which makes sense for something like spin. But what about for something like position? Surely when a particle's wave function collapses to a particular point in space from some interaction, there is a world for every possible value that its position could have, right? Which is presumably an uncountable infinity of branches created from a single collapse event (or a very large number if you think space is discrete).
I'd love to know if you have any thoughts on this, though.
I'm far from an expert on many worlds or QM, but I don't think there has to be a binary decision, or any sort of _decision_ at all, actually, in order for the worlds to "split" -- just any sort interaction that would cause the "collapse" of the wavefunction.
I presume the reason it's often presented in terms of binary decisions in pop-sci presentations is because it's just easier to explain that way. It's similar to how SR is often described in terms of different conscious observers, even though it's equally valid for inanimate objects, and all that actually matters is that we have different reference frames/coordinate systems, regardless of whether there's a conscious observers in either frame.
The whole idea of a "branch" is very pop-sci in the first place. A "world" in MWI is not a physical place you can go to, it's just a term in the wavefunction of the universe. Universal wavefunction evolves according to the regular Schrodinger equation and you can mentally split the wavefunction into non-overlapping parts according to their macroscopic state and call them "worlds". Then the entire wavefunction is just a sum of all these "worlds" that we've come up with for our own convenience, and since they are not overlapping in the wavefunction, they basically don't interact with each other. And there is no problem with uncountably infinite sums, that's just an integral
The binary I use in my modeling if the branching reality of all possible timelines is what I usually call contraction and expansion. Or stability and change. Or 0 and 1. What that binary means on a given level of reality's evolution is different, because it's a different kind of relationship. If you look at what Pascal's triangle represents geometrically, starting with -1D emptiness on the top, and one new dimension (on the right side) as you go down, you get all possible combinations of triangular geometric patterns, starting with a space (-1D), then a point (0D), then a line (1D), then a triangle (2D), then a tetrahedron (3D), and so on, adding one dimension per row, and generating complexity of relationships between spaces, points, lines, etc.
I've recently started using a series of questions for each new dimension. It's usually Why?, When?, How?, and Where for the top 4 rows. Why? is a given, the singular (non-binary) category at the top of Pascal's triangle, which is answered "because" or with a definition of whatever we want to start with, such as a self (cogito ergo sum!). Then we ask where is it? It can either be in the past (contracted, unchanged), or the future (expanded, changed), in our binary split universe. Then we ask how is it? And the binary branching is either a familiar process (contracted, unchanged), or a novel process (expanded, changed). Then we ask where is it? And the binary branches are either here (internal, contracted, unchanged) or there (external, expanded, changed). And so on, with more specific kinds of questions as we get more detailed observations of the possible paths.
(I have some nice diagrams of these, but alas, RUclips doesn't really like links and doesn't allow images in comments. You can find me on Twitter, though, with this username, where I share stuff like this.)
@@Lucky10279 "I presume the reason it's often presented in terms of binary decisions in pop-sci presentations is because it's just easier to explain that way. "
That's a natural-enough presumption: if you don't understand a field deeply it's natural to imagine that, when experts give you a wordy description of something, that they're merely trying to make a complex concept relatable. It happens so often that it becomes expected. However, with the "many worlds interpretation", the wordy description is all there is, and when you scratch beneath the surface, you find there's nothing there at all! Despite many proponents' statements to the contrary, if you simply remove the collapse postulate from quantum mechanics, you do _not_ get many worlds. At least nobody has been able to show that you do. The project of actually obtaining the many worlds out without accidentally putting them in has been attempted since Everett himself, without success. A large part of the reason why the project has been a failure is precisely that there's no natural, consistent "measure" for an uncountable infinity of possible histories.
In David Wallace's book he talks about this. Yes many things like position are continua, not binary or discrete states. So how do you count branches in those cases?
The way he describes it, think about a radial plane wave front in the position basis. Actually think about it in 2D so we're talking about circles. A wave front is continuous, so technically there are infinite branches or "points" in position. But events close to each other in Hilbert space (quantum possibility space) will stay close to each other, which is to say a vast number of points along the wavefront will be indistinguishable, so there's no sense calling them separate branches. His point was, counting a branch as "separate" has to do with our phenomenology of differences in physical events. It's not a property in whatever is mediating the wave; it's an emergent property about us (or whatever) in observing the thing.
