I attended a seminar by Feynman on this subject at the University of Alaska Fairbanks sometime in the early 80s. I was amazed as he wrote out a multiterm equation on the blackboard, each term representing a probability that could have any value. He showed how all the meaningless terms cancelled out, leaving a real probability as the solution. What a shame that the seminar wasn't filmed.
Half of that quote was inspired by one of Scott Aaronson’s blog posts. He’s written a lot about quantum information and complexity theory, and he even talks about implications for various topics in philosophy. I highly recommend taking a look!
That is misleading, though, since in quantum theory, "observation" does not refer to anything you think the word refers to based on its coloquial definition.
@@angelmendez-rivera351 you have no idea what I think the word observation refers to. In the case of quantum physics, observation has a somewhat circular definition of it is when a wave function collapses; when a possible superposition collapses to a single eigenstate corresponding to an observable physical property. The behavior of these possible superpositions, or wave functions when "unobserved" i.e when it is not collapsed, is governed by the Schrodinger equation, or the dirac equation, if you want to be more precise. None of this is contradictory to the quote shown at the end of this video. A ket is by all accounts, an information packet. Quantum physics studies the behavior of these objects when they are not collapsed.
@@brandonklein1 *you have no idea what I think the word observation refers to.* My apologies. I used the pronoun "you" deictically. I am not referring to you, Brandon Klein, specifically. I probably should have used the pronoun "one" to avoid ambiguity. *In the case of quantum physics, observation has a somewhat circular definition of it is when a wave function collapses; when a possible superposition collapses to a single eigenstate corresponding to an observable physical property.* Perhaps a text may provide this naive definition as a starting point for discussion, but this is most definitely not the actual definition physicists use. *None of this is contradictory to the quote shown at the end of this video.* I never said there were any contradictions anywhere. My claim is simply that the quote is misleading. As in, technically accurate, but it does not mean what most people would think it means, and so it communicates the wrong idea to most people.
Wow! That means so much coming from you. Your channel was a big part of my journey into physics, especially when I was self-teaching some quantum mechanics and watching RUclips videos to build up intuition. I distinctly remember some “aha!” moments I had while watching your videos on interference and spin. Thanks a lot! This made my day.
This is great. I tried to prove that no probability distribution can explain the correlation of two entangled photons in a Bells inequality experiment. It turns out that a negative probability of some of the “lambda” combinations explains the observations just fine.
That’s a neat connection! Thanks for sharing that. To be clear, negative probabilities should absolutely be considered a problem if they’re assigned to directly observable events. If a proof leads you to a negative probability assigned to an observable event, then that should certainly be considered a contradiction. But if the negative probability pops up in some “intermediate” transition corresponding to an event that is not directly observable, then things are okay. This is all meant to tease the idea that we can formulate quantum mechanics as a calculation of “probability amplitudes,” complex numbers that we add up for all possible paths and then take the square magnitude to get the final probability. The “negative probabilities” we see pop up here are analogous to the fact that probability amplitudes can interfere before we take the square magnitude of the final result.
@@oosmanbeekawoo I calculate for self check my correctly understanding of calculate algorithm and essence of the video. And when my answer did not agree with what was in the video, it caused bad feelings. After spending some time double-checking it in my head, I picked up the calculator and realized there was an error in the video.
The path integral is no different to how you would compute the interference pattern of a plane complex-valued wave. Just take square modulus on the detector to get spatial probability distribution
Wavefunctions in quantum mechanics have a *phase* which means they may cancel out when you add them up. But that isn't a negative probability. To calculate a probability you have to square a (normalized) wavefunction, which necessarily means probabilities *are* between 0 and 1. To be honest I think presenting QM as negative probabilities is a good example of the "quantum mechanics is spooky" rhetoric which appears all to often in popular science, and only serves to make people believe that quantum mechanics explains consciousness or whatever else without ever actually learning the physics itself.
I would disagree. The facts that wavefunctions exist, and that their magnitude squared equals probability are axioms of quantum mechanics. There isn't a reason why those facts should be true. It just happens to work out in the math, and it predicts what we actually observe. But just like in ordinary mechanics, where we can analyze motion using different philosophies (Hamiltonian vs Lagrangian), we can analyze quantum mechanics using different philosophies as well. As long as a certain philosophy matches our observations, we can say that it's valid, and that it's just one way to look at things, among other ways to look at things. Feynman's formulation of quantum mechanics with negative probabilities, if it is complete and consistent (which I don't know because I'm not familiar with it), then it is also a valid way of looking at quantum mechanics -- a different paradygm of the same thing
@@karolakkolo123 Thanks for replying! I'm not sure that I have been convinced, but I hope you make more videos in the future anyway, it is very well made
Thanks for your comment. You are correct that quantum mechanics is not just probability with minus signs, and I warn against this conclusion in the video. All I wanted to do was draw a connection between the logical consistency of negative probabilities and the idea of interference in quantum mechanics, inspired by a paper that Feynman wrote late in his life. It does *not* represent a complete formulation of quantum mechanics by any means. It is true, though, that there is alternative to the Schrödinger wave function method of quantum mechanics. It’s called the path integral formulation of quantum mechanics, and involves the calculation of probability amplitudes (which are complex numbers) whose square magnitude gives the probability of an event. I was hoping to tease in this video that you can do quantum mechanics without wave functions, but I realize that has been confusing or easy to misinterpret for some viewers.
Well, even besides Feynman's path integral formulation, there is another mathematical formalism for quantum mechanics in which negative probabilities occur even more plainly, called the Wigner phase space formulation. In it, we represent the state of a quantum system as a quasiprobability distribution on phase space (the space of all possible combinations of the positions and momenta of the particles), which is a real-valued function that behaves exactly like a (joint) probability distribution for the purposes of calculating the expected values of observables and the marginal probability distributions for position or momentum, except that it can actually be negative in some regions of phase space. It turns out that the regions where the Wigner function is negative are small enough that they are impossible to directly observe experimentally (since the state of a particle cannot be localized to arbitrarily small regions of phase space due to the Heisenberg uncertainty principle), but there is still some disagreement and mystery about what exactly these negative probabilities mean philosophically.
Well I may be a year late, but this video is great! I had so many "aha!" moments from disparate areas of maths/science. (Even the very briefly mentioned relationship of AND with + and XOR with * finally made me understand how Boolean Logic relates to probability theory!) The quote at the end is especially good, I'll be keeping that one in mind as I study Quantum Mechanics!
What the heck? Your video has me chomping at the bit, for more. This is not a criticism but you barely hinted at how -ve probabilities could be used in describing the quantum effects. Subbed and collapsed my wave function on the [like] button in the hopes your next video comes out soon.