Then you can think about it like points along a circumference as a circle's radius grows. There are an infinite number of points along the circumference for both the small and large circle. But I think we'd say the large circle has "more branches" (in the position basis) because the separation in position is greater as you take proportional steps down the circumference, so the emergent phenomenology is going to have more countable differences in that sense.
I think there is a mathematically clearer or more formal way to describe that, and Wallace does a better job explaining it than I did here. But I think you get the gist of it.
In another world I completely understand your video
hey love your videos.
I dont really get the problem here. at 5:28 why did you assign the "x" branch 1/2 and "a" branch 1/2. in mwt a quantum measurement causes an infinite number or large finite number of branches to split and 1/3 of those branches would split to "a" and 2/3 would split to "x".
That reminds me, I've been meaning to watch Everything Everywhere All at Once again. I expect to experience a world where that's happened quite soon.
It seems to me that once you accept Everett's original proposition, that the observer enters a superposition upon measuring, self locating uncertainty is a fairly obvious way to define the probability. You even get your own amplitude to work with.
This!
Cool video!
Counting the branches however still works when using the right branches. An experiment with chanes 1/3 (red) to 2/3 (blue) isn't splitting into two worlds, but three. There are now two people who measure blue and one red. Depending on what number the probabilities are represented in I guess we technically split into many many or even infinitely many worlds.
Awesome food for thought though!
Wouldn't this rule out irrational probabilities?
@@fg8557 only for some very weird irrational numbers. Any number that can be represented by a program can exist as a probability here, assuming we have countably infinitely many worlds.
Numbers that do exist are n-th roots, eulerian, logarithm, technically complex ones (are there complex probabilities?)...all of which can be represented as a program 'creating' infinitely many worlds
@@ArvedRockt How many worlds do you get for a probability of root 2? For a probability of 0.5 do you get 2 worlds with 1 of each outcome or 4 worlds with 2 of each outcome (or 3/6 or 4/8, etc), or even infinitely many worlds at each wave function collapse? I mean, the real answer is you can make up whatever answer you want and the math will still work, which is the main problem with interpreting quantum mechanics.
Then you’re allowing for different branches that aren’t orthogonal to each other in which case the born rule won’t be respected anyway
I think I missed something, but this felt like explaining the probability of an event by saying that the result is biased by a proportion determined by the expected outcome, but then saying that the expected outcome is based on the probability of the event. Isn't this circular?
There is no uncertainty before you do the experiment because both outcomes happen.
After the experiment, you don't know which version of yourself you are, this is called indexical uncertainty.
What I find interesting after repeating the experiment many times is that there will be a version of you which sees very unlikely results (e.g. red 100 times in a row).
Let's hope that there is a version of you who actually read Everett's thesis and who noticed the glaring mistake in the second sentence that renders all of MWI complete intellectual nonsense. Maybe not in this universe? :-)
@@lepidoptera9337 Can you be more specific?
@@martinkunev9911 Everett simply didn't know that quantum mechanics is an ensemble theory and that the wave function is NOT a description of an individual system. It's a description of a quantum mechanical ensemble, i.e. it describes an infinite repetition of the same experiment. He treats it as if it was the description of one system... and that logical error is what blows up one universe into an infinite number of parallel ones. MWI is a trivial counting mistake. ;-)
the branch tracking probability change is like the monty hall problem
I have been thinking the same thing. Monty Hall problem, if we can compare it to MWI, is a branching problem. The player decides on a strategy of "always switch", the odds of winning are roughly 2/3. This is reported to match statistics when players use that strategy. And that player who decides on a strategy ahead of time, creats the branches for the worlds at the get-go. Players who adopt no strategy create their branches further along the branched tree of worlds. I realize it is maybe incorrect to say players "create branches" merely by deciding or not deciding on a strategy but I'm not sure how else to frame it. Some people make much of the host knowing which door has the car. The host has a branching also, but his is set by the game format. A robot could do it.
If we describe the universal wave function as | U > = | R > + | B > (two worlds where you either experienced Red or Blue). What is then the difference between |U> where you experience Red , and |U> where you experience Blue. Since the universal wave function is the same in both cases, there has to be something outside the wave function that is different. The universal wave function is supposed to represent the state of the universe. If the universal wave function describes everything in the universe, where does that leave thing not described by it?
Many worlds is the most flagrant violation of Ockham's razor imaginable!
It's only a guiding notion, no one claims it has to be. Hickam's dictum springs to mind, which suggests a theory can have as many worlds as it needs.
Ironically it tries to be the simplest by eliminating extra math that is required with the single world interpretations.
Hallo there, my personal interpretation of the identity problem ("which world will you end up in?") is that it's wrong to think about you in terms of individual person. I think a change of paradigm is necessary, for which you are everyone. You experience being me and other people, separately, but simultaneously. This works the same of course for the many world identity problem: you experience all the branches simultaneously, not only one, though in each branch you think you perceive only that branch.
At 11:13, what if you just saw 3 reds in a row?
What if you repeat the experiment another 3 times, and you get another 3 reds?
What if every time you repeat the experiment 3 times in a row you get 3 reds?
In that case, what would expect to get if you were to repeat the experiment another 3 times in a row?
Why can't I like a video more than once??
Perhaps, if the many worlds already exist in a higher-dimensional multiverse (some kind of block-multiverse), the probability problem could be solved with some notion of distance. A metric relating probability to distance. Perhaps one outcome is more "likely" because that universe is closer and therefore "easier" to access.
In this way, there could be some kind of law of least action to guarantee that the nearest universe is more likely than the most distant ones.
Just maybe. It is an idea that is not clear to me. But it seems that the metric on Hilbert spaces for quantum states (and their components) could be related to this metric, because it is directly related to the probability of each state.
I don't know, just that it's something that has given me a lot to think about.
What do you think?
I don't see how MWI can accomodate correct probabilities of outcomes, except if it is regarded as a probability measure without "worlds", kind of like Copenhagen. The MWI is a philosophical concept, not a physics concept.
MWI is a trivial counting mistake. You can find the source of that error in the second sentence of Everett's thesis. :-)
Very interesting, 4:30 This looks super close to the Monty hall problem....
This experiment she does in the final part of the video would end up disconfirming the born rule in most but not all branches. So if one believes in MWI, then one must believe that one has ended up in a very rare world where the born rule is confirmed by simple 50/50 splitting.
There must be something going on that is beyond human comprehension.
Yes, it's the fact that most humans are incapable of learning even the most trivial facts about physics. To me, as a physicist, that is absolutely beyond comprehension because all of this stuff is trivial. There are hard physical problems, but this is not one of them. :-)
The quantum multiverse may be a bit like a landscape with many roads in it. That all the roads exists doesn't mean we actually drive along all of them.
Hmmm i always thought that the probabilities come from the rules of quantum mechanics and in many worlds all the expected outcome happen and we just happen to be one of it (so that the probabilities is independent of interpretation)
maybe i'm missing something...
in all the counter examples, why does there need to only be 2 worlds? like for the red/blue example, why cant you just have 3 total words: 2 worlds with blue and 1 with red, or like 3k worlds (where k is huge)? in that case you'd get that the p(blue) = #worlds with blue/#worlds = 2/3 or =2k/3k as you'd expect. like sure the 2 blue worlds might be equivalent wrt the color, but might have other differences we don't care about.
I’m unsatisfied EVERY time I listen to a QM video, read a QM article or book, or THINK about QM. I’m pretty certain this state will continue until I go to my grave.
Why in the red vs blue, 1/3 vs 2/3 example, does the number of worlds have to correspond to the number of experience types? Why can't there be 1 world where you experience red and 2 where you experience blue?
7:20
Possible gibberish but potentially an interesting thought.
While you were explaining this using your pictures,
the original state with the particle seems to act as a "Let" statement whereby you are determining the probable exist of the particle without respect to its state being that the sun total is one, then working backwards from its existence where one would say
Let particle P exist.
You then say:
Particle PsubR or P(R) [depending upon one's requirement for the variable use case]
Plus PsubB or P(B) = 1P(1)
Or,
Let particle P exist as P(1) = P(R) + P(B)
which == PsubR + PsubB = PsubRB = P
Then, there's the recursive interaction of the original state pre-check as part of the branch for each succession as the check is done without respect to time. Furthermore, the theoretical system isn't restricted by a strict adherence to quantitative segments (strict branch probability) and could also lean towards the LIM to Probability of each approaching to true probability as the segments are defined as t -> 0
Because, there is a time requirement to perform the check that isn't taken into account through the illustration as shown. So that, it is taken to be that it occurs instantaneously as an unstated assumption.
I suppose the biggest difference between math and physics is to say whether we assume time is instantaneous, taken into account or not relevant to values under consideration.