The disappearance of the interference effect is not really a mystery. It is because measurement decoheres the system so that states of the environment (ourselves and the lab and the rest of the world) become correlated. It's called the Everett interpretation, though it is more fact than mere interpretation. The path integral formulation is not really any different from 'standard' Quantum mechanics (operator formalism), it's just an alternate way to express the same equations. We use different mathematical formulations in different contexts, depending on which makes the problem easier to solve.
It's not nonsense to say that a particle went through both slits. The uncertainty principle is the reason why one cannot know which slit. That's also the reason why the slit dimensions have to be similar to the particle dimensions (i.e., comparable to the dimensions laid out by the uncertainty principle, to the extent that the particles behave quantum mechanically when comparable to such dimensions. if the slits are moved apart sufficienty, the interference goes away because the dimensions become larger than those laid out by the uncertainty principle) I find it to be a bit over the top to invoke negative probability in explaining the double slit experiment.
It's honestly very simple: particles are waves. That's it. I know they are quantised excitations rather than arbitrary ones, and things get a lot more complicated with QFT, but the simple correct explanation is that they are waves and there is no issue with waves spreading amongst multiple slits. There is a phenomenon of pop-sci communicators trying to make it sound more difficult to understand so that they can make it appear more mysterious and interesting. They appear as particles due to decoherence which leads to splitting of multiple worlds (Everett interpretation). This should not really be called interpretation as it is a logical consequence of the theory, it's just geocentrism all over again with people wanting to believe they are at the centre of everything, wanting to believe there could not be prorated parallel realities etc even though it's a logical consequence of extremely well-validated theory... Anyway, in this case I think the video creator just doesn't know the subject matter.
@@wizard7314 I like Everett. He simplified the theory, removed the "ad-hoc rules", removed the "measurement problem" and yet still can explain how our every-day experience emerge from a universe following the Schroedinger equation. Awesome! The other interpretations look so clumsy to me, in comparison. But the other "interpretations" also work and get the same results. As far as I know, we have no data that would allow us to rule out one over the others. So I'd say it is just cautious to call Everett's work an "interpretation". Got nothing to do with my "ego"... But if I ever find out, that my "parallel me" is still together with my highschool crush... then ... then... grrrr Screw you Everett!!!
Its got complex numbers in there as well. Multiply for and, add for or. With complex numbers. The probabilities you observe are the squares of the amplitude. (x+iy => x^2+y^2) And you have a big chunk of quantum mechanics.
QM even has imaginary pretty probability for wavefunctions, by which you have to combine two of them (even for the same particle) to arrive at the real peobabilities for its position. Btw, quantum 1/2-spin particles are spinors, meaning they lie along the border of a 4d hypersphere, which also has interpretation 2d vector of complex numbers, so this is probabilly ehy the quantum probability distribution function comes into play.
This idea that there's a switch from 'clump' to interference when going from single to double slit is an assumed model that does not look to be consistent with the physics of photon grating experiments. For example, the pattern formed when a single slit is present is not a bell curve, it is another wider but quite clear pattern also predicted by quantum mechanics (and classical electromagnetic waves) with a form of sinc^2(theta) with wave-like lobes that are spaced at minima given by theta at lambda/n*d. It has a beautiful series of smaller lobes on either side of the central maximum. The double-slit then superimposes narrower fringes and adding more slits narrows the peaks so that all particles become concentrated into bright lines. where all the energy goes to peaks. By artificially replacing the actual single slit pattern with a bell curve it seems one is adding a questionable notion that the single slit pattern is like a random scattering pattern similar to bullets going through an aperture. This presumption has been repeated so often I think it has become a sort of apriori trope that pre-determines the possible conclusions. The shape and width of both patterns, single and double, have a direct analytic relationship that can be calculated from QM and the result is that the expectation function for the cross-beam momentum that this added to the trajectory is given by the magnitude of the Fourier transform of the aperture pattern divided by Plack's constant. This pattern depends only on the shape of the scattering aperture and is completely independent of the type of incident particle (matter/photon) or the incident momentum. To me, this is utterly stunning and makes all the talk of wave-particle duality seem as inadequate as using epicycles and deferents to explain orbital mechanics. It is as if the scattering takes a snapshot of the allowed cross-beam momentum spectrum available at the time of transit, which then becomes visible by allowing the beam to travel undisturbed far enough to show the pattern macroscopically, and the surprising thing is that the expectation function for scattering momentum is utterly independent of the type of particle or its incident momentum. Any interaction that detects a particle at the time it traverses the slits will add a random impulse that will smear out that pattern by effectively convolving the slit scattering expectation function with another scattering function. Perhaps the best way to understand this experiment is to give up the accepted notion that we can only explain it by thinking of the incident particle as a wave that interferes around a passive barrier. A great paper by Carolyne M. Van Vliet "Linear momentum quantization in periodic structures II" is a start.
@@wizard7314 That is not true. When the slits are larger than the wavelength, the scattering function is still simply, clearly, and precisely given by a Sinc(x)^2 function that has wave-like periodic side lobes as you can see on any basic diffraction textbook. At no time does the function revert to a particle bell curve. Both the single and double slit patterns are diffraction patterns that are also matched by using quantum mechanics. At all times QM predicts that both Single and Doule slit the scattering expectation functions have a momentum spectrum the Fourier transform of the aperture pattern divided by Planck's constant. At no time does closing one slit cause particles to stop behaving according to a wave function, classical or quantum.
@@wizard7314 What? ,you don't even realise that momentum expectation functions are calculated by using quantum mechanics, not classical mechanics? Try again, the momentum expectation function as calculated by QM across the beam is the Fourier transform of of the aperture divided by Planck's constant. Besides, it's not 'my' explanation it is clearly laid out in several papers. Go read LINEAR MOMENTUM QUANTIZATION STRUCTURES by K. M. VAN VLIET Physica 1967, or the Second Paper Physica A 389 (2010) 15851593. I
Yes, the bell curve is an idealisation, it's more complicated in real life. But the pattern from two slits with detectors is still the sum of the patterns from individual slits, whereas two slits without detectors gives extra interference.
But don't the detectors have to interact with the particles in order to detect them? This would somewhat explain different results in these experiments.
If negative probability are possible then probabilities above 1 are possible too.what do you think is maximum positive and negative probability ?does it extends to infinity or 2.there are many things left out.