Still, good video.
Also, you seemed to hesitate with the connotation of 'expect' with its convention as a term in Statistics which may have been an instance of lacking a better word rather than any deficit of comprehension of either. More precisely, would did we expect from a random RUclips commenter regarding their knowledge of the statistical expectation given that the existence of the comment provides a non-zero until you get to the part where I then say:
TL:DR
OP doesn't know what they're talking about.
But, which OP? OP(V) or OP(C)? XD
N2S 4:10
why not put randomness in between? like many universes of you drinking the same coffe but being served by a different person because of the universe that person is, which it might look different for them but not for you. idk if im explaining myself good lol
There is no randomness in quantum mechanics. Random physical processes cause dissipation and we have not been able to observe any dissipation in quantum mechanics (for one thing stable matter could not exist). The theory is simply based on statistical independence of individual experiments in an ensemble. Statistical independence is NOT the same as randomness. Most people simply don't understand the assumptions of the theory.
OK, now I know why you had that strange configuration in another video of your phone taped to 1 cardboard box sitting on top of another box. I didn't realize that you were filming a writing surface.
The certainty with which you state 'but I know there is another world...' is unbelieveble. I love the things are not as they seem part . However I am not convinced that there are mw, 'there are no worlds' makes more sense to me.
We do see this world, so there is no obvious evidance that we actually dont. Similarly like we have no evidance about the other world. Though for both the argument can be made. Would be too long to make it here...
This reminds me a lot of the Sleeping Beauty Paradox. Is there a connection there?
In the Sleeping Beauty Paradox, you are told that you will fall asleep for a number of days, and the prince will then flip a coin. The prince will wake you up on Monday and ask what side the coin landed on.
Irrelevant of what you guess, if the coin landed on tails the prince will give you a pill that erases your memory and puts you back to sleep. He will then wake you up on Tuesday and ask what side the coin landed on.
Whenever you are woken up, you have no way of knowing what day it is. Given you know the rules ahead of time, what is the probability that you will be correct if you guess tails?
Why not consider probability a lateral extent of the branch, a kind of width, and count the branches like that?
If there two outcomes in MW one with near infinite possibility and the other with near zero possibility, this means nothing because both events will occur. The two versions of me will see both. Am I missing something.
Is it not true that quantum superposition implies that particles are not merely here or there, in one state or another, but actually in a combined state of possibilities? Hence explanations which look upon blue and red objects as wholly discrete (represented here by colour) seems misleading, in that it gives a false impression. Nor do the probability of all quantum events remain the same over time. Radioactive elements decay so, the probability of a cat being dead in the box increases over time. So the equations used to predict the outcome can never be exactly calculated.
No, that is not true. A quantum is always in one place: the one where it was detected. Without that detection the quantum does not even exist.
So you define the probabilities with the word "expected proportion". But isn't this self-referential? Can you define what "expected" means without using the concept of probability of the outcomes in the first place?
Na, toss a coin, you expect half the outcomes to be heads. Probabilities will always be a ratio, and you can predict what that outcome will be. No circular reference at all. I think you've confused proportion with probability, they are not the same thing.
@@fatsquirrel75 I thought the point of the definition by expectance was to not rely on proportions.
What if observing the red/blue state does not create two worlds but 3? Two worlds where you see the blue and one where you see red. This makes it so we can keep the relatively intuitive idea that P of red= worlds with red/all worlds.
I mean, this is a problem with probability even without many worlds or quantum mechanics, right? What does it really mean to say there's a 50% chance of rain? Conventional intuition is like you conclude here -- if you experience this day 100 times, you will expect to experience rain 50 of those days. Likewise, if you run a quantum experiment 100 times, you will expect to experience a certain result 50 of those times. You mention that this idea applies equally to all QM interpretations, but I think it's even broader than that.
The diagram at 11:07 is incomplete… in some universes the experiment will be conducted only once, in other universes the experiment will be conducted only twice, etc
I think the problem with branch counting is simplification. It's more like for all the outcomes there are 100 worlds, in 33 of them you get red in 67 you get blue, 2 outcome with correct probability. The simplistic branch counting is like saying it's 50% for any outcome because it either happens or it doesn't.
The whole idea of branches is that you have a superposition of a couple of states, each of which are orthogonal to each other, and you wanna say that each term represents a branch that exists physically. If you measure a two level system, you only have two orthogonal terms, so only two branches.