We meet probability distributions in the theory of Brownian motion. If we have two overlapping distributions, then they merely add up to a cumulative distribution, and all the probabilities are positive. However in quantum mechanics we observe destructive interference. How can that be? I will make a suggestion. There is more than one way to travel faster than light, at least according to the Minkowski formalism which I will take as representing something real. In the way that exchanges timelike and spacelike intervals we can have an oscillation cycling through a series of transformations which is capable of destructive interference with itself. In the other way we can have tachyonic Brownian motion. If two or more detectors are trying to capture our entity, then the randomness of the TBM ensures that only one detector is triggered. Here we do have a probability distribution which can exhibit destructive interference with itself. Quantum mechanical behaviour is imaginable, but at the price of having to venture into the superluminal world. Bell's Theorem implies that we should be willing to pay that price. I would emphasise that the wavelike behaviour and the TBM are orthogonal to each other, so this is not just schoolboyish musing. In computer simulations of fluid mechanics, Brownian motion of vorticity is one way of modelling the two-dimensional Navier-Stokes equation, as originally proposed by Alexandre Chorin. The fluid mechanics simulation makes use of a random number generator and I would like to work out how to include a RNG in a computer simulation of quantum mechanics. Tachyonic Brownian motion is one thing to think about because it does not directly mess up the Schroedinger equation. I would expect it to be apparent during the nonlinear interaction between matter and the electromagnetic field.
at (e.g.) 12:28, where the sum of the 2 waves and the interference graph is shown, it is worth noting that both measure the magnitude of a complex valued function, scaled such that the integral over all real numbers is 1. Naturally, we could expect to see 2 totally different results when we compare the sum of magnitudes and the magnitude of the sum. By the law of triangles, the sum of magnitudes is always more than the magnitude of the sum; the increase in probability comes from the scaling such that the integral is 1
So, I'm pretty sure your diagram at 7:14 explaining negative probabilities is wrong. The idea of "we added a path and the probability went down" is correct, but only with the stipulation that all other probabilities must stay the same. For instance, instead of a negative probability, take a really small probability. P(p→2|1 path) = 1•.8 = .8 P(p→2|2 paths) = .7*.8 + .3•.01 = .563 We have made the probability go down without negative probabilities. This is because we changed the probabilities that allow he particle to go to box 2. If instead we put the block *after* the first node, so the particle has a 30% chance (the first node) of not going into box 2 at all. The probability with the block = .7•.8 + .3•0 = 0.56 Probability without that block should make the probability go up because probability has to be higher than 0, but with negative probability, the probability goes down.
this video is such a slay omfg reminds me of PBS space time, Sci Show, 3Blue1brown! the animation was sexy and helpful and most importantly the concept is SO interesting to me but ALWAYS feels so abstract
The implication of the negative probability is that you were wrong about the other probabilities, that the combined experiment altered the probability in some way you hadn't anticipated.
You did not give an example of negative probabilities, because quantum wave function values are NOT probabilities; they merely yield probabilities when you take their magnitude squared. They are analogous to the linear predictor in a logistic regression model, which yields a probability when you apply the logistic function to it.
Here's a question for people who know what they're talking about. How do we know it's observation that changes things, instead of something we currently can't avoid doing when observing?
accepting negative intermediate probability has nothing to do with certainty but simply with the weight of this path, if this probability is 0 we are completely certain nothing went through there and still everything works fine, the number must be small enough so positive probabilities from other path outweight the one with negative value
I am not sure what you are referring to by a σ-field, since this is not standard mathematical terminology used in the literature. The more accurate description is that (Χ, Σ, μ) is a probability space if and only if it is a measure space and μ(X) = 1. (X, Σ, μ) is a measure space if and only if (X, Σ) is a σ-ring, and μ : Σ -> {t : t in R} is σ-additive with μ({}) = 0. Perhaps you are using σ-field to refer to a σ-ring, but this is obscuring terminology, and besides, you failed to mention that μ({}) = 0.
Your notation is wrong. The transition probability P(S -> 2) is the conditional probability P(2 | S). The conditioning information goes to the right of the bar.
How does the math work though? A measure can't be used to describe negative probability because it assumes nonnegativity. Are signed measures used? Or something completely different?
You may be interested in 'quasiprobability distributions'. I am not too familiar with them, but I think in this case you'd ascribe a probability density function over the collection of possible paths. Although the PDF is not nonnegative, the integrated density over paths that lead to a given point are. Apart from this, I think the math in the video is slightly wrong as a comparison to QM. Instead of negative, allow complex 'probability amplitudes' (the technical term) and then take the square modulus of the final result to get the probability. Using only negatives, and not taking the square, is a bit strange and I'm not sure if it can correctly model the experiment.
Aren't there more parameters impacting the bands seen behind? The ratio of distance between the source, slits, screen as well as distance between the two slits.
can we think negative probability as opposite directed probability ? all probabilities flow to the destination nodes. but -0.4 probability explains escaping from destination and that view also explains what does probability value greater than one (1.4 probability) means at that node. directed probability seems like a vector. a value vith direction.
Great, though it is not the act of observing the particle that makes it stop acting like a wave, it is the photons needed to measure the particle's position that cause it to stop acting like a wave. In other words, an interaction. This is also how the heisenberg uncertainty principle works, because to measure the particle's position you need to hit it with a photon to measure it, and that changes its speed just a bit.
Thanks for your comment. I encourage you to keep an open mind about what causes the wave function collapse, however. It is fundamentally about information leaking into the environment, not just about interaction. I recommend watching Looking Glass Universe’s video about measurement for an well-explained argument about why any old interaction with the environment doesn’t necessarily cause the wave function to collapse. Your explanation in terms of interaction with a photon is enticing at first, but doesn’t tell the full story.
@@StevenG22 So i watched the video, and yeah that goes well into my belief that you can make an information theory without observers. You can work with interactions and uncertainty alone to have information there
Couldn't a situation with positrons and electrons make this not weird anymore? Imagine you have charge in S and it travels to (1),(2) but along the way some positron-electron pairs might be produced. If you first talk about percentages then maybe -50% of the charge reaches (1), and 150% of the charge reaches (2). They must sum to 100% because the total charge is conserved. This might feel weird in the language of probabilities but I guess if an electron is emitted from S then the probability of the electron arriving at (1) is -50% and at (2) is 150%.* And this doesn't seem all that counterintuitive. Note*: I thought about whether to say "the electron arrives" or "an electron arrives" and I had to choose "the".
This was a really nice explanation and visual, I loved it. It also makes me wonder if it’s possible to formulate quantum mechanics, not by using complex numbers, but by introducing negative probabilities instead.
Thanks for your comment! I’ve also wondered this, but I caution you not to take the conclusions from this video too far. The mathematical structure of quantum theory definitely needs complex numbers. However, there has been some nice work addressing the question of why the need for complex numbers is philosophically appealing. Some of Scott Aaronson’s blog posts dive into this question really well, so I highly recommend taking a look at those.
By the same argument, the 'probabilities' on the left can be of any type-imaginary, complex, quaternion, ...-so long as, after addition, they appear 'reasonable' on the right. So going forward, feel free to quote me instead of Richard Feynman: _"The idea of _*_complex_*_ and _*_quaternion probability_*_ may be no more mysterious than something like complex current and quaternion rotations, which are concepts that we use fairly often in electrical engineering and computer graphics respectively."_ - Niranjan Hanasoge, 2021.
Thanks for your question. Every time an electron reaches the detector screen, it is registered as a “spot,” rather than as a smeared out intensity. This is the part that cannot be explained by wave mechanics alone. It is also true that when we put “which-way detectors” at the two slits, they always register a “flash” at one slit or the other, and never both at the same time. A wave alone couldn’t cause these discrete events.
Nice video but there's a problem with your exposition of the subject IMO. The 2 parts don't properly relate to each other. The negative probabilities from the first part don't explain _at all_ the results of the second part. In particular it's clearly not symmetric. You can't put negative probabilities on A and B and still have a valid result. And I don't think you can even fix that with a more complex tree. There's a reason quantum mechanics uses complex numbers for amplitudes...
That's a good question and we have no fucking idea. That's the most mindblowing bit of science to me: every experiment we've done confirms the observer effect, but we have no actual explanation for it. It's mind-boggling.
Particles are just another form of energy. And as all energy in out universe, energy is never at a single point, energy is always spread out within an area of varying size. So the energy that makes up a particle can split up and pass two slits at once, after all it's just energy. Only when a particle interacts with other energy, this interaction must have on tiny spot where it started and where most of it took place and that's where we then "locate" the particle. But that's not because the particle really is exactly and only there, that's because this is the spot were we saw the particle interacting with its environment and thus at this spot the majority of the energy of the particle is located; at least during a brief moment in time. And as every detector must interact with the particle to detect something, adding detectors forces the vast majority of energy that makes up a particle to go through one or the other slit, while it can freely pass through both of them if no interaction is forced upon it. The reason why particles look so "locality based" to us is that in our world they are constantly interacting with other particles or energy (e.g. light photons) and thus we always seem to have an exact locality for a particle. Yet put a particle into a perfect vacuum that is isolated from all known radiation and then tell me where it is. Right, you can't. It could be everywhere within that vacuum and maybe it even is.
We can only "watch" a particle if it and our instrumentation interact. This interaction is always local and discrete... very NOT like a wave. Discrete and local are particle properties, but these interactions disturb our instrument and the particle field -- these disturbances propagate outward from the location of the interaction as a wave.
11:38 this is actually not correct: there is still inference with "which way" detectors (just a different one) and you actually get one blob. See here: ruclips.net/video/RQv5CVELG3U/видео.html
It feels like you're mixing apples and oranges here. A quantum probability amplitude is not a probability - the square of the magnitude of the probability amplitude is a probability. And the magnitude of a complex number is never negative, much less its square. You may have a point, but you failed to explain it. The video makes it seem like you're simply confused and don't know what you are talking about.
Thanks for your honest comment. I will try to address your point here. The video simply claims that asking under what circumstances probabilities can be negative leads to the idea of interference in the absence of which-way information. It makes *no* claim that quantum mechanics is just probability with minus signs (in fact, it explicitly warns that this is not the case). It’s simply making a connection between the logical consistency of negative probabilities and the idea of interference in quantum theory. I do not claim that this is how we do calculations in quantum mechanics. I just wanted to start from a seemingly silly math question and find that it at least gives hints of a connection to quantum mechanics. I understand that it’s easy to take this video the wrong way, and that’s an oversight on my part. Ideally, a viewer not trained in quantum mechanics will not take the claims of this random RUclips video further than intended, and a viewer trained in quantum mechanics will know exactly how far to take these claims.
Largely misleading to confuse complex amplitude with a probability. Also you have never seen a double slit experiment in real life, or else you’d know a single slit generates a diffraction pattern much like a wave does. If you see two ‘blobs’ as indicated, you are doing your slits horribly wrong.
So, I'm pretty sure your diagram at 7:14 explaining negative probabilities is wrong. The idea of "we added a path and the probability went down" is correct, but only with the stipulation that all other probabilities must stay the same. For instance, instead of a negative probability, take a really small probability. P(p→2|1 path) = 1•.8 = .8 P(p→2|2 paths) = .7*.8 + .3•.01 = .563 We have made the probability go down without negative probabilities. This is because we changed the probabilities that allow he particle to go to box 2. If instead we put the block *after* the first node, so the particle has a 30% chance (the first node) of not going into box 2 at all. The probability with the block = .7•.8 + .3•0 = 0.56 Probability without that block should make the probability go up because probability has to be higher than 0, but with negative probability, the probability goes down.
"Opening more paths can decrease the flow of particles" amazing how this can actually happen in traffic
Makes sense that a line of traffic can interfere with itself
genius, curious to see if someone had already measured the (negative) values in that context
Note: This doesn't apply perfectly for all types of traffic (most notably cars) because there is such a thing called induced demand.
Maybe traffic is a wave.
Called tapping the left lane
I attended a seminar by Feynman on this subject at the University of Alaska Fairbanks sometime in the early 80s. I was amazed as he wrote out a multiterm equation on the blackboard, each term representing a probability that could have any value. He showed how all the meaningless terms cancelled out, leaving a real probability as the solution. What a shame that the seminar wasn't filmed.
That ending quote is absolutely fantastic. Quantum theory is about information, and how it behaves when unobserved.
Half of that quote was inspired by one of Scott Aaronson’s blog posts. He’s written a lot about quantum information and complexity theory, and he even talks about implications for various topics in philosophy. I highly recommend taking a look!
@@StevenG22 Thank you!
That is misleading, though, since in quantum theory, "observation" does not refer to anything you think the word refers to based on its coloquial definition.
@@angelmendez-rivera351 you have no idea what I think the word observation refers to. In the case of quantum physics, observation has a somewhat circular definition of it is when a wave function collapses; when a possible superposition collapses to a single eigenstate corresponding to an observable physical property. The behavior of these possible superpositions, or wave functions when "unobserved" i.e when it is not collapsed, is governed by the Schrodinger equation, or the dirac equation, if you want to be more precise. None of this is contradictory to the quote shown at the end of this video. A ket is by all accounts, an information packet. Quantum physics studies the behavior of these objects when they are not collapsed.
@@brandonklein1 *you have no idea what I think the word observation refers to.*
My apologies. I used the pronoun "you" deictically. I am not referring to you, Brandon Klein, specifically. I probably should have used the pronoun "one" to avoid ambiguity.
*In the case of quantum physics, observation has a somewhat circular definition of it is when a wave function collapses; when a possible superposition collapses to a single eigenstate corresponding to an observable physical property.*
Perhaps a text may provide this naive definition as a starting point for discussion, but this is most definitely not the actual definition physicists use.
*None of this is contradictory to the quote shown at the end of this video.*
I never said there were any contradictions anywhere. My claim is simply that the quote is misleading. As in, technically accurate, but it does not mean what most people would think it means, and so it communicates the wrong idea to most people.