@@jezer8325 sure, but the branches are not equal, so treating them as if they are is like saying every outcome has a 50% chance of happening. If you had 3 branches with 2 being blue and 1 being red that would actually give you the correct distribution of probability. If the model doesn't match actual reality you can't get mad at reality for being wrong.
@@chiepah2 It would give you the results you expect but that's because you reverse engineered a definition of 'branch' that's consistent with the 'branch counting' method but is not a relevant in any other way. The change you made that fits reality doesn't fit with the rest of the model. Your idea has as much explaining power as simply stating that the probability of being in each branch follows Born's rule. And maybe that's fine, but either way you're going to need to fit that into an extra postulate in place of the one we removed when moving from the Copenhagen interpretation to the MW interpretation. Hopefully the next video will explain how you can derive the rule without having to simply assert it.
@@jezer8325 ah, I see, thanks for the explanation, that makes sense. You don't really know what the probability is until you calculate it, so you wouldn't know how many versions of the same branch to add until after you calculate probability. If you know the probability you aren't adding anything by including additional branches of the same kind.
I find the feature of many worlds that you mentioned "it's really important that *you* only experience one world in many worlds" problematic. What definition of *you* are you using? The person you were before measurement of a particle's state is now gone, survived only by the two *you's* that measured the particle. I argue that *you* still actually experience both branches, the only thing to do is to let go of the traditional notion of *you* and see that both measurers are you: *you* who measured outcome 1 and *you* who measured outcome two. Isn't this what it means for an organism to have a life tree? Isn't this why it doesn't even make sense to ask "what is the probability that *you* end up one one branch or the other?"?
With the branch counting why are you assuming only 2 worlds, 1 for blue and 1 for red? How do we know there aren't 4 worlds where red are experienced and 8 worlds where blue is experienced? Then the # of branches where red is experienced / # of total branches would be 1/3 as needed.
perhaps the "world" splits into all probabilities. Two blue and one red. You get two blue worlds and one red world. If the probability is fifty four to forty six you create fifty four blue and forty six red. Is there some force stopping the creation of multiple identical worlds? I dont see why there should be.
Now you've just created a separate black box entity that can determine which outcome happens in a universe. It literally has to be able to create a universe with a specific configuration. But if you've done that, what is the point of a many worlds theory? Occam's razor would insist that that black box would be used to determine the evolution of a single universe than to do the exact same thing to a potentially infinite number of newly created ones.
So instead of that black box creating exactly 44 identical universes for outcome blue and 46 identical universes for outcome red, it simply would allow the existing universe to evolve with outcome blue 44/90 percent of the time and outcome red 46/90 percent of the time. This black box would be doing the exact same type _hand wavium_ as many worlds, just with much less of it and without the need to create entire new universes.
in any branch in a timeline, say you want 2 choices, thinking if i do it, other me has no choice in the matter. well, a whole lot of conditions existed before that determine which branch you are on that have these yes/no forks. there is not only your Personal yes/no fork but so many branches up stream that also came to this fork. across ALL of these, the probability can approach a statistical value. there is unknown # of you's arriving at this choice
What's the meaning of a world being more likely than other when, after the experiment, both exist.
The branch counting argument feels silly
Things can have only 2 possible outcomes without those outcomes necessarily being equally weighted. For example, you either will be struck by lightning tomorrow or you won't. But that doesn't mean the probability is 50/50
This argument is very unconvincing compared to the arguments for MW.
Can we use the world theory to figure out the probability for genetics?
I really have a problem w Many Worlds for the very reason you made this video, but between time 10:40 and 11:30 you glossed over the crux of the problem w Expected experience....if red being 1/3 of the time.... in your diagram there were 8 observers that had each observed the experiment 3 times, and each one had a different observed probability. If u expand the experiment a million more times, there is no way that all observers end up seeing the same expected value of 1/3 red. I have no idea why many worlds is always a binary split (into 2 worlds) but it makes it impossible to get probabilities other than 50/50. Your original intuition was correct, I think. I have not heard an explanation that properly shows otherwise. Note I did watch your next referenced vídeo on the born rule, it didn't help. Thanks.
At 4:03 you mentioned there are "three worlds", shouldn't that be "three energy states"?
This just proves that the many worlds doesn't exist....not just on probabilities being wrong, but the very basics of energy dispersion not matching field draw under an observed event collapsing. There MIGHT be other universes, but it has nothing to do with ours splitting.