#SoME1 is the best thing that happened to SciComm this year. Waiting for your next video!!
That ending ❤️❤️❤️
I loved this video! Looking forward to more from you!
Wow! That means so much coming from you. Your channel was a big part of my journey into physics, especially when I was self-teaching some quantum mechanics and watching RUclips videos to build up intuition. I distinctly remember some “aha!” moments I had while watching your videos on interference and spin. Thanks a lot! This made my day.
This is great. I tried to prove that no probability distribution can explain the correlation of two entangled photons in a Bells inequality experiment. It turns out that a negative probability of some of the “lambda” combinations explains the observations just fine.
That’s a neat connection! Thanks for sharing that.
To be clear, negative probabilities should absolutely be considered a problem if they’re assigned to directly observable events. If a proof leads you to a negative probability assigned to an observable event, then that should certainly be considered a contradiction. But if the negative probability pops up in some “intermediate” transition corresponding to an event that is not directly observable, then things are okay.
This is all meant to tease the idea that we can formulate quantum mechanics as a calculation of “probability amplitudes,” complex numbers that we add up for all possible paths and then take the square magnitude to get the final probability. The “negative probabilities” we see pop up here are analogous to the fact that probability amplitudes can interfere before we take the square magnitude of the final result.
That would have been a great realisation after a lot of work! Well done
Oh snap. I hope someone puts out a nice informative video about exactly that. *hint *hint Steven
You have your probabilities confused for point "B." Either 2-->0.56+0.18=0.74 and
3-->0.12 or you have labeled the probabilities from B backwards.
Thank you. This was addressed in a previous comment, and the correction is listed in the description.
Haha! Who the heck goes to calculate that!
@@oosmanbeekawoo I calculate for self check my correctly understanding of calculate algorithm and essence of the video. And when my answer did not agree with what was in the video, it caused bad feelings. After spending some time double-checking it in my head, I picked up the calculator and realized there was an error in the video.
Wow, that little fact blew my mind. I wait for the video of Feynman's interpretation like a little child in Christmas
The path integral is no different to how you would compute the interference pattern of a plane complex-valued wave. Just take square modulus on the detector to get spatial probability distribution
Wavefunctions in quantum mechanics have a *phase* which means they may cancel out when you add them up. But that isn't a negative probability. To calculate a probability you have to square a (normalized) wavefunction, which necessarily means probabilities *are* between 0 and 1. To be honest I think presenting QM as negative probabilities is a good example of the "quantum mechanics is spooky" rhetoric which appears all to often in popular science, and only serves to make people believe that quantum mechanics explains consciousness or whatever else without ever actually learning the physics itself.
I would disagree. The facts that wavefunctions exist, and that their magnitude squared equals probability are axioms of quantum mechanics. There isn't a reason why those facts should be true. It just happens to work out in the math, and it predicts what we actually observe. But just like in ordinary mechanics, where we can analyze motion using different philosophies (Hamiltonian vs Lagrangian), we can analyze quantum mechanics using different philosophies as well. As long as a certain philosophy matches our observations, we can say that it's valid, and that it's just one way to look at things, among other ways to look at things. Feynman's formulation of quantum mechanics with negative probabilities, if it is complete and consistent (which I don't know because I'm not familiar with it), then it is also a valid way of looking at quantum mechanics -- a different paradygm of the same thing
@@karolakkolo123 Thanks for replying! I'm not sure that I have been convinced, but I hope you make more videos in the future anyway, it is very well made
@@simondwilkinson oh, it wasn't me who made the video haha, but yeah
Thanks for your comment.
You are correct that quantum mechanics is not just probability with minus signs, and I warn against this conclusion in the video. All I wanted to do was draw a connection between the logical consistency of negative probabilities and the idea of interference in quantum mechanics, inspired by a paper that Feynman wrote late in his life. It does *not* represent a complete formulation of quantum mechanics by any means.
It is true, though, that there is alternative to the Schrödinger wave function method of quantum mechanics. It’s called the path integral formulation of quantum mechanics, and involves the calculation of probability amplitudes (which are complex numbers) whose square magnitude gives the probability of an event. I was hoping to tease in this video that you can do quantum mechanics without wave functions, but I realize that has been confusing or easy to misinterpret for some viewers.
Well, even besides Feynman's path integral formulation, there is another mathematical formalism for quantum mechanics in which negative probabilities occur even more plainly, called the Wigner phase space formulation. In it, we represent the state of a quantum system as a quasiprobability distribution on phase space (the space of all possible combinations of the positions and momenta of the particles), which is a real-valued function that behaves exactly like a (joint) probability distribution for the purposes of calculating the expected values of observables and the marginal probability distributions for position or momentum, except that it can actually be negative in some regions of phase space. It turns out that the regions where the Wigner function is negative are small enough that they are impossible to directly observe experimentally (since the state of a particle cannot be localized to arbitrarily small regions of phase space due to the Heisenberg uncertainty principle), but there is still some disagreement and mystery about what exactly these negative probabilities mean philosophically.
Well I may be a year late, but this video is great! I had so many "aha!" moments from disparate areas of maths/science. (Even the very briefly mentioned relationship of AND with + and XOR with * finally made me understand how Boolean Logic relates to probability theory!)
The quote at the end is especially good, I'll be keeping that one in mind as I study Quantum Mechanics!
What the heck? Your video has me chomping at the bit, for more. This is not a criticism but you barely hinted at how -ve probabilities could be used in describing the quantum effects. Subbed and collapsed my wave function on the [like] button in the hopes your next video comes out soon.
The last sentence opens the door to so much more! Fantastic video!
This is a great video! You taught this very concisely and brought light to a topic I did not know about.
The disappearance of the interference effect is not really a mystery. It is because measurement decoheres the system so that states of the environment (ourselves and the lab and the rest of the world) become correlated. It's called the Everett interpretation, though it is more fact than mere interpretation.
The path integral formulation is not really any different from 'standard' Quantum mechanics (operator formalism), it's just an alternate way to express the same equations. We use different mathematical formulations in different contexts, depending on which makes the problem easier to solve.
It's not nonsense to say that a particle went through both slits. The uncertainty principle is the reason why one cannot know which slit. That's also the reason why the slit dimensions have to be similar to the particle dimensions (i.e., comparable to the dimensions laid out by the uncertainty principle, to the extent that the particles behave quantum mechanically when comparable to such dimensions. if the slits are moved apart sufficienty, the interference goes away because the dimensions become larger than those laid out by the uncertainty principle) I find it to be a bit over the top to invoke negative probability in explaining the double slit experiment.
It's honestly very simple: particles are waves. That's it.
I know they are quantised excitations rather than arbitrary ones, and things get a lot more complicated with QFT, but the simple correct explanation is that they are waves and there is no issue with waves spreading amongst multiple slits.
There is a phenomenon of pop-sci communicators trying to make it sound more difficult to understand so that they can make it appear more mysterious and interesting.
They appear as particles due to decoherence which leads to splitting of multiple worlds (Everett interpretation). This should not really be called interpretation as it is a logical consequence of the theory, it's just geocentrism all over again with people wanting to believe they are at the centre of everything, wanting to believe there could not be prorated parallel realities etc even though it's a logical consequence of extremely well-validated theory...
Anyway, in this case I think the video creator just doesn't know the subject matter.
@@wizard7314 I like Everett. He simplified the theory, removed the "ad-hoc rules", removed the "measurement problem" and yet still can explain how our every-day experience emerge from a universe following the Schroedinger equation. Awesome!
The other interpretations look so clumsy to me, in comparison.
But the other "interpretations" also work and get the same results. As far as I know, we have no data that would allow us to rule out one over the others.
So I'd say it is just cautious to call Everett's work an "interpretation".
Got nothing to do with my "ego"...
But if I ever find out, that my "parallel me" is still together with my highschool crush... then ... then... grrrr
Screw you Everett!!!
Nice exposition. Thought provoking. Thanks
Just discovered this gem, I hope there more coming!
Its got complex numbers in there as well.
Multiply for and, add for or. With complex numbers. The probabilities you observe are the squares of the amplitude. (x+iy => x^2+y^2)
And you have a big chunk of quantum mechanics.
Thanks for the video!
QM even has imaginary pretty probability for wavefunctions, by which you have to combine two of them (even for the same particle) to arrive at the real peobabilities for its position. Btw, quantum 1/2-spin particles are spinors, meaning they lie along the border of a 4d hypersphere, which also has interpretation 2d vector of complex numbers, so this is probabilly ehy the quantum probability distribution function comes into play.
if you write s-->1 then you have to write the probability of 1 knowing s or p(1|s) not p(s|1)
That’s true. Thanks for catching that.
Just scratch my head for a while seeing p(s|1) 🤣
This idea that there's a switch from 'clump' to interference when going from single to double slit is an assumed model that does not look to be consistent with the physics of photon grating experiments.
For example, the pattern formed when a single slit is present is not a bell curve, it is another wider but quite clear pattern also predicted by quantum mechanics (and classical electromagnetic waves) with a form of sinc^2(theta) with wave-like lobes that are spaced at minima given by theta at lambda/n*d. It has a beautiful series of smaller lobes on either side of the central maximum. The double-slit then superimposes narrower fringes and adding more slits narrows the peaks so that all particles become concentrated into bright lines. where all the energy goes to peaks.
By artificially replacing the actual single slit pattern with a bell curve it seems one is adding a questionable notion that the single slit pattern is like a random scattering pattern similar to bullets going through an aperture. This presumption has been repeated so often I think it has become a sort of apriori trope that pre-determines the possible conclusions.
The shape and width of both patterns, single and double, have a direct analytic relationship that can be calculated from QM and the result is that the expectation function for the cross-beam momentum that this added to the trajectory is given by the magnitude of the Fourier transform of the aperture pattern divided by Plack's constant. This pattern depends only on the shape of the scattering aperture and is completely independent of the type of incident particle (matter/photon) or the incident momentum. To me, this is utterly stunning and makes all the talk of wave-particle duality seem as inadequate as using epicycles and deferents to explain orbital mechanics.
It is as if the scattering takes a snapshot of the allowed cross-beam momentum spectrum available at the time of transit, which then becomes visible by allowing the beam to travel undisturbed far enough to show the pattern macroscopically, and the surprising thing is that the expectation function for scattering momentum is utterly independent of the type of particle or its incident momentum.
Any interaction that detects a particle at the time it traverses the slits will add a random impulse that will smear out that pattern by effectively convolving the slit scattering expectation function with another scattering function.
Perhaps the best way to understand this experiment is to give up the accepted notion that we can only explain it by thinking of the incident particle as a wave that interferes around a passive barrier. A great paper by Carolyne M. Van Vliet "Linear momentum quantization in periodic structures II" is a start.
A single slit produces something 'like' bell curve when the slit is appreciably larger than the wavelength of the light.
Your explanation about adding a certain momentum distribution to the particles is spurious. It is not a classical effect.
@@wizard7314 That is not true. When the slits are larger than the wavelength, the scattering function is still simply, clearly, and precisely given by a Sinc(x)^2 function that has wave-like periodic side lobes as you can see on any basic diffraction textbook. At no time does the function revert to a particle bell curve. Both the single and double slit patterns are diffraction patterns that are also matched by using quantum mechanics. At all times QM predicts that both Single and Doule slit the scattering expectation functions have a momentum spectrum the Fourier transform of the aperture pattern divided by Planck's constant. At no time does closing one slit cause particles to stop behaving according to a wave function, classical or quantum.
@@wizard7314 What? ,you don't even realise that momentum expectation functions are calculated by using quantum mechanics, not classical mechanics?
Try again, the momentum expectation function as calculated by QM across the beam is the Fourier transform of of the aperture divided by Planck's constant.
Besides, it's not 'my' explanation it is clearly laid out in several papers. Go read
LINEAR MOMENTUM QUANTIZATION
STRUCTURES
by K. M. VAN VLIET Physica 1967, or
the Second Paper Physica A 389 (2010) 15851593. I
Yes, the bell curve is an idealisation, it's more complicated in real life. But the pattern from two slits with detectors is still the sum of the patterns from individual slits, whereas two slits without detectors gives extra interference.
But don't the detectors have to interact with the particles in order to detect them? This would somewhat explain different results in these experiments.
If negative probability are possible then probabilities above 1 are possible too.what do you think is maximum positive and negative probability ?does it extends to infinity or 2.there are many things left out.
We meet probability distributions in the theory of Brownian motion. If we have two overlapping distributions, then they merely add up to a cumulative distribution, and all the probabilities are positive. However in quantum mechanics we observe destructive interference. How can that be? I will make a suggestion.
There is more than one way to travel faster than light, at least according to the Minkowski formalism which I will take as representing something real. In the way that exchanges timelike and spacelike intervals we can have an oscillation cycling through a series of transformations which is capable of destructive interference with itself. In the other way we can have tachyonic Brownian motion. If two or more detectors are trying to capture our entity, then the randomness of the TBM ensures that only one detector is triggered. Here we do have a probability distribution which can exhibit destructive interference with itself. Quantum mechanical behaviour is imaginable, but at the price of having to venture into the superluminal world. Bell's Theorem implies that we should be willing to pay that price. I would emphasise that the wavelike behaviour and the TBM are orthogonal to each other, so this is not just schoolboyish musing.