About 01:10
Your basic assumption that an experiment with n possible outcomes will get reality split into exactly n realities, here n being 2,...
_...there will be one version of yourself who sees the outcome A and another who sees the outcome B._
...might be false to begin with. It might split into a huge number N words instead, in p(A)∙N of them the outcome will be A and in p(B)∙N of them it will be B.
The thing with the many worlds theory is that it’s based on your actions. The probability of me choosing the red or blue is based off of my opinion and which I like better. It’s every time you make a decision you split off.
human choice has absolutely no impact on many worlds. humans are not magical beings, we are made out of atoms following the rules of physics. there is no such thing as free will.
The thing I don't understand is why people would bother discrediting certain branches from existing.
If you believe in the many worlds theory, then you know that everything can happen somewhere in those branches...
The branch might not relate closely to your universe, but you have to understand the conundrum that multiple branching universes cause.
If you go backwards and start branching forward, are you sure there isn't a universe where this becomes more likely?
It seems to me that its not that it is impossible. but rather you lack the ability to ever come across that possbility in your mind.
There's alot of questions left to answer. Is the universe existence itself or is their many layers to this existence that we don't know.
Is Quantum mechanics a small example of the chaotic nature that helped create existence? If we believe in the chaotic mess that is quantum probability. Then its not too farfetched into believing existence is governed by more chaotic ???? that we could never hope to wrap our heads around.
I think many of us question why existence happens the way it does. Why did existence decide to shape in the way it did. I think we all agree that before existence there was no rules. So why would each existence come about with the same fundamental logic and rules. Can't it think of something better or is it really unoriginal. No pressure. I mean it has no time at all to decide something.
Perhaps it did. I like this idea because I find it proposterous that existence would shape itself like this and this alone. There are no rules and yet unlimited rules to try out. It would be a creative shame to stick to just one rule set.
So if you take that into account, the many worlds theory more than supports the impossible branches out there....
It also helps explain where the possible end point for these branches might exist.
Since the fundamentals can be altered infinitely, then the many world branches may stop at universes where Quantum mechanics are different from our own. Making a universe that does not support the many world theory. The best part of this may be the fact that if you genuinely consider this,
you may conclude that this world is that very same world. Meaning I just made a religion on the idea that the many world theory is right, but just false in this one. Which sounds like absolute nonsense, but Its impossible to disprove it.
All this just to say... I f'd your mom.
I think people misunderstand probability. If a random experiment has two possible outcomes, that does not necessarily mean that their probability is 50-50. Or 33% in case of 3 possible outcomes. Probabilities can be different based on actual experimental data or some other properties. Say I have put two balls inside a box and you have to pick one up randomly. But Ball 1 is twice the size of Ball 2, so may be you will pick Ball 1 more often than Ball 2. Just because you pick up the balls randomly and it has two possible outcomes do not mean both the outcomes are equally probable. We can see that say after 100 times, you picked up Ball 1: 75% and Ball 2: 25% of the times.
You're A vs. X is incorrect. A is 1/3rd since X = B or C. For example if it is known that people live to 100 years old and every age group is equally represented, then choosing a 1 year vs. any other age group is not 50% for a year old and 50% for all ages over 1. That is just bad math.
What if, when the measurement is made, there were not two worlds where each of the states of the particle is measured, but three worlds where one measures one state and the other two measure the other state? Could that solve the contradiction?
If we consider that after a measurement two worlds appear without any possibility of empirical verification, what difference would it make to consider that more than two worlds are created?
Assuming this were true, the different probabilities of measuring different properties would be an indication of how many worlds are being created when making each measurement.
I hope I'm not talking nonsense :S
This doesn't really work, but in a more complicated way. In quantum mechanics some parts of the wavefunction are allowed to cancel each other out, since it's just regular mathematical sums. However, branches can't really cancel each other out, and if you say they can, they you'd have to provide exact formulas for when they do and which branches do, which is even more complicated than just using QM with amplitudes instead of probabilities
you can calculate the probablity of which world you will end up in after entanlgement.
Yes, with Copenhagen. MWI tells you nothing about it. MWI is simply nonsense. ;-)
Actually mathematically when the probability of a state A is bigger than state B, it means number of world where A happens is more than B. So the branch counting is clearly valid, but you're doing it wrongly. Because there are many worlds where A happens it's not just 1.