In computer simulations of fluid mechanics, Brownian motion of vorticity is one way of modelling the two-dimensional Navier-Stokes equation, as originally proposed by Alexandre Chorin. The fluid mechanics simulation makes use of a random number generator and I would like to work out how to include a RNG in a computer simulation of quantum mechanics. Tachyonic Brownian motion is one thing to think about because it does not directly mess up the Schroedinger equation. I would expect it to be apparent during the nonlinear interaction between matter and the electromagnetic field.
at (e.g.) 12:28, where the sum of the 2 waves and the interference graph is shown, it is worth noting that both measure the magnitude of a complex valued function, scaled such that the integral over all real numbers is 1.
Naturally, we could expect to see 2 totally different results when we compare the sum of magnitudes and the magnitude of the sum. By the law of triangles, the sum of magnitudes is always more than the magnitude of the sum; the increase in probability comes from the scaling such that the integral is 1
So, I'm pretty sure your diagram at 7:14 explaining negative probabilities is wrong.
The idea of "we added a path and the probability went down" is correct, but only with the stipulation that all other probabilities must stay the same.
For instance, instead of a negative probability, take a really small probability.
P(p→2|1 path) = 1•.8 = .8
P(p→2|2 paths) = .7*.8 + .3•.01 = .563
We have made the probability go down without negative probabilities. This is because we changed the probabilities that allow he particle to go to box 2.
If instead we put the block *after* the first node, so the particle has a 30% chance (the first node) of not going into box 2 at all.
The probability with the block = .7•.8 + .3•0 = 0.56
Probability without that block should make the probability go up because probability has to be higher than 0, but with negative probability, the probability goes down.
The numbers you put in red didn't show well on the screen
this video is such a slay omfg reminds me of PBS space time, Sci Show, 3Blue1brown! the animation was sexy and helpful and most importantly the concept is SO interesting to me but ALWAYS feels so abstract
and you've made it clear!
Thanks for the encouraging comment!
Should be at 5:22
P(S->2) = 0.56 + 0.18
I'm not sure if anyone saw it.
Thank you for making this!!
The implication of the negative probability is that you were wrong about the other probabilities, that the combined experiment altered the probability in some way you hadn't anticipated.
do the video on the half integral interpretation
how about imaginary porbabilities ?
You did not give an example of negative probabilities, because quantum wave function values are NOT probabilities; they merely yield probabilities when you take their magnitude squared. They are analogous to the linear predictor in a logistic regression model, which yields a probability when you apply the logistic function to it.
Incredibile content, congrats and hope u do these more :)
9:58 not quite true, the particle would still diffract and interfere with itelf and form a sin(x)/x shape, not a bell curve
Wow this was great
Here's a question for people who know what they're talking about. How do we know it's observation that changes things, instead of something we currently can't avoid doing when observing?
Negative probability is used all the time in quantum computing to describe how wave functions will collapse. :D
accepting negative intermediate probability has nothing to do with certainty but simply with the weight of this path, if this probability is 0 we are completely certain nothing went through there and still everything works fine, the number must be small enough so positive probabilities from other path outweight the one with negative value
Steven you're amazing 🤩
At 7:30. Is it illustrative of the Monty Hall paradox?
How would the measure of the space work? Would it even be a probability space
A probability is a non-negative, countably additive, normalized mapping of events in a sigma field onto the space of real numbers.
I am not sure what you are referring to by a σ-field, since this is not standard mathematical terminology used in the literature. The more accurate description is that (Χ, Σ, μ) is a probability space if and only if it is a measure space and μ(X) = 1. (X, Σ, μ) is a measure space if and only if (X, Σ) is a σ-ring, and μ : Σ -> {t : t in R} is σ-additive with μ({}) = 0. Perhaps you are using σ-field to refer to a σ-ring, but this is obscuring terminology, and besides, you failed to mention that μ({}) = 0.
@@angelmendez-rivera351 They probably meant σ-algebra. And by "normalized": μ({}) = 0 and μ(X) = 1.
Great video, thank you. Interesting is: What qualifies as an "observer" in this?
Your notation is wrong. The transition probability P(S -> 2) is the conditional probability P(2 | S). The conditioning information goes to the right of the bar.
How does the math work though? A measure can't be used to describe negative probability because it assumes nonnegativity. Are signed measures used? Or something completely different?
You may be interested in 'quasiprobability distributions'. I am not too familiar with them, but I think in this case you'd ascribe a probability density function over the collection of possible paths. Although the PDF is not nonnegative, the integrated density over paths that lead to a given point are.
Apart from this, I think the math in the video is slightly wrong as a comparison to QM. Instead of negative, allow complex 'probability amplitudes' (the technical term) and then take the square modulus of the final result to get the probability. Using only negatives, and not taking the square, is a bit strange and I'm not sure if it can correctly model the experiment.
6:05 Heh, the compression did not like that red text.
At 10:56, That is the wave theory of probability.
Aren't there more parameters impacting the bands seen behind? The ratio of distance between the source, slits, screen as well as distance between the two slits.
can we think negative probability as opposite directed probability ? all probabilities flow to the destination nodes. but -0.4 probability explains escaping from destination and that view also explains what does probability value greater than one (1.4 probability) means at that node.
directed probability seems like a vector. a value vith direction.
When will be the next video? T_T
Very nice video!
Great video!!!
but whats a negative distance? that it gets shorter?
Great job!
5:30 - Uh, the last time I checked 0.3*0.6 is 0.18, not 0.12. Ooops...
That was great!
Great, though it is not the act of observing the particle that makes it stop acting like a wave, it is the photons needed to measure the particle's position that cause it to stop acting like a wave. In other words, an interaction. This is also how the heisenberg uncertainty principle works, because to measure the particle's position you need to hit it with a photon to measure it, and that changes its speed just a bit.
Thanks for your comment. I encourage you to keep an open mind about what causes the wave function collapse, however. It is fundamentally about information leaking into the environment, not just about interaction. I recommend watching Looking Glass Universe’s video about measurement for an well-explained argument about why any old interaction with the environment doesn’t necessarily cause the wave function to collapse. Your explanation in terms of interaction with a photon is enticing at first, but doesn’t tell the full story.
@@StevenG22 i believe you can make an information theory based on particles still, though ill check that video out, thanks
@@StevenG22 So i watched the video, and yeah that goes well into my belief that you can make an information theory without observers. You can work with interactions and uncertainty alone to have information there
Couldn't a situation with positrons and electrons make this not weird anymore?
Imagine you have charge in S and it travels to (1),(2) but along the way some positron-electron pairs might be produced. If you first talk about percentages then maybe -50% of the charge reaches (1), and 150% of the charge reaches (2). They must sum to 100% because the total charge is conserved.
This might feel weird in the language of probabilities but I guess if an electron is emitted from S then the probability of the electron arriving at (1) is -50% and at (2) is 150%.*
And this doesn't seem all that counterintuitive.
Note*: I thought about whether to say "the electron arrives" or "an electron arrives" and I had to choose "the".
0.68 and 0.18 were wrong ...... 0.3x0.4=0.12
Your comment about conditional probabilities at 2:11 makes no sense
This was a really nice explanation and visual, I loved it. It also makes me wonder if it’s possible to formulate quantum mechanics, not by using complex numbers, but by introducing negative probabilities instead.
Thanks for your comment! I’ve also wondered this, but I caution you not to take the conclusions from this video too far. The mathematical structure of quantum theory definitely needs complex numbers. However, there has been some nice work addressing the question of why the need for complex numbers is philosophically appealing. Some of Scott Aaronson’s blog posts dive into this question really well, so I highly recommend taking a look at those.
can u put subtitles? for deaf people and stuff
By the same argument, the 'probabilities' on the left can be of any type-imaginary, complex, quaternion, ...-so long as, after addition, they appear 'reasonable' on the right.
So going forward, feel free to quote me instead of Richard Feynman: _"The idea of _*_complex_*_ and _*_quaternion probability_*_ may be no more mysterious than something like complex current and quaternion rotations, which are concepts that we use fairly often in electrical engineering and computer graphics respectively."_ - Niranjan Hanasoge, 2021.
who came from 3blue1brown?
This is SoME afterall
😱💥🤕 Mind blow!
can probabilities be negative? Kolmogorov would like to have a word with you.
You know, of all the Sci-Fi tech to become or to have some element of realism.... the infinite improbability dive.... was not one of them.
I've just started to watch the video, let's see if my guess that this is based on a Scott Aaronson's book, course or blog post is correct
Well, there is no direct answer in the video, but I have a strong suspicion :)
Wow!
Why would you still want to call them particles, if they behave like waves? Can't you just call them waves, and get rid of quantum mechanics?
Thanks for your question. Every time an electron reaches the detector screen, it is registered as a “spot,” rather than as a smeared out intensity. This is the part that cannot be explained by wave mechanics alone. It is also true that when we put “which-way detectors” at the two slits, they always register a “flash” at one slit or the other, and never both at the same time. A wave alone couldn’t cause these discrete events.
@@StevenG22 Thank you for explanation!
arent probabalities complex numbers in QM?
Nice video but there's a problem with your exposition of the subject IMO. The 2 parts don't properly relate to each other. The negative probabilities from the first part don't explain _at all_ the results of the second part. In particular it's clearly not symmetric. You can't put negative probabilities on A and B and still have a valid result. And I don't think you can even fix that with a more complex tree. There's a reason quantum mechanics uses complex numbers for amplitudes...
How do particles "know" that they're being observed?
That's a good question and we have no fucking idea.
That's the most mindblowing bit of science to me: every experiment we've done confirms the observer effect, but we have no actual explanation for it. It's mind-boggling.
Particles are just another form of energy. And as all energy in out universe, energy is never at a single point, energy is always spread out within an area of varying size. So the energy that makes up a particle can split up and pass two slits at once, after all it's just energy. Only when a particle interacts with other energy, this interaction must have on tiny spot where it started and where most of it took place and that's where we then "locate" the particle. But that's not because the particle really is exactly and only there, that's because this is the spot were we saw the particle interacting with its environment and thus at this spot the majority of the energy of the particle is located; at least during a brief moment in time. And as every detector must interact with the particle to detect something, adding detectors forces the vast majority of energy that makes up a particle to go through one or the other slit, while it can freely pass through both of them if no interaction is forced upon it. The reason why particles look so "locality based" to us is that in our world they are constantly interacting with other particles or energy (e.g. light photons) and thus we always seem to have an exact locality for a particle. Yet put a particle into a perfect vacuum that is isolated from all known radiation and then tell me where it is. Right, you can't. It could be everywhere within that vacuum and maybe it even is.
very good curry
We can only "watch" a particle if it and our instrumentation interact. This interaction is always local and discrete... very NOT like a wave. Discrete and local are particle properties, but these interactions disturb our instrument and the particle field -- these disturbances propagate outward from the location of the interaction as a wave.
Or it just can be said that there is a finite speed of expansion of event influence
11:38 this is actually not correct: there is still inference with "which way" detectors (just a different one) and you actually get one blob.
See here: ruclips.net/video/RQv5CVELG3U/видео.html
Strange indeed
You have a negative probability of being killed by a polar bear on a Florida beach.
moaaaaaaaaaaaaaar!
It feels like you're mixing apples and oranges here. A quantum probability amplitude is not a probability - the square of the magnitude of the probability amplitude is a probability. And the magnitude of a complex number is never negative, much less its square.
You may have a point, but you failed to explain it. The video makes it seem like you're simply confused and don't know what you are talking about.
Thanks for your honest comment. I will try to address your point here.
The video simply claims that asking under what circumstances probabilities can be negative leads to the idea of interference in the absence of which-way information. It makes *no* claim that quantum mechanics is just probability with minus signs (in fact, it explicitly warns that this is not the case). It’s simply making a connection between the logical consistency of negative probabilities and the idea of interference in quantum theory. I do not claim that this is how we do calculations in quantum mechanics. I just wanted to start from a seemingly silly math question and find that it at least gives hints of a connection to quantum mechanics.
I understand that it’s easy to take this video the wrong way, and that’s an oversight on my part. Ideally, a viewer not trained in quantum mechanics will not take the claims of this random RUclips video further than intended, and a viewer trained in quantum mechanics will know exactly how far to take these claims.
Largely misleading to confuse complex amplitude with a probability. Also you have never seen a double slit experiment in real life, or else you’d know a single slit generates a diffraction pattern much like a wave does. If you see two ‘blobs’ as indicated, you are doing your slits horribly wrong.
Just commented on it lol, yeah it should be a sinc(x)**2 function not a gaussian blob
nani????
Probabilities can't be negative, amplitudes can. 🤓
So, I'm pretty sure your diagram at 7:14 explaining negative probabilities is wrong.
The idea of "we added a path and the probability went down" is correct, but only with the stipulation that all other probabilities must stay the same.
For instance, instead of a negative probability, take a really small probability.
P(p→2|1 path) = 1•.8 = .8
P(p→2|2 paths) = .7*.8 + .3•.01 = .563
We have made the probability go down without negative probabilities. This is because we changed the probabilities that allow he particle to go to box 2.
If instead we put the block *after* the first node, so the particle has a 30% chance (the first node) of not going into box 2 at all.
The probability with the block = .7•.8 + .3•0 = 0.56
Probability without that block should make the probability go up because probability has to be higher than 0, but with negative probability, the probability goes down.