For example if you have a fair dice, clearly your probability of getting 6 is 1/6 since the you only have one 6 in a dice. But if you hava a fair dice where you change number 5 to 6 such that there are 2 number 6 in your new dice. The probability of getting number six now is 2/6=1/3. That's because the number of world where number 6 happen is more than others.
Which one of these many worlds has cheap gas and low inflation and water fountains that have fruit punch?
You've made a mistake sorry, you have the branch with X and A each with probablity 1/2, thats not correct, X has a probablity of 2/3 and A of 1/3, so this mistake is what lead to the calculations being incorrect. You say "our rule tells us they should both be a half" what? No, not all measurements must be 50, 50 outomes... when meausuring position for example, it takes on a continuum of values. I just don't understand why you assign equal probablity to both A and x just because we are not sure which it will be, thats not correct at all, you can't just assume that of two possible measurement results the odds are always 50/50, thats defintely not true.
Curious if you have read “something deeply hidden”
7:20 now we enter fantasy land
7:38 Why does one version see red and one blue? Isn't it more likely that both versions see blue?
The conclusion at 5:35 is incorrect… the probability of each outcome is exactly 1.
The probability of any past event is always 1, no matter how unlikely that event might be, ie what is the probability that someone is struck by lightning 10 times in 1 day and survive, given that they been struck by lightning 10 times in 1 day and survived? The answer is 1!
I have never been all that convinced by the many worlds interpretation of quantum mechanics or by the spontaneous collapse theories but you can't just assign an equal probability to all the worlds happening and expect that to make any sense because when dealing with infinites things are a little more complicated, I said infinities because there would be an infinite number of outcomes that all happen due to a measurement but you can group those into worlds that are not statistically dissimilar enough from each other to be considered different. Some worlds are going to be more likely than other worlds and the probability in those theories would be the probability that you find yourself in a world where x happened and not y rather than what the probability is of x happening instead of y. This is the basic understanding you have to have when dealing with this interpretation of quantum mechanics. When you use the branch counting method you are classifying two types of world with the properties you are looking for and as such you can't just assign a probability to the 2 groupings of the worlds from the fact that you made 2 groupings because that destroys probability entirely.
I'm sorry, what is the "problem" mentioned in the title? The way I see it, MW works perfectly
Some of the smileys look very sad. Maybe they expected another outcome of their experiment.
In first explanation, what if there were 3 worlds, 2 of them with blue and 1 with red ... But then the number of total worlds would be different for every situation (probability). One solution of this could be the infinite world interpretation where we have infinity many worlds. Can we explain it this way?
Im not a physicist so please correct me if I'm wrong about anything
Instead of each branch being equally likely, I like to think of the branches as having a thickness to them that is proportional to the probability of the corresponding event. Almost as if you are flowing through a pipe, you are more likely to end up in the world at the end of the thicker branch. As time progresses, each world gets smaller and smaller, but at each event or 'intersection', we describe the probability of going to another, smaller world based on the proportion of the cross sectional area of each path.
This is incoherent nonsense.
@@negativevariance1363 if a water company were to supply two houses, it wouldn’t use two separate pipes. There would be a water main that would branch off to each of the houses. This could be drawn to show two separate branches, making it appear that each house would get equal amounts of water. However, if the pipe for house A had a cross-sectional area that was twice as large as the pipe to house B, house A would receive twice as much water as house B. The junction where 2 parts of water goes to house A and one part of water goes to house B is the ‘event’ such as when a quantum measurement is taken. Both houses get water just as both states composing the particle’s superposition is observed albeit in different worlds instead of different houses. If we were to think of ourselves as the water, we split into the two worlds just as water splits into the two houses, but just as any one particle of water is twice as likely to go to house A as house B, we are twice as likely of ending up in the world where state A is observed rather than state B.
I believe the line-thickness model is used by RUclipsr Minutephysics if I am remembering correctly.
@@negativevariance1363 not really, just like a Markov chain that doesn't loop back to itself ever, where you end up depends purely on the probability of events at your current state. They just want to reflect the probability with thickness rather than a number. Perfectly fine if that helps them visualise it.
@@fatsquirrel75 Assigning a "probability" to a branch that happens with certainty is incoherent and meaningless, no matter what analogy is used.
What's flowing through the pipe?
Very nice and healthy hair!
so if from an actual person's experience it behaves the same as copenhagen, how could we ever tell if the other worlds were there or not